Two box plots can have the same median and different interquartile ranges. The median describes the middle of the ordered values. The interquartile range, or IQR, is the upper quartile minus the lower quartile. It tells you how wide the middle half of the data is.
The 2027 SEC G3 Mathematics K310 syllabus includes box plots, quartiles and measures of spread. When comparing two plots, write one statement about centre and another about spread if the question asks for both.
- Read both plots against their numerical scales.
- Find each median and both quartiles.
- Subtract the lower quartile from the upper quartile.
- State which group has the wider middle half.
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Compare the numbers before the shapes
A long box on the page can be misleading if two plots are drawn on different scales. Read the coordinates of its ends before comparing widths. Use the variable and unit in your sentence.
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Worked example | Two groups of journey times
Group A has a lower quartile of 18 minutes, a median of 22 minutes and an upper quartile of 26 minutes. Group B has a lower quartile of 16 minutes, a median of 22 minutes and an upper quartile of 30 minutes.
Both groups have a median journey time of 22 minutes. Group A has an IQR of 8 minutes and Group B has an IQR of 14 minutes. The middle half of Group B’s journey times is more spread out. You would need the minimum and maximum values to compare the full ranges.
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Write the comparison in context
Say “Group B has the greater IQR, 14 minutes compared with 8 minutes for Group A.” If you describe this as greater variability, specify that you are talking about the middle half.
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Frequently asked questions
Do equal medians mean equal means?
The median and mean describe centre in different ways. The supplied quartiles alone do not establish the means.