Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 15

Question 1

A data set has 11 values. If the smallest value is removed, which of the following is most likely to change significantly?

Accepted Answer

Mean

Answer

Removing an extreme low value has a greater effect on the mean (which sums all values) than on the median or IQR, which depend on middle values.

Question 2

A dataset has values 6, 8, 10, 12, 14. Each value is doubled. What happens to the standard deviation?

Accepted Answer

It is doubled.

Answer

Multiplying all values by a constant k multiplies the standard deviation by k; doubling all values doubles the standard deviation.

Question 3

A dataset of 5 values has a mean of 10 and a range of 12. The minimum is 4. What is the maximum?

Accepted Answer

16

Answer

Maximum = Minimum + Range = 4 + 12 = 16.

Question 4

The dot plot shows daily high temperatures (°F) for 10 days: 72, 74, 74, 75, 76, 77, 77, 78, 80, 85. What is the interquartile range?

Accepted Answer

4

Answer

Sorted: 72,74,74,75,76,77,77,78,80,85. Q1 = median of lower half {72,74,74,75,76} = 74; Q3 = median of upper half {77,77,78,80,85} = 78; IQR = 78 − 74 = 4.

Question 5

A researcher reports that the median household income in a city is $52,000 while the mean is $78,000. Which explanation best accounts for this difference?

Accepted Answer

A small number of very high incomes pull the mean upward.

Answer

A few very wealthy households create extreme high values (outliers) that pull the mean up well above the median, which is unaffected by those extremes.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 15