- A random sample of distances travelled to work for 120 commuters from a train station in Devon is recorded. The distances travelled, to the nearest mile, are summarised below.
| Distance (to the nearest mile) | Number of commuters |
| 0-9 | 10 |
| 10-19 | 19 |
| 20-29 | 43 |
| 30-39 | 25 |
| 40-49 | 8 |
| 50-59 | 6 |
| 60-69 | 5 |
| 70-79 | 3 |
| 80-89 | 1 |
For this distribution:
a estimate the median.
The mid-point of each class was represented by \(x\) and its corresponding frequency by \(f\). The mid-point of the lowest class was taken to be 4.75 giving:
$$\Sigma f x = 3552.5 \text { and } \Sigma f x ^ { 2 } = 138043.125$$
b Estimate the mean and the standard deviation of this distribution.
c Explain why the median is less than the mean for these data.
[0pt]
[BLANK PAGE]