Which statement about the mean is true?

Which statement about the mean is true?

• A. It is easily distorted by extreme values.
• B. It is unaffected by outliers.
• C. It cannot be calculated if the data are skewed.
• D. It is always the most representative measure.

Answer: (A)

The mean is a measure of central tendency that sums all values and divides by the number of observations, so every data point influences it. Because of this, extreme values have a big impact: a single very high or very low score can pull the average toward itself. In distributions that are skewed, this pulling effect becomes pronounced, so the mean may not represent what is typical for most observations. For example, in a small set like 1, 2, 3, 4, 100, the mean is about 22, while the median is 3, showing how the extreme value skews the mean. Because of this sensitivity, the mean is not always the most representative measure; in skewed data or when outliers are present, the median often provides a better sense of a “typical” value. It is false that the mean is unaffected by outliers, false that you can’t compute it with skewed data, and false that it is always the best measure.

The mean is a measure of central tendency that sums all values and divides by the number of observations, so every data point influences it. Because of this, extreme values have a big impact: a single very high or very low score can pull the average toward itself. In distributions that are skewed, this pulling effect becomes pronounced, so the mean may not represent what is typical for most observations. For example, in a small set like 1, 2, 3, 4, 100, the mean is about 22, while the median is 3, showing how the extreme value skews the mean. Because of this sensitivity, the mean is not always the most representative measure; in skewed data or when outliers are present, the median often provides a better sense of a “typical” value. It is false that the mean is unaffected by outliers, false that you can’t compute it with skewed data, and false that it is always the best measure.