5. The following grouped frequency distribution summarises the number of minutes, to the nearest minute, that a random sample of 200 motorists were delayed by roadworks on a stretch of motorway.
| Delay (mins) | Number of motorists |
| \(4 - 6\) | 15 |
| \(7 - 8\) | 28 |
| 9 | 49 |
| 10 | 53 |
| \(11 - 12\) | 30 |
| \(13 - 15\) | 15 |
| \(16 - 20\) | 10 |
- Using graph paper represent these data by a histogram.
- Give a reason to justify the use of a histogram to represent these data.
- Use interpolation to estimate the median of this distribution.
- Calculate an estimate of the mean and an estimate of the standard deviation of these data.
One coefficient of skewness is given by
$$\frac { 3 ( \text { mean - median } ) } { \text { standard deviation } } .$$
- Evaluate this coefficient for the above data.
- Explain why the normal distribution may not be suitable to model the number of minutes that motorists are delayed by these roadworks.