The given stem-and-leaf plot represents the amount of tips received by servers in a restaurant in one night. When examining stem-and-leaf plots, it is essential to ensure that the plot accurately and clearly represents the data distribution. Let's analyze the given options to determine why the plot might be misleading:
1. The plot shows that the data is skewed.
- While skewness can make interpretation challenging, this option alone does not explain why the plot is misleading in its representation.
2. There is not an equal number of data points for each stem.
- This is true. The plot shows an uneven distribution of data points across the stems. In a well-constructed stem-and-leaf plot, there would ideally be a more balanced representation of data points within each stem to reflect the distribution accurately. The absence of an equal number of data points for each stem makes it harder to interpret the distribution of the data accurately and could lead to misinterpretation.
3. The plot shows duplicate data points.
- Showing duplicate data points is not inherently misleading, as it can be part of the data. The concern is not about duplicates but about the overall clarity and representation of the data.
4. The stem does not clearly show the outlier.
- This statement may be relevant in some cases, but from the given plot, it does not appear to be the primary reason for being misleading. The main issue identified is more about the distribution and representation of data across stems.
Therefore, the correct reason why the plot is misleading is that there is not an equal number of data points for each stem. This imbalance in the number of data points across different stems hinders an accurate and easily interpretable representation of the data distribution.
Hence, the correct and detailed answer is: There is not an equal number of data points for each stem.
