Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 8 — Questions and Answers
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?
- Mean decreases; median stays the same or decreases slightly (Correct answer)
- Mean increases; median increases
- Mean stays the same; median decreases
- Both mean and median increase
Correct answer: Mean decreases; median stays the same or decreases slightly
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:
- The same for both datasets
- 10 times smaller for the first dataset (Correct answer)
- 10 times larger for the first dataset
- Cannot be compared
Correct answer: 10 times smaller for the first dataset
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?
- 7 (Correct answer)
- 8
- 9
- 16
Correct answer: 7
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:
- Increase both mean and median significantly
- Increase the mean substantially but barely affect the median (Correct answer)
- Increase the median substantially but barely affect the mean
- Have no effect on either the mean or the median
Correct answer: Increase the mean substantially but barely affect the median
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:
- 0
- 5 (Correct answer)
- 10
- 50
Correct answer: 5
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).
Question 6: A histogram shows customer wait times in minutes: most customers wait 3–5 minutes, but a few wait over 20 minutes. The distribution is right-skewed. Which statement is correct?
- The mean equals the median
- The mean is less than the median
- The mean is greater than the median (Correct answer)
- The median is greater than the mode
Correct answer: The mean is greater than the median
The long right tail (customers waiting 20+ minutes) pulls the mean above the median in a right-skewed distribution.
Question 7: The scores on a 10-point quiz for 5 students are: 6, 7, 8, 9, and x. If the mean is 8, what is x?
- 10 (Correct answer)
- 9
- 8
- 7
Correct answer: 10
Sum = 8 × 5 = 40; 6 + 7 + 8 + 9 + x = 40; 30 + x = 40; x = 10.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 8
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?