Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 8

Question 1

A dataset of 6 values has a mean of 10 and a median of 9. If the largest value is removed, which is most likely?

Accepted Answer

Mean decreases; median stays the same or decreases slightly

Answer

The largest value is likely above the mean, so removing it decreases the mean; the median, based on middle values, may shift only slightly.

Question 2

The standard deviation of {3, 6, 9, 12, 15} compared to {30, 60, 90, 120, 150} is:

Accepted Answer

10 times smaller for the first dataset

Answer

The second dataset is the first multiplied by 10, so its standard deviation is 10 times larger; equivalently, the first has a standard deviation 10 times smaller.

Question 3

A data set is: 14, 14, 16, 17, 19, 21, 22, 23, 25, 30. What is the IQR?

Accepted Answer

7

Answer

Lower half {14,14,16,17,19} has median 16 (Q1); upper half {21,22,23,25,30} has median 23 (Q3); IQR = 23 − 16 = 7.

Question 4

A researcher collects income data from a neighborhood. She finds the mean income is $90,000 but the median is $55,000. A newcomer with an income of $1,000,000 moves in. This would most likely:

Accepted Answer

Increase the mean substantially but barely affect the median

Answer

The million-dollar income is an extreme outlier that dramatically raises the mean, while the median—resistant to extremes—barely moves.

Question 5

A symmetric distribution has mean 50. The values 45, 50, and 55 each appear equally often. This distribution has standard deviation closest to:

Accepted Answer

5

Answer

The values are all within 5 units of the mean of 50, so the standard deviation is approximately 5 (the average deviation from the mean).

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 8