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

• A. $\mathrm{mean}$ is equal to the $\mathrm{median}$.
• B. $\mathrm{mean}$ is greater than the $\mathrm{median}$.
• C. There is no consistent relationship between the $\mathrm{mean}$ and the $\mathrm{median}$.
• D. $\mathrm{mean}$ is less than the $\mathrm{median}$.

Answer: (B)

Verified step by step guidance

1. Understand the concept of skewness: A distribution that is skewed right (positively skewed) has a longer tail on the right side, meaning there are some unusually large values.
2. Recall the definitions of mean and median: The mean is the average of all data points, while the median is the middle value when data is ordered.
3. Consider how extreme values affect the mean and median: In a right-skewed distribution, the large values in the tail pull the mean to the right, increasing it more than the median.
4. Compare the mean and median in a right-skewed distribution: Because the mean is influenced by extreme values and the median is not, the mean tends to be greater than the median.
5. Conclude the typical relationship: For a right-skewed distribution, the mean is usually greater than the median.