Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 2

Question 1

A dataset has values 5, 5, 5, 5, 5. What is the standard deviation of this dataset?

Accepted Answer

0

Answer

When all values are identical, there is no spread from the mean, so the standard deviation is 0.

Question 2

Which of the following datasets has the greatest range?

Accepted Answer

{5, 15, 25, 35, 100}

Answer

The range is max minus min: Set B has 100 − 5 = 95, which is larger than 40, 40, or 40 for the others.

Question 3

The median of the dataset {3, 7, 9, 12, 15, x} is 10.5. What is the value of x?

Accepted Answer

12

Answer

With 6 values sorted, the median is the average of the 3rd and 4th values: (9 + x) / 2 = 10.5 gives x = 12.

Question 4

A dot plot shows quiz scores for 12 students. The scores cluster around 85 with one score of 20. If the outlier is removed, which of the following will change the most?

Accepted Answer

Mean

Answer

The mean is sensitive to outliers; removing the score of 20 will increase the mean substantially more than it shifts the median.

Question 5

Dataset: {4, 6, 8, 10, 12}. Each value is multiplied by 3. What happens to the mean and standard deviation?

Accepted Answer

Mean triples; standard deviation triples

Answer

Multiplying every value by 3 scales both the mean and the standard deviation by a factor of 3.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 2