June 2019 p63 q7
2386
The times in minutes taken by 13 pupils at each of two schools in a cross-country race are recorded in the table below.
| Thaters School |
38 |
43 |
48 |
52 |
54 |
56 |
57 |
58 |
58 |
61 |
62 |
66 |
75 |
| Whitefay Park School |
45 |
47 |
53 |
56 |
56 |
61 |
64 |
66 |
69 |
73 |
75 |
78 |
83 |
- Draw a back-to-back stem-and-leaf diagram to illustrate these times with Thaters School on the left.
- Find the interquartile range of the times for pupils at Thaters School.
Solution
(i)
| Thaters School |
Stem |
Whitefay Park School |
|
8
|
3 |
|
|
3
8
|
4 |
5
7
|
|
8
7
6
4
2
|
5 |
3
6
6
|
|
6
2
1
|
6 |
1
4
6
9
|
|
5
|
7 |
3
5
8
|
|
8
|
8 |
3
|
Key: \( 8 \mid 4 \mid 5 \) represents \(48\) minutes (Thaters School) and \(45\) minutes (Whitefay Park School).
(ii) Ordered times (Thaters): 38, 43, 48, 52, 54, 56, 57, 58, 58, 61, 62, 66, 75.
Lower quartile \(Q_1 = \frac{48 + 52}{2} = 50\).
Upper quartile \(Q_3 = \frac{61 + 62}{2} = 61.5\).
Interquartile range \( \text{IQR} = Q_3 - Q_1 = 61.5 - 50 = 11.5 \) minutes.
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