The distribution of income tends to be skewed to the right. Suppose you are running for a congressional seat and wish to portray that the average income in your district is low. Which measure of central tendency, the mean or the median, would you report? Why?

Verified step by step guidance

1. Understand the difference between the mean and the median as measures of central tendency: the mean is the arithmetic average, while the median is the middle value when data are ordered.
2. Recognize that a right-skewed distribution has a long tail on the right side, meaning there are some unusually high income values that pull the mean upward.
3. Know that in a right-skewed distribution, the mean is typically greater than the median because the high values increase the average more than the middle value.
4. Since you want to portray the average income as low, consider which measure (mean or median) will give a lower value in a right-skewed distribution.
5. Conclude that reporting the median is more appropriate because it is less affected by extreme high incomes and better represents the typical income 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 long tail on the right side, meaning there are a few very high values that pull the mean upward, making it larger than the median.

Mean as a Measure of Central Tendency

The mean is the arithmetic average of all data points. It is sensitive to extreme values or outliers, so in a right-skewed distribution, the mean is typically higher than most data points, reflecting the influence of large incomes.

Median as a Measure of Central Tendency

The median is the middle value when data are ordered from smallest to largest. It is resistant to outliers and skewness, providing a better representation of a 'typical' income in a right-skewed distribution.