Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 5 — Questions and Answers
Question 1: A frequency table shows: Score 70 (frequency 3), Score 80 (frequency 5), Score 90 (frequency 2). What is the mean score?
- 80
- 79 (Correct answer)
- 78
- 81
Correct answer: 79
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}?
- Replace 10 with 11
- Replace 18 with 17
- Replace 14 with 50 (Correct answer)
- Replace 12 with 13
Correct answer: Replace 14 with 50
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?
- 45 (Correct answer)
- 30
- 15
- 25
Correct answer: 45
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?
- It is the mean
- It is the mode
- It is the median (Correct answer)
- It is the maximum
Correct answer: It is the median
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?
- Class A's scores are more consistent
- Class B's scores are more consistent (Correct answer)
- Both classes performed the same overall
- Class A has a higher median
Correct answer: Class B's scores are more consistent
A lower standard deviation indicates less variability, so Class B's scores are more consistent (more tightly clustered around the mean).
Question 6: The dataset {x, 8, 11, 14, 17} has a mean of 12. What is the value of x?
- 10 (Correct answer)
- 12
- 11
- 8
Correct answer: 10
Sum = 12 × 5 = 60; x + 8 + 11 + 14 + 17 = 60, so x = 60 − 50 = 10.
Question 7: A dataset has an outlier that is extremely large. Removing the outlier would most likely:
- Decrease the mean and decrease the median
- Decrease the mean and have little effect on the median (Correct answer)
- Increase the mean and decrease the median
- Have no effect on the mean or median
Correct answer: Decrease the mean and have little effect on the median
A large outlier inflates the mean; removing it decreases the mean significantly, while the median—resistant to outliers—barely changes.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 5
A frequency table shows: Score 70 (frequency 3), Score 80 (frequency 5), Score 90 (frequency 2).
What is the mean score?