Quartiles and box plots · Year 12
In Year 12 you get fluent with: comparing distributions.
Averages tell you a typical value. Measures of spread tell you how much the data vary. Quartiles split ordered data into four equal parts. A box plot shows the minimum, quartiles, median and maximum at a glance.
Key facts
- Range = maximum − minimum. One extreme value can change it a lot.
- Q1 is the median of the lower half and Q3 is the median of the upper half. With an odd number of values, leave the median out of both halves.
- Interquartile range IQR = Q3 − Q1: the spread of the middle 50%.
- An outlier is more than 1.5 × IQR below Q1 or above Q3.
- A box plot shows the minimum, Q1, median, Q3 and maximum on a scale.
- To compare data sets, compare the medians (average) and the IQRs (consistency).
Worked examples
Example 1
The box plots show test marks for two classes. Compare them.
Answer: A scored higher on average; B was more consistent