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.

The standard deviation of the distribution of house age is about 16 years. Interpret this value.

a. The age of all houses in the sample is within 16 years of the mean.

b. The gap between the youngest and oldest house is 16 years.

c. The age of all the houses in the sample is 16 years from the mean.

d. The gap between the first quartile and the third quartile is 16 years.

e. The age of the houses in the sample typically varies by about 16 years from the mean age.

Short answer

The correct option is (e)

e. The age of the houses in the sample typically varies by about 16 years from the mean age.

Step-by-step solution

Step 1. Given information.

a. The age of all houses in the sample is within 16 years of the mean.

b. The gap between the youngest and oldest house is 16 years.

c. The age of all the houses in the sample is 16 years from the mean.

d. The gap between the first quartile and the third quartile is 16 years.

e. The age of the houses in the sample typically varies by about 16 years from the mean age.

Step 2.  The best option.

16 years is the standard deviation.

The standard deviation describes the data values' average deviation from the mean.

The following is a correct interpretation: The average house age of the 52 houses in the data set differs by about 16 years from the mean house age.

The correct response is thus: (e) The average age of the houses in the sample is about 16 years older than the mean age.

Note that: (b) refers to the range, whereas (d) refers to the interquartile range. (a) a and (c) are incorrect because the age of the house can be more than one standard deviation from the mean.

As a result:

e. The age of the houses in the sample typically varies by about 16 years from the mean age.