How to teach boxplots and the five-number summary
Year 9 to Year 10 (ages 14 to 16)
A boxplot summarises a data set using five key values (minimum, lower quartile, median, upper quartile, maximum), letting you compare the centre and spread of two or more data sets at a glance rather than listing every point.
How to teach it
- Review finding a median on sorted data first, since a quartile is just a median of a half.
- Teach the five-number summary in order: minimum, Q1 (median of the lower half), median, Q3 (median of the upper half), maximum.
- Introduce the interquartile range (IQR = Q3 - Q1) as a spread measure that resists outliers better than the full range.
- Compare two data sets with the same median but different IQRs, so students see that 'centre' and 'spread' are separate ideas.
- Only once the numbers are secure, connect them to the visual boxplot (a box from Q1 to Q3 with whiskers to the min and max).
Worked example
Sorted data: 12, 15, 18, 22, 25, 29, 33, 38 Minimum = 12, maximum = 38 Median = (22 + 25) / 2 = 23.5 Q1 = median of 12, 15, 18, 22 = (15 + 18) / 2 = 16.5 Q3 = median of 25, 29, 33, 38 = (29 + 33) / 2 = 31 IQR = 31 - 16.5 = 14.5
Common mistakes
- Forgetting to sort the data before finding any of the five numbers.
- Adding the two squares instead of subtracting when finding the IQR (Q3 - Q1, not Q3 + Q1).
- Assuming a bigger range always means a bigger IQR, missing that one outlier can inflate the range while barely changing the IQR.
- Comparing only the medians of two data sets and ignoring the spread (IQR) entirely.
Frequently asked questions
What is the five-number summary?
The five-number summary is the minimum, lower quartile (Q1), median, upper quartile (Q3) and maximum of a sorted data set. Together these five values describe a data set's centre and spread without listing every point.
How do you find the lower and upper quartiles?
Sort the data, find the overall median, then find the median of the lower half (that is Q1) and the median of the upper half (that is Q3). This is the same 'find the middle' skill used for the median, applied twice more.
What does the interquartile range (IQR) measure?
The IQR is Q3 minus Q1, the spread of the middle 50 per cent of the data. It ignores the most extreme quarter at each end, so a single outlier affects the IQR far less than it affects the full range.
What year is boxplots and the five-number summary taught?
In the Australian Curriculum, comparing data distributions starts at Year 9 (AC9M9ST03) and boxplots specifically are named at Year 10 (AC9M10ST02), building directly on the Year 7 median skill.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.