On an IQ scale where the current white American mean is set at 100 (SD = 15), the distribution for Americans as a whole has now fallen to about 96 (SD = 15.8). Now imagine a racist psychologist who was too lazy to score anyone’s IQ test results. She simply looked at the person’s face and assigned them the average score of their race:
Black Americans: IQ 85
Native Americans: IQ 86
Hispanic Americans: IQ 89
Southeast Asian Americans: IQ 92
White Americans: 100
East Asian Americans: 104
Indian Americans: 110
Jewish Americans: 110
When she calculated the average score of her sample, it clocked in at 96, which is now the U.S. average. She was very pleased with herself. Her scoring method worked!
However when her boss checked her work he was not pleased. He said that while the mean score of her sample looked good, the standard deviation was only 6.6. How can that be he asked. All the other samples of American IQ were showing a standard deviation of 15.8.
Standard deviation is the standard amount by which people vary from the mean. It is calculated by taking the average squared deviation from the mean. If the SD is large, it means there’s a lot of variability in the sample. If the SD is small, it means everyone is clustered around the average.
The reason the racist psychologist got such a small SD is that by assigning everyone the average IQ of their race, she eliminated all the IQ variability that exists within races, leaving only the IQ variability that exists between races.
So can she get the SD up to 15.8 while maintaining the perfect correlation between IQ and race? By simply converting all her IQs in her sample into Z scores:
Z score = (obtained score – mean)/SD
Z score = (obtained score – 96)/6.6
And then converting the Z scores into new IQ scores with mean of 96 and an SD of 15.8:
New IQ score = Z score(15.8) + 96
With this conversion, the IQs of every member of each race were as follows:
Black Americans: IQ 70
Native Americans: IQ 72
Hispanic Americans: IQ 79
Southeast Asian Americans: IQ 86
White Americans: 106
East Asian Americans: 115
Indian Americans: 130
Jewish Americans: 130
The racist psychologist began to laugh with evil glee. For now her sample had as much IQ variability as every other, but the correlation between IQ and race remained perfect. She had simply transferred the within race IQ variation she had removed into between race IQ variation.