# Quartile deviation

© Paul Cooijmans

## Explanation

This quartile deviation is half the difference between the 3^{rd} and 1^{st} quartile (the two points that enclose the middle 50% of the population). It is a measure of spread, like the standard deviation, but unlike the latter it is also meaningful in non-linear situations and non-normal distributions. In a normal distribution, the quartile deviation is about two thirds the size of the standard deviation (actually .6745 σ); it has thus a more human-friendly size than the rather large standard deviation. The size of the quartile deviation corresponds roughly to what one intuitively feels as a "level", and in fact the grades of Sir Francis Galton's scale for intelligence, which he devised before the standard deviation came in use, are in size very close to a quartile deviation.

Other measures of spread are the mean deviation (less sensitive to outliers than is the standard deviation, but also primarily useful on linear scales), the variance, and the range (which logically makes a good pair with the quartile deviation in non-linear situations).