Question

the data set shows the ages of all participants in two yoga classes. complete parts (a) through (d) below.

3:00 p.m. class
41, 60, 73, 77, 51, 62
68, 35, 53, 64, 74, 69
59, 73, 55, 75, 68, 76
74, 38, 77

8:00 p.m. class
18, 18, 19, 24, 19, 29
19, 20, 39, 22, 56, 25
24, 19, 18, 43, 23, 71
18, 31, 20, 25, 44, 31

(a) make a back to back stem-and-leaf plot to display the data.

3:00 p.m. class | | 8:00 p.m. class
1
2
3
4
5
6
7

key: 1|0 = 10
(use ascending order.)

Explanation:

Sort the data for both classes

3:00 P.M. Class:
Raw: 41, 60, 73, 77, 51, 62, 68, 35, 53, 64, 74, 69, 59, 73, 55, 75, 68, 76, 74, 38, 77
Sorted:

• 30s: 35, 38
• 40s: 41
• 50s: 51, 53, 55, 59
• 60s: 60, 62, 64, 68, 68, 69
• 70s: 73, 73, 74, 74, 75, 76, 77, 77

8:00 P.M. Class:
Raw: 18, 18, 19, 24, 19, 29, 19, 20, 39, 22, 56, 25, 24, 19, 18, 43, 23, 71, 18, 31, 20, 25, 44, 31
Sorted:

• 10s: 18, 18, 18, 18, 19, 19, 19, 19
• 20s: 20, 20, 22, 23, 24, 24, 25, 25, 29
• 30s: 31, 31, 39
• 40s: 43, 44
• 50s: 56
• 60s: None
• 70s: 71

Extract leaves for the plot

3:00 P.M. Class (leaves ordered outwards from the stem, i.e., ascending from right to left):

• Stem 3: 8, 5
• Stem 4: 1
• Stem 5: 9, 5, 3, 1
• Stem 6: 9, 8, 8, 4, 2, 0
• Stem 7: 7, 7, 6, 5, 4, 4, 3, 3

8:00 P.M. Class (leaves ordered outwards from the stem, i.e., ascending from left to right):

• Stem 1: 8, 8, 8, 8, 9, 9, 9, 9
• Stem 2: 0, 0, 2, 3, 4, 4, 5, 5, 9
• Stem 3: 1, 1, 9
• Stem 4: 3, 4
• Stem 5: 6
• Stem 6: (blank)
• Stem 7: 1

Answer:

The completed back-to-back stem-and-leaf plot is:

$$\begin{array}{r|c|l} \text{3:00 P.M. Class} & \text{Stem} & \text{8:00 P.M. Class} \\ \hline & 1 & \text{88889999} \\ & 2 & \text{002344559} \\ \text{85} & 3 & \text{119} \\ \text{1} & 4 & \text{34} \\ \text{9531} & 5 & \text{6} \\ \text{988420} & 6 & \\ \text{77654433} & 7 & \text{1} \\ \end{array}$$

Key: \(1|0 = 10\)