Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 1 — Questions and Answers
Question 1: A dataset of 7 values has a mean of 12. If a new value of 12 is added to the dataset, what happens to the mean?
- The mean increases
- The mean decreases
- The mean stays the same (Correct answer)
- The mean cannot be determined
Correct answer: The mean stays the same
Adding a value equal to the mean does not change the mean, since it contributes proportionally to both the sum and the count.
Question 2: The dot plot shows the number of hours students studied: 1, 1, 2, 3, 3, 3, 4, 5, 5, 8. Which measure of center best represents this dataset if the goal is to avoid distortion from the outlier?
- Mean
- Median (Correct answer)
- Mode
- Range
Correct answer: Median
The median is resistant to outliers, so it better represents the center when an extreme value like 8 is present.
Question 3: Dataset A: {2, 4, 6, 8, 10} and Dataset B: {4, 5, 6, 7, 8}. Both datasets have the same mean. Which dataset has the greater standard deviation?
- Dataset A (Correct answer)
- Dataset B
- Both have equal standard deviation
- Standard deviation cannot be compared
Correct answer: Dataset A
Dataset A's values are more spread out from the mean of 6, so it has a greater standard deviation than Dataset B.
Question 4: A box plot shows the following five-number summary: Min=10, Q1=20, Median=35, Q3=50, Max=80. What is the interquartile range (IQR)?
- 70
- 45
- 30 (Correct answer)
- 15
Correct answer: 30
The IQR equals Q3 minus Q1, which is 50 − 20 = 30.
Question 5: A class of 10 students scored: 70, 72, 74, 75, 76, 78, 79, 80, 82, 84. What is the median score?
- 76
- 77 (Correct answer)
- 78
- 75
Correct answer: 77
With 10 values, the median is the average of the 5th and 6th values: (76 + 78) / 2 = 77.
Question 6: A histogram shows heights of plants. The distribution is strongly skewed right. Which statement about the mean and median is most likely true?
- Mean > Median (Correct answer)
- Mean < Median
- Mean = Median
- Mean and median are both equal to the mode
Correct answer: Mean > Median
In a right-skewed distribution, the mean is pulled toward the higher tail and is greater than the median.
Question 7: The ages of five employees are 24, 27, 29, 31, and 34. If a new employee aged 62 joins, what is the effect on the mean and median?
- Both the mean and median increase significantly
- The mean increases more than the median (Correct answer)
- The median increases more than the mean
- Neither the mean nor the median changes
Correct answer: The mean increases more than the median
The mean is pulled substantially by the outlier (62), while the median only shifts slightly from 29 to 30.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 1
A dataset of 7 values has a mean of 12.
If a new value of 12 is added to the dataset, what happens to the mean?