Measures of location and spread

Describe the centre of a dataset, measure its variation and explain what the summaries mean.

Start with the available lessons below. Further lessons on grouped data, quartiles, standard deviation and coding are being prepared.

Mean, median and modeCalculate and interpret three ways to summarise the centre of data. Move an extreme value, compare the measures and practise with original worked questions.
Averages from frequency tablesUse frequencies to calculate exact means, locate medians and identify modes. Explore a table, solve unknown-frequency problems and check original worked practice.
Combining meansRecover totals from group means, combine unequal groups correctly and update a mean when observations are added or removed. Original manual model and worked practice.
Estimates from grouped dataEstimate a mean from class midpoints, locate a median class and recognise information lost by grouping. Compare possible original datasets with the same frequencies.
Quartiles and percentiles of listed dataLocate quartiles and percentiles in ordered lists and frequency tables, with an explicit rank convention, learner-operated model and original worked practice.
Linear interpolation for grouped dataEstimate medians, quartiles and percentiles using cumulative frequency and class boundaries. Explore a manual graph and practise the interpolation formula with worked solutions.
Range and interpercentile spreadCompare range, interquartile range and interpercentile ranges, including extreme values, grouped estimates and cautious contextual interpretation.
Variance and standard deviationBuild variance from squared deviations, use the shortcut formula and distinguish descriptive denominator n from sample denominator n minus one. Original model, animation and practice.
Standard deviation from frequency tablesCalculate weighted variance and standard deviation for exact frequency data, estimate them from grouped midpoints, and explain what the summaries cannot reveal.