Normal Distribution

I mention things like normal distributions and standard deviations pretty frequently around here so I thought it was about time that I elaborated on it a bit. The graph above illustrates what is known as a “normal distribution”. In a normal distribution the mean, median, and mode are all the same. “Mean” is the average, i.e. the sum of values divided by the number of values. One half of all values are above the “median”, one half below. And the “mode” is the most frequently occurring value.

In a normal distribution 68% of all values are within what’s called a “standard deviation” from the mean. The standard deviation is sometimes represented by the Greek letter sigma (sort of an “o” with a squiggle at the top, “σ”). 95% are within two standard deviations and 99.7% are within three standard deviations.

There are all sort of things that are believed to occur in an approximately normal distribution, e.g. wages, intelligence as measured by IQ scores, the logarithm of stock market indices, measurement errors in the physical sciences, and so on.

The IQs of people in the professions, i.e. doctors, lawyers, etc. tend to be between one standard deviation and two standard deviations above the mean. In general, people with lower IQs can’t hack it and people with higher IQs aren’t interested. There are exceptions at both ends of the spectrum.

The IQs of college students tend to be at the mean or above and that appears to be cross-cultural, i.e. as true in Japan as it is in the United States.

That, for example, is why, when our political leadership points to the importance of higher education, I invariably respond “What do you plan to do with the other half of the people?”