Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 9

Question 1

A dataset contains the values 8, 11, 14, 14, 17, 20, 23. What is the mean of this dataset?

Accepted Answer

15.3

Answer

8+11+14+14+17+20+23 = 107; mean = 107 ÷ 7 ≈ 15.3.

Question 2

A dataset of 8 values has a mean of 16. If every value in the dataset is increased by 4, what is the new mean?

Accepted Answer

20

Answer

Adding a constant k to every value increases the mean by k, so the new mean is 16 + 4 = 20.

Question 3

The data values 3, 5, 7, 9, 11, 13, and 15 form an arithmetic sequence. What is the relationship between the mean and the median of this dataset?

Accepted Answer

The mean and median are equal.

Answer

In a symmetric distribution such as an arithmetic sequence, the mean and median are always equal; both equal 9 here.

Question 4

A dataset of 10 test scores has a mean of 80. One score of 40 is removed. What is the new mean of the remaining 9 scores?

Accepted Answer

84.4

Answer

Total sum = 80 × 10 = 800; after removing 40, the new sum = 760; new mean = 760 ÷ 9 ≈ 84.4.

Question 5

Which of the following describes a dataset where the median is a more appropriate measure of center than the mean?

Accepted Answer

A dataset with a few extremely large values that skew the distribution

Answer

The median is preferred when outliers are present because it is resistant to extreme values, unlike the mean which is pulled toward them.

Bluebook SAT Practice Test