Which central tendency measure is most affected by outliers?

Which central tendency measure is most affected by outliers?

• A. Median
• B. Mean
• C. Mode
• D. Range

Answer: (B)

Outliers throw off measures that rely on every value in the data. The mean is calculated by adding all observations and dividing by the count, so an extreme value pulls the average toward itself. If you have results clustered around typical values and one very large or very small number, the mean shifts toward that outlier, even though most of the data didn’t change. The median, on the other hand, is the middle value once the data are sorted, so it depends on order rather than the magnitude of the observations and tends to stay put in the presence of outliers. The mode is simply the most frequent value and may remain unchanged unless the outlier somehow becomes the most common value—in many cases it isn’t affected. The range measures spread (max minus min) rather than center, so it’s not the central tendency that’s being described. With these ideas in mind, the mean is the central tendency measure most affected by outliers.

Outliers throw off measures that rely on every value in the data. The mean is calculated by adding all observations and dividing by the count, so an extreme value pulls the average toward itself. If you have results clustered around typical values and one very large or very small number, the mean shifts toward that outlier, even though most of the data didn’t change. The median, on the other hand, is the middle value once the data are sorted, so it depends on order rather than the magnitude of the observations and tends to stay put in the presence of outliers. The mode is simply the most frequent value and may remain unchanged unless the outlier somehow becomes the most common value—in many cases it isn’t affected. The range measures spread (max minus min) rather than center, so it’s not the central tendency that’s being described. With these ideas in mind, the mean is the central tendency measure most affected by outliers.