2. The following grouped frequency distribution summarises the number of minutes, to the nearest minute, that a random sample of 100 motorists were delayed by roadworks on a stretch of motorway one Monday.
| Delay (minutes) | Number of motorists (f) | Delay midpoint (x) |
| 3-6 | 38 | 4.5 |
| 7-8 | 25 | 7.5 |
| 9-10 | 18 | 9.5 |
| 11-15 | 12 | 13 |
| 16-20 | 7 | 18 |
(You may use \(\sum \mathrm { f } x ^ { 2 } = 8096.25\) )
A histogram has been drawn to represent these data.
The bar representing a delay of (3-6) minutes has a width of 2 cm and a height of 9.5 cm .
- Calculate the width and the height of the bar representing a delay of (11-15) minutes.
- Use linear interpolation to estimate the median delay.
- Calculate an estimate of the mean delay.
- Calculate an estimate of the standard deviation of the delays.
One coefficient of skewness is given by \(\frac { 3 ( \text { mean } - \text { median } ) } { \text { standard deviation } }\)
- Evaluate this coefficient for the above data, giving your answer to 2 significant figures.
On the following Friday, the coefficient of skewness for the delays on this stretch of motorway was - 0.22
- State, giving a reason, how the delays on this stretch of motorway on Friday are different from the delays on Monday.