Question

The distribution of annual incomes for U.S. households is positively skewed. If the Census Bureau reports a median annual income of $57,450, this implies that the mean annual income is

a) about the same.
b) larger.
c) smaller.
d) either larger or smaller, but it's impossible to decide on the basis of the available information.

Answer 1

The correct answer is that the mean annual income would be larger than the median in a positively skewed distribution. This means that there are a number of households with very high incomes that raise the average above the median.

Step-by-step explanation:

The correct answer is option b) larger. When a distribution is positively skewed, there is a long tail on the right side, indicating there are a number of households with incomes much higher than the median. This can pull the mean up, causing it to be higher than the median. By understanding the skewness of the distribution, we can infer that the mean is greater than the median. This is further corroborated by data from the American Community Survey which provides a range for the mean U.S. household income significantly above the reported median. Although specific numbers for the mean income were not given in this case, the positively skewed distribution suggests that the mean will be on the higher end.

Keeping this in mind, when examining the income distribution of a smaller sample, we would calculate shares of total income for each quintile to see how the income is actually distributed across the population. However, this would be a separate exercise from determining the relationship between the mean and median in a positively skewed distribution.