Solution
(i) The back-to-back stem-and-leaf diagram is constructed as follows:
| Bronlea |
Stem |
Rogate |
|
6
3
0
|
0 |
4
5
7
7
|
|
7
4
3
1
|
1 |
0
1
3
5
6
8
|
|
8
7
5
4
|
2 |
2
1
2
3
3
6
|
|
3
2
3
|
3 |
4
|
|
5
4
|
4 |
|
Key: \( 3 \mid 1 \mid 5 \) represents \(13\) kph for Bronlea and \(15\) kph for Rogate.
(ii) Median for Bronlea (ordered): \(3, 6, 13, 14, 17, 21, 22, 24, 25, 27, 28, 32, 33, 45\). Median \(=\) 8th value \(= 23\ \text{kph}\).
Rogate (ordered): \(4, 5, 7, 7, 10, 11, 13, 15, 16, 18, 23, 23, 26, 34\). \(Q_1 = 7,\ Q_3 = 23\). IQR \(= 23 - 7 = 16\).
(iii) From the diagram, Rogate is less windy than Bronlea.