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File:Standard deviation diagram.svg

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Original file(SVG file, nominally 400 × 200 pixels, file size: 17 KB)


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% because of rounding for presentation.)
Français : Courbe de distribution normale montrant l'écart type. Chaque bande verticale a une largeur d'un écart type et les pourcentages indiquent leur valeur approximative rapportée à la population totale. Note : du fait des arrondis, le total est de 99,8 % au lieu de 100%.
Source Own work, based (in concept) on figure by Jeremy Kemp, on 2005-02-09
Author M. W. Toews
Other versions


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R logo.svg
This chart was created with R:

R code

svg(filename = "Standard deviation diagram.svg", width = 7, height = 3.5)
par(mar = c(2, 2, 0, 0))

# # 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="", ylab="")

# 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(mu - 3 * sigma, mu - 2 * sigma, mu - sigma, mu,
                                   mu + sigma, mu + 2 * sigma, mu + 3 * sigma))

# Add percent densities to each division (rounded to 1 decimal place), between x and x+1
text(c((0:3) + 0.5, (0:-3) - 0.5), c(0.16, 0.05, 0.04, 0.02),
     sprintf("%.1f%%", 100 * (pnorm(1:4) - pnorm(0:3))),
     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))

File history

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current02:06, 15 January 2015Thumbnail for version as of 02:06, 15 January 2015400 × 200 (17 KB)GliderMavenAverage is now zero not mu
11:08, 7 April 2007Thumbnail for version as of 11:08, 7 April 2007400 × 200 (14 KB)Petter Strandmark== Summary == Standard deviation diagram, based an original graph by Jeremy Kemp, in 2005-02-09 []. This figure was started in R using: <pre> x <- seq(-4,4,.1) plot(x,dnorm(x),type

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