Under what data conditions is the median preferred over the mean?

• A. The data are perfectly symmetric with no outliers.
• B. The data are skewed or contain outliers.
• C. The data are measured on a ratio scale.
• D. There are multiple distinct modes.

Answer: (B)

When describing the center of a data set, the median is favored when the data are skewed or have outliers because it is resistant to extreme values. The median is the middle value when the numbers are arranged in order, so a few very large or very small observations don’t pull it in one direction. In contrast, the mean uses every value, so outliers or a long tail can pull it toward the tail and give a center that doesn’t reflect where most observations lie.

If the data are perfectly symmetric with no outliers, the mean and median coincide, so either can describe the center well. Data measured on a ratio scale doesn’t automatically require the median over the mean; both can be used, though symmetry and outliers still guide which is more representative. Having multiple distinct modes doesn’t determine the best measure of center either; the median’s advantage comes mainly from robustness to skew and outliers, not distribution shape aspects like modality.

So the best description occurs when the data are skewed or contain outliers.