If a data set has a mean of 32 and a median of 35, the distribution is skewed toward the left. Which statement best expresses this?

If a data set has a mean of 32 and a median of 35, the distribution is skewed toward the left. Which statement best expresses this?

• A. Normal distribution
• B. Skewed to the left
• C. Skewed to the right
• D. Uniform distribution

Answer: (B)

When a dataset is skewed, the mean shifts toward the tail because it’s sensitive to extreme values. A left (negatively) skew means the tail extends to the lower values, pulling the mean downward relative to the median. Here the mean is 32 and the median is 35, so the mean lies to the left of the median, indicating left-skew. This fits the idea of a distribution with a longer or heavier left tail. A normal distribution would have the mean and median equal, and a right-skew would have the mean greater than the median, so those options don’t match the given numbers.

When a dataset is skewed, the mean shifts toward the tail because it’s sensitive to extreme values. A left (negatively) skew means the tail extends to the lower values, pulling the mean downward relative to the median. Here the mean is 32 and the median is 35, so the mean lies to the left of the median, indicating left-skew. This fits the idea of a distribution with a longer or heavier left tail. A normal distribution would have the mean and median equal, and a right-skew would have the mean greater than the median, so those options don’t match the given numbers.