Problem

Apply this center policy: use the mean for roughly symmetric data without outliers, and use the median when skew or outliers would pull the mean. For symmetric data with \(\text{no}~\text{outliers}\), which complete response correctly applies the center policy?

Big Picture

What this problem is really about

Let distribution shape determine the center measure. The mean uses every value and works well when symmetry and the absence of outliers keep it representative, while the median’s resistance matters when skew or influential extremes would pull the mean away from the typical data.

Answer choices

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selected center = mean; trigger = symmetric with no outliers; property = mean uses every value and is not being distorted under this condition

selected center = median; trigger = symmetric with no outliers; property = median is treated as always best despite mean using every undistorted value

selected center = median; trigger = symmetry; property = other values are treated as irrelevant despite no distortion of the mean

selected center = mean; trigger = outliers are treated as present; property = mean is selected despite the policy calling for median when outliers pull it

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Apply this center policy: use the mean for roughly symmetric data without outliers, and use the median when skew or outliers would pull the mean. For symmetric data with \(\text{no}~\text{outliers}\), which complete response correctly applies the center policy?

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