Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 1

Question 1

A dataset of 7 values has a mean of 12. If a new value of 12 is added to the dataset, what happens to the mean?

Accepted Answer

The mean stays the same

Answer

Adding a value equal to the mean does not change the mean, since it contributes proportionally to both the sum and the count.

Question 2

The dot plot shows the number of hours students studied: 1, 1, 2, 3, 3, 3, 4, 5, 5, 8. Which measure of center best represents this dataset if the goal is to avoid distortion from the outlier?

Accepted Answer

Median

Answer

The median is resistant to outliers, so it better represents the center when an extreme value like 8 is present.

Question 3

Dataset A: {2, 4, 6, 8, 10} and Dataset B: {4, 5, 6, 7, 8}. Both datasets have the same mean. Which dataset has the greater standard deviation?

Accepted Answer

Dataset A

Answer

Dataset A's values are more spread out from the mean of 6, so it has a greater standard deviation than Dataset B.

Question 4

A box plot shows the following five-number summary: Min=10, Q1=20, Median=35, Q3=50, Max=80. What is the interquartile range (IQR)?

Accepted Answer

30

Answer

The IQR equals Q3 minus Q1, which is 50 − 20 = 30.

Question 5

A class of 10 students scored: 70, 72, 74, 75, 76, 78, 79, 80, 82, 84. What is the median score?

Accepted Answer

77

Answer

With 10 values, the median is the average of the 5th and 6th values: (76 + 78) / 2 = 77.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 1