7 The incomes of a sample of 918 households on an island are given in the table below.
| Income | | \(( x\) thousand pounds \()\) |
| \(0 \leqslant x \leqslant 20\) | \(20 < x \leqslant 40\) | \(40 < x \leqslant 60\) | \(60 < x \leqslant 100\) | \(100 < x \leqslant 200\) |
| Frequency | 238 | 365 | 142 | 128 | 45 |
- Draw a histogram to illustrate the data.
- Calculate an estimate of the mean income.
- Calculate an estimate of the standard deviation of the incomes.
- Use your answers to parts (ii) and (iii) to show there are almost certainly some outliers in the sample. Explain whether or not it would be appropriate to exclude the outliers from the calculation of the mean and the standard deviation.
- The incomes were converted into another currency using the formula \(y = 1.15 x\). Calculate estimates of the mean and variance of the incomes in the new currency.