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Five-number summaries
Calculate minimum, lower quartile, median, upper quartile and maximum for four or six datasets with 9–13 observations.
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Draw box-and-whisker plots
Find five-number summaries for three datasets, then draw each box plot on its labeled axis. Choose data lengths, order and number range.
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Sort the data for calculation, complete the five-number summary, then draw the box from Q1 to Q3, mark the median and extend whiskers to the minimum and maximum.
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Customize this worksheetUse a consistent quartile convention
Sort before calculating. For odd-length datasets, exclude the overall median from both halves; find each half’s median for Q1 and Q3. Average middle pairs exactly. Whiskers reach the observed minimum and maximum, with no separate outlier rule.
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Learning objective
What this activity builds
Connect ordered observations with quartiles, a median and minimum-to-maximum whiskers.
Worked example
For 1, 2, 3, 4, 5, 6, 7, 8, 9, what is the five-number summary?
1, 2.5, 5, 7.5, 9.
Exclude the overall median 5 from the halves. The lower half median is (2 + 3)/2 and the upper half median is (7 + 8)/2.
Teaching notes
Make the practice count
- Select dataset lengths from 9–13. Three tasks balance the selected lengths as far as the number of tasks allows.
- For an odd dataset, exclude the overall median from both halves before finding Q1 and Q3. For an even half, average its middle two values.
- Whiskers reach the observed minimum and maximum; these tasks do not use an outlier-fence rule.
- The axis may start above zero. Locate a value relative to the stated origin, including half-unit quartiles.
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