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?

Rationale

A stem-and-leaf plot must show the information needed for the student to determine the mean of the data.

A stem-and-leaf plot organizes data points while retaining the original values, allowing easy calculation of the mean. By displaying each temperature value clearly, it facilitates the addition of all values necessary for mean computation.

A (A box-and-whisker plot) YOUR ANSWER

A box-and-whisker plot summarizes data by displaying the median, quartiles, and possible outliers, but it does not provide individual data points. Consequently, while it offers a visual summary of data distribution, it lacks the specific temperature values needed to calculate the mean.

B (A stem-and-leaf plot) CORRECT

A stem-and-leaf plot effectively displays individual temperature values by organizing them into stems (the leading digits) and leaves (the trailing digits). This format allows the student to see all daily high temperatures at a glance, making it straightforward to sum the values and divide by the number of days to find the mean.

C (A circle graph) YOUR ANSWER

A circle graph (or pie chart) presents data as parts of a whole, which is useful for showing proportions but not for calculating the mean. It typically displays categorical data rather than numerical values, thus failing to provide the necessary daily temperature readings for mean calculation.

D (A histogram) YOUR ANSWER

A histogram displays the frequency distribution of numerical data through bars representing bins of values. While it offers insights into data distribution, it aggregates the data into ranges, obscuring individual temperature values needed for calculating the mean. Without specific values, the mean cannot be accurately determined.

Conclusion

To determine the mean of daily high temperatures recorded by the student, a stem-and-leaf plot is essential as it displays individual data points clearly. Other options, such as box-and-whisker plots, circle graphs, and histograms, either summarize the data or present it in a way that does not allow for straightforward mean calculation. Thus, the stem-and-leaf plot serves as the most effective tool for this purpose.

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?

A stem-and-leaf plot must show the information needed for the student to determine the mean of the data.

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