Problem
\begin{tabular}{|c|c|} \hline \begin{tabular}{l} (a) For these data, which measures of \\ central tendency take more than one value? \\ Choose all that apply. \end{tabular} & \begin{tabular}{l} $\square$ Mean \\ Median \\ Mode \\ None of these measures \end{tabular} \\ \hline \begin{tabular}{l} (b) Suppose that the measurement -5 (the \\ smallest measurement in the data set) were \\ replaced by -42 . Which measures of central \\ tendency would be affected by the change? \\ Choose all that apply. \end{tabular} & \begin{tabular}{l} Mean \\ Median \\ Mode \\ None of these measures \end{tabular} \\ \hline \begin{tabular}{l} (c) Suppose that, starting with the original \\ data set, the smallest measurement were \\ removed. Which measures of central \\ tendency would be changed from those of \\ the original data set? Choose all that apply. \end{tabular} & \begin{tabular}{l} Mean \\ Median \\ Mode \\ None of these measures \end{tabular} \\ \hline \begin{tabular}{l} (d) Which of the following best describes the \\ distribution of the original data? Choose only \\ one. \end{tabular} & \begin{tabular}{l} Negatively skewed \\ Positively skewed \\ Roughly. symmetrical \end{tabular} \\ \hline \end{tabular}
Solution
Step 1 ：The question is asking about the measures of central tendency which can take more than one value. The measures of central tendency are mean, median, and mode.
Step 2 ：The mean is the average of the data set, the median is the middle value when the data set is ordered, and the mode is the most frequently occurring value in the data set.
Step 3 ：The mean and median can only take one value for a given data set. However, the mode can take more than one value if there are multiple values that occur most frequently.
Step 4 ：Therefore, the mode is the measure of central tendency that can take more than one value.
Step 5 ：Final Answer: \(\boxed{\text{Mode}}\)
