Solution
(i) Back-to-back stem-and-leaf diagram:
| Team A |
|
Team B |
|
7 |
5
7
9
|
|
4
4
2
|
8 |
2
3
4
6
|
|
9
8
7
6
1
|
9 |
4
5
6
|
|
9
7
4
0
|
10 |
1
8
|
|
6
5
|
11 |
1
3
5
|
|
2
|
12 |
|
Key: \( 1 \mid 9 \mid 4 \) means \(91\ \text{kg}\) (Team A) and \(94\ \text{kg}\) (Team B).
(ii) Interquartile range for Team A:
Ordered weights: 82, 84, 84, 91, 96, 97, 98, 99, 100, 104, 107, 109, 115, 116, 122.
\( Q_1 = 91,\quad Q_3 = 109 \)
\( \text{IQR} = Q_3 - Q_1 = 109 - 91 = 18\ \text{kg}. \)
(iii) New player in Team B:
\( \sum_{15} = 1399 \)
\( \dfrac{1399 + x}{16} = 93.9 \)
\( 1399 + x = 16 \times 93.9 = 1502.4 \)
\( x = 1502.4 - 1399 = 103.4 \ \text{kg} \approx 103\ \text{kg}. \)