A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?

Verified step by step guidance

1. Understand the shape of the distribution: A right-skewed distribution means the tail on the right side (higher values) is longer or stretched out compared to the left side.
2. Recall the definitions of mean and median: The mean is the arithmetic average of all data points, while the median is the middle value when the data is ordered.
3. Consider the effect of skewness on the mean: In a right-skewed distribution, the few large values in the tail pull the mean toward the right, increasing its value.
4. Consider the effect of skewness on the median: The median is less affected by extreme values because it depends on the middle position, not the magnitude of values.
5. Conclude which measure is larger: Because the mean is influenced by the high-value outliers in the right tail, the mean will likely be larger than the median in a right-skewed distribution.

Key Concepts

Skewness of a Distribution

Skewness describes the asymmetry of a data distribution. A right-skewed distribution has a longer tail on the right side, indicating that there are some unusually large values pulling the distribution in that direction.

Mean as a Measure of Central Tendency

The mean is the arithmetic average of all data points. It is sensitive to extreme values, so in a right-skewed distribution, the mean is pulled toward the higher values in the tail.

Median as a Measure of Central Tendency

The median is the middle value when data are ordered. It is less affected by extreme values, so in a right-skewed distribution, the median remains closer to the bulk of the data than the mean.