Averages & Spread

This unit covers the mean, median and mode, averages from frequency and grouped tables, choosing an appropriate average, range and interquartile range, quartiles and percentiles, standard deviation, box plots, outliers and skewness at Higher tier.

The calculations are mostly straightforward; the marks are in the choices and the interpretation. Questions almost always ask you to justify which average suits the data, and the reason usually concerns outliers — the median is unaffected by them and the mean is not. Comparing two distributions requires both an average and a measure of spread, each stated in context. Students lose marks by giving bare numbers without interpretation, by pairing the median with the standard deviation rather than the interquartile range, and by forgetting the final square root when calculating standard deviation.