2.4.2—Descriptive statistics

The mean, median and mode describe different centres: the arithmetic average, the middle ordered value and the most frequent value. Range and standard deviation describe spread, not the size of the centre.

Use the median when extreme values would pull the mean away from a typical case. A small spread means scores cluster around the chosen centre; it does not by itself prove a measure is reliable or valid.

For 2, 3, 3, 4 and 18, the mean is 6 and the median is 3. The outlier is part of the evidence: report it, check how it arose, and justify any decision to analyse it separately rather than deleting it silently.

There is no universally best summary. Match the statistic to the scale, distribution and research question; never treat a single central value as the whole dataset.

For ordered data, the semi-interquartile range is (Q3 − Q1) / 2, so it describes the spread of the middle 50% and resists extreme scores. Standard deviation describes typical distance from the mean and is most informative alongside the distribution and mean. For 2, 3, 3, 4, 18, Q1 = 2.5 and Q3 = 11, so SIQR = (11 − 2.5) / 2 = 4.25; state the units of the original scores when reporting any measure of spread.