Norms

The Dreaded Bell Curve

For the normal distribution, the values less than one standard deviation away from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%.

The 68–95–99.7 rule is a shorthand of the values lie within one, two and three standard deviations of the mean, respectively.

Let's take something simple like IQ. The mean IQ is 100. Using the shorthand method, 68 of one hundred test subjects will be within one standard deviation from the mean of 100. That standard deviation is 15 points. So, under the single standard deviation from 100, 34 people will be between 100 and 115 and 34 people will be between 100 and 85.

95 people will be in the group testing from 70 to 130, two standard deviations on either side of the mean. This mean 5 % of those tested will lie outside the two standard deviations, that is 2.5% will be below 70 and 2.5% will be above 130.

 

It is just great that 2.5 per cent of the population will have IQs higher than 130. But what about the other end of the curve? 2.5% of the population will test below 70? Google says the current population of the U.S. is 321 million. So 2.5% of that means there are 8,025,000 people in the U.S. with IQs less than 70. Expressing their God-given constitutional rights. Buying weapons. Voting.

Should the current problems in the U.S. surprise anybody?

Well, maybe 2.5% are surprised.