5. An antiques shop recorded the value of items stolen to the nearest pound during each week for a year giving the data in the table below.
| Value of goods stolen (£) | Number of weeks |
| 0-199 | 31 |
| 200-399 | 6 |
| 400-599 | 3 |
| 600-799 | 4 |
| 800-999 | 5 |
| 1000-1999 | 2 |
| 2000-2999 | 1 |
Letting \(x\) represent the mid-point of each group and using the coding \(y = \frac { x - 699.5 } { 200 }\),
- find \(\sum\) fy.
- estimate to the nearest pound the mean and standard deviation of the value of the goods stolen each week using your value for \(\sum f y\) and \(\sum f y ^ { 2 } = 424\).
(6 marks)
The median for these data is \(\pounds 82\). - Explain why the manager of the shop might be reluctant to use either the mean or the median in summarising these data.
(3 marks)