The stem-and-leaf plot below shows the amount of tips received by the servers in a restaurant in one night.
\begin{tabular}{l|lll}
0 & 9 & & \\
1 & 2 & 4 & 7 \\
2 & 3 & 6 & 6 \\
3 & 1 & 2 & 2 \\
5 & 9
\end{tabular}
Why is the plot misleading?
A. The plot shows that the data is skewed.
B. There is not an equal number of data points for each stem.
C. The plot shows duplicate data points.
D. The stem does not clearly show the outlier.
Answer (1)
The stem-and-leaf plot displays the data points: 9, 12, 14, 17, 23, 26, 26, 31, 32, 32, 59.
The number of data points for each stem is unequal.
Unequal data points per stem can cause misinterpretations.
The plot is misleading because there is not an equal number of data points for each stem: T h ere i s n o t an e q u a l n u mb ero fd a t a p o in t s f ore a c h s t e m .
Explanation
Analyze the problem We are given a stem-and-leaf plot representing the amount of tips received by servers. Our goal is to identify why this plot might be misleading. Let's analyze the plot and the answer options.
Identify data points The stem-and-leaf plot shows the following data points: 9, 12, 14, 17, 23, 26, 26, 31, 32, 32, and 59. The stems represent the tens digit, and the leaves represent the ones digit.
Evaluate the reasons Now, let's evaluate the given reasons:
The plot shows that the data is skewed: While the data might be skewed, this isn't inherently misleading. Stem-and-leaf plots can effectively show skewness.
There is not an equal number of data points for each stem: This is true. Some stems have more leaves than others. This can be misleading if someone assumes each stem represents an equal number of data points.
The plot shows duplicate data points: This is also true (e.g., 26, 26, 32, 32). However, showing duplicates is a feature of stem-and-leaf plots, not a flaw.
The stem does not clearly show the outlier: The outlier, 59, is clearly shown in the plot.
Therefore, the most accurate reason for why the plot might be misleading is the unequal number of data points for each stem.
Conclusion The plot is misleading because there is not an equal number of data points for each stem. This can lead to misinterpretations about the distribution of the data.
Examples
Stem-and-leaf plots are useful for quickly visualizing data, such as test scores in a class. If a teacher wants to see the distribution of scores, a stem-and-leaf plot can show how many students scored in each ten-point range (e.g., 60s, 70s, 80s). However, if some ranges have many more scores than others, it could give a misleading impression unless the viewer is aware of the varying number of data points per stem. This is similar to understanding the distribution of income in a city, where some income brackets have far more people than others, which can skew the perception of average income.
