- As part of their job, taxi drivers record the number of miles they travel each day. A random sample of the mileages recorded by taxi drivers Keith and Asif are summarised in the back-toback stem and leaf diagram below.
| Totals | | | | | | | Asif | | Totals |
| (9) | | 8 | 7 | 4 | 3 | 2 | 1 | 1 | 0 | 18 | 4 | 4 | 5 | 7 | | | | | (4) |
| (11) | 9 | 8 | 6 | 5 | 4 | 3 | 3 | 1 | 1 | 19 | 5 | 7 | 8 | 9 | 9 | | | | (5) |
| (6) | | | | 8 | 7 | 4 | 2 | 2 | 0 | 20 | 0 | 2 | 2 | 4 | 4 | 8 | | | (6) |
| (6) | | | | 9 | 4 | 3 | 1 | 0 | 0 | 21 | 2 | 3 | 5 | 6 | 6 | 7 | 9 | | (7) |
| (4) | | | | | | 6 | 4 | 1 | 1 | 22 | 1 | 1 | 2 | 4 | 5 | 5 | 8 | | (7) |
| (2) | | | | | | | | 2 | 0 | 23 | 1 | 1 | 3 | 4 | 6 | 6 | 7 | 8 | (8) |
| (2) | | | | | | | | 7 | 1 | 24 | 2 | 4 | 8 | 9 | | | | | (4) |
| (1) | | | | | | | | | 9 | 25 | 4 | | | | | | | | (1) |
| (2) | | | | | | | | 9 | 3 | 26 | | | | | | | | | (0) |
Key: 0184 means 180 for Keith and 184 for Asif
The quartiles for these two distributions are summarised in the table below.
| Keith | Asif |
| Lower quartile | 191 | \(a\) |
| Median | \(b\) | 218 |
| Upper quartile | 221 | \(c\) |
- Find the values of \(a , b\) and \(c\).
Outliers are values that lie outside the limits
$$Q _ { 1 } - 1.5 \left( Q _ { 3 } - Q _ { 1 } \right) \text { and } Q _ { 3 } + 1.5 \left( Q _ { 3 } - Q _ { 1 } \right) .$$
- On graph paper, and showing your scale clearly, draw a box plot to represent Keith's data.
- Comment on the skewness of the two distributions.