5.1.3—Averages and spread

Mean, median and mode describe location. Range, interquartile range, variance and standard deviation describe spread; each responds differently to outliers and skew.

Use the mean when all values and squared deviations are meaningful, the median for skewed or ordinal data, and state which spread measure matches the centre.

One extreme value can raise the mean and standard deviation while leaving the median and IQR almost unchanged.

A larger mean does not imply greater variability, and “average” is not automatically the arithmetic mean.