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June 2010 p63 q6
2497
The lengths of some insects of the same type from two countries, X and Y, were measured. The stem-and-leaf diagram shows the results.
| Country X | Country Y | |||
|---|---|---|---|---|
| (10) | 9 7 6 6 6 4 4 3 2 0 | 80 | ||
| (18) | 8 8 7 7 6 6 5 5 5 4 4 3 3 2 2 0 | 81 | 1 1 2 2 3 3 3 5 5 6 7 8 9 | (13) |
| (16) | 9 9 9 8 8 7 7 6 5 5 3 2 1 1 0 0 | 82 | 0 0 1 2 3 3 q 4 5 6 6 7 8 8 | (15) |
| (16) | 8 7 6 5 5 5 3 3 2 2 1 1 1 0 0 | 83 | 0 1 2 2 4 4 4 5 5 6 7 7 7 8 9 | (17) |
| (11) | 8 7 6 5 5 4 4 3 3 1 1 | 84 | 0 1 2 4 4 5 5 6 7 7 7 8 9 | (15) |
| 85 | 1 2 r 3 3 5 5 6 7 8 8 | (12) | ||
| 86 | 0 1 2 2 3 5 5 8 9 9 | (11) |
Key: 5 | 81 | 3 means an insect from country X has length 0.815 cm and an insect from country Y has length 0.813 cm.
- Find the median and interquartile range of the lengths of the insects from country X.
- The interquartile range of the lengths of the insects from country Y is 0.028 cm. Find the values of \(q\) and \(r\).
- Represent the data by means of a pair of box-and-whisker plots in a single diagram on graph paper.
- Compare the lengths of the insects from the two countries.
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