S3.2StatisticsCore

Box Plots

A box plot summarises a data set with five numbers: the minimum, the three quartiles and the maximum. It shows the spread and skew at a glance, and is perfect for comparing two data sets side by side.

25 min Representations of Data

Edexcel AS Level Maths: 3.2 Box Plots (Quartiles and Outliers)Curated by Kepler, not produced by us. Watch it before the notes below.

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What you'll be able to do

Identify the five-number summary
Draw a box plot
Show outliers on a box plot
Compare two data sets using box plots

The five-number summary

A box plot is built from five values: the minimum, lower quartile $Q_1$ , median $Q_2$ , upper quartile $Q_3$ , and the maximum. The box spans $Q_1$ to $Q_3$ (the IQR), with a line at the median; whiskers reach to the smallest and largest non-outlier values.

\text{min}, \ Q_1, \ Q_2, \ Q_3, \ \text{max}

The five-number summary.

Showing outliers

If there are outliers, the whisker stops at the most extreme value that is $\textbf{not}$ an outlier, and each outlier is marked with a cross ( $\times$ ).

Tip — Whiskers go to the last value inside the fences; plot outliers separately as crosses.

Comparing data

Two box plots on the same scale make comparison easy: compare a measure of location (e.g. medians) and a measure of spread (e.g. IQRs), and always interpret in context.

Example 1Box A has median 50, Box B median 40. What can you say?

1Compare the medians.

AnswerA’s values are typically higher than B’s

Formula recap

\{\text{min}, Q_1, Q_2, Q_3, \text{max}\}

Five-number summary.

\text{box} = Q_1 \to Q_3 \ (\text{IQR})

The box shows the middle 50%.

Common mistakes to avoid

Drawing whiskers all the way to an outlier.

Whiskers stop at the last non-outlier; outliers are crosses.

Comparing only one feature when comparing data sets.

Compare both a location measure and a spread measure, in context.

Key takeaways

Box plot = min, Q₁, median, Q₃, max.
The box is the IQR; whiskers reach the extreme non-outliers; outliers are crosses.
Compare medians (location) and IQRs (spread) in context.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Related lessons

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Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.