Suppose the numbers of hours worked per week by $400$ statistics students are entered into a graphing calculator. Which of the following statistics can be directly obtained from the calculator's $1-\mathrm{Var}\mathrm{Stats}$ function?

• A. Only the minimum and maximum values
• B. The interquartile range and the mode
• C. Only the mode and range of the data set
• D. The mean, median, and standard deviation of the data set

Answer: (D)

Verified step by step guidance

1. Understand what the 1-Var Stats function on a graphing calculator typically provides. This function is designed to calculate summary statistics for a single variable data set.
2. Recall that the 1-Var Stats function usually outputs the following key statistics: the mean (\(\bar{x}\)), the median, the standard deviation (\(s\) or \(\sigma\)), the minimum and maximum values, the sum of the data, and sometimes quartiles.
3. Note that the mode (the most frequently occurring value) is generally not provided by the 1-Var Stats function because it requires frequency counting rather than summary calculations.
4. Recognize that the interquartile range (IQR) can be calculated if the calculator provides the first quartile (\(Q_1\)) and third quartile (\(Q_3\)), but not all calculators display these quartiles directly in the 1-Var Stats output.
5. Conclude that the statistics you can directly obtain from the 1-Var Stats function include the mean, median, and standard deviation, which are measures of central tendency and spread.