6. The number of people visiting a new art gallery each day is recorded over a three-month period and the results are summarised in the table below.
| Number of visitors | Number of days |
| 400-459 | 3 |
| 460-479 | 8 |
| 480-499 | 13 |
| 500-519 | 12 |
| 520-539 | 18 |
| 540-559 | 11 |
| 560-599 | 9 |
| 600-699 | 5 |
- Draw a histogram on graph paper to illustrate these data.
In order to calculate summary statistics for the data it is coded using \(y = \frac { x - 509.5 } { 10 }\), where \(x\) is the mid-point of each class.
- Find \(\sum\) fy.
You may assume that \(\sum f y ^ { 2 } = 2041\).
- Using these values for \(\sum f y\) and \(\sum f y ^ { 2 }\), calculate estimates of the mean and standard deviation of the number of visitors per day.
(6 marks)