- A random sample of 35 homeowners was taken from each of the villages Greenslax and Penville and their ages were recorded. The results are summarised in the back-to-back stem and leaf diagram below.
| Totals | Greenslax | | Penville | | Totals |
| (2) | | | | | | 8 | 7 | 2 | 5 | 5 | 6 | 7 | 8 | 8 | 9 | | | | (7) |
| (3) | | | | | 9 | 8 | 7 | 3 | 1 | 1 | 1 | 2 | 3 | 4 | 4 | 5 | 6 | 9 | (11) |
| (4) | | | | 4 | 4 | 4 | 0 | 4 | 0 | 1 | 2 | 4 | 7 | | | | | | (5) |
| (5) | | | 6 | 6 | 5 | 2 | 2 | 5 | 0 | 0 | 5 | 5 | 5 | | | | | | (5) |
| (7) | 8 | 6 | 5 | 4 | 2 | 1 | 1 | 6 | 2 | 5 | 6 | 6 | | | | | | | (4) |
| (8) | 8 | 6 | 6 | 4 | 3 | 1 | 1 | 7 | 0 | 5 | | | | | | | | | (2) |
| (5) | | | 9 | 8 | 4 | 3 | 2 | 8 | | | | | | | | | | | (0) |
| (1) | | | | | | | 4 | 9 | 9 | | | | | | | | | | (1) |
Key: 7 | 3 | 1 means 37 years for Greenslax and 31 years for Penville
Some of the quartiles for these two distributions are given in the table below.
| Greenslax | Penville |
| Lower quartile, \(Q _ { 1 }\) | \(a\) | 31 |
| Median, \(Q _ { 2 }\) | 64 | 39 |
| Upper quartile, \(Q _ { 3 }\) | \(b\) | 55 |
- Find the value of \(a\) and the value of \(b\).
An outlier is a value that falls either
$$\begin{aligned}
& \text { more than } 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right) \text { above } Q _ { 3 }
& \text { or more than } 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right) \text { below } Q _ { 1 }
\end{aligned}$$ - On the graph paper opposite draw a box plot to represent the data from Penville. Show clearly any outliers.
- State the skewness of each distribution. Justify your answers.
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