Question

a tax consultant analyzes the distribution of income tax payments and finds it is highly skewed to the right. which statement best describes the characteristics of this distribution? the distribution has a symmetrical shape. the mean is greater than the median. the median is greater than the mean. the mean and median are approximately equal.

Explanation:

In a right - skewed (positively skewed) distribution, the tail of the distribution is on the right side. The mean is pulled in the direction of the tail (towards the larger values in the right - skewed case), while the median is the middle value that is less affected by extreme values in the tail. So, in a right - skewed distribution, the mean is greater than the median.

• For the option "The distribution has a symmetrical shape", a right - skewed distribution is not symmetrical, so this is incorrect.
• For the option "The mean and median are approximately equal", this is true for a symmetrical distribution, not a right - skewed one, so this is incorrect.
• For the option "The median is greater than the mean", this is the case for a left - skewed (negatively skewed) distribution, not a right - skewed one, so this is incorrect.

Answer:

The mean is greater than the median.