How does a right-skewed distribution affect the mean relative to the median?

How does a right-skewed distribution affect the mean relative to the median?

• A. In a right-skewed distribution, the mean is less than the median.
• B. In a right-skewed distribution, the mean is greater than the median.
• C. In a right-skewed distribution, the mean equals the median.
• D. In a right-skewed distribution, the median is greater than the mean.

Answer: (B)

In a right-skewed distribution, a few unusually large values stretch the tail to the right. The mean incorporates every observation, so those extreme values pull it upward. The median, being the middle value, is less affected by those outliers and stays closer to the bulk of the data. So the mean ends up larger than the median in a right-skewed distribution. For example, with data like 1, 2, 3, 4, 100, the median is 3, while the mean is (1+2+3+4+100)/5 = 22. This shows how the extreme value raises the average beyond the central value. In contrast, left-skew would pull the mean below the median, and symmetric distributions have the mean and median close together.

In a right-skewed distribution, a few unusually large values stretch the tail to the right. The mean incorporates every observation, so those extreme values pull it upward. The median, being the middle value, is less affected by those outliers and stays closer to the bulk of the data. So the mean ends up larger than the median in a right-skewed distribution.

For example, with data like 1, 2, 3, 4, 100, the median is 3, while the mean is (1+2+3+4+100)/5 = 22. This shows how the extreme value raises the average beyond the central value. In contrast, left-skew would pull the mean below the median, and symmetric distributions have the mean and median close together.