31. During a certain year, a student recorded the daily high temperature in a city for each day in the month of April. Which of the following displays MUST show the information needed for the student to be able to determine the mean of the data?
Answer: B
A stem-and-leaf plot must show the information needed to determine the mean of the data.
A stem-and-leaf plot effectively organizes data while retaining the original values, allowing the student to calculate the mean directly from the displayed numbers.
A) A box-and-whisker plot
A box-and-whisker plot summarizes data through five-number summaries, including the minimum, first quartile, median, third quartile, and maximum. While it provides insight into the data distribution and variability, it does not display individual data points necessary for calculating the mean.
B) A stem-and-leaf plot
A stem-and-leaf plot presents each data point in a way that maintains their values, which allows for straightforward calculations of the mean. This format displays the data in an organized manner, making it easy for the student to sum the values and find the average.
C) A circle graph
A circle graph, or pie chart, represents data in proportional segments and is used primarily for categorical data. It does not showcase individual temperature values, thus making it impossible for the student to calculate the mean from this type of display.
D) A histogram
A histogram displays the frequency distribution of data but groups data into intervals (bins). While it provides a visual representation of data distribution, it does not allow for direct access to individual temperature values needed to compute the mean.
Conclusion
The stem-and-leaf plot is the only option that allows for direct access to individual data points, enabling the calculation of the mean. In contrast, the other options either summarize the data or present it in a form that obscures individual values, making them inadequate for determining the mean.