Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 16

Question 1

A class of 30 students has a mean exam score of 80. A second class of 20 students has a mean score of 70. What is the combined mean for all 50 students?

Accepted Answer

76

Answer

Combined mean = (30×80 + 20×70) ÷ 50 = (2400 + 1400) ÷ 50 = 3800 ÷ 50 = 76.

Question 2

The data values 1, 4, 9, 16, 25 represent perfect squares. The mean is 11. Which value is farthest from the mean?

Accepted Answer

25

Answer

Distances from mean 11: |1−11|=10, |4−11|=7, |9−11|=2, |16−11|=5, |25−11|=14; the value 25 is farthest.

Question 3

A data set has a mean of 50 and a standard deviation of 8. A data point has a value of 66. How many standard deviations above the mean is this value?

Accepted Answer

2

Answer

Z-score = (66 − 50) ÷ 8 = 16 ÷ 8 = 2 standard deviations above the mean.

Question 4

A dot plot shows the number of hours 9 students practiced guitar each week: 1, 2, 3, 3, 4, 5, 5, 6, 7. If the outlier 1 is removed, which of the following changes?

Accepted Answer

The range decreases, and the mean increases.

Answer

Removing the minimum (1) decreases the range from 6 to 5, and removing a below-mean value increases the mean.

Question 5

A bimodal distribution has two peaks at 20 and 60 with a valley in between. Which statement best describes the mean?

Accepted Answer

The mean is approximately 40, between the two peaks.

Answer

If both peaks are roughly symmetric and equal in size, the mean falls in the middle of the two peaks, approximately at 40.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 16