(a) Back-to-back stem-and-leaf diagram (stem = tens, leaf = units; Dados on the left, Linva on the right):
| Dados |
Stem |
Linva |
|
8
6
|
0 |
0
2
9
|
|
6
5
2
0
0
|
1 |
0
1
2
5
6
|
|
8
2
|
2 |
|
|
6
|
3 |
2
6
|
|
2
|
4 |
0
|
Key: \( 6 \mid 3 \mid 2 \) means \(36\) cm (Dados) and \(32\) cm (Linva).
(b) Dados ordered: 6, 8, 10, 10, 12, 15, 16, 22, 28, 36, 42.
Median \(= 15\ \text{cm}\).
Lower quartile \(Q_1 = 10\ \text{cm}\), upper quartile \(Q_3 = 28\ \text{cm}\).
Interquartile range: \( \text{IQR} = Q_3 - Q_1 = 28 - 10 = 18\ \text{cm}. \)
(c) Linva: median \(=12\ \text{cm}\), \(Q_1=9\ \text{cm}\), \(Q_3=32\ \text{cm}\) so \( \text{IQR}=23\ \text{cm} \).
Dados has higher central tendency (median \(15\ \text{cm}\) vs \(12\ \text{cm}\)) but smaller spread (IQR \(18\ \text{cm}\) vs \(23\ \text{cm}\)).
On average the snowfall in Davos is higher.
The amount of snowfall in Linva varies more than in Davos.