For 4, 6, 7, 9, 10, 12, 13, 15, 40, find Q1, Q3 and the IQR, and decide whether 40 is an outlier.

Q1 = 6.5, Q3 = 14, IQR = 7.5. The upper limit is 14 + 11.25 = 25.25, so 40 is an outlier

Class A has a median of 64 and an IQR of 10. Class B has a median of 71 and an IQR of 22. Which class scored higher typically, and which was more consistent?

Class B scored higher typically; Class A was more consistent

A box plot has Q1 = 30, median 40 and Q3 = 60, with whiskers of similar length. Describe the skew.

Positively skewed, because the box is longer above the median

Free worksheet · Australian Curriculum

Box plot worksheets with answers

A box plot shows a data set's five-number summary at a glance. Learn to find the quartiles, draw and read the plot and spot outliers, then practise with fresh questions and worked solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Box plots, explained

From a list of numbers to a five-number summary and a box plot. Quartiles here use the method common in Australian schools: when there's an odd number of values, leave the median out of both halves.

1. The five-number summary

A box plot is built from five numbers: the minimum, the lower quartile $Q_1$ , the median, the upper quartile $Q_3$ and the maximum. The box runs from $Q_1$ to $Q_3$ with a line at the median, and the whiskers reach out to the minimum and maximum.

2. Quartiles with an odd number of values

Order the data and find the median. Leave the median out, then find the median of each half. For 3, 5, 6, 8, 9, 11, 14:

median $= 8$
lower half $3, 5, 6$ , so $Q_1 = 5$
upper half $9, 11, 14$ , so $Q_3 = 11$

Five-number summary: 3, 5, 8, 11, 14.

3. Quartiles with an even number of values

Split the ordered data into two equal halves. For 2, 4, 5, 7, 8, 10, 12, 15:

median $= \dfrac{7 + 8}{2} = 7.5$
lower half 2, 4, 5, 7, so $Q_1 = \dfrac{4 + 5}{2} = 4.5$
upper half 8, 10, 12, 15, so $Q_3 = \dfrac{10 + 12}{2} = 11$

4. The interquartile range (IQR)

The IQR is the width of the box, and it measures the spread of the middle half of the data:

$\text{IQR} = Q_3 - Q_1$

For the even example above, $\text{IQR} = 11 - 4.5 = 6.5$ . About half the data lies inside the box.

5. Outliers

A value is an outlier if it lies more than $1.5 \times \text{IQR}$ below $Q_1$ or above $Q_3$ . For 1, 3, 4, 5, 6, 7, 30: $Q_1 = 3$ , $Q_3 = 7$ and $\text{IQR} = 4$ , so the upper limit is

$7 + 1.5 \times 4 = 13$

$30$ is above $13$ , so it's an outlier. On a box plot, the whisker stops at the largest value that isn't an outlier and the outlier is marked with a cross.

6. Reading and comparing box plots

To compare two groups, compare their medians (which is higher, typically) and their IQRs (which is more spread out). If the box and whisker are longer above the median, the data is positively skewed; if longer below, it's negatively skewed.

Quick check: 10 questions

Try each one, then open the answer.

Find the five-number summary of 2, 4, 6, 8, 10.
Answer
2, 3, 6, 9, 10
Find the median of 12, 15, 17, 20, 22, 25.
Answer
$18.5$
A data set has $Q_1 = 14$ and $Q_3 = 23$ . Find the IQR.
Answer
$9$
Find $Q_1$ and $Q_3$ for 1, 2, 4, 6, 7, 8, 9, 12.
Answer
$Q_1 = 3$ and $Q_3 = 8.5$
A box plot has a minimum of $12$ and a maximum of $47$ . What is the range?
Answer
$35$
About what percentage of the data lies between $Q_1$ and $Q_3$ ?
Answer
About $50\%$
For 4, 6, 7, 9, 10, 12, 13, 15, 40, find $Q_1$ , $Q_3$ and the IQR, and decide whether $40$ is an outlier.
Answer
$Q_1 = 6.5$ , $Q_3 = 14$ , $\text{IQR} = 7.5$ . The upper limit is $14 + 11.25 = 25.25$ , so $40$ is an outlier
Find the five-number summary of 15, 18, 20, 21, 24, 26, 29, 31, 33, 35, 38.
Answer
15, 20, 26, 33, 38
Class A has a median of $64$ and an IQR of $10$ . Class B has a median of $71$ and an IQR of $22$ . Which class scored higher typically, and which was more consistent?
Answer
Class B scored higher typically; Class A was more consistent
A box plot has $Q_1 = 30$ , median $40$ and $Q_3 = 60$ , with whiskers of similar length. Describe the skew.
Answer
Positively skewed, because the box is longer above the median

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 10 worksheetStatistics Year 9 worksheetComparing data sets Year 7 worksheetDot plots and stem-and-leaf plots Year 9 worksheetStatistics

Questions

What are the five numbers in a box plot?

The minimum, the lower quartile, the median, the upper quartile and the maximum.

How do you find quartiles when there is an odd number of values?

Find the median, leave it out, then find the median of the lower half for the lower quartile and of the upper half for the upper quartile. This is the method most Australian schools use.

How do you know if a value is an outlier on a box plot?

Work out 1.5 times the interquartile range. A value further than that below the lower quartile or above the upper quartile is an outlier.

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