Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 5

Question 1

A frequency table shows: Score 70 (frequency 3), Score 80 (frequency 5), Score 90 (frequency 2). What is the mean score?

Accepted Answer

79

Answer

Mean = (70×3 + 80×5 + 90×2) / (3+5+2) = (210+400+180)/10 = 790/10 = 79.

Question 2

Which of the following would most increase the standard deviation of the dataset {10, 12, 14, 16, 18}?

Accepted Answer

Replace 14 with 50

Answer

Replacing the middle value with 50 introduces a very large outlier far from the mean, dramatically increasing the spread.

Question 3

The range of a dataset is 30 and the minimum is 15. What is the maximum?

Accepted Answer

45

Answer

Range = Maximum − Minimum, so Maximum = Range + Minimum = 30 + 15 = 45.

Question 4

A histogram shows that 50% of values fall below the 6th bar. What does this suggest about the 6th bar's value relative to the dataset?

Accepted Answer

It is the median

Answer

The value at which 50% of the data falls below is the median by definition.

Question 5

Two classes took the same test. Class A has mean 72 and standard deviation 8. Class B has mean 72 and standard deviation 3. Which statement is true?

Accepted Answer

Class B's scores are more consistent

Answer

A lower standard deviation indicates less variability, so Class B's scores are more consistent (more tightly clustered around the mean).

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