Question

Realtors collect data in order to serve their clients more effectively. In a recent week, data on the age of all homes sold in a particular area were collected and displayed in this histogram.

Which of the following is most likely true?

a. mean > median, range < IQR

b. mean < median, range < IQR

c. mean > median, range > IQR

d. mean < median, range > IQR

e. mean = median, range > IQR

Short answer

The correct option is (c)

(c) mean>median, range>IQR

Step-by-step solution

Step 1. Given information.

a. mean > median, range < IQR

b. mean < median, range < IQR

c. mean > median, range > IQR

d. mean < median, range > IQR

e. mean = median, range > IQR

Step 2.  The best option.

The distribution is skewed to the right because the highest bars in the histogram are on the left, with a tail of smaller bars on the right. This implies that the distribution contains some data with unusually large values.

The mean is not resistant, whereas the median is. This implies that the mean is more influenced by unusually large data values than the median, and thus the mean will be greater than the median (as the mean increases due to the unusually large data values).

The range is the difference between the maximum and minimum of the distribution, whereas the interquartile range IQR is the difference between the third and first quartiles (at 75% of the sorted data set) (at 25 percent of the sorted data set). As a result, the range is greater than the interquartile range IQR because the minimum is less than the first quartile and the third quartile is less than the maximum.

As a result:

(c) mean>median, range>IQR