2 Katy works as a clerical assistant for a small company. Each morning, she collects the company's post from a secure box in the nearby Royal Mail sorting office.
Katy's supervisor asks her to keep a daily record of the number of letters that she collects.
Her records for a period of 175 days are summarised in the table.
| Daily number of letters (x) | Number of days (f) |
| 0-9 | 5 |
| 10-19 | 16 |
| 20 | 23 |
| 21 | 27 |
| 22 | 31 |
| 23 | 34 |
| 24 | 16 |
| 25-29 | 10 |
| 30-34 | 5 |
| 35-39 | 3 |
| 40-49 | 4 |
| 50 or more | 1 |
| Total | 175 |
- For these data:
- state the modal value;
- determine values for the median and the interquartile range.
- The most letters that Katy collected on any of the 175 days was 54. Calculate estimates of the mean and the standard deviation of the daily number of letters collected by Katy.
- During the same period, a total of 280 letters was also delivered to the company by private courier firms.
Calculate an estimate of the mean daily number of all letters received by the company during the 175 days.