File:IQ curve (2).svg

Summary

    Description Current IQ tests typically have standard scores such that the mean score is 100 with each standard deviation from the mean counting for 15 IQ points.[1] The plot shows, assuming that such scores have a normal distribution, the percentage of people getting a score versus the score itself, from 55 to 145 IQ, that is over a span of six standard deviations. Spans are represented with different colors for each standard deviation above or below the mean. The plot was created with the following gnuplot code:
    SVG development
    InfoField
    Source code
    InfoField

    Gnuplot code

    set terminal svg name 'IQ_curve' size 600,480 font ',10' rounded
set output 'IQ_curve.svg'

mu    = 100.0
sigma = 15.0
from  = 55
to    = 145

# Normal distribution:
# (continuos normalization approximation, good to ~10 digits in this case)
P(x) = exp(-(x - mu)**2 / (2 * sigma**2)) / (sqrt(2 * pi) * sigma) * 100
# By sigma intervals:
oddsi(x) = (int(abs(x - mu) / sigma) % 2) ^ (x < mu)
Pm(x) =               (x == mu)  ? P(x) : 1/0 # sample at mu
Po(x) = ( oddsi(x) && (x != mu)) ? P(x) : 1/0 # samples in odd sigma intervals
Pe(x) = (!oddsi(x) && (x != mu)) ? P(x) : 1/0 # samples in even sigma intervals

set key off
set border 3
set xlabel 'IQ'
set xtics 10 out nomirror
set mxtics 2
set ylabel 'Population, %'
set ytics 1 out nomirror
set mytics 2
set samples (to - from + 1)
set style function impulses
plot [x = from:to] \
 Pm(x) lw 2, \
 Po(x) lw 2, \
 Pe(x) lw 2
    Date
    Source Own work
    Author Alessio Damato, Mikhail Ryazanov

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    attribution share alike
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    You are free:
    • to share – to copy, distribute and transmit the work
    • to remix – to adapt the work
    Under the following conditions:
    • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
    • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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    Category:Self-published work Category:Images with Gnuplot source code Category:Intelligence quotient Category:Normal distribution Category:Psychometrics Category:XY plots
    1. ↑ Kaufman, A.S. (2009) IQ Testing 101, New York (NY): Springer Publishing, pp. 104−109 ISBN: 978-0-8261-0629-2.
    Category:CC-BY-SA-2.5,2.0,1.0 Category:CC-BY-SA-3.0-migrated Category:GFDL Category:Images with Gnuplot source code Category:Intelligence quotient Category:License migration redundant Category:Normal distribution Category:Pages with non-numeric formatnum arguments Category:Psychometrics Category:Self-published work Category:Translation possible - SVG Category:Valid SVG created with Gnuplot code:Charts Category:XY plots