Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 7

Question 1

Which of the following changes would NOT affect the median of a dataset?

Accepted Answer

Changing the largest value to an even larger number

Answer

Changing only the largest value (which is already above the median) does not move the middle position, so the median is unaffected.

Question 2

A dataset has values 10, 20, 30, 40, and 50. The mean is 30 and the range is 40. If every value is increased by 5, the new mean and range are:

Accepted Answer

Mean=35, Range=40

Answer

Adding 5 to every value increases the mean by 5 (to 35) but does not change the range, since max and min both shift by the same amount.

Question 3

A frequency histogram shows test scores. The bars have heights: 50-59: 2 students, 60-69: 4 students, 70-79: 8 students, 80-89: 6 students, 90-99: 2 students. What is the modal class?

Accepted Answer

70-79

Answer

The modal class is the interval with the highest frequency; the 70-79 interval has 8 students, the most of any group.

Question 4

The mean of a dataset is 25 and the standard deviation is 5. If a value of 40 is added to the dataset, what happens?

Accepted Answer

Mean increases; standard deviation increases

Answer

Adding 40 (above the mean) pulls the mean upward and also increases the spread since 40 is far from the current center.

Question 5

The data set {5, 8, 10, 12, 15} has a mean of 10. Which value, if replaced by 30, would cause the greatest increase in standard deviation?

Accepted Answer

10

Answer

Replacing the middle value (10, which equals the mean) with 30 creates the greatest deviation from the mean for that position, maximally increasing spread.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 7