This task processes the raw RNA-seq gene expression data by performing multiple normalization steps to prepare it for downstream differential expression and integrative analysis. The steps include:
These normalized matrices will be used in PCA, correlation analysis with methylation data, and visualization tasks.
Step 2.1: Load Counts + Metadata
# Load raw RNA-seq count matrix (genes × samples)
# Rows = genes, Columns = sample IDs (accessions)
rna_counts <- read.delim("GSE224377_raw_counts_GRCh38.p13_NCBI (1).tsv", row.names = 1)
# Load sample metadata (contains Accession IDs, Titles, Age, Gender, etc.)
rna_meta <- read.csv("metadata-new.csv")
# Match sample IDs between counts and metadata
# This step ensures that the sample columns in rna_counts match the metadata rows
# We replace column names of the count matrix using matched sample names from metadata
colnames(rna_counts) <- rna_meta$X[match(colnames(rna_counts), rna_meta$Accession)]
# Optional (more explicit Dr. Noha style):
# ord <- match(colnames(rna_counts), rna_meta$Accession)
# rna_meta <- rna_meta[ord[which(!is.na(ord))], ]
# rna_counts <- rna_counts[, which(!is.na(ord))]
# Extract patient ID and sample type from the 'Title' column
# Example Title: "Patient1, Lesion" → patient = Patient1, sample.type = Lesion
rna_meta <- rna_meta %>%
separate(Title, into = c("patient", "sample.type"), sep = ",", fill = "right") %>%
mutate(sample.type = trimws(sample.type)) # Remove any extra spaces around the sample typeStep 2.2: Histogram of Raw Counts
#Histogram of Raw Counts
pdf("Histogram_0_Raw_Counts.pdf")
apply(rna_counts, 2, function(x) hist(x, breaks=60))## $`1A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000
##
## $counts
## [1] 39327 16 12 2 1 2 1 1 5 1 5 1
## [13] 0 1 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 1
##
## $density
## [1] 1.997511e-04 8.126778e-08 6.095083e-08 1.015847e-08 5.079236e-09
## [6] 1.015847e-08 5.079236e-09 5.079236e-09 2.539618e-08 5.079236e-09
## [11] 2.539618e-08 5.079236e-09 0.000000e+00 5.079236e-09 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`1B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000
##
## $counts
## [1] 39306 30 8 3 5 2 1 4 2 2 0 0
## [13] 1 1 0 0 0 0 5 4 1 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 1
##
## $density
## [1] 1.996445e-04 1.523771e-07 4.063389e-08 1.523771e-08 2.539618e-08
## [6] 1.015847e-08 5.079236e-09 2.031694e-08 1.015847e-08 1.015847e-08
## [11] 0.000000e+00 0.000000e+00 5.079236e-09 5.079236e-09 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-08 2.031694e-08
## [21] 5.079236e-09 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000
##
## $counts
## [1] 39337 11 5 5 1 1 2 1 5 1 6 0
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 1
##
## $density
## [1] 9.990095e-05 2.793580e-08 1.269809e-08 1.269809e-08 2.539618e-09
## [6] 2.539618e-09 5.079236e-09 2.539618e-09 1.269809e-08 2.539618e-09
## [11] 1.523771e-08 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000
##
## $counts
## [1] 39332 14 5 1 2 9 0 2 0 5 0 0
## [13] 0 0 0 5 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 1
##
## $density
## [1] 1.997765e-04 7.110931e-08 2.539618e-08 5.079236e-09 1.015847e-08
## [6] 4.571312e-08 0.000000e+00 1.015847e-08 0.000000e+00 2.539618e-08
## [11] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 2.539618e-08 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000
##
## $counts
## [1] 39321 13 6 11 2 3 3 1 0 0 3 5
## [13] 0 1 0 5 0 0 1 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 1
##
## $density
## [1] 1.997206e-04 6.603007e-08 3.047542e-08 5.587160e-08 1.015847e-08
## [6] 1.523771e-08 1.523771e-08 5.079236e-09 0.000000e+00 0.000000e+00
## [11] 1.523771e-08 2.539618e-08 0.000000e+00 5.079236e-09 0.000000e+00
## [16] 2.539618e-08 0.000000e+00 0.000000e+00 5.079236e-09 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000
##
## $counts
## [1] 39319 20 3 9 1 1 2 2 3 0 5 6
## [13] 0 2 0 1 0 0 0 1 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 1
##
## $density
## [1] 1.997105e-04 1.015847e-07 1.523771e-08 4.571312e-08 5.079236e-09
## [6] 5.079236e-09 1.015847e-08 1.015847e-08 1.523771e-08 0.000000e+00
## [11] 2.539618e-08 3.047542e-08 0.000000e+00 1.015847e-08 0.000000e+00
## [16] 5.079236e-09 0.000000e+00 0.000000e+00 0.000000e+00 5.079236e-09
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000 380000 385000 390000
##
## $counts
## [1] 39319 17 5 7 2 4 2 1 1 1 3 1
## [13] 5 0 1 0 5 0 0 1 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 0 0 0 1
##
## $density
## [1] 1.997105e-04 8.634701e-08 2.539618e-08 3.555465e-08 1.015847e-08
## [6] 2.031694e-08 1.015847e-08 5.079236e-09 5.079236e-09 5.079236e-09
## [11] 1.523771e-08 5.079236e-09 2.539618e-08 0.000000e+00 5.079236e-09
## [16] 0.000000e+00 2.539618e-08 0.000000e+00 0.000000e+00 5.079236e-09
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [76] 0.000000e+00 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500 377500 382500 387500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000
##
## $counts
## [1] 39327 16 7 1 3 4 6 1 6 2 0 1
## [13] 0 0 1 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 1
##
## $density
## [1] 9.987556e-05 4.063389e-08 1.777733e-08 2.539618e-09 7.618854e-09
## [6] 1.015847e-08 1.523771e-08 2.539618e-09 1.523771e-08 5.079236e-09
## [11] 0.000000e+00 2.539618e-09 0.000000e+00 0.000000e+00 2.539618e-09
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
##
## $counts
## [1] 39337 7 9 3 3 1 1 2 0 1 5 1
## [13] 5 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 1
##
## $density
## [1] 9.990095e-05 1.777733e-08 2.285656e-08 7.618854e-09 7.618854e-09
## [6] 2.539618e-09 2.539618e-09 5.079236e-09 0.000000e+00 2.539618e-09
## [11] 1.269809e-08 2.539618e-09 1.269809e-08 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000 510000 520000 530000 540000
##
## $counts
## [1] 39331 14 2 5 3 3 2 0 6 2 6 0
## [13] 0 0 1 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 1
##
## $density
## [1] 9.988572e-05 3.555465e-08 5.079236e-09 1.269809e-08 7.618854e-09
## [6] 7.618854e-09 5.079236e-09 0.000000e+00 1.523771e-08 5.079236e-09
## [11] 1.523771e-08 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-09
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
## [51] 505000 515000 525000 535000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000 510000 520000 530000 540000 550000 560000 570000 580000 590000
## [61] 600000 610000 620000 630000 640000 650000 660000 670000 680000 690000
## [71] 700000 710000
##
## $counts
## [1] 39336 6 7 3 4 0 2 2 0 0 3 0
## [13] 0 1 0 0 1 4 0 5 0 1 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 1
##
## $density
## [1] 9.989842e-05 1.523771e-08 1.777733e-08 7.618854e-09 1.015847e-08
## [6] 0.000000e+00 5.079236e-09 5.079236e-09 0.000000e+00 0.000000e+00
## [11] 7.618854e-09 0.000000e+00 0.000000e+00 2.539618e-09 0.000000e+00
## [16] 0.000000e+00 2.539618e-09 1.015847e-08 0.000000e+00 1.269809e-08
## [21] 0.000000e+00 2.539618e-09 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
## [51] 505000 515000 525000 535000 545000 555000 565000 575000 585000 595000
## [61] 605000 615000 625000 635000 645000 655000 665000 675000 685000 695000
## [71] 705000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000 510000 520000 530000 540000 550000 560000
##
## $counts
## [1] 39337 3 11 5 4 2 1 0 6 0 1 5
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 1
##
## $density
## [1] 9.990095e-05 7.618854e-09 2.793580e-08 1.269809e-08 1.015847e-08
## [6] 5.079236e-09 2.539618e-09 0.000000e+00 1.523771e-08 0.000000e+00
## [11] 2.539618e-09 1.269809e-08 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
## [51] 505000 515000 525000 535000 545000 555000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000 380000 385000 390000
##
## $counts
## [1] 39313 23 6 4 2 3 2 2 1 1 1 6
## [13] 0 7 0 1 0 0 1 1 0 1 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 0 0 0 1
##
## $density
## [1] 1.996800e-04 1.168224e-07 3.047542e-08 2.031694e-08 1.015847e-08
## [6] 1.523771e-08 1.015847e-08 1.015847e-08 5.079236e-09 5.079236e-09
## [11] 5.079236e-09 3.047542e-08 0.000000e+00 3.555465e-08 0.000000e+00
## [16] 5.079236e-09 0.000000e+00 0.000000e+00 5.079236e-09 5.079236e-09
## [21] 0.000000e+00 5.079236e-09 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [76] 0.000000e+00 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500 377500 382500 387500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000
##
## $counts
## [1] 39333 11 2 8 0 6 7 2 0 1 2 0
## [13] 1 1 1 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 1
##
## $density
## [1] 9.989080e-05 2.793580e-08 5.079236e-09 2.031694e-08 0.000000e+00
## [6] 1.523771e-08 1.777733e-08 5.079236e-09 0.000000e+00 2.539618e-09
## [11] 5.079236e-09 0.000000e+00 2.539618e-09 2.539618e-09 2.539618e-09
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000
##
## $counts
## [1] 39335 7 7 5 4 1 3 0 0 6 7 0
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 1
##
## $density
## [1] 9.989588e-05 1.777733e-08 1.777733e-08 1.269809e-08 1.015847e-08
## [6] 2.539618e-09 7.618854e-09 0.000000e+00 0.000000e+00 1.523771e-08
## [11] 1.777733e-08 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 2.539618e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000 380000 385000
##
## $counts
## [1] 39301 29 12 2 4 3 0 3 2 0 0 2
## [13] 0 7 3 3 1 0 0 0 1 1 0 1
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 0 0 1
##
## $density
## [1] 1.996191e-04 1.472978e-07 6.095083e-08 1.015847e-08 2.031694e-08
## [6] 1.523771e-08 0.000000e+00 1.523771e-08 1.015847e-08 0.000000e+00
## [11] 0.000000e+00 1.015847e-08 0.000000e+00 3.555465e-08 1.523771e-08
## [16] 1.523771e-08 5.079236e-09 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 5.079236e-09 5.079236e-09 0.000000e+00 5.079236e-09 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [76] 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500 377500 382500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10A`
## $breaks
## [1] 0 20000 40000 60000 80000 100000 120000 140000 160000 180000
## [11] 200000 220000 240000 260000 280000 300000 320000 340000 360000 380000
## [21] 400000 420000 440000 460000 480000 500000 520000 540000 560000 580000
## [31] 600000 620000 640000 660000 680000 700000 720000 740000 760000 780000
## [41] 800000 820000 840000 860000
##
## $counts
## [1] 39338 7 11 1 5 1 5 0 6 0 1 0
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 1
##
## $density
## [1] 4.995175e-05 8.888663e-09 1.396790e-08 1.269809e-09 6.349045e-09
## [6] 1.269809e-09 6.349045e-09 0.000000e+00 7.618854e-09 0.000000e+00
## [11] 1.269809e-09 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 1.269809e-09
##
## $mids
## [1] 10000 30000 50000 70000 90000 110000 130000 150000 170000 190000
## [11] 210000 230000 250000 270000 290000 310000 330000 350000 370000 390000
## [21] 410000 430000 450000 470000 490000 510000 530000 550000 570000 590000
## [31] 610000 630000 650000 670000 690000 710000 730000 750000 770000 790000
## [41] 810000 830000 850000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000
##
## $counts
## [1] 39311 22 8 7 4 1 2 1 0 1 3 2
## [13] 0 0 6 0 0 5 0 2 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 1
##
## $density
## [1] 1.996698e-04 1.117432e-07 4.063389e-08 3.555465e-08 2.031694e-08
## [6] 5.079236e-09 1.015847e-08 5.079236e-09 0.000000e+00 5.079236e-09
## [11] 1.523771e-08 1.015847e-08 0.000000e+00 0.000000e+00 3.047542e-08
## [16] 0.000000e+00 0.000000e+00 2.539618e-08 0.000000e+00 1.015847e-08
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 5.079236e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"dev.off()## png
## 2Step 2.3: Filter Genes with >90% Zeros
# Calculate the proportion of zero counts for each gene
# For each row (gene), count how many samples have a count of 0, then divide by total number of samples
zero_prop <- rowSums(rna_counts == 0) / ncol(rna_counts)
# Filter out genes where more than 90% of samples have zero counts
# Retain genes expressed in at least 10% of samples
rna_counts_filtered <- rna_counts[zero_prop < 0.9, ]
# Save the filtered count matrix to a CSV file for reference
write.csv(rna_counts_filtered, "Filtered_counts_less90perc_zeros.csv")
# Plot histograms of the filtered counts for each sample to visualize count distributions
pdf("Histogram_Filtered_counts_less90perc_zeros.pdf")
apply(rna_counts_filtered, 2, function(x) hist(x, breaks = 60))## $`1A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000
##
## $counts
## [1] 27716 16 12 2 1 2 1 1 5 1 5 1
## [13] 0 1 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 1
##
## $density
## [1] 1.996470e-04 1.152530e-07 8.643976e-08 1.440663e-08 7.203314e-09
## [6] 1.440663e-08 7.203314e-09 7.203314e-09 3.601657e-08 7.203314e-09
## [11] 3.601657e-08 7.203314e-09 0.000000e+00 7.203314e-09 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`1B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000
##
## $counts
## [1] 27695 30 8 3 5 2 1 4 2 2 0 0
## [13] 1 1 0 0 0 0 5 4 1 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 1
##
## $density
## [1] 1.994958e-04 2.160994e-07 5.762651e-08 2.160994e-08 3.601657e-08
## [6] 1.440663e-08 7.203314e-09 2.881325e-08 1.440663e-08 1.440663e-08
## [11] 0.000000e+00 0.000000e+00 7.203314e-09 7.203314e-09 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-08 2.881325e-08
## [21] 7.203314e-09 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000
##
## $counts
## [1] 27726 11 5 5 1 1 2 1 5 1 6 0
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 1
##
## $density
## [1] 9.985954e-05 3.961822e-08 1.800828e-08 1.800828e-08 3.601657e-09
## [6] 3.601657e-09 7.203314e-09 3.601657e-09 1.800828e-08 3.601657e-09
## [11] 2.160994e-08 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000
##
## $counts
## [1] 27721 14 5 1 2 9 0 2 0 5 0 0
## [13] 0 0 0 5 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 1
##
## $density
## [1] 1.996831e-04 1.008464e-07 3.601657e-08 7.203314e-09 1.440663e-08
## [6] 6.482982e-08 0.000000e+00 1.440663e-08 0.000000e+00 3.601657e-08
## [11] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 3.601657e-08 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000
##
## $counts
## [1] 27710 13 6 11 2 3 3 1 0 0 3 5
## [13] 0 1 0 5 0 0 1 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 1
##
## $density
## [1] 1.996038e-04 9.364308e-08 4.321988e-08 7.923645e-08 1.440663e-08
## [6] 2.160994e-08 2.160994e-08 7.203314e-09 0.000000e+00 0.000000e+00
## [11] 2.160994e-08 3.601657e-08 0.000000e+00 7.203314e-09 0.000000e+00
## [16] 3.601657e-08 0.000000e+00 0.000000e+00 7.203314e-09 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000
##
## $counts
## [1] 27708 20 3 9 1 1 2 2 3 0 5 6
## [13] 0 2 0 1 0 0 0 1 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 1
##
## $density
## [1] 1.995894e-04 1.440663e-07 2.160994e-08 6.482982e-08 7.203314e-09
## [6] 7.203314e-09 1.440663e-08 1.440663e-08 2.160994e-08 0.000000e+00
## [11] 3.601657e-08 4.321988e-08 0.000000e+00 1.440663e-08 0.000000e+00
## [16] 7.203314e-09 0.000000e+00 0.000000e+00 0.000000e+00 7.203314e-09
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000 380000 385000 390000
##
## $counts
## [1] 27708 17 5 7 2 4 2 1 1 1 3 1
## [13] 5 0 1 0 5 0 0 1 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 0 0 0 1
##
## $density
## [1] 1.995894e-04 1.224563e-07 3.601657e-08 5.042319e-08 1.440663e-08
## [6] 2.881325e-08 1.440663e-08 7.203314e-09 7.203314e-09 7.203314e-09
## [11] 2.160994e-08 7.203314e-09 3.601657e-08 0.000000e+00 7.203314e-09
## [16] 0.000000e+00 3.601657e-08 0.000000e+00 0.000000e+00 7.203314e-09
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [76] 0.000000e+00 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500 377500 382500 387500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000
##
## $counts
## [1] 27716 16 7 1 3 4 6 1 6 2 0 1
## [13] 0 0 1 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 1
##
## $density
## [1] 9.982352e-05 5.762651e-08 2.521160e-08 3.601657e-09 1.080497e-08
## [6] 1.440663e-08 2.160994e-08 3.601657e-09 2.160994e-08 7.203314e-09
## [11] 0.000000e+00 3.601657e-09 0.000000e+00 0.000000e+00 3.601657e-09
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
##
## $counts
## [1] 27726 7 9 3 3 1 1 2 0 1 5 1
## [13] 5 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 1
##
## $density
## [1] 9.985954e-05 2.521160e-08 3.241491e-08 1.080497e-08 1.080497e-08
## [6] 3.601657e-09 3.601657e-09 7.203314e-09 0.000000e+00 3.601657e-09
## [11] 1.800828e-08 3.601657e-09 1.800828e-08 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000 510000 520000 530000 540000
##
## $counts
## [1] 27720 14 2 5 3 3 2 0 6 2 6 0
## [13] 0 0 1 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 1
##
## $density
## [1] 9.983793e-05 5.042319e-08 7.203314e-09 1.800828e-08 1.080497e-08
## [6] 1.080497e-08 7.203314e-09 0.000000e+00 2.160994e-08 7.203314e-09
## [11] 2.160994e-08 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-09
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
## [51] 505000 515000 525000 535000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000 510000 520000 530000 540000 550000 560000 570000 580000 590000
## [61] 600000 610000 620000 630000 640000 650000 660000 670000 680000 690000
## [71] 700000 710000
##
## $counts
## [1] 27725 6 7 3 4 0 2 2 0 0 3 0
## [13] 0 1 0 0 1 4 0 5 0 1 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 1
##
## $density
## [1] 9.985593e-05 2.160994e-08 2.521160e-08 1.080497e-08 1.440663e-08
## [6] 0.000000e+00 7.203314e-09 7.203314e-09 0.000000e+00 0.000000e+00
## [11] 1.080497e-08 0.000000e+00 0.000000e+00 3.601657e-09 0.000000e+00
## [16] 0.000000e+00 3.601657e-09 1.440663e-08 0.000000e+00 1.800828e-08
## [21] 0.000000e+00 3.601657e-09 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
## [51] 505000 515000 525000 535000 545000 555000 565000 575000 585000 595000
## [61] 605000 615000 625000 635000 645000 655000 665000 675000 685000 695000
## [71] 705000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000 510000 520000 530000 540000 550000 560000
##
## $counts
## [1] 27726 3 11 5 4 2 1 0 6 0 1 5
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 1
##
## $density
## [1] 9.985954e-05 1.080497e-08 3.961822e-08 1.800828e-08 1.440663e-08
## [6] 7.203314e-09 3.601657e-09 0.000000e+00 2.160994e-08 0.000000e+00
## [11] 3.601657e-09 1.800828e-08 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
## [51] 505000 515000 525000 535000 545000 555000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7A`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000 380000 385000 390000
##
## $counts
## [1] 27702 23 6 4 2 3 2 2 1 1 1 6
## [13] 0 7 0 1 0 0 1 1 0 1 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 0 0 0 1
##
## $density
## [1] 1.995462e-04 1.656762e-07 4.321988e-08 2.881325e-08 1.440663e-08
## [6] 2.160994e-08 1.440663e-08 1.440663e-08 7.203314e-09 7.203314e-09
## [11] 7.203314e-09 4.321988e-08 0.000000e+00 5.042319e-08 0.000000e+00
## [16] 7.203314e-09 0.000000e+00 0.000000e+00 7.203314e-09 7.203314e-09
## [21] 0.000000e+00 7.203314e-09 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [76] 0.000000e+00 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500 377500 382500 387500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7B`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000 450000 460000 470000 480000 490000
## [51] 500000
##
## $counts
## [1] 27722 11 2 8 0 6 7 2 0 1 2 0
## [13] 1 1 1 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 1
##
## $density
## [1] 9.984513e-05 3.961822e-08 7.203314e-09 2.881325e-08 0.000000e+00
## [6] 2.160994e-08 2.521160e-08 7.203314e-09 0.000000e+00 3.601657e-09
## [11] 7.203314e-09 0.000000e+00 3.601657e-09 3.601657e-09 3.601657e-09
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000 445000 455000 465000 475000 485000 495000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9A`
## $breaks
## [1] 0 10000 20000 30000 40000 50000 60000 70000 80000 90000
## [11] 100000 110000 120000 130000 140000 150000 160000 170000 180000 190000
## [21] 200000 210000 220000 230000 240000 250000 260000 270000 280000 290000
## [31] 300000 310000 320000 330000 340000 350000 360000 370000 380000 390000
## [41] 400000 410000 420000 430000 440000
##
## $counts
## [1] 27724 7 7 5 4 1 3 0 0 6 7 0
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 1
##
## $density
## [1] 9.985233e-05 2.521160e-08 2.521160e-08 1.800828e-08 1.440663e-08
## [6] 3.601657e-09 1.080497e-08 0.000000e+00 0.000000e+00 2.160994e-08
## [11] 2.521160e-08 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 3.601657e-09
##
## $mids
## [1] 5000 15000 25000 35000 45000 55000 65000 75000 85000 95000
## [11] 105000 115000 125000 135000 145000 155000 165000 175000 185000 195000
## [21] 205000 215000 225000 235000 245000 255000 265000 275000 285000 295000
## [31] 305000 315000 325000 335000 345000 355000 365000 375000 385000 395000
## [41] 405000 415000 425000 435000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000 380000 385000
##
## $counts
## [1] 27690 29 12 2 4 3 0 3 2 0 0 2
## [13] 0 7 3 3 1 0 0 0 1 1 0 1
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 0 0 1
##
## $density
## [1] 1.994598e-04 2.088961e-07 8.643976e-08 1.440663e-08 2.881325e-08
## [6] 2.160994e-08 0.000000e+00 2.160994e-08 1.440663e-08 0.000000e+00
## [11] 0.000000e+00 1.440663e-08 0.000000e+00 5.042319e-08 2.160994e-08
## [16] 2.160994e-08 7.203314e-09 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 7.203314e-09 7.203314e-09 0.000000e+00 7.203314e-09 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [76] 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500 377500 382500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10A`
## $breaks
## [1] 0 20000 40000 60000 80000 100000 120000 140000 160000 180000
## [11] 200000 220000 240000 260000 280000 300000 320000 340000 360000 380000
## [21] 400000 420000 440000 460000 480000 500000 520000 540000 560000 580000
## [31] 600000 620000 640000 660000 680000 700000 720000 740000 760000 780000
## [41] 800000 820000 840000 860000
##
## $counts
## [1] 27727 7 11 1 5 1 5 0 6 0 1 0
## [13] 0 0 0 0 0 0 0 0 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 1
##
## $density
## [1] 4.993157e-05 1.260580e-08 1.980911e-08 1.800828e-09 9.004142e-09
## [6] 1.800828e-09 9.004142e-09 0.000000e+00 1.080497e-08 0.000000e+00
## [11] 1.800828e-09 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 1.800828e-09
##
## $mids
## [1] 10000 30000 50000 70000 90000 110000 130000 150000 170000 190000
## [11] 210000 230000 250000 270000 290000 310000 330000 350000 370000 390000
## [21] 410000 430000 450000 470000 490000 510000 530000 550000 570000 590000
## [31] 610000 630000 650000 670000 690000 710000 730000 750000 770000 790000
## [41] 810000 830000 850000
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10B`
## $breaks
## [1] 0 5000 10000 15000 20000 25000 30000 35000 40000 45000
## [11] 50000 55000 60000 65000 70000 75000 80000 85000 90000 95000
## [21] 100000 105000 110000 115000 120000 125000 130000 135000 140000 145000
## [31] 150000 155000 160000 165000 170000 175000 180000 185000 190000 195000
## [41] 200000 205000 210000 215000 220000 225000 230000 235000 240000 245000
## [51] 250000 255000 260000 265000 270000 275000 280000 285000 290000 295000
## [61] 300000 305000 310000 315000 320000 325000 330000 335000 340000 345000
## [71] 350000 355000 360000 365000 370000 375000
##
## $counts
## [1] 27700 22 8 7 4 1 2 1 0 1 3 2
## [13] 0 0 6 0 0 5 0 2 0 0 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0
## [49] 0 0 0 0 0 0 0 0 0 0 0 0
## [61] 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 1
##
## $density
## [1] 1.995318e-04 1.584729e-07 5.762651e-08 5.042319e-08 2.881325e-08
## [6] 7.203314e-09 1.440663e-08 7.203314e-09 0.000000e+00 7.203314e-09
## [11] 2.160994e-08 1.440663e-08 0.000000e+00 0.000000e+00 4.321988e-08
## [16] 0.000000e+00 0.000000e+00 3.601657e-08 0.000000e+00 1.440663e-08
## [21] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [31] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [46] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [51] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [56] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [61] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [66] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [71] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 7.203314e-09
##
## $mids
## [1] 2500 7500 12500 17500 22500 27500 32500 37500 42500 47500
## [11] 52500 57500 62500 67500 72500 77500 82500 87500 92500 97500
## [21] 102500 107500 112500 117500 122500 127500 132500 137500 142500 147500
## [31] 152500 157500 162500 167500 172500 177500 182500 187500 192500 197500
## [41] 202500 207500 212500 217500 222500 227500 232500 237500 242500 247500
## [51] 252500 257500 262500 267500 272500 277500 282500 287500 292500 297500
## [61] 302500 307500 312500 317500 322500 327500 332500 337500 342500 347500
## [71] 352500 357500 362500 367500 372500
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"dev.off()## png
## 2Step 2.4: TMM Normalization
# Create a DGEList object (Digital Gene Expression list) from the filtered count matrix
# This is required for edgeR normalization and downstream differential expression analysis
dge <- DGEList(counts = rna_counts_filtered)
# Apply TMM (Trimmed Mean of M-values) normalization to account for library size and composition bias
# This step calculates scaling factors to make samples more comparable
dge <- calcNormFactors(dge, method = "TMM")Step 2.5: log2(CPM + 1)
# Convert raw counts to log2 Counts Per Million (CPM) using edgeR's `cpm()` function
# log = TRUE applies log2 transformation; prior.count = 1 avoids taking log(0)
rna_log_cpm <- cpm(dge, log = TRUE, prior.count = 1)
# Save the normalized log2 CPM matrix to a CSV file
write.csv(rna_log_cpm, "RNA_log2_CPM_TMM_filtered.csv")
# Generate histograms for each sample's log2 CPM distribution (QC visualization)
pdf("Histogram_RNA_log2_CPM_TMM_filtered.pdf")
apply(rna_log_cpm, 2, function(x) hist(x, breaks = 60))## $`1A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5
##
## $counts
## [1] 6537 0 2333 0 1454 1842 1166 1338 1313 1208 1700 1391 1452 1296 1185
## [16] 1016 774 590 428 245 189 105 83 45 16 10 8 8 10 4
## [31] 2 3 12 1 0 0 0 1
##
## $density
## [1] 4.708806e-01 0.000000e+00 1.680533e-01 0.000000e+00 1.047362e-01
## [6] 1.326850e-01 8.399064e-02 9.638033e-02 9.457951e-02 8.701603e-02
## [11] 1.224563e-01 1.001981e-01 1.045921e-01 9.335494e-02 8.535927e-02
## [16] 7.318567e-02 5.575365e-02 4.249955e-02 3.083018e-02 1.764812e-02
## [21] 1.361426e-02 7.563479e-03 5.978750e-03 3.241491e-03 1.152530e-03
## [26] 7.203314e-04 5.762651e-04 5.762651e-04 7.203314e-04 2.881325e-04
## [31] 1.440663e-04 2.160994e-04 8.643976e-04 7.203314e-05 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`1B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0
##
## $counts
## [1] 5948 0 1814 2091 739 1589 1033 1196 1458 1352 1415 1437 1435 1282 1236
## [16] 1010 840 642 435 305 169 127 78 51 22 16 9 5 7 4
## [31] 7 2 8 2 0 0 1
##
## $density
## [1] 4.284531e-01 0.000000e+00 1.306681e-01 1.506213e-01 5.323249e-02
## [6] 1.144607e-01 7.441023e-02 8.615163e-02 1.050243e-01 9.738880e-02
## [11] 1.019269e-01 1.035116e-01 1.033675e-01 9.234648e-02 8.903296e-02
## [16] 7.275347e-02 6.050783e-02 4.624527e-02 3.133441e-02 2.197011e-02
## [21] 1.217360e-02 9.148208e-03 5.618585e-03 3.673690e-03 1.584729e-03
## [26] 1.152530e-03 6.482982e-04 3.601657e-04 5.042319e-04 2.881325e-04
## [31] 5.042319e-04 1.440663e-04 5.762651e-04 1.440663e-04 0.000000e+00
## [36] 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5
##
## $counts
## [1] 6135 0 2186 0 1465 1926 743 1622 1585 1715 1481 1643 1556 1361 1171
## [16] 951 726 542 352 228 144 87 58 24 12 6 4 3 5 6
## [31] 4 5 2 4 11 1 0 0 0 1
##
## $density
## [1] 4.419233e-01 0.000000e+00 1.574644e-01 0.000000e+00 1.055285e-01
## [6] 1.387358e-01 5.352062e-02 1.168377e-01 1.141725e-01 1.235368e-01
## [11] 1.066811e-01 1.183504e-01 1.120836e-01 9.803710e-02 8.435080e-02
## [16] 6.850351e-02 5.229606e-02 3.904196e-02 2.535566e-02 1.642355e-02
## [21] 1.037277e-02 6.266883e-03 4.177922e-03 1.728795e-03 8.643976e-04
## [26] 4.321988e-04 2.881325e-04 2.160994e-04 3.601657e-04 4.321988e-04
## [31] 2.881325e-04 3.601657e-04 1.440663e-04 2.881325e-04 7.923645e-04
## [36] 7.203314e-05 0.000000e+00 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25 16.75 17.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0
##
## $counts
## [1] 7287 0 0 2321 1509 1106 941 1919 1402 1334 1468 1514 1485 1194 1049
## [16] 921 688 550 385 258 172 91 59 36 17 8 8 10 3 6
## [31] 1 10 2 5 5 0 0 0 1
##
## $density
## [1] 5.249055e-01 0.000000e+00 0.000000e+00 1.671889e-01 1.086980e-01
## [6] 7.966865e-02 6.778318e-02 1.382316e-01 1.009905e-01 9.609220e-02
## [11] 1.057446e-01 1.090582e-01 1.069692e-01 8.600756e-02 7.556276e-02
## [16] 6.634252e-02 4.955880e-02 3.961822e-02 2.773276e-02 1.858455e-02
## [21] 1.238970e-02 6.555015e-03 4.249955e-03 2.593193e-03 1.224563e-03
## [26] 5.762651e-04 5.762651e-04 7.203314e-04 2.160994e-04 4.321988e-04
## [31] 7.203314e-05 7.203314e-04 1.440663e-04 3.601657e-04 3.601657e-04
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25 16.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5
##
## $counts
## [1] 6508 0 2062 1372 962 1360 996 1387 1337 1374 1454 1382 1463 1345 1187
## [16] 1006 787 595 429 274 183 101 79 40 25 9 5 4 10 6
## [31] 6 1 9 6 0 0 0 1
##
## $density
## [1] 4.687916e-01 0.000000e+00 1.485323e-01 9.882946e-02 6.929588e-02
## [6] 9.796506e-02 7.174500e-02 9.990996e-02 9.630830e-02 9.897353e-02
## [11] 1.047362e-01 9.954979e-02 1.053845e-01 9.688457e-02 8.550333e-02
## [16] 7.246533e-02 5.669008e-02 4.285972e-02 3.090222e-02 1.973708e-02
## [21] 1.318206e-02 7.275347e-03 5.690618e-03 2.881325e-03 1.800828e-03
## [26] 6.482982e-04 3.601657e-04 2.881325e-04 7.203314e-04 4.321988e-04
## [31] 4.321988e-04 7.203314e-05 6.482982e-04 4.321988e-04 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0
##
## $counts
## [1] 6133 0 2087 1356 955 1815 805 1201 1402 1350 1561 1430 1449 1441 1183
## [16] 1071 758 589 427 277 175 99 78 44 22 13 7 3 9 2
## [31] 4 9 8 1 0 0 1
##
## $density
## [1] 4.417792e-01 0.000000e+00 1.503332e-01 9.767693e-02 6.879164e-02
## [6] 1.307401e-01 5.798667e-02 8.651180e-02 1.009905e-01 9.724473e-02
## [11] 1.124437e-01 1.030074e-01 1.043760e-01 1.037997e-01 8.521520e-02
## [16] 7.714749e-02 5.460112e-02 4.242752e-02 3.075815e-02 1.995318e-02
## [21] 1.260580e-02 7.131280e-03 5.618585e-03 3.169458e-03 1.584729e-03
## [26] 9.364308e-04 5.042319e-04 2.160994e-04 6.482982e-04 1.440663e-04
## [31] 2.881325e-04 6.482982e-04 5.762651e-04 7.203314e-05 0.000000e+00
## [36] 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5
##
## $counts
## [1] 5537 0 1777 2088 731 1592 1091 1324 1372 1537 1434 1603 1575 1405 1245
## [16] 1075 781 546 362 253 175 84 77 33 15 8 7 5 7 6
## [31] 2 10 6 1 0 0 0 1
##
## $density
## [1] 3.988475e-01 0.000000e+00 1.280029e-01 1.504052e-01 5.265622e-02
## [6] 1.146768e-01 7.858815e-02 9.537187e-02 9.882946e-02 1.107149e-01
## [11] 1.032955e-01 1.154691e-01 1.134522e-01 1.012066e-01 8.968125e-02
## [16] 7.743562e-02 5.625788e-02 3.933009e-02 2.607599e-02 1.822438e-02
## [21] 1.260580e-02 6.050783e-03 5.546551e-03 2.377093e-03 1.080497e-03
## [26] 5.762651e-04 5.042319e-04 3.601657e-04 5.042319e-04 4.321988e-04
## [31] 1.440663e-04 7.203314e-04 4.321988e-04 7.203314e-05 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0
##
## $counts
## [1] 4831 1756 1216 1583 1070 1106 1292 1257 1263 1424 1524 1524 1591 1449 1301
## [16] 1084 831 618 373 260 142 114 53 37 15 6 11 5 4 2
## [31] 6 12 3 1 0 0 1
##
## $density
## [1] 3.479921e-01 1.264902e-01 8.759229e-02 1.140285e-01 7.707545e-02
## [6] 7.966865e-02 9.306681e-02 9.054565e-02 9.097785e-02 1.025752e-01
## [11] 1.097785e-01 1.097785e-01 1.146047e-01 1.043760e-01 9.371511e-02
## [16] 7.808392e-02 5.985954e-02 4.451648e-02 2.686836e-02 1.872862e-02
## [21] 1.022871e-02 8.211777e-03 3.817756e-03 2.665226e-03 1.080497e-03
## [26] 4.321988e-04 7.923645e-04 3.601657e-04 2.881325e-04 1.440663e-04
## [31] 4.321988e-04 8.643976e-04 2.160994e-04 7.203314e-05 0.000000e+00
## [36] 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0
##
## $counts
## [1] 7677 0 0 1923 1345 1004 883 1298 1469 1718 1622 1452 1581 1295 1138
## [16] 980 761 576 350 233 175 105 68 40 13 10 5 3 4 4
## [31] 1 9 4 3 3 7 5 0 0 0 1
##
## $density
## [1] 5.529984e-01 0.000000e+00 0.000000e+00 1.385197e-01 9.688457e-02
## [6] 7.232127e-02 6.360526e-02 9.349901e-02 1.058167e-01 1.237529e-01
## [11] 1.168377e-01 1.045921e-01 1.138844e-01 9.328291e-02 8.197371e-02
## [16] 7.059247e-02 5.481722e-02 4.149109e-02 2.521160e-02 1.678372e-02
## [21] 1.260580e-02 7.563479e-03 4.898253e-03 2.881325e-03 9.364308e-04
## [26] 7.203314e-04 3.601657e-04 2.160994e-04 2.881325e-04 2.881325e-04
## [31] 7.203314e-05 6.482982e-04 2.881325e-04 2.160994e-04 2.160994e-04
## [36] 5.042319e-04 3.601657e-04 0.000000e+00 0.000000e+00 0.000000e+00
## [41] 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25 16.75 17.25 17.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0
##
## $counts
## [1] 6255 0 1921 1341 1020 1428 1045 1567 1408 1442 1516 1489 1374 1314 1125
## [16] 944 791 603 414 278 183 101 69 59 20 6 5 5 11 1
## [31] 3 5 6 7 7 1 0 0 1
##
## $density
## [1] 4.505673e-01 0.000000e+00 1.383757e-01 9.659643e-02 7.347380e-02
## [6] 1.028633e-01 7.527463e-02 1.128759e-01 1.014227e-01 1.038718e-01
## [11] 1.092022e-01 1.072573e-01 9.897353e-02 9.465154e-02 8.103728e-02
## [16] 6.799928e-02 5.697821e-02 4.343598e-02 2.982172e-02 2.002521e-02
## [21] 1.318206e-02 7.275347e-03 4.970286e-03 4.249955e-03 1.440663e-03
## [26] 4.321988e-04 3.601657e-04 3.601657e-04 7.923645e-04 7.203314e-05
## [31] 2.160994e-04 3.601657e-04 4.321988e-04 5.042319e-04 5.042319e-04
## [36] 7.203314e-05 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25 16.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5
##
## $counts
## [1] 9115 0 0 1537 1060 862 758 1251 1390 1723 1496 1335 1448 1301 1139
## [16] 937 737 533 425 241 181 88 79 43 27 8 5 4 3 2
## [31] 3 7 3 4 4 3 1 11 0 0 0 1
##
## $density
## [1] 6.565820e-01 0.000000e+00 0.000000e+00 1.107149e-01 7.635512e-02
## [6] 6.209256e-02 5.460112e-02 9.011345e-02 1.001261e-01 1.241131e-01
## [11] 1.077616e-01 9.616424e-02 1.043040e-01 9.371511e-02 8.204574e-02
## [16] 6.749505e-02 5.308842e-02 3.839366e-02 3.061408e-02 1.735999e-02
## [21] 1.303800e-02 6.338916e-03 5.690618e-03 3.097425e-03 1.944895e-03
## [26] 5.762651e-04 3.601657e-04 2.881325e-04 2.160994e-04 1.440663e-04
## [31] 2.160994e-04 5.042319e-04 2.160994e-04 2.881325e-04 2.881325e-04
## [36] 2.160994e-04 7.203314e-05 7.923645e-04 0.000000e+00 0.000000e+00
## [41] 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25 16.75 17.25 17.75 18.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5
##
## $counts
## [1] 6868 0 0 2135 1488 1023 1597 1611 1611 1458 1392 1563 1375 1220 1081
## [16] 924 726 569 354 271 187 95 78 38 34 13 9 5 1 3
## [31] 5 11 4 3 6 6 0 0 0 1
##
## $density
## [1] 4.947236e-01 0.000000e+00 0.000000e+00 1.537907e-01 1.071853e-01
## [6] 7.368990e-02 1.150369e-01 1.160454e-01 1.160454e-01 1.050243e-01
## [11] 1.002701e-01 1.125878e-01 9.904556e-02 8.788042e-02 7.786782e-02
## [16] 6.655862e-02 5.229606e-02 4.098685e-02 2.549973e-02 1.952098e-02
## [21] 1.347020e-02 6.843148e-03 5.618585e-03 2.737259e-03 2.449127e-03
## [26] 9.364308e-04 6.482982e-04 3.601657e-04 7.203314e-05 2.160994e-04
## [31] 3.601657e-04 7.923645e-04 2.881325e-04 2.160994e-04 4.321988e-04
## [36] 4.321988e-04 0.000000e+00 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25 16.75 17.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0
##
## $counts
## [1] 5162 1921 1323 920 1407 1310 940 1316 1361 1355 1433 1599 1529 1398 1224
## [16] 1064 832 597 396 242 157 101 80 28 14 16 6 4 4 4
## [31] 4 13 4 0 0 0 1
##
## $density
## [1] 3.718350e-01 1.383757e-01 9.529984e-02 6.627048e-02 1.013506e-01
## [6] 9.436341e-02 6.771115e-02 9.479561e-02 9.803710e-02 9.760490e-02
## [11] 1.032235e-01 1.151810e-01 1.101387e-01 1.007023e-01 8.816856e-02
## [16] 7.664326e-02 5.993157e-02 4.300378e-02 2.852512e-02 1.743202e-02
## [21] 1.130920e-02 7.275347e-03 5.762651e-03 2.016928e-03 1.008464e-03
## [26] 1.152530e-03 4.321988e-04 2.881325e-04 2.881325e-04 2.881325e-04
## [31] 2.881325e-04 9.364308e-04 2.881325e-04 0.000000e+00 0.000000e+00
## [36] 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0
##
## $counts
## [1] 5105 1810 1138 1654 1087 1126 1304 1018 1226 1376 1515 1521 1524 1440 1242
## [16] 1093 841 636 422 234 158 112 80 29 18 15 7 2 4 6
## [31] 7 8 4 2 0 0 1
##
## $density
## [1] 3.677292e-01 1.303800e-01 8.197371e-02 1.191428e-01 7.830002e-02
## [6] 8.110931e-02 9.393121e-02 7.332973e-02 8.831262e-02 9.911759e-02
## [11] 1.091302e-01 1.095624e-01 1.097785e-01 1.037277e-01 8.946515e-02
## [16] 7.873222e-02 6.057987e-02 4.581307e-02 3.039798e-02 1.685575e-02
## [21] 1.138124e-02 8.067711e-03 5.762651e-03 2.088961e-03 1.296596e-03
## [26] 1.080497e-03 5.042319e-04 1.440663e-04 2.881325e-04 4.321988e-04
## [31] 5.042319e-04 5.762651e-04 2.881325e-04 1.440663e-04 0.000000e+00
## [36] 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5
##
## $counts
## [1] 6372 0 1354 1764 1265 904 1381 1214 1443 1279 1592 1554 1496 1417 1229
## [16] 1029 794 602 399 250 138 107 79 34 17 10 6 2 6 6
## [31] 4 4 12 1 0 0 0 1
##
## $density
## [1] 4.589951e-01 0.000000e+00 9.753287e-02 1.270665e-01 9.112192e-02
## [6] 6.511795e-02 9.947776e-02 8.744823e-02 1.039438e-01 9.213038e-02
## [11] 1.146768e-01 1.119395e-01 1.077616e-01 1.020710e-01 8.852872e-02
## [16] 7.412210e-02 5.719431e-02 4.336395e-02 2.874122e-02 1.800828e-02
## [21] 9.940573e-03 7.707545e-03 5.690618e-03 2.449127e-03 1.224563e-03
## [26] 7.203314e-04 4.321988e-04 1.440663e-04 4.321988e-04 4.321988e-04
## [31] 2.881325e-04 2.881325e-04 8.643976e-04 7.203314e-05 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0
##
## $counts
## [1] 5839 1757 1158 904 1319 1330 1160 1303 1241 1315 1457 1438 1392 1315 1195
## [16] 1052 769 606 429 291 181 107 78 53 22 8 12 2 7 2
## [31] 3 15 3 1 0 0 1
##
## $density
## [1] 4.206015e-01 1.265622e-01 8.341437e-02 6.511795e-02 9.501171e-02
## [6] 9.580407e-02 8.355844e-02 9.385918e-02 8.939312e-02 9.472357e-02
## [11] 1.049523e-01 1.035836e-01 1.002701e-01 9.472357e-02 8.607960e-02
## [16] 7.577886e-02 5.539348e-02 4.365208e-02 3.090222e-02 2.096164e-02
## [21] 1.303800e-02 7.707545e-03 5.618585e-03 3.817756e-03 1.584729e-03
## [26] 5.762651e-04 8.643976e-04 1.440663e-04 5.042319e-04 1.440663e-04
## [31] 2.160994e-04 1.080497e-03 2.160994e-04 7.203314e-05 0.000000e+00
## [36] 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10A`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0
##
## $counts
## [1] 5302 1408 1052 837 1303 1346 1577 1282 1332 1664 1557 1567 1558 1414 1173
## [16] 972 787 559 403 258 154 97 66 34 10 8 3 4 4 4
## [31] 10 2 5 5 7 0 0 0 1
##
## $density
## [1] 3.819197e-01 1.014227e-01 7.577886e-02 6.029173e-02 9.385918e-02
## [6] 9.695660e-02 1.135963e-01 9.234648e-02 9.594814e-02 1.198631e-01
## [11] 1.121556e-01 1.128759e-01 1.122276e-01 1.018549e-01 8.449487e-02
## [16] 7.001621e-02 5.669008e-02 4.026652e-02 2.902935e-02 1.858455e-02
## [21] 1.109310e-02 6.987214e-03 4.754187e-03 2.449127e-03 7.203314e-04
## [26] 5.762651e-04 2.160994e-04 2.881325e-04 2.881325e-04 2.881325e-04
## [31] 7.203314e-04 1.440663e-04 3.601657e-04 3.601657e-04 5.042319e-04
## [36] 0.000000e+00 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25 16.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10B`
## $breaks
## [1] -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
## [16] 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
## [31] 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5
##
## $counts
## [1] 7258 0 1464 1028 1538 1131 1141 1216 1290 1402 1336 1538 1401 1253 1155
## [16] 990 785 608 466 257 190 104 77 56 21 9 9 7 10 2
## [31] 3 6 6 7 0 0 0 1
##
## $density
## [1] 5.228165e-01 0.000000e+00 1.054565e-01 7.405006e-02 1.107870e-01
## [6] 8.146948e-02 8.218981e-02 8.759229e-02 9.292274e-02 1.009905e-01
## [11] 9.623627e-02 1.107870e-01 1.009184e-01 9.025752e-02 8.319827e-02
## [16] 7.131280e-02 5.654601e-02 4.379615e-02 3.356744e-02 1.851252e-02
## [21] 1.368630e-02 7.491446e-03 5.546551e-03 4.033856e-03 1.512696e-03
## [26] 6.482982e-04 6.482982e-04 5.042319e-04 7.203314e-04 1.440663e-04
## [31] 2.160994e-04 4.321988e-04 4.321988e-04 5.042319e-04 0.000000e+00
## [36] 0.000000e+00 0.000000e+00 7.203314e-05
##
## $mids
## [1] -2.25 -1.75 -1.25 -0.75 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25
## [13] 3.75 4.25 4.75 5.25 5.75 6.25 6.75 7.25 7.75 8.25 8.75 9.25
## [25] 9.75 10.25 10.75 11.25 11.75 12.25 12.75 13.25 13.75 14.25 14.75 15.25
## [37] 15.75 16.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"dev.off()## png
## 2Step 2.6: Z-score Normalization
# Perform z-score normalization (standardization) across genes (rows)
# Each value is transformed to (x - mean) / sd per gene
GE_z <- scale(rna_log_cpm)
# Save the z-score normalized expression matrix to a CSV file
write.csv(GE_z, "RNA_TMM_log2_zscore.csv")
# Generate histograms to visualize the distribution of z-scores for each sample
pdf("Histogram_RNA_TMM_log2_zscore.pdf")
apply(GE_z, 2, function(x) hist(x, breaks = 60))## $`1A`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0
##
## $counts
## [1] 6537 0 0 0 2333 0 0 1454 1037 805 625 541 939 758 682
## [16] 752 959 955 947 851 887 809 760 732 653 707 583 476 403 342
## [31] 281 229 155 127 101 89 55 56 37 29 11 9 8 3 6
## [46] 6 3 7 5 2 0 2 2 1 6 6 1 0 0 0
## [61] 0 0 1
##
## $density
## [1] 2.3544030254 0.0000000000 0.0000000000 0.0000000000 0.8402665226
## [6] 0.0000000000 0.0000000000 0.5236808932 0.3734918062 0.2899333693
## [11] 0.2251035476 0.1948496308 0.3381955700 0.2730055826 0.2456329912
## [16] 0.2708445885 0.3453988835 0.3439582208 0.3410768954 0.3065009905
## [21] 0.3194669548 0.2913740321 0.2737259139 0.2636412750 0.2351881866
## [26] 0.2546371331 0.2099765892 0.1714388619 0.1451467675 0.1231766613
## [31] 0.1012065550 0.0824779399 0.0558256798 0.0457410409 0.0363767333
## [36] 0.0320547452 0.0198091122 0.0201692779 0.0133261300 0.0104448046
## [41] 0.0039618224 0.0032414911 0.0028813254 0.0010804970 0.0021609941
## [46] 0.0021609941 0.0010804970 0.0025211597 0.0018008284 0.0007203314
## [51] 0.0000000000 0.0007203314 0.0007203314 0.0003601657 0.0021609941
## [56] 0.0021609941 0.0003601657 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`1B`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8
##
## $counts
## [1] 5948 0 0 1814 0 1217 874 739 613 976 735 563 731 832 826
## [16] 724 885 882 858 855 853 821 782 771 726 656 551 507 415 369
## [31] 288 204 197 132 83 85 67 47 31 25 16 7 14 6 4
## [46] 4 2 4 4 2 4 3 2 0 10 0 0 0 0 0
## [61] 1
##
## $density
## [1] 2.1422654421 0.0000000000 0.0000000000 0.6533405366 0.0000000000
## [6] 0.4383216279 0.3147848010 0.2661624347 0.2207815595 0.3515217000
## [11] 0.2647217720 0.2027732757 0.2632811093 0.2996578426 0.2974968486
## [16] 0.2607599496 0.3187466234 0.3176661264 0.3090221502 0.3079416532
## [21] 0.3072213218 0.2956960202 0.2816495588 0.2776877364 0.2614802809
## [26] 0.2362686836 0.1984512876 0.1826039978 0.1494687556 0.1329011345
## [31] 0.1037277147 0.0734737979 0.0709526382 0.0475418693 0.0298937511
## [36] 0.0306140825 0.0241311003 0.0169277868 0.0111651360 0.0090041419
## [41] 0.0057626508 0.0025211597 0.0050423195 0.0021609941 0.0014406627
## [46] 0.0014406627 0.0007203314 0.0014406627 0.0014406627 0.0007203314
## [51] 0.0014406627 0.0010804970 0.0007203314 0.0000000000 0.0036016568
## [56] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2A`
## $breaks
## [1] -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
## [16] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
## [31] 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
## [46] 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5
## [61] 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5
##
## $counts
## [1] 6135 0 0 0 0 2186 0 1465 0 1072 854 743 630 992 867
## [16] 718 916 799 1073 927 869 939 872 766 710 735 629 511 465 393
## [31] 369 232 217 147 128 112 63 58 43 26 24 10 12 7 4
## [46] 2 3 1 2 2 3 1 5 3 3 3 2 1 2 1
## [61] 6 6 0 0 0 0 0 0 1
##
## $density
## [1] 2.2096164236 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [6] 0.7873221682 0.0000000000 0.5276427156 0.0000000000 0.3860976049
## [11] 0.3075814875 0.2676030974 0.2269043760 0.3572843508 0.3122636413
## [16] 0.2585989555 0.3299117594 0.2877723753 0.3864577706 0.3338735818
## [21] 0.3129839726 0.3381955700 0.3140644697 0.2758869080 0.2557176301
## [26] 0.2647217720 0.2265442103 0.1840446605 0.1674770394 0.1415451108
## [31] 0.1329011345 0.0835584369 0.0781559517 0.0529443544 0.0461012066
## [36] 0.0403385557 0.0226904376 0.0208896092 0.0154871241 0.0093643076
## [41] 0.0086439762 0.0036016568 0.0043219881 0.0025211597 0.0014406627
## [46] 0.0007203314 0.0010804970 0.0003601657 0.0007203314 0.0007203314
## [51] 0.0010804970 0.0003601657 0.0018008284 0.0010804970 0.0010804970
## [56] 0.0010804970 0.0007203314 0.0003601657 0.0007203314 0.0003601657
## [61] 0.0021609941 0.0021609941 0.0000000000 0.0000000000 0.0000000000
## [66] 0.0000000000 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.35 -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25
## [13] -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95
## [25] 1.05 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15
## [37] 2.25 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35
## [49] 3.45 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55
## [61] 4.65 4.75 4.85 4.95 5.05 5.15 5.25 5.35 5.45
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`2B`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0 5.1 5.2
##
## $counts
## [1] 7287 0 0 0 0 2321 0 0 1509 0 1106 941 703 1216 972
## [16] 828 936 764 899 858 853 832 731 724 596 608 545 492 385 345
## [31] 293 237 182 142 107 96 63 43 26 28 21 14 5 5 5
## [46] 4 8 3 2 2 3 1 1 9 1 2 5 0 0 5
## [61] 0 0 0 0 1
##
## $density
## [1] 2.6245272825 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [6] 0.8359445345 0.0000000000 0.0000000000 0.5434900054 0.0000000000
## [11] 0.3983432379 0.3389159013 0.2531964704 0.4379614623 0.3500810373
## [16] 0.2982171799 0.3371150729 0.2751665766 0.3237889429 0.3090221502
## [21] 0.3072213218 0.2996578426 0.2632811093 0.2607599496 0.2146587430
## [26] 0.2189807311 0.1962902935 0.1772015127 0.1386637853 0.1242571583
## [31] 0.1055285431 0.0853592653 0.0655501531 0.0511435260 0.0385377274
## [36] 0.0345759049 0.0226904376 0.0154871241 0.0093643076 0.0100846389
## [41] 0.0075634792 0.0050423195 0.0018008284 0.0018008284 0.0018008284
## [46] 0.0014406627 0.0028813254 0.0010804970 0.0007203314 0.0007203314
## [51] 0.0010804970 0.0003601657 0.0003601657 0.0032414911 0.0003601657
## [56] 0.0007203314 0.0018008284 0.0000000000 0.0000000000 0.0018008284
## [61] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95 5.05 5.15
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3A`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0
##
## $counts
## [1] 6508 0 0 0 2062 0 1372 962 0 1360 515 872 703 594 793
## [16] 867 929 736 963 771 916 875 862 734 669 653 559 498 421 321
## [31] 291 223 176 139 102 76 44 52 40 22 17 11 4 7 3
## [46] 1 3 4 10 2 2 4 1 1 7 6 1 0 0 0
## [61] 0 0 1
##
## $density
## [1] 2.3439582208 0.0000000000 0.0000000000 0.0000000000 0.7426616243
## [6] 0.0000000000 0.4941473078 0.3464793805 0.0000000000 0.4898253196
## [11] 0.1854853232 0.3140644697 0.2531964704 0.2139384117 0.2856113812
## [16] 0.3122636413 0.3345939132 0.2650819377 0.3468395462 0.2776877364
## [21] 0.3299117594 0.3151449667 0.3104628129 0.2643616063 0.2409508374
## [26] 0.2351881866 0.2013326130 0.1793625068 0.1516297497 0.1156131821
## [31] 0.1048082118 0.0803169458 0.0633891590 0.0500630290 0.0367368990
## [36] 0.0273725914 0.0158472898 0.0187286152 0.0144066270 0.0079236449
## [41] 0.0061228165 0.0039618224 0.0014406627 0.0025211597 0.0010804970
## [46] 0.0003601657 0.0010804970 0.0014406627 0.0036016568 0.0007203314
## [51] 0.0007203314 0.0014406627 0.0003601657 0.0003601657 0.0025211597
## [56] 0.0021609941 0.0003601657 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`3B`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9
##
## $counts
## [1] 6133 0 0 2087 0 1356 0 955 752 559 931 704 606 778 893
## [16] 703 933 909 869 861 908 833 843 791 683 659 576 456 424 335
## [31] 275 225 176 137 102 64 51 51 39 24 13 14 11 4 4
## [46] 2 2 4 6 1 0 4 3 11 3 0 1 0 0 0
## [61] 0 1
##
## $density
## [1] 2.2088960922 0.0000000000 0.0000000000 0.7516657663 0.0000000000
## [6] 0.4883846569 0.0000000000 0.3439582208 0.2708445885 0.2013326130
## [11] 0.3353142446 0.2535566361 0.2182603998 0.2802088961 0.3216279489
## [16] 0.2531964704 0.3360345759 0.3273905997 0.3129839726 0.3101026472
## [21] 0.3270304340 0.3000180083 0.3036196650 0.2848910499 0.2459931569
## [26] 0.2373491806 0.2074554295 0.1642355484 0.1527102467 0.1206555015
## [31] 0.0990455610 0.0810372771 0.0633891590 0.0493426976 0.0367368990
## [36] 0.0230506033 0.0183684495 0.0183684495 0.0140464614 0.0086439762
## [41] 0.0046821538 0.0050423195 0.0039618224 0.0014406627 0.0014406627
## [46] 0.0007203314 0.0007203314 0.0014406627 0.0021609941 0.0003601657
## [51] 0.0000000000 0.0014406627 0.0010804970 0.0039618224 0.0010804970
## [56] 0.0000000000 0.0003601657 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4A`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0
##
## $counts
## [1] 5537 0 0 1777 1133 0 955 731 641 951 783 595 813 858 738
## [16] 967 830 892 926 910 918 877 835 786 716 672 595 467 398 310
## [31] 261 194 164 132 106 58 55 50 37 18 18 7 4 5 5
## [46] 2 3 7 2 3 3 1 2 9 1 5 1 0 0 0
## [61] 0 0 1
##
## $density
## [1] 1.9942373492 0.0000000000 0.0000000000 0.6400144066 0.4080677111
## [6] 0.0000000000 0.3439582208 0.2632811093 0.2308661985 0.3425175581
## [11] 0.2820097245 0.2142985773 0.2928146948 0.3090221502 0.2658022690
## [16] 0.3482802089 0.2989375113 0.3212677832 0.3335134162 0.3277507654
## [21] 0.3306320908 0.3158652980 0.3007383396 0.2830902215 0.2578786242
## [26] 0.2420313344 0.2142985773 0.1681973708 0.1433459391 0.1116513596
## [31] 0.0940032415 0.0698721412 0.0590671709 0.0475418693 0.0381775617
## [36] 0.0208896092 0.0198091122 0.0180082838 0.0133261300 0.0064829822
## [41] 0.0064829822 0.0025211597 0.0014406627 0.0018008284 0.0018008284
## [46] 0.0007203314 0.0010804970 0.0025211597 0.0007203314 0.0010804970
## [51] 0.0010804970 0.0003601657 0.0007203314 0.0032414911 0.0003601657
## [56] 0.0018008284 0.0003601657 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`4B`
## $breaks
## [1] -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
## [16] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
## [31] 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
## [46] 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5
## [61] 4.6 4.7 4.8 4.9 5.0
##
## $counts
## [1] 4831 0 0 1756 1216 0 884 1293 476 775 626 783 627 676 796
## [16] 864 753 820 943 952 879 868 951 828 788 740 680 590 496 426
## [31] 340 252 208 161 109 81 63 75 37 26 21 15 9 2 4
## [46] 9 2 3 3 3 0 2 5 7 6 2 1 1 0 0
## [61] 0 0 0 1
##
## $density
## [1] 1.7399603818 0.0000000000 0.0000000000 0.6324509274 0.4379614623
## [6] 0.0000000000 0.3183864578 0.4656942193 0.1714388619 0.2791283991
## [11] 0.2254637133 0.2820097245 0.2258238790 0.2434719971 0.2866918783
## [16] 0.3111831442 0.2712047542 0.2953358545 0.3396362327 0.3428777238
## [21] 0.3165856294 0.3126238070 0.3425175581 0.2982171799 0.2838105529
## [26] 0.2665226004 0.2449126598 0.2124977490 0.1786421754 0.1534305781
## [31] 0.1224563299 0.0907617504 0.0749144607 0.0579866739 0.0392580587
## [36] 0.0291734198 0.0226904376 0.0270124257 0.0133261300 0.0093643076
## [41] 0.0075634792 0.0054024851 0.0032414911 0.0007203314 0.0014406627
## [46] 0.0032414911 0.0007203314 0.0010804970 0.0010804970 0.0010804970
## [51] 0.0000000000 0.0007203314 0.0018008284 0.0025211597 0.0021609941
## [56] 0.0007203314 0.0003601657 0.0003601657 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.35 -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25
## [13] -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95
## [25] 1.05 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15
## [37] 2.25 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35
## [49] 3.45 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55
## [61] 4.65 4.75 4.85 4.95
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5A`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4
##
## $counts
## [1] 7677 0 0 0 0 1923 0 0 1345 0 1004 883 707 1157 903
## [16] 749 969 914 1126 886 860 869 819 747 721 606 558 467 403 347
## [31] 250 193 143 124 108 77 53 51 28 22 12 5 9 3 3
## [46] 1 2 2 5 1 0 1 6 5 1 3 1 3 1 6
## [61] 5 0 0 0 0 0 1
##
## $density
## [1] 2.7649918963 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [6] 0.6925985954 0.0000000000 0.0000000000 0.4844228345 0.0000000000
## [11] 0.3616063389 0.3180262921 0.2546371331 0.4167116874 0.3252296056
## [16] 0.2697640915 0.3490005402 0.3291914281 0.4055465514 0.3191067891
## [21] 0.3097424815 0.3129839726 0.2949756888 0.2690437601 0.2596794525
## [26] 0.2182603998 0.2009724473 0.1681973708 0.1451467675 0.1249774896
## [31] 0.0900414191 0.0695119755 0.0515036917 0.0446605439 0.0388978930
## [36] 0.0277327571 0.0190887808 0.0183684495 0.0100846389 0.0079236449
## [41] 0.0043219881 0.0018008284 0.0032414911 0.0010804970 0.0010804970
## [46] 0.0003601657 0.0007203314 0.0007203314 0.0018008284 0.0003601657
## [51] 0.0000000000 0.0003601657 0.0021609941 0.0018008284 0.0003601657
## [56] 0.0010804970 0.0003601657 0.0010804970 0.0003601657 0.0021609941
## [61] 0.0018008284 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [66] 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95 5.05 5.15 5.25 5.35
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`5B`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0 5.1 5.2 5.3
##
## $counts
## [1] 6255 0 0 0 1921 0 1341 1020 774 654 545 918 796 647 850
## [16] 959 933 956 874 925 775 772 788 762 648 600 549 477 412 345
## [31] 294 219 176 151 98 60 65 48 36 34 24 6 4 2 4
## [46] 3 3 3 8 0 1 3 3 3 3 2 7 7 0 1
## [61] 0 0 0 0 0 1
##
## $density
## [1] 2.2528363047 0.0000000000 0.0000000000 0.0000000000 0.6918782640
## [6] 0.0000000000 0.4829821718 0.3673689897 0.2787682334 0.2355483522
## [11] 0.1962902935 0.3306320908 0.2866918783 0.2330271925 0.3061408248
## [16] 0.3453988835 0.3360345759 0.3443183865 0.3147848010 0.3331532505
## [21] 0.2791283991 0.2780479020 0.2838105529 0.2744462453 0.2333873582
## [26] 0.2160994057 0.1977309562 0.1717990276 0.1483882586 0.1242571583
## [31] 0.1058887088 0.0788762831 0.0633891590 0.0543850171 0.0352962363
## [36] 0.0216099406 0.0234107690 0.0172879525 0.0129659643 0.0122456330
## [41] 0.0086439762 0.0021609941 0.0014406627 0.0007203314 0.0014406627
## [46] 0.0010804970 0.0010804970 0.0010804970 0.0028813254 0.0000000000
## [51] 0.0003601657 0.0010804970 0.0010804970 0.0010804970 0.0010804970
## [56] 0.0007203314 0.0025211597 0.0025211597 0.0000000000 0.0003601657
## [61] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [66] 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95 5.05 5.15 5.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6A`
## $breaks
## [1] -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
## [16] 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
## [31] 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2
## [46] 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7
## [61] 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5
##
## $counts
## [1] 9115 0 0 0 0 1537 0 0 1060 862 758 623 628 959 820
## [16] 1042 888 900 891 853 944 766 804 743 613 563 470 411 327 270
## [31] 233 155 123 107 53 53 56 27 29 19 7 4 3 5 1
## [46] 1 3 1 1 3 6 1 2 3 2 2 2 3 1 5
## [61] 5 1 0 0 0 0 1
##
## $density
## [1] 3.2829101387 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [6] 0.5535746443 0.0000000000 0.0000000000 0.3817756168 0.3104628129
## [11] 0.2730055826 0.2243832163 0.2261840447 0.3453988835 0.2953358545
## [16] 0.3752926346 0.3198271205 0.3241491086 0.3209076175 0.3072213218
## [21] 0.3399963983 0.2758869080 0.2895732037 0.2676030974 0.2207815595
## [26] 0.2027732757 0.1692778678 0.1480280929 0.1177741761 0.0972447326
## [31] 0.0839186026 0.0558256798 0.0443003782 0.0385377274 0.0190887808
## [36] 0.0190887808 0.0201692779 0.0097244733 0.0104448046 0.0068431478
## [41] 0.0025211597 0.0014406627 0.0010804970 0.0018008284 0.0003601657
## [46] 0.0003601657 0.0010804970 0.0003601657 0.0003601657 0.0010804970
## [51] 0.0021609941 0.0003601657 0.0007203314 0.0010804970 0.0007203314
## [56] 0.0007203314 0.0007203314 0.0010804970 0.0003601657 0.0018008284
## [61] 0.0018008284 0.0003601657 0.0000000000 0.0000000000 0.0000000000
## [66] 0.0000000000 0.0003601657
##
## $mids
## [1] -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15 -0.05
## [13] 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15
## [25] 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25 2.35
## [37] 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45 3.55
## [49] 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65 4.75
## [61] 4.85 4.95 5.05 5.15 5.25 5.35 5.45
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`6B`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5
##
## $counts
## [1] 6868 0 0 0 0 2135 0 1488 0 1023 910 687 1144 894 804
## [16] 999 839 886 847 845 920 760 781 670 633 590 541 458 409 352
## [31] 261 211 188 132 124 75 52 61 39 28 19 21 11 6 7
## [46] 2 3 3 0 1 2 5 0 10 2 3 3 0 6 6
## [61] 0 0 0 0 0 0 0 1
##
## $density
## [1] 2.4736178642 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [6] 0.7689537187 0.0000000000 0.5359265262 0.0000000000 0.3684494868
## [11] 0.3277507654 0.2474338196 0.4120295336 0.3219881145 0.2895732037
## [16] 0.3598055105 0.3021790023 0.3191067891 0.3050603278 0.3043399964
## [21] 0.3313524221 0.2737259139 0.2812893931 0.2413110031 0.2279848730
## [26] 0.2124977490 0.1948496308 0.1649558797 0.1473077616 0.1267783180
## [31] 0.0940032415 0.0759949577 0.0677111471 0.0475418693 0.0446605439
## [36] 0.0270124257 0.0187286152 0.0219701062 0.0140464614 0.0100846389
## [41] 0.0068431478 0.0075634792 0.0039618224 0.0021609941 0.0025211597
## [46] 0.0007203314 0.0010804970 0.0010804970 0.0000000000 0.0003601657
## [51] 0.0007203314 0.0018008284 0.0000000000 0.0036016568 0.0007203314
## [56] 0.0010804970 0.0010804970 0.0000000000 0.0021609941 0.0021609941
## [61] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [66] 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95 5.05 5.15 5.25 5.35 5.45
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7A`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0
##
## $counts
## [1] 5162 0 1921 0 1323 920 0 1407 497 813 666 743 653 745 810
## [16] 781 778 974 900 891 947 840 799 796 716 688 574 500 392 372
## [31] 278 201 174 112 82 65 64 48 35 19 18 4 7 10 4
## [46] 2 2 3 3 3 2 2 7 7 1 3 0 0 0 0
## [61] 0 0 1
##
## $density
## [1] 1.8591752206 0.0000000000 0.6918782640 0.0000000000 0.4764991896
## [6] 0.3313524221 0.0000000000 0.5067531064 0.1790023411 0.2928146948
## [11] 0.2398703404 0.2676030974 0.2351881866 0.2683234288 0.2917341977
## [16] 0.2812893931 0.2802088961 0.3508013686 0.3241491086 0.3209076175
## [21] 0.3410768954 0.3025391680 0.2877723753 0.2866918783 0.2578786242
## [26] 0.2477939852 0.2067350981 0.1800828381 0.1411849451 0.1339816316
## [31] 0.1001260580 0.0723933009 0.0626688277 0.0403385557 0.0295335854
## [36] 0.0234107690 0.0230506033 0.0172879525 0.0126057987 0.0068431478
## [41] 0.0064829822 0.0014406627 0.0025211597 0.0036016568 0.0014406627
## [46] 0.0007203314 0.0007203314 0.0010804970 0.0010804970 0.0010804970
## [51] 0.0007203314 0.0007203314 0.0025211597 0.0025211597 0.0003601657
## [56] 0.0010804970 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`7B`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0
##
## $counts
## [1] 5105 0 1810 0 1138 949 705 1087 392 1040 528 636 707 725 769
## [16] 843 870 835 892 902 881 889 844 782 738 678 619 490 421 359
## [31] 265 220 150 107 82 74 64 42 33 14 19 6 12 3 5
## [46] 3 0 1 5 4 0 7 8 0 3 2 1 0 0 0
## [61] 0 0 1
##
## $density
## [1] 1.8386457771 0.0000000000 0.6518998739 0.0000000000 0.4098685395
## [6] 0.3417972267 0.2539168017 0.3915000900 0.1411849451 0.3745723033
## [11] 0.1901674770 0.2290653701 0.2546371331 0.2611201153 0.2769674050
## [16] 0.3036196650 0.3133441383 0.3007383396 0.3212677832 0.3248694399
## [21] 0.3173059607 0.3201872862 0.3039798307 0.2816495588 0.2658022690
## [26] 0.2441923285 0.2229425536 0.1764811813 0.1516297497 0.1292994778
## [31] 0.0954439042 0.0792364488 0.0540248514 0.0385377274 0.0295335854
## [36] 0.0266522600 0.0230506033 0.0151269584 0.0118854673 0.0050423195
## [41] 0.0068431478 0.0021609941 0.0043219881 0.0010804970 0.0018008284
## [46] 0.0010804970 0.0000000000 0.0003601657 0.0018008284 0.0014406627
## [51] 0.0000000000 0.0025211597 0.0028813254 0.0000000000 0.0010804970
## [56] 0.0007203314 0.0003601657 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9A`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9 5.0
##
## $counts
## [1] 6372 0 0 1354 0 956 808 676 1083 410 736 933 709 838 678
## [16] 857 790 973 928 921 885 913 838 796 710 647 560 499 417 343
## [31] 262 230 144 124 68 78 49 60 26 21 13 8 4 7 4
## [46] 2 1 5 2 1 4 4 1 3 6 7 0 0 0 0
## [61] 0 0 1
##
## $density
## [1] 2.2949756888 0.0000000000 0.0000000000 0.4876643256 0.0000000000
## [6] 0.3443183865 0.2910138664 0.2434719971 0.3900594273 0.1476679272
## [11] 0.2650819377 0.3360345759 0.2553574644 0.3018188367 0.2441923285
## [16] 0.3086619845 0.2845308842 0.3504412030 0.3342337475 0.3317125878
## [21] 0.3187466234 0.3288312624 0.3018188367 0.2866918783 0.2557176301
## [26] 0.2330271925 0.2016927787 0.1797226724 0.1501890870 0.1235368269
## [31] 0.0943634072 0.0828381055 0.0518638574 0.0446605439 0.0244912660
## [36] 0.0280929227 0.0176481181 0.0216099406 0.0093643076 0.0075634792
## [41] 0.0046821538 0.0028813254 0.0014406627 0.0025211597 0.0014406627
## [46] 0.0007203314 0.0003601657 0.0018008284 0.0007203314 0.0003601657
## [51] 0.0014406627 0.0014406627 0.0003601657 0.0010804970 0.0021609941
## [56] 0.0025211597 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85 4.95
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`9B`
## $breaks
## [1] -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1
## [16] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
## [31] 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1
## [46] 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6
## [61] 4.7 4.8 4.9
##
## $counts
## [1] 5839 0 0 1757 1158 0 904 747 1085 817 623 537 923 688 786
## [16] 802 896 793 839 856 918 795 743 763 734 633 630 463 387 374
## [31] 288 226 194 134 102 70 62 50 37 30 15 13 4 7 8
## [46] 1 2 4 3 2 3 0 9 7 2 1 0 0 0 0
## [61] 0 1
##
## $density
## [1] 2.1030073834 0.0000000000 0.0000000000 0.6328110931 0.4170718531
## [6] 0.0000000000 0.3255897713 0.2690437601 0.3907797587 0.2942553575
## [11] 0.2243832163 0.1934089681 0.3324329191 0.2477939852 0.2830902215
## [16] 0.2888528723 0.3227084459 0.2856113812 0.3021790023 0.3083018188
## [21] 0.3306320908 0.2863317126 0.2676030974 0.2748064109 0.2643616063
## [26] 0.2279848730 0.2269043760 0.1667567081 0.1393841167 0.1347019629
## [31] 0.1037277147 0.0813974428 0.0698721412 0.0482622006 0.0367368990
## [36] 0.0252115973 0.0223302719 0.0180082838 0.0133261300 0.0108049703
## [41] 0.0054024851 0.0046821538 0.0014406627 0.0025211597 0.0028813254
## [46] 0.0003601657 0.0007203314 0.0014406627 0.0010804970 0.0007203314
## [51] 0.0010804970 0.0000000000 0.0032414911 0.0025211597 0.0007203314
## [56] 0.0003601657 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0000000000 0.0003601657
##
## $mids
## [1] -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15
## [13] -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05
## [25] 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25
## [37] 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45
## [49] 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65
## [61] 4.75 4.85
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10A`
## $breaks
## [1] -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
## [16] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
## [31] 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
## [46] 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5
## [61] 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3
##
## $counts
## [1] 5302 0 0 1408 0 1052 837 704 599 939 796 937 732 630 878
## [16] 756 968 885 916 884 947 940 845 819 773 669 586 566 496 412
## [31] 302 265 237 151 142 74 78 58 53 31 19 20 6 2 5
## [46] 2 2 2 2 4 2 2 7 3 1 2 3 6 0 7
## [61] 0 0 0 0 0 0 1
##
## $density
## [1] 1.9095984153 0.0000000000 0.0000000000 0.5071132721 0.0000000000
## [6] 0.3788942914 0.3014586710 0.2535566361 0.2157392401 0.3381955700
## [11] 0.2866918783 0.3374752386 0.2636412750 0.2269043760 0.3162254637
## [16] 0.2722852512 0.3486403746 0.3187466234 0.3299117594 0.3183864578
## [21] 0.3410768954 0.3385557356 0.3043399964 0.2949756888 0.2784080677
## [26] 0.2409508374 0.2110570863 0.2038537727 0.1786421754 0.1483882586
## [31] 0.1087700342 0.0954439042 0.0853592653 0.0543850171 0.0511435260
## [36] 0.0266522600 0.0280929227 0.0208896092 0.0190887808 0.0111651360
## [41] 0.0068431478 0.0072033135 0.0021609941 0.0007203314 0.0018008284
## [46] 0.0007203314 0.0007203314 0.0007203314 0.0007203314 0.0014406627
## [51] 0.0007203314 0.0007203314 0.0025211597 0.0010804970 0.0003601657
## [56] 0.0007203314 0.0010804970 0.0021609941 0.0000000000 0.0025211597
## [61] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [66] 0.0000000000 0.0003601657
##
## $mids
## [1] -1.35 -1.25 -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25
## [13] -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95
## [25] 1.05 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15
## [37] 2.25 2.35 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35
## [49] 3.45 3.55 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55
## [61] 4.65 4.75 4.85 4.95 5.05 5.15 5.25
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
##
## $`10B`
## $breaks
## [1] -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
## [16] 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
## [31] 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2
## [46] 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7
## [61] 4.8 4.9
##
## $counts
## [1] 7258 0 0 1464 0 1028 846 692 619 937 716 637 865 821 700
## [16] 885 835 928 847 872 843 774 721 709 632 600 489 430 341 319
## [31] 226 152 157 102 64 58 51 40 26 11 11 6 6 5 1
## [46] 7 9 1 1 3 1 4 2 10 2 0 0 0 0 0
## [61] 1
##
## $density
## [1] 2.6140824779 0.0000000000 0.0000000000 0.5272825500 0.0000000000
## [6] 0.3702503151 0.3047001621 0.2492346479 0.2229425536 0.3374752386
## [11] 0.2578786242 0.2294255357 0.3115433099 0.2956960202 0.2521159733
## [16] 0.3187466234 0.3007383396 0.3342337475 0.3050603278 0.3140644697
## [21] 0.3036196650 0.2787682334 0.2596794525 0.2553574644 0.2276247074
## [26] 0.2160994057 0.1761210157 0.1548712408 0.1228164956 0.1148928507
## [31] 0.0813974428 0.0547451828 0.0565460112 0.0367368990 0.0230506033
## [36] 0.0208896092 0.0183684495 0.0144066270 0.0093643076 0.0039618224
## [41] 0.0039618224 0.0021609941 0.0021609941 0.0018008284 0.0003601657
## [46] 0.0025211597 0.0032414911 0.0003601657 0.0003601657 0.0010804970
## [51] 0.0003601657 0.0014406627 0.0007203314 0.0036016568 0.0007203314
## [56] 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
## [61] 0.0003601657
##
## $mids
## [1] -1.15 -1.05 -0.95 -0.85 -0.75 -0.65 -0.55 -0.45 -0.35 -0.25 -0.15 -0.05
## [13] 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15
## [25] 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15 2.25 2.35
## [37] 2.45 2.55 2.65 2.75 2.85 2.95 3.05 3.15 3.25 3.35 3.45 3.55
## [49] 3.65 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65 4.75
## [61] 4.85
##
## $xname
## [1] "x"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"dev.off()## png
## 2Step 2.7: Min-Max Normalization
# Define a function to perform min-max normalization for each vector (gene across samples)
# The values are scaled to the range [-1, 1]
minmax_norm <- function(x) {
# If all values are identical (to avoid division by zero), return a vector of zeros
if (max(x) == min(x)) return(rep(0, length(x)))
# Apply min-max scaling formula: scaled_x = 2 * (x - min) / (max - min) - 1
2 * (x - min(x)) / (max(x) - min(x)) - 1
}
# Apply min-max normalization across columns (i.e., for each sample)
GE_minmax <- apply(rna_log_cpm, 2, minmax_norm)
# Save the min-max normalized matrix to CSV
write.csv(GE_minmax, "RNA_TMM_log2_minmax_scaled.csv")