4. A researcher measured the foot lengths of a random sample of 120 ten-year-old children. The lengths are summarised in the table below.
| Foot length, \(l\), (cm) | Number of children |
| \(10 \leqslant l < 12\) | 5 |
| \(12 \leqslant l < 17\) | 53 |
| \(17 \leqslant l < 19\) | 29 |
| \(19 \leqslant l < 21\) | 15 |
| \(21 \leqslant l < 23\) | 11 |
| \(23 \leqslant l < 25\) | 7 |
- Use interpolation to estimate the median of this distribution.
- Calculate estimates for the mean and the standard deviation of these data.
One measure of skewness is given by
$$\text { Coefficient of skewness } = \frac { 3 ( \text { mean } - \text { median } ) } { \text { standard deviation } }$$
- Evaluate this coefficient and comment on the skewness of these data.
Greg suggests that a normal distribution is a suitable model for the foot lengths of ten-year-old children.
- Using the value found in part (c), comment on Greg's suggestion, giving a reason for your answer.