Statistics Quest

Describing Data

Summarise a dataset with the right measures of centre, spread and shape.

Frequency tables, mean, median and mode, weighted and geometric means, variance and standard deviation, quartiles and percentiles, z-scores, outliers, skewness and kurtosis, robust summaries and grouped data — calculated on real datasets and interpreted in context.

Lessons

  1. 1Frequency and relative frequencyBuild and read frequency, relative-frequency and cumulative-frequency tables, including simple two-way tables.25 minFree
  2. 2Mean, median and modeCalculate the mean, median and mode, and choose the measure that honestly represents the centre of a dataset.25 minFree
  3. 3Weighted and geometric meansCalculate weighted means and geometric means, and decide when each one — rather than the ordinary mean — answers the question.30 minFree
  4. 4Variance and standard deviationCalculate the range, variance and standard deviation, choose between the sample (n − 1) and population (n) versions, and interpret a standard deviation in context.30 minFree
  5. 5Quartiles and percentilesCalculate percentiles, quartiles and the interquartile range with the type 7 method, find a percentile rank, and explain why different software can report slightly different quartiles.30 minFree
  6. 6Five-number summary and outliersGive a five-number summary, read and build a box plot, flag outliers with the 1.5 × IQR rule, and decide sensibly what to do with them.30 minFree
  7. 7z-scores and relative standingStandardise values with z-scores, convert back from z to the original units, compare values measured on different scales, and use the empirical rule only where it applies.25 minFree
  8. 8Shape: skewness and kurtosisDescribe the shape of a distribution — symmetry, skew, modality and tails — and calculate and interpret skewness and excess kurtosis.30 minFree
  9. 9Robust summaries and relative spreadCalculate resistant summaries — the median absolute deviation, trimmed and winsorized means — and the coefficient of variation, and judge when each is appropriate.30 minFree
  10. 10Grouped dataEstimate the mean, standard deviation and median from a grouped frequency table, and explain why these are approximations.25 minFree
  11. 11Choosing and reporting summariesChoose summaries that fit each variable's type and shape, present them in a clear summary table with sensible precision, and write a summary sentence a decision-maker can trust.25 minFree