A school canteen records the number of snack items sold each day over two separate weeks. The box plots compare the daily sales for Week 1 and Week 2. 01020...
Question 1 Report
A school canteen records the number of snack items sold each day over two separate weeks. The box plots compare the daily sales for Week 1 and Week 2.
- Write down the median number of snack items sold in Week 1. (1)
- Work out the interquartile range for Week 1. (1)
- Work out the interquartile range for Week 2. (1)
- Referring to both the medians and the interquartile ranges, state which week had more consistent daily sales. (2)
Answer Details
Reading a box plot means taking the median directly from the line inside the box, and the interquartile range from the gap between the two ends of the box; comparing both statistics together, not just one, gives a fuller picture of which week's sales were more consistent.
- Week 1's median line sits at: \[ \text{median} = 20 \text{ items} \] [1 mark]
- Week 1's box runs from \(15\) to \(25\): \[ \text{IQR} = 25-15 = 10 \text{ items} \] [1 mark]
- Week 2's box runs from \(12\) to \(29\): \[ \text{IQR} = 29-12 = 17 \text{ items} \] [1 mark]
- Week 1 has a similar median to Week 2 (so a similar typical level of daily sales), but a smaller interquartile range, \(10\) compared with \(17\), so Week 1 had more consistent daily sales. [2 marks]
Comparing only the medians would suggest the two weeks were much the same, but the interquartile ranges show Week 2's sales swung much more widely from day to day; this is exactly why both a "typical value" and a "spread" measure are needed to compare two data sets properly.
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