Math  /  Data & Statistics

QuestionOur class recorded the temperature at noon each day for 36 school days in the spring. The lowest temperature (in F{ }^{\circ} \mathrm{F} ) was 80 , and the highest was 87 . The table gives the mean, median, range, and interquartile range (IQR) of the data set.
Summary values Mean Median Range IQR 83.5 83.5 7 3 \begin{tabular}{|c|c|} \hline \begin{tabular}{l} (a) Select the best description of spread for the data set. \\ The difference between the largest and smallest \\ temperature (in F{ }^{\circ} \mathrm{F} ) is 7 . (This is the range.) \\ The difference between the largest and smallest \\ temperature (in F{ }^{\circ} \mathrm{F} ) is 83.5 . (This is the mean.) \\ The difference between the largest and smallest \\ temperature (in F{ }^{\circ} \mathrm{F} ) is 36 . (This is the number of days the \\ temperature was recorded.) \end{tabular} & \begin{tabular}{l} (b) Select the best description of center for the data set. \\ Based on the range, we see that the "average" \\ temperature (in F{ }^{\circ} \mathrm{F} ) was about 7 . \\ Based on the mean and median, we see that the \\ "average" temperature (in F{ }^{\circ} \mathrm{F} ) was about 83 or 84 . \\ Based on the IQR, we see that the "average" \\ temperature (in F{ }^{\circ} \mathrm{F} ) was about 3 . \end{tabular} \\ \hline \end{tabular}

Studdy Solution
Analyze the given descriptions of center:
1. "Based on the range, we see that the 'average' temperature (in F{}^{\circ} \mathrm{F}) was about 7." This description incorrectly identifies the range as the average temperature.
2. "Based on the mean and median, we see that the 'average' temperature (in F{}^{\circ} \mathrm{F}) was about 83 or 84." This description correctly identifies the mean and median as measures of the average temperature.
3. "Based on the IQR, we see that the 'average' temperature (in F{}^{\circ} \mathrm{F}) was about 3." This description incorrectly identifies the IQR as the average temperature.

The correct description of center is: "Based on the mean and median, we see that the 'average' temperature (in F{}^{\circ} \mathrm{F}) was about 83 or 84."
Solution: (a) The best description of spread for the data set is: "The difference between the largest and smallest temperature (in F{}^{\circ} \mathrm{F}) is 7." (b) The best description of center for the data set is: "Based on the mean and median, we see that the 'average' temperature (in F{}^{\circ} \mathrm{F}) was about 83 or 84."

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