Question

A report states that the mean household income last year for a certain rural county was $44.100 and the median was $35,300. If a histogram were constructed for the incomes of all households in the county, would you expect it to be skewed to the right to the left, or approximately symmetric?

A) skewed right
B) skewed left
C) approximately symmetric

Answer 1

The histogram of incomes would be skewed to the right because the mean is higher than the median, indicating the presence of higher income outliers.

Step-by-step explanation:

When the mean household income in a county is higher than the median, as in the case where the mean is $44,100 and the median is $35,300, this is an indication that the higher income households are pulling the mean up, suggesting that there are some households with significantly higher incomes. Therefore, you would expect the histogram of incomes to be skewed to the right (A), since the longer tail of the distribution is on the right side, indicating the presence of higher income outliers. It is important to note that when the mean is affected by outliers, the median can often provide a better indication of the typical income within the population because it is not influenced by extreme values. For the purposes of descriptive statistics and data visualization, understanding the shape of the distribution provides insight into income inequality and distribution within the community.