Question

the following histogram shows the ages, in years, of the people who attended a documentary at a movie theater.
based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages?
a the mean and the median are equal in value because the distribution is symmetric.
b the mean is most likely less than the median because the distribution is skewed to the right.
c the mean is most likely less than the median because the distribution is skewed to the left.
d the mean is most likely greater than the median because the distribution is skewed to the right.
e the mean is most likely greater than the median because the distribution is skewed to the left.

Explanation:

Step1: Identify distribution shape

The histogram has a longer tail on the right - hand side, so it is right - skewed.

Step2: Recall mean - median relationship for skewed distributions

In a right - skewed distribution, the mean is pulled in the direction of the tail. The median is the middle value and is less affected by extreme values. So, the mean is greater than the median in a right - skewed distribution.

Answer:

D. The mean is most likely greater than the median because the distribution is skewed to the right.