Track 3 · Visualising and Exploring Data · Lesson 8 of 11
ECDFs and Q-Q plots
Read proportions, medians and percentiles from an empirical cumulative distribution function, compare groups with ECDFs, and judge departures from normality with a normal Q-Q plot.
A school network wants to know what share of students score below 60, and whether exam scores are close enough to normal for the usual methods. Histograms make both questions awkward; an ECDF answers the first directly, and a Q-Q plot answers the second far more sharply than eyeballing a bell curve.
The empirical cumulative distribution function (ECDF) gives, for every value , the proportion of observations less than or equal to . Drawn as a chart it is a staircase that starts at 0 on the left, climbs by at each observation (more where values are tied), and reaches 1 at the maximum. There are no bins and no bandwidth: every observation is shown.
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It has 9 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Read proportions, medians and percentiles from an ECDF
- Compare groups with overlaid ECDFs: further right means larger values
- Recognise skew, heavy tails and light tails from the shape of a normal Q-Q plot
- Judge whether a departure from normality matters, without treating a test as proof