Box Plots (Box-and-Whisker Diagrams)

Grade 6

The five-figure summary

A box plot (also called a box-and-whisker diagram) displays five key values for a data set on a number line: the minimum, lower quartile (LQ), median, upper quartile (UQ), and maximum.

The box covers the middle 50% of data (LQ to UQ). The whiskers extend from the box to the minimum and maximum.

Drawing a box plot

EXAMPLE
Five-figure summary for a data set: min = 10, LQ = 25, median = 35, UQ = 50, max = 70. Draw the box plot.
Draw a number line covering at least 10 to 70. Draw a vertical line at 25 (LQ) and at 50 (UQ). Join them to form a box. Draw a vertical line at 35 (median) inside the box. Draw a whisker from 25 to 10 (min), and another from 50 to 70 (max). Box from 25 to 50, median line at 35, whiskers to 10 and 70.

Interpreting a box plot

A box plot lets you see spread and skew at a glance. If the median line is closer to the LQ, the data is positively skewed (more data in the lower half). If it's closer to the UQ, it's negatively skewed.

Read the IQR directly as the width of the box: UQ − LQ. You don't need to look anything up — it's drawn right there for you.

Comparing two box plots

If you have two box plots on the same scale, compare medians (who scores higher on average) and IQRs (who is more consistent). Mention both in your answer — a comparison answer that only talks about one measure will usually drop a mark.
Nova
Try this one

A cumulative frequency graph is drawn for the heights of 60 plants. A student reads the following values from the graph:

  • lower quartile \( = 24 \) cm
  • median \( = 33 \) cm
  • upper quartile \( = 41 \) cm

(a) Work out the interquartile range. [2]

(b) Explain what the interquartile range tells you about the heights of the plants. [1]

Nova's hint:

This tests the meaning and calculation of the interquartile range.

Ask yourself: 'which two quartiles do I subtract, and which order?' The interquartile range describes how spread out the middle half of the data is — a smaller value means more consistent data.

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