Twenty-nine executives reported the number of telephone calls made during a randomly selected week as shown here. Construct a stem and leaf plot for the data and analyze the results.

Question

38
53
53
56
69
89
94
41
58
68
66
69
89
52
50
70
83
81
80
90
74
50
70
83
59
75
78
73
92
Arrange the leaves in order from smallest to largest

Answer 1

To create a stem-and-leaf plot, we first need to organize the data into two parts: the stem and the leaf. The stem represents all but the last digit of each data point, while the leaf represents the last digit.

Step 1: Organize the Data

The data is: 38, 53, 53, 56, 69, 89, 94, 41, 58, 68, 66, 69, 89, 52, 50, 70, 83, 81, 80, 90, 74, 50, 70, 83, 59, 75, 78, 73, 92

Step 2: Identify Stems and Leaves

• The stems will be the tens digits (e.g., 30, 40, 50, etc.).
• The leaves will be the units digits.

Step 3: Create the Stem-and-Leaf Plot

Let's arrange the data and assign stems and leaves accordingly:

| Stem | Leaf | |------|-------| | 3 | 8 | | 4 | 1 | | 5 | 0, 0, 2, 3, 3, 6, 8, 9 | | 6 | 6, 8, 9, 9 | | 7 | 0, 0, 3, 4, 5, 8 | | 8 | 0, 1, 3, 9, 9 | | 9 | 0, 2, 4 |

Each leaf for a particular stem is the last digit of the data points that begin with the tens digit representing the stem.

Final Stem-and-Leaf Plot

Stem | Leaf
3    | 8
4    | 1
5    | 0, 0, 2, 3, 3, 6, 8, 9
6    | 6, 8, 9, 9
7    | 0, 0, 3, 4, 5, 8
8    | 0, 1, 3, 9, 9
9    | 0, 2, 4

Step 4: Analyze the Results

1. Distribution:

   • The most common range seems to be in the 50s and 70s.
   • The 50s have 8 entries (50, 50, 52, 53, 53, 56, 58, 59) while the 70s have 6 entries (70, 70, 73, 74, 75, 78).

2. Range:

   • The smallest value is 38 and the largest value is 94, giving a range of 94 - 38 = 56, which indicates a fairly diverse set of data points.

3. Insights:

   • The data set is skewed towards the lower end (with many entries in the 50s and 60s) but extends up to the 90s.
   • There are duplicate values in the 50s and the 80s, indicating that certain numbers of calls were made more frequently during the selected week.

4. Central Trend:

   • It may be beneficial to calculate the mean, median, and mode for further insights into the central tendency and to understand the data distribution better.

This stem-and-leaf plot gives us an organized way to visualize the data and analyze the pattern of telephone calls made by executives.