GCSE Box Plots — Examiner's Guide | The Maths and Science Tutor

Box plots are quick to draw, quick to read — and one of the easier topics to lose marks on, because the comparison sentences at the end have a very specific format that examiners are looking for. This guide walks through how to build a box plot from a five-number summary, how to read information off it, and exactly what to write when comparing two distributions.

The five-number summary

A box plot is built from five numbers, in order:

Minimum — the smallest value in the dataset
Lower quartile (Q1) — the 25th percentile
Median (Q2) — the middle value
Upper quartile (Q3) — the 75th percentile
Maximum — the largest value

The "box" is the middle 50% of the data — from Q1 to Q3. The "whiskers" extend out to the minimum and maximum.

Drawing a box plot — step by step

Worked example 1

The five-number summary for 30 students' test scores is: minimum 22, Q1 = 41, median = 56, Q3 = 68, maximum 89.

Draw a horizontal scale that covers the full range (in this case 20 to 90).
Draw a small vertical line at the minimum (22) and another at the maximum (89).
Draw a rectangle from Q1 (41) to Q3 (68).
Draw a vertical line through the box at the median (56).
Draw horizontal whiskers from the minimum to Q1, and from Q3 to the maximum.

Reading values off a box plot

Once it's drawn, you can read off any of the five numbers, plus:

Range = maximum − minimum
Interquartile range (IQR) = Q3 − Q1

For our example: range = 89 − 22 = 67. IQR = 68 − 41 = 27.

Comparing two box plots — the marks question

The comparison question is where the marks are. The examiner wants two distinct comparisons:

An average comparison using the median.
A spread comparison using the IQR (or sometimes the range).

Both comparisons need a contextual interpretation — a sentence that ties the maths back to the question.

Worked example 2 — comparison phrasing

Class A test scores: median 56, IQR 27. Class B test scores: median 64, IQR 18.

Average: "Class B has a higher median (64) than Class A (56), so on average Class B scored higher."

Spread: "Class B has a smaller IQR (18) than Class A (27), so the middle 50% of scores in Class B are more consistent / less spread out."

Examiner's note: Always use the word "median" (or "average") in the first comparison, and "IQR" (or "spread", "consistency") in the second. Vague answers like "Class B did better" without quoting the median lose half the marks. The mark scheme is looking for one mark per statistic and one mark per interpretation.

The mistakes that cost the most marks

Mistake 1 — Forgetting the contextual sentence. "The median is higher" earns one mark; "The median is higher, so the team scored more goals on average" earns two.

Mistake 2 — Comparing both averages and not the spread (or vice versa). The mark scheme wants one of each. Two median comparisons earns the marks for one.

Mistake 3 — Quoting the wrong stat. Range (max − min) is more affected by extreme values than IQR. If the question asks about consistency or "the middle of the data", use IQR.

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Box Plots — An Examiner's Guide