Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 7 — Questions and Answers
Question 1: Which of the following changes would NOT affect the median of a dataset?
- Changing the largest value to an even larger number (Correct answer)
- Removing the smallest value
- Adding a value equal to the current median
- Changing the smallest value to a still-smaller number
Correct answer: Changing the largest value to an even larger number
Changing only the largest value (which is already above the median) does not move the middle position, so the median is unaffected.
Question 2: A dataset has values 10, 20, 30, 40, and 50. The mean is 30 and the range is 40. If every value is increased by 5, the new mean and range are:
- Mean=30, Range=40
- Mean=35, Range=45
- Mean=35, Range=40 (Correct answer)
- Mean=30, Range=45
Correct answer: Mean=35, Range=40
Adding 5 to every value increases the mean by 5 (to 35) but does not change the range, since max and min both shift by the same amount.
Question 3: A frequency histogram shows test scores. The bars have heights: 50-59: 2 students, 60-69: 4 students, 70-79: 8 students, 80-89: 6 students, 90-99: 2 students. What is the modal class?
- 60-69
- 70-79 (Correct answer)
- 80-89
- 90-99
Correct answer: 70-79
The modal class is the interval with the highest frequency; the 70-79 interval has 8 students, the most of any group.
Question 4: The mean of a dataset is 25 and the standard deviation is 5. If a value of 40 is added to the dataset, what happens?
- Mean increases; standard deviation increases (Correct answer)
- Mean decreases; standard deviation decreases
- Mean increases; standard deviation decreases
- Mean stays the same; standard deviation increases
Correct answer: Mean increases; standard deviation increases
Adding 40 (above the mean) pulls the mean upward and also increases the spread since 40 is far from the current center.
Question 5: The data set {5, 8, 10, 12, 15} has a mean of 10. Which value, if replaced by 30, would cause the greatest increase in standard deviation?
- 5
- 8
- 10 (Correct answer)
- 15
Correct answer: 10
Replacing the middle value (10, which equals the mean) with 30 creates the greatest deviation from the mean for that position, maximally increasing spread.
Question 6: A box plot shows: Min=5, Q1=15, Median=22, Q3=30, Max=42. Which interval contains approximately 50% of the data?
- 5 to 42
- 15 to 30 (Correct answer)
- 5 to 22
- 22 to 42
Correct answer: 15 to 30
The box (Q1 to Q3) in a box plot represents the middle 50% of the data, from 15 to 30.
Question 7: A teacher calculates class mean scores: Quiz 1 mean = 70, Quiz 2 mean = 80. The class took both quizzes with 20 students each. What is the mean score across both quizzes combined?
- 75 (Correct answer)
- 150
- 70
- 80
Correct answer: 75
Since both groups are the same size (20 students), the combined mean is simply (70 + 80) / 2 = 75.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 7
Which of the following changes would NOT affect the median of a dataset?