Question

a tax policy researcher examines the distribution of household incomes and observes it is highly skewed to the left. which statement best describes the characteristics of this distribution? the mean is greater than the median. the median is greater than the mean. the distribution has a symmetrical shape. the mean and median are approximately equal.

Explanation:

For a left - skewed (negatively skewed) distribution of household incomes:

• A symmetrical shape is incorrect as left - skewed means the distribution is not symmetrical.
• In a left - skewed distribution, the mean is pulled towards the left (lower values) by the tail, so the median (which is less affected by extreme values in the tail) is greater than the mean.
• The mean being greater than the median is characteristic of a right - skewed (positively skewed) distribution.
• Mean and median being approximately equal is characteristic of a symmetrical distribution.

Answer:

The median is greater than the mean.