Key ideas
- The median (Q₂) is the middle value of the ordered data. It tells you the average.
- The lower quartile (Q₁) is the middle of the lower half. The upper quartile (Q₃) is the middle of the upper half.
- The interquartile range is IQR = Q₃ − Q₁. A bigger IQR means the data is more varied.
- The five-figure summary (min, Q₁, median, Q₃, max) is all you need to draw a box plot.
The time, in minutes, that 11 pupils in Class A spent reading one evening is shown:
25, 18, 34, 12, 30, 22, 41, 15, 27, 36, 20 (a) Find the median and interquartile range for Class A. (3) (b) Class B had a median of 29 minutes and an interquartile range of 9 minutes. Make two valid statements comparing the reading times of the two classes. (2) (c) Class B’s box plot is drawn below. Construct a box plot for Class A on the same scale. (2) (7 marks)
25, 18, 34, 12, 30, 22, 41, 15, 27, 36, 20 (a) Find the median and interquartile range for Class A. (3) (b) Class B had a median of 29 minutes and an interquartile range of 9 minutes. Make two valid statements comparing the reading times of the two classes. (2) (c) Class B’s box plot is drawn below. Construct a box plot for Class A on the same scale. (2) (7 marks)
Data: 25, 18, 34, 12, 30, 22, 41, 15, 27, 36, 20
Ordered (n = 11): 12, 15, 18, 20, 22, 25, 27, 30, 34, 36, 41
In plain EnglishWrite the values from smallest to largest and count them. There are 11. Tick each one off as you use it so none go missing.
(a) Median
Ordered (n = 11) — split into two halves:
12, 15, 18, 20, 2225Q227, 30, 34, 36, 41
Median = 25 ✓1
In plain EnglishSplit the list into two equal halves. With 11 values there are 5 in each half, and 25 is left on its own in the middle. Circle it: that's the median.
(a) Quartiles
Split each half into two:
12, 1518Q120, 2225Q227, 3034Q336, 41
Q1 = 18, Q3 = 34 ✓2
In plain EnglishNow split each half in two. The middle of the lower half is Q₁. The middle of the upper half is Q₃.
(a) Interquartile range
IQR = Q3 − Q1
= 34 − 18 = 16 minutes ✓3
In plain EnglishTake the lower quartile away from the upper quartile. It's a time, so include the units: minutes.
(b) Compare
| Class A | Class B | |
|---|---|---|
| Median | 25 min | 29 min |
| IQR | 16 min | 9 min |
Median: On average, Class A spent less time reading than Class B, since 25 < 29. ✓4
IQR: The times Class A spent reading were more varied than those of Class B, since 16 > 9. ✓5
In plain EnglishPut both classes side by side. A lower median means less time reading on average. A bigger IQR means the times are more varied. Always say what you're comparing: the reading times. Then quote the numbers to show how you decided: 25 < 29 and 16 > 9.
(c) Box plot
| Min | Q1 | Q2 | Q3 | Max |
|---|---|---|---|---|
| 12 | 18 | 25 | 34 | 41 |
Box from 18 to 34, median line at 25 ✓6
Whiskers to 12 and 41 ✓7
In plain EnglishUse your five numbers. Draw the box from Q₁ (18) to Q₃ (34) with a line at the median (25). Then draw whiskers out to the smallest (12) and largest (41) values. Use a ruler and check each value against the scale.
⚠ Order the data first. The median and quartiles can only be found from an ordered list. Working from the list as given is the most common way to lose these marks.
⚠ Interpreting the IQR. A bigger IQR means the values are more varied. Say what is varied — “the reading times” — not just “Class A was more varied”.
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Your turn
Order the data first! Stuck? Tap Need a hint? for one clue at a time. Each worked solution shows where the marks are given.
Past paper questions
Ready for exam-style questions? Use these links to practise median, quartiles, interquartile range and box plot questions from real SQA papers. Remember: order the data first, and link each comparison statement to the context of the question.
Median and IQR: past paper questions by topicEvery SQA past paper and specimen question on the median and interquartile range in one PDF, with answers. Start here.maths.scot Open ↗ (opens in a new tab) National 5 Maths: median, quartiles & IQR questionsEvery National 5 Maths question on the median, quartiles and interquartile range (2017–2025), each with a link to its marking scheme. Papers before 2023 ask for the semi-interquartile range. That is just the IQR ÷ 2.dynamicmaths.co.uk Open ↗ (opens in a new tab) Applications of Maths: quartiles, IQR & box plotsExtra practice from National 5 Applications of Maths papers (2018–2025), including box plot questions. The method is exactly the same, and there are no stem-and-leaf questions in this list.dynamicmaths.co.uk Open ↗ (opens in a new tab)