Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 12

Question 1

A dataset of 9 numbers has a mean of 22. The sum of 8 of the numbers is 180. What is the 9th number?

Accepted Answer

18

Answer

Total sum = 22 × 9 = 198; 9th number = 198 − 180 = 18.

Question 2

Which measure of spread is most affected by a single extreme outlier?

Accepted Answer

Range

Answer

The range uses only the maximum and minimum values, so a single extreme outlier directly changes the range more dramatically than the IQR or standard deviation.

Question 3

The scores 50, 60, 70, 80, and 90 form a dataset. A new value of 70 is added. Which statement about the updated dataset is true?

Accepted Answer

The mode changes from undefined to 70.

Answer

Originally all values are distinct, so there is no mode; adding a second 70 creates a mode of 70 while the mean stays at 70 and the median remains 70.

Question 4

A histogram shows the following distribution of ages in a group: most values cluster between 20 and 30, with a few values near 70. This distribution is best described as:

Accepted Answer

Right-skewed

Answer

The bulk of data is on the lower end with a few high values creating a tail to the right, which is the definition of a right-skewed (positively skewed) distribution.

Question 5

The IQR of a dataset is 18. Using the 1.5 × IQR rule, an outlier is any value more than 1.5 × IQR above Q3. If Q3 = 54, what is the outlier threshold?

Accepted Answer

81

Answer

Upper outlier threshold = Q3 + 1.5 × IQR = 54 + 1.5 × 18 = 54 + 27 = 81.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 12