Let's analyze the provided stem-and-leaf plot to understand why it might be misleading. We'll go step by step to consider all possible issues that might make the plot misleading:
### Step-by-Step Analysis
1. Stem-and-Leaf Plot Overview:
```
| 0 | 9 |
| 1 | 247 |
| 2 | 3668|
| 3 | 12245|
| 5 | 9 |
```
2. Stem-and-Leaf Data Points:
- 0: 9 (1 data point)
- 1: 2, 4, 7 (3 data points)
- 2: 3, 6, 6, 8 (4 data points)
- 3: 1, 2, 2, 4, 5 (5 data points)
- 5: 9 (1 data point)
3. Given Choices:
- The plot shows that the data is skewed.
- There is not an equal number of data points for each stem.
- The plot shows duplicate data points.
- The stem does not clearly show the outlier.
4. Analyzing Each Choice:
- Skewed Data:
While the data distribution is somewhat uneven, this is not the primary reason the plot is misleading since a skewed distribution can still be accurately represented.
- Equal Number of Data Points for Each Stem:
Let's count the number of data points for each stem:
- Stem 0: 1 data point
- Stem 1: 3 data points
- Stem 2: 4 data points
- Stem 3: 5 data points
- Stem 5: 1 data point
Clearly, there is not an equal number of data points for each stem. This inconsistency could be misleading when interpreting the distribution of data.
- Duplicate Data Points:
Duplicate data points exist, as seen in the stem 2 with two instances of 6 and stem 3 with two instances of 2. However, this merely indicates repetition within a data set, which is not inherently misleading.
- Outlier Representation:
There's only one outlier in this data set (stem 5: 9). While an outlier exists, the plot does include all data points and does not fail to show it. This choice is not the most reflective of why the plot is misleading.
5. Conclusion:
Among the choices, the one that best explains why the plot is misleading is the unequal number of data points for each stem.
### Final Answer:
The plot is misleading because:
There is not an equal number of data points for each stem.
