What's With the Jews

April 18, 2018

Just watched CBC documentary “What’s With The Jews” and one of the assertions seemed counterintuitive. It said that if the average IQ of a population is only slightly shifted from the average, this has a disproportionate influence over the tail end of the distribution. So, if the average IQ of the Jewish population is only 10 points above the general average, the number of people with an IQ of 145 or higher is going to be 6 times more than in the general population.

Let us assume that the IQ is normally distributed with a standard deviation of 15 points (see http://www.i3mindware.com/what-is-an-iq-test-and-iq-score). Than the IQ of the general population is given by¹:

$$ f(x)=\frac{dnorm(x,100,\sigma)}{dnorm(100,100,\sigma)} \;\text{wtith}\;\sigma=15 $$

The IQ of the Jewish population is given by: $g(x) = \frac{dnorm(1,110,\sigma)}{dnorm(110,110,\sigma)}$ and their ratio is $r(x) = g(x)/f(x)$

Let us evaluate these at some significant points (taken from the same site):

High average - IQ = 110 #

$$ \eqalign{ x_1 &= 110 \cr f(x_1) &= 0.801 \cr g(x_1) &= 1 \cr r(x_1) &= 1.249 } $$

In the Jewish population there are about 25% more people with this IQ.

Mensa membership - IQ = 130 #

$$ \eqalign{ x_2 &= 130 \cr f(x_2) &= 0.135 \cr g(x_2) &= 0.411 \cr r(x_2) &= 3.038 } $$

In the Jewish population there are about 3 people with this IQ for every gentile of the same IQ.

Highly gifted people - IQ = 140 #

$$ \eqalign{ x_3 &= 140 \cr f(x_3) &= 0.029 \cr g(x_3) &= 0.135 \cr r(x_3) &= 4.738 } $$

Now for each gentile there are almost 5 people in the Jewish population with the same IQ

Here is a graph showing what a difference the tail of normal distribution makes.

Looking at these numbers, it is not so surprising that among the Nobel laureates, a group that presumably has a very high IQ, the Ashkenazi Jews occupy such a preeminent position.

Also it is hard not to speculate on the contribution that centuries of persecutions and pogroms have had.

$dnorm$ is the Mathcad function that generates the probability density for a normal distribution: $dnorm(x,\mu,\sigma)=\frac{1}{\sqrt{2\pi}\sigma}\exp[\frac{-1}{2\sigma^2}(x-\mu)^2]$ ↩︎