6. The times, in seconds, spent in a queue at a supermarket by 85 randomly selected customers, are summarised in the table below.
| Time (seconds) | Number of customers, \(f\) |
| 0-30 | 2 |
| 30-60 | 10 |
| 60-70 | 17 |
| 70-80 | 25 |
| 80-100 | 25 |
| 100-150 | 6 |
A histogram was drawn to represent these data. The \(30 - 60\) group was represented by a bar of width 1.5 cm and height 1 cm .
- Find the width and the height of the \(70 - 80\) group.
- Use linear interpolation to estimate the median of this distribution.
Given that \(x\) denotes the midpoint of each group in the table and
$$\sum f x = 6460 \quad \sum f x ^ { 2 } = 529400$$
- calculate an estimate for
- the mean,
- the standard deviation,
for the above 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.