The stem-and-leaf plot provided shows the amount of tips received by the servers in a restaurant in one night. Here is the plot represented again for clarity:
```
| Stem | Leaf |
|------|-----------------------------------------------|
| 0 | 9 |
| 1 | 247 |
| 2 | 3668 |
| 3 | 12245 |
| 4 | 9 |
```
We are given several options for why this plot might be misleading:
1. The plot shows that the data is skewed.
2. There is not an equal number of data points for each stem.
3. The plot shows duplicate data points.
4. The stem does not clearly show the outlier.
Let's evaluate each option one by one:
1. The plot shows that the data is skewed.
- Skewness refers to the asymmetry of the data distribution. While the plot may show evidence of skewness (an uneven distribution of tips in the brackets shown), this can be typical, and skewing itself does not directly make the plot misleading.
2. There is not an equal number of data points for each stem.
- A stem-and-leaf plot is meant to give a quick visual impression of the distribution and frequency of data points. Here, we can see there is not an equal number of data points for each stem. For example:
- Stem 1 has three data points (2, 4, 7).
- Stem 2 has four data points (3, 6, 6, 8).
- Stems like 3 and 4 may or may not have comparable distributions.
The unequal number of data points across the stems can lead to a misleading interpretation of the dataset as it may suggest ranges with fewer or more frequent occurrences of tips inaccurately.
3. The plot shows duplicate data points.
- If the plot showed duplicate data points, we would expect to see repeated leaves under the same stem, which appears very minimally. Thus, while possible, it does not seem the main problem here.
4. The stem does not clearly show the outlier.
- If there were an outlier, it would typically be evident by looking at the stems and leaves. Each interval is divided, but there's no clear indication that a stem fails to display an outlier.
Given these points, the main issue with the stem-and-leaf plot is that there is not an equal number of data points for each stem. The unequal distribution of data points across the stems can mislead viewers when interpreting the data.
Therefore, the correct answer is: There is not an equal number of data points for each stem.
