Question

tax data
tms-sc financial math cr sem b
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 median is greater than the mean.
the mean and median are approximately equal.
the mean is greater than the median.
the distribution has a symmetrical shape.

Explanation:

To determine the correct statement for a left - skewed (negatively skewed) distribution of household incomes:

1. Recall the properties of skewed distributions:

• In a left - skewed distribution, the tail of the distribution is on the left (lower) side. The mean is pulled in the direction of the tail. So, in a left - skewed distribution, the median is greater than the mean.
• For a symmetric distribution, the mean and median are approximately equal. But the problem states the distribution is highly skewed to the left, so the distribution is not symmetric.
• Let's analyze each option:
• Option "The median is greater than the mean": This is consistent with the property of a left - skewed distribution.
• Option "The mean and median are approximately equal": This is true for a symmetric distribution, not a left - skewed one.
• Option "The mean is greater than the median": This is the property of a right - skewed (positively skewed) distribution.
• Option "The distribution has a symmetrical shape": The problem states it is highly skewed to the left, so it is not symmetrical.

Answer:

The median is greater than the mean.