The table below shows the distance from the basketball goal that Juan was standing when he successfully made a basket.

What is the mean absolute deviation of the distance that Juan stood from the basketball goal when he successfully made a basket?

A. 1.125
Correct!

B. 7.625
Incorrect. This number is the mean of the distances, but the question asks for the mean absolute deviation of the distances.

C. 9
Incorrect. This number is the sum of the absolute deviations of the distance Juan was from the basketball goal. Divide this number by the number of shots to get the mean absolute deviation.

D. 61
Incorrect. This number is the sum of the distances Juan was from the basketball goal. Next, determine the mean and the absolute deviation of each shot from the mean, and then calculate the average of the absolute deviations.

The list below shows the ages of ten randomly selected customers in a bookstore.

22    38    25    19    31
30    42    45    27    30

What is the mean absolute deviation of the ages of this group of customers?

A. 30.9
Incorrect. This number is the mean age of this group of customers. Use the mean to calculate the absolute deviation from the mean of each customer’s age, and then determine the mean absolute deviation.

B. 30
Incorrect. This number is the median age of this group of customers, but the question asks for the mean absolute deviation.

C. 26
Incorrect. This number is the range of the ages of this group of customers, but the question asks for the mean absolute deviation.

D. 6.48
Correct!

The table below shows the high temperatures in Dallas, Texas for the past 10 days.

Which of the following is the best statement about this set of temperatures?

A. The mean absolute deviation is 92.6°F, meaning that the typical temperature deviated from the mean by 92.6°F during this 10-day period.
Incorrect. The mean temperature in this 10-day period is 92.6°F. The typical temperature deviation from the mean is given by the mean absolute deviation, not the mean.

B. The mean absolute deviation is 5.28°F, meaning that the typical temperature deviated from the mean by 5.28°F during this 10-day period.
Correct!

C. The mean temperature is 92.6°F, meaning that temperature deviated from normal by about 5.28°F.
Incorrect. The mean absolute deviation is 5.28°F, and the mean temperature for this 10-day period is 92.6°F. You do not know what the normal temperature for this 10-day period is, so you cannot make a conclusion about a daily temperature’s deviation from normal.

D. The mean absolute deviation is 5.28°F, meaning that every day during this 10-day period, the temperature deviated from the mean by 5.28°F.
Incorrect. The mean absolute deviation is 5.28°F, but the interpretation of the mean absolute deviation is incorrect. Mean absolute deviation describes the average, or typical, deviation from the mean for each day’s temperature. It doesn’t necessarily imply that the temperature had the same deviation from the mean each day.

Stephanie registered for a baby shower, and the prices for six items from her registry are $19, $48, $25, $99, $75, and $31. What is the mean absolute deviation of this set of item prices?

A. $25
Correct!

B. $49.50
Incorrect. This number is the mean of the six prices, but the question asks for the mean absolute deviation.

C. $15
Incorrect. The sum of the absolute deviations is $150, but there are only six prices, not ten, so divide the sum by six.

D. $39.50
Incorrect. This number is the median of the six prices, but the question asks for the mean absolute deviation.

In 2014, there were nine justices on the United States Supreme Court. The table below shows the name of each justice and the number of years of service on the Supreme Court for that justice.

What is the mean absolute deviation of the lengths of service for these nine justices?

A. 16 years
Incorrect. This number is the mean length of service, but the question asks for the mean absolute deviation.

B. 8 4 9 years
Correct!

C. 24 years
Incorrect. This number is the range of the years of service, but the question asks for the mean absolute deviation.

D. 8.4 years
Incorrect. When calculating the mean absolute deviation, you divide the sum of the absolute deviations, 76, by the number of justices, 9. When you do, you get 8 with 4 left over. To write the remainder of 4, use a fraction of instead of writing the 4 in the tenths place.