7 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.
The times taken by pupils at Whitefay Park School are denoted by \(x\) minutes. - Find the value of \(\Sigma ( x - 60 ) ^ { 2 }\).
- It is given that \(\Sigma ( x - 60 ) = 46\). Use this result, together with your answer to part (iii), to find the variance of \(x\).
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