Choosing a delivery firm from two five-number summaries
Choosing a delivery firm from two five-number summaries
IP 2
7 marks
The delivery times, in minutes, of \(80\) orders from each of two firms are summarised below.
| Firm | Minimum | Lower quartile | Median | Upper quartile | Maximum |
|---|---|---|---|---|---|
| A | \(18\) | \(24\) | \(28\) | \(31\) | \(45\) |
| B | \(22\) | \(26\) | \(27\) | \(28\) | \(34\) |
- Find the range and the interquartile range for each firm.[2]
- Compare the two firms' delivery times, commenting on a measure of centre and a measure of spread.[2]
- A customer needs an order delivered within \(30\) minutes. Use the quartiles to explain which firm is more likely to meet this.[2]
- Explain why the range is a poor measure of spread for firm \(A\).[1]
Solution:
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Answer:(a) A: \(27\), \(7\) B: \(12\), \(2\) (b) Similar medians; B much more consistent (c) B (\(Q_3=28<30\)) (d) It depends on the single extreme value \(45\)
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