Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 6 — Questions and Answers
Question 1: The test scores for 11 students, listed in order, are: 60, 63, 67, 70, 72, 75, 78, 80, 84, 88, 92. What is the median score?
- 72
- 75 (Correct answer)
- 78
- 70
Correct answer: 75
With 11 values, the median is the 6th value in the ordered list, which is 75.
Question 2: In a symmetric distribution, the mean is 40 and the standard deviation is 6. What value is 1.5 standard deviations above the mean?
- 46
- 49 (Correct answer)
- 52
- 43
Correct answer: 49
1.5 standard deviations above the mean: 40 + 1.5(6) = 40 + 9 = 49.
Question 3: A dot plot shows these values: 3, 3, 4, 4, 4, 5, 5, 6, 6, 10. Which value is an outlier that most distorts the mean?
- 3
- 4
- 6
- 10 (Correct answer)
Correct answer: 10
The value 10 is much larger than the rest of the data (which clusters between 3 and 6) and pulls the mean upward.
Question 4: A dataset of salaries has a mean of $65,000 and a median of $55,000. This suggests the distribution is:
- Symmetric
- Left-skewed
- Right-skewed (Correct answer)
- Uniform
Correct answer: Right-skewed
When mean > median, high-value outliers pull the mean upward, indicating right skew.
Question 5: For the dataset {2, 4, 4, 4, 5, 5, 7, 9}, what is the difference between the mean and the mode?
- 1 (Correct answer)
- 0.5
- 2
- 0
Correct answer: 1
Mean = (2+4+4+4+5+5+7+9)/8 = 40/8 = 5; Mode = 4 (appears 3 times); Difference = 5 − 4 = 1.
Question 6: A histogram shows a roughly uniform distribution of data. In this case, what is most likely true about the mean and median?
- Mean > Median
- Mean < Median
- Mean ≈ Median (Correct answer)
- Mean = 0
Correct answer: Mean ≈ Median
In a symmetric or uniform distribution, the mean and median are approximately equal.
Question 7: The interquartile range (IQR) of a dataset is 12. A value is considered an outlier if it falls more than 1.5 × IQR below Q1. If Q1 = 20, below what value would a data point be an outlier?
- 2 (Correct answer)
- 8
- 14
- 38
Correct answer: 2
Lower fence = Q1 − 1.5 × IQR = 20 − 1.5(12) = 20 − 18 = 2; values below 2 are outliers.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 6
The test scores for 11 students, listed in order, are: 60, 63, 67, 70, 72, 75, 78, 80, 84, 88, 92.
What is the median score?