Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 9 — Questions and Answers
Question 1: A dataset contains the values 8, 11, 14, 14, 17, 20, 23. What is the mean of this dataset?
- 14
- 15
- 15.3 (Correct answer)
- 16
Correct answer: 15.3
8+11+14+14+17+20+23 = 107; mean = 107 ÷ 7 ≈ 15.3.
Question 2: A dataset of 8 values has a mean of 16. If every value in the dataset is increased by 4, what is the new mean?
- 16
- 18
- 20 (Correct answer)
- 64
Correct answer: 20
Adding a constant k to every value increases the mean by k, so the new mean is 16 + 4 = 20.
Question 3: The data values 3, 5, 7, 9, 11, 13, and 15 form an arithmetic sequence. What is the relationship between the mean and the median of this dataset?
- The mean is greater than the median.
- The median is greater than the mean.
- The mean and median are equal. (Correct answer)
- It cannot be determined without more information.
Correct answer: The mean and median are equal.
In a symmetric distribution such as an arithmetic sequence, the mean and median are always equal; both equal 9 here.
Question 4: A dataset of 10 test scores has a mean of 80. One score of 40 is removed. What is the new mean of the remaining 9 scores?
- 80
- 82
- 84.4 (Correct answer)
- 86
Correct answer: 84.4
Total sum = 80 × 10 = 800; after removing 40, the new sum = 760; new mean = 760 ÷ 9 ≈ 84.4.
Question 5: Which of the following describes a dataset where the median is a more appropriate measure of center than the mean?
- A symmetric bell-shaped distribution
- A dataset with no outliers and roughly equal spread
- A dataset with a few extremely large values that skew the distribution (Correct answer)
- A uniform distribution where all values appear equally often
Correct answer: A dataset with a few extremely large values that skew the distribution
The median is preferred when outliers are present because it is resistant to extreme values, unlike the mean which is pulled toward them.
Question 6: The five-number summary of a dataset is: Min = 4, Q1 = 12, Median = 19, Q3 = 28, Max = 50. What is the range?
- 16
- 19
- 34
- 46 (Correct answer)
Correct answer: 46
Range = Max − Min = 50 − 4 = 46.
Question 7: A teacher records quiz scores for 6 students: 72, 75, 80, 80, 85, 88. What is the mode?
- 75
- 80 (Correct answer)
- 82
- 88
Correct answer: 80
The mode is the value that appears most frequently; 80 appears twice while all other values appear once.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 9
A dataset contains the values 8, 11, 14, 14, 17, 20, 23.
What is the mean of this dataset?