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Statistics & Probability · Higher
Box plots Box plots (box-and-whisker diagrams) display the five-number summary of a data set: minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum.
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Revising box plots the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Box plots GCSE” on the site for the complete guide.
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Key facts to remember 1 Box plots show: minimum, Q1, median, Q3, maximum. 2 The box spans from Q1 to Q3 (the middle 50% of the data). 3 The whiskers extend to the minimum and maximum. 4 IQR = Q3 − Q1 — measures the spread of the middle 50%. 5 Use box plots to compare two data sets — compare medians and IQRs. 6 Outliers may be shown as crosses beyond the whiskers. ✍️
Worked examples Example 1 Draw a box plot for: min = 12, Q1 = 18, median = 24, Q3 = 30, max = 40.
Working
Draw a number line covering 12 to 40 Mark Q1 = 18 and Q3 = 30, draw a box between them Mark the median = 24 inside the box Draw whiskers from the box to min = 12 and max = 40 Answer Box from 18 to 30, median line at 24, whiskers to 12 and 40
Example 2 Class A: median 65, IQR 20. Class B: median 72, IQR 8. Compare the two classes.
Working
Class B has a higher median (72 > 65) so generally scored higher Class A has a larger IQR (20 > 8) so results are more spread out / less consistent Class B was more consistent Answer Class B scored higher on average (median 72 vs 65); Class A had more variation (IQR 20 vs 8).
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Common mistakes ✗ Confusing the whisker ends with the mean — whiskers show min and max, not mean.
✗ Comparing only medians without comparing spread (IQR) when asked to "compare".
✗ Drawing the box to the mean rather than the quartiles.
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Exam tips ✓ When asked to "compare" box plots, always comment on both average (median) and spread (IQR).
✓ Use comparative language: "Class A had a higher median than Class B" — don't just list the values.
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