Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 3 — Questions and Answers
Question 1: The mode of the dataset {2, 3, 3, 5, 7, 7, 7, 9} is:
- 3
- 7 (Correct answer)
- 5
- 9
Correct answer: 7
The mode is the value that appears most often; 7 appears three times, more than any other value.
Question 2: Two datasets each have 10 values and the same mean of 20. Dataset X has values all between 18 and 22, while Dataset Y has values ranging from 5 to 35. Which has the greater standard deviation?
- Dataset X
- Dataset Y (Correct answer)
- They are equal
- Cannot be determined from this information
Correct answer: Dataset Y
Dataset Y's values are much more spread out from the mean, resulting in a greater standard deviation.
Question 3: A box plot has whiskers extending from 10 to 90, with Q1=30 and Q3=70. A data point at 95 would be classified as:
- Within the IQR
- A mild outlier (Correct answer)
- Exactly at Q3
- Cannot be determined
Correct answer: A mild outlier
The IQR is 40, and 1.5 × 40 = 60, so the upper fence is Q3 + 60 = 130; 95 is outside the whisker (90) but below the fence, making it a mild outlier.
Question 4: A dataset of 9 values has a median of 15. A 10th value of 15 is added. What happens to the median?
- The median increases to more than 15
- The median decreases to less than 15
- The median remains 15 (Correct answer)
- The median cannot be determined
Correct answer: The median remains 15
Adding 15 places it in the middle of the sorted dataset; the median of the 10-value dataset averages the 5th and 6th values, both near 15, keeping the median at 15.
Question 5: The histogram below shows the distribution of test scores in a class. The distribution is left-skewed (skewed toward lower values). Which is most likely true?
- Mean > Median > Mode
- Mode > Median > Mean (Correct answer)
- Mean = Median = Mode
- Median > Mean > Mode
Correct answer: Mode > Median > Mean
In a left-skewed distribution, the long tail pulls the mean left, so Mode > Median > Mean.
Question 6: Students' weekly study hours: 2, 4, 4, 5, 6, 6, 6, 8, 10. What is the mean number of study hours?
- 5
- 5.67 (Correct answer)
- 6
- 5.5
Correct answer: 5.67
The sum is 2+4+4+5+6+6+6+8+10 = 51; dividing by 9 gives 51/9 ≈ 5.67.
Question 7: If a constant of 10 is added to every value in a dataset, what happens to the mean and standard deviation?
- Mean increases by 10; standard deviation stays the same (Correct answer)
- Mean increases by 10; standard deviation increases by 10
- Mean stays the same; standard deviation increases by 10
- Both mean and standard deviation increase by 10
Correct answer: Mean increases by 10; standard deviation stays the same
Adding a constant shifts every value equally, increasing the mean by that constant while leaving the spread (standard deviation) unchanged.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 3
The mode of the dataset {2, 3, 3, 5, 7, 7, 7, 9} is: