ACT Measures of Center Practice

Data Set A consists of the 8 numbers listed below. Data Set B consists of the8 numbers in A and a 9th number, which is greater than 90. How will the mean and median of B compare to the mean and the median of A?

63, 77, 77, 81, 83, 88, 95, 97

• The mean and the median of B will each be greater than the mean and median of A.

• The mean and the median of B will each be less than the mean and the median of A.

• The mean and the median of B will each be the same as the mean and the median of A.

• The mean of B will be the same as the mean of A, and the median of B will be greater than the median of A.

• The mean of B will be greater than the mean of A, and the median of B will be the same as the median of A.

Jose is doing an experiment to determine whether a high-protein food affects the ability of white mice to find their way through a maze. The mice in the experimental group were given the high-protein food; the mice in the control group were given regular food. Jen then timed the mice as they found their way through the maze. The table below shows the results.

The average time the mice in the experimental group took to find their way through the maze was how many seconds less than the average time taken by the mice in the control group?

• 8

• 11

• 13

• 16

• 19

The average of 10 test scores is x. When the highest score and the lowest score are removed from the 10 scores, the average is y. Which of the following is an expression for the average of the highest score and the lowest score?

Mele earned scores of 75, 70, 92, 95, and 97 points ( a total of 429 points) on the first 5 tests in Economics II. Solving which of the following equations for s gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests?

The median of a set of data containing 9 items was found. Four data items were added to the set. Two of these items were greater than the original median, and the other 2 items were less than the original median. Which of the following statements must be true about the median of the new data set?

• It is the average of the 2 new lower values.

• It is the same as the original median.

• It is the average of the 2 new higher values.

• It is greater than the original median.

• It is less than the original median.

The sign of a is positive. The sign of b is negative. If it can be determined, what is the sign of the mean of a and b?

• Positive

• Negative

• Both positive and negative

• Neither positive nor negative

• Cannot be determined from the given information

Halle is bowling a series of 3 games. She has bowled 2 of 3 games with scores of 148 and 176.

What score will Halle need to earn in her 3rd game to have an average score of 172 for the 3 games?

• 165

• 172

• 182

• 192

• 200

Pete has an average score of exactly x points on 4 equally weighted tests. How many points higher than x must Pete score on the 5th equally weighted test to raise his average score after the 5th test to x + 2 points?

• 2

• 4

• 5

• 8

• 10

The mean of the set of 5 numbers {42, 3, 11, 27, x} is 24, and the median of the set of 4 numbers {53, 8, 29, y} is 38. If it can be determined, which of the following values is equal to x - y?

• -38

• -10

• 10

• 38

• Cannot be determined from the given information