the choices below are data sets. in the choices, w is a constant. each choice has the same mean. which…

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures the dispersion of data from the mean. Larger deviations from the mean result in a larger standard deviation.

Step2: Analyze option A

The data points in option A are $w - 2,w - 1,w,w + 1,w + 2$. The deviations from the mean (which is $w$) are $- 2,-1,0,1,2$.

Step3: Analyze option B

The data points in option B are $w - 2,w - 2,w,w + 2,w + 2$. The deviations from the mean (which is $w$) are $- 2,-2,0,2,2$.

Step4: Analyze option C

The data points in option C are $w - 3,w - 1,w,w + 1,w + 3$. The deviations from the mean (which is $w$) are $-3,-1,0,1,3$.

Step5: Analyze option D

The data points in option D are $w - 3,w,w,w,w + 3$. The deviations from the mean (which is $w$) are $-3,0,0,0,3$.

Step6: Compare the magnitudes of deviations

The magnitudes of the non - zero deviations in option A are $1,2$. In option B are $2$. In option C are $1,3$. In option D are $3$. Since the set in option C has the largest non - zero deviations from the mean among all the options, it has the greatest standard deviation.

Answer:

C. $w - 3,w - 1,w,w + 1,w + 3$