Chapter 4 The Average and the Standard Deviation

4.1 Chapter Notes

Nice quote from Galton heads the chapter. I first read this quote in “The Empire of Chance,” and there it seemed to be a pointed criticism of Adolphe Quetelet and his obsession with “l’homme moyen.”

The chapter introduces the mean, the median, and the impact on these of long-right tailed distributions (like income).

The chapter then introduces the root mean square:

The R.M.S of a list of \(n\) \(x_i\)’s is

\[ \sqrt{\frac{\sum(x_i^2)}{n}} \]

We then get the standard deviation, a measure of the size of deviations from the mean.

The (population) standard deviation is the root mean square of the deviations from the mean.

\[ s.d. = \sqrt{\frac{\sum(x_i - \overline{x})^2}{n}} \]

There is some mention of the sample standard deviation (where we use n-1 instead), denoted in the book as \(SD^+\), with a promise to explain the difference in more in chapter 26.