Ohio Assessments for Educators (OAE) Mathematics Practice Exam

If the median is greater than the mean, what can be inferred about the skewness of the data?

1. The data is negatively skewed or left skewed

2. The data is positively skewed or right skewed

3. The data is perfectly symmetrical

4. The data is not skewed

The correct answer is: The data is negatively skewed or left skewed

When the median is greater than the mean, it indicates that the distribution of the data is negatively skewed, also known as left skewed. In a negatively skewed distribution, the tail on the left side of the distribution is longer or fatter than the right side. This often means that there are a few extremely low values pulling the mean down, while the majority of the values are concentrated on the higher end. As a result, the median, which represents the middle value of the dataset, tends to be higher than the mean. In contrast, if the median were less than the mean, it would suggest a positively skewed distribution, where the tail on the right side is longer. Perfectly symmetrical data would yield a median equal to the mean, indicating no skewness. Therefore, when the median exceeds the mean, it strongly suggests that the data shows negative skewness.