Answer:
A stem-and-leaf plot is a graphical representation of a dataset that organizes the data in a way that allows you to see the distribution and patterns of the data. In a stem-and-leaf plot, the data is split into two parts: the stem and the leaf. The stem represents the larger digits of the data, and the leaf represents the smaller digits. Here's how to construct and interpret a stem-and-leaf plot for the provided movie duration data:
Data: 92, 94, 99, 99, 96, 105, 105, 108, 111, 119, 119, 87, 87, 88, 91, 46, 66, 75, 79, 92, 93
1. First, arrange the data in ascending order:
46, 66, 75, 79, 87, 87, 88, 91, 92, 92, 93, 94, 96, 99, 99, 105, 105, 108, 111, 119, 119
2. Determine the "stems" and "leaves." The stem consists of the tens digit, and the leaf consists of the units digit. For example, for the data point "46," the stem is "4," and the leaf is "6."
3. Create a table with two columns. The left column represents the stems, and the right column represents the leaves. List the stems in ascending order with a vertical line separating the stems and leaves.
```
Stems | Leaves
-------------------
4 | 6
6 | 6 6
7 | 5 9
8 | 7 7 8
9 | 1 2 2 3 4 5 9 9
10 | 5 5 8
11 | 1 9 9
```
Now, let's interpret the stem-and-leaf plot:
- The stem-and-leaf plot shows the distribution of movie durations.
- The stems represent the tens digit of the data, and the leaves represent the units digit.
- For example, there are two movies with durations in the 40s (stem "4"), one with a duration of 46 minutes and another with a duration of 66 minutes.
- There are two movies with durations in the 70s (stem "7"), with durations of 75 and 79 minutes.
- The most common duration seems to be in the 90s (stem "9"), with several movies having durations in this range (e.g., 92, 92, 93, 94, 96, 99, 99).
- The longest duration is 119 minutes (stem "11").
The stem-and-leaf plot provides a visual representation of the distribution of movie durations, making it easy to identify patterns and central tendencies in the data.
Explanation: