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File:Standard deviation diagram.svg


English: Normal distribution curve that illustrates standard deviations. Each band has 1 standard deviation, and the labels indicate the approximate proportion of area (note: these add up to 99.8%, and not 100% due to rounding for presentation.)
Date 7 April 2007
Source Own work, based (in concept) on figure by Jeremy Kemp, on 2005-02-09
Author Mwtoews

Figure source code

This figure was made with R using:

# # External package to generate four shades of blue
# library(RColorBrewer)
# cols <- rev(brewer.pal(4, "Blues"))
cols <- c("#2171B5", "#6BAED6", "#BDD7E7", "#EFF3FF")

# Sequence between -4 and 4 with 0.1 steps
x <- seq(-4, 4, 0.1)

# Plot an empty chart with tight axis boundaries, and axis lines on bottom and left
plot(x, type="n", xaxs="i", yaxs="i", xlim=c(-4, 4), ylim=c(0, 0.4),
     bty="l", xaxt="n", xlab="x-value", ylab="probability density")

# Function to plot each coloured portion of the curve, between "a" and "b" as a
# polygon; the function "dnorm" is the normal probability density function
polysection <- function(a, b, col, n=11){
    dx <- seq(a, b, length.out=n)
    polygon(c(a, dx, b), c(0, dnorm(dx), 0), col=col, border=NA)
    # draw a white vertical line on "inside" side to separate each section
    segments(a, 0, a, dnorm(a), col="white")

# Build the four left and right portions of this bell curve
for(i in 0:3){
    polysection(   i, i+1,  col=cols[i+1]) # Right side of 0
    polysection(-i-1,  -i,  col=cols[i+1]) # Left right of 0

# Black outline of bell curve
lines(x, dnorm(x))

# Bottom axis values, where sigma represents standard deviation and mu is the mean
axis(1, at=-3:3, labels=expression(-3*sigma, -2*sigma, -1*sigma, mu,
                                    1*sigma,  2*sigma,  3*sigma))

# Add percent densities to each division (rounded to 1 decimal place), between x and x+1
pd <- sprintf("%.1f%%", 100*(pnorm(1:4) - pnorm(0:3)))
text(c((0:3)+0.5,(0:-3)-0.5), c(0.16, 0.05, 0.04, 0.02), pd, col=c("white","white","black","black"))
segments(c(-2.5, -3.5, 2.5, 3.5), dnorm(c(2.5, 3.5)), c(-2.5, -3.5, 2.5, 3.5), c(0.03, 0.01))\
This chart was created with R.


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