In a right-skewed distribution, which of the following is typically true about the relationship between the $\mathrm{mean}$ and the $\mathrm{median}$?

• A. The $\mathrm{mean}$ and $\mathrm{median}$ cannot be compared in a right-skewed distribution.
• B. The $\mathrm{mean}$ is greater than the $\mathrm{median}$.
• C. The $\mathrm{mean}$ is less than the $\mathrm{median}$.
• D. The $\mathrm{mean}$ is equal to the $\mathrm{median}$.

Answer: (B)

Verified step by step guidance

1. Understand the concept of skewness: In a right-skewed distribution, the tail on the right side (higher values) is longer or fatter than the left side.
2. Recall how mean and median behave in skewed distributions: The mean is sensitive to extreme values (outliers), while the median is more robust and represents the middle value.
3. In a right-skewed distribution, the extreme high values pull the mean to the right, making it larger than the median.
4. Therefore, the typical relationship in a right-skewed distribution is that the mean is greater than the median.
5. This contrasts with a left-skewed distribution where the mean is usually less than the median, and a symmetric distribution where the mean equals the median.