Comparing Measures of Center and Variability

Which statement is true?

• The mode is misleading because it is in the center of the data points.

• The mean is misleading because the outlier skews the mean down.

• The median is misleading because it is in the center of the data.

• The range is misleading because it is too large.

Enzo’s mean score is 44. Zahra’s mean score is 38. How much greater is the mean absolute deviation for Zahra's scores than for Enzo's scores?

• 1.2

• 4.4

• 5.6

• 6.0

Theo recorded the means and mean absolute deviations of his language arts and Biology scores. He found the difference in the means of the scores of the two subjects. What is the approximate ratio of the difference in the means to each of the mean absolute deviations?

• 2

• 5

• 18

• 28

Joaquin and Trisha are playing a game in which the lower median wins the game. Their scores are shown below. Joaquin’s scores: 75, 72, 85, 62, 58, 91 Trisha’s scores: 92, 90, 55, 76, 91, 74 Which supports the conclusion that Joaquin won the game?

• Joaquin won because the median of his scores is 73.5 and the median of Trisha’s scores is 83.

• Joaquin won because the median of his scores is 83 and the median of Trisha’s scores is 73.5.

• Trisha won because the median of her scores is 73.5 and the median of Joaquin’s scores is 83.

• Trisha won because the median of her scores is 83 and the median of Joaquin’s scores is 73.5.

What is the mean absolute deviation of her math scores?

• 5.4

• 6.4

• 7.8

• 8.8

Darius and Barb are playing a video game in which the higher score wins the game. Their scores are shown below.Darius’s scores: 96, 54, 120, 87, 123Barb’s scores: 92, 98, 96, 94, 110Barb says that she is the winner. Darius says that it is a tie. Who is correct?

• Barb is correct if both the mean and median scores are considered.

• Barb is correct if only the median score is considered.

• Darius is correct if both the mean and median scores are considered.

• Darius is correct if only the median score is considered.

The difference of the means is found and then compared to each of the mean absolute deviations. Which is true?

• The difference between the mean times is about equal to the mean absolute deviation of the data sets.

• The difference between the mean times is about 2 times the mean absolute deviation of the data sets.

• The difference between the mean times is about 5 times the mean absolute deviation of the data sets.

• The difference between the mean times is about 16 times the mean absolute deviation of the data sets.

Which statement comparing the modes to the ranges is true?

• The modes differ by 40 and the ranges differ by 40.

• The modes differ by 20 and the ranges differ by 20.

• The modes differ by 40, but the ranges differ by 20.

• The modes differ by 20, but the ranges differ by 40.

What is the ratio of the difference in the means to the Mean Absolute Deviation of Team B?

• 0.09

• 0.15

• 0.25

• 0.65

Step 1 Add Scores: 76+62+94+80=312

Step 2 Divide the sum of the scores by 4: 312/4 = 78 Step 3 Add the difference between the mean and each score: (76-78)+(62-78)+(94-78)+(80-78)=0

Step 4 Divide by 4: 0/4 = 0

• Step 1

• Step 2

• Step 3

• Step 4