Chapter 8 Variance

A measure of center such as the mean is not enoguh to summarize the information of a variable. We also need a measure of the amount of variability. Synonym terms are variation, spread, scatter, and dispersion.

There are several ways to measure spread:

• overall range: \(max(X) - min(X)\)

• interquartile range \(Q_3(X) - Q_1(X)\)

• the length between two quantiles

• variance (and its square root the standard deviation)

Because of its relevance and importance for statistical learning methods, we will focus on the variance.