6 The daily rainfall, \(x \mathrm {~mm}\), in a certain village is recorded on 250 consecutive days. The results are summarised in the following cumulative frequency table.
| Rainfall, \(x \mathrm {~mm}\) | \(x \leqslant 20\) | \(x \leqslant 30\) | \(x \leqslant 40\) | \(x \leqslant 50\) | \(x \leqslant 70\) | \(x \leqslant 100\) |
| Cumulative frequency | 52 | 94 | 142 | 172 | 222 | 250 |
- On the grid, draw a cumulative frequency graph to illustrate the data.
- On 100 of the days, the rainfall was \(k \mathrm {~mm}\) or more. Use your graph to estimate the value of \(k\).
- Calculate estimates of the mean and standard deviation of the daily rainfall in this village.