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 Video by Zeeshan Zamurred Representations of Data

Edexcel AS Level Maths: 3.2 Box Plots (Quartiles and Outliers)Watch the full walkthrough 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.

min, Q_{1}, Q_{2}, Q_{3}, max

The five-number summary.

Showing outliers

If there are outliers, the whisker stops at the most extreme value that is $not$ 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.

1Compare the medians.

AnswerA’s values are typically higher than B’s

Formula recap

{min, Q_{1}, Q_{2}, Q_{3}, max}

Five-number summary.

box = Q_{1} \to Q_{3} (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

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