(a) The back-to-back stem-and-leaf diagram is drawn with the Lions on the left and the Tigers on the right. The stems represent the tens digit, and the leaves represent the units digit:
| Lions |
Stem |
Tigers |
|
9
|
16 |
|
|
9
8
|
17 |
9
|
|
9
7
6
1
|
18 |
0
3
4
7
|
|
0
0
|
19 |
0
1
4
5
7
|
|
6
|
20 |
1
|
Key: \( 1 \mid 8 \mid 3 \) means 181 cm (Lions) and 183 cm (Tigers).
(b) Arrange the Lions' heights in ascending order:
169, 178, 179, 180, 181, 186, 187, 189, 190, 190, 196
The median is the 6th value: \( \text{Median} = 186 \) cm.
Lower quartile (LQ) is the median of the first half: \( LQ = 179 \) cm.
Upper quartile (UQ) is the median of the second half: \( UQ = 190 \) cm.
\( IQR = UQ - LQ = 190 - 179 = 11 \) cm.
(c) Comparisons:
- The Tigers are generally taller than the Lions, as their median height (190 cm) is greater than the Lions’ median (186 cm).
- The Tigers have a larger spread, as their upper quartile is higher, indicating more variation in player heights.