Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 10 — Questions and Answers
Question 1: A dataset is: 5, 10, 15, 20, 25, 30, 200. Removing the value 200 would most likely:
- Decrease the mean and increase the median
- Decrease both the mean and the median
- Decrease the mean but leave the median relatively unchanged (Correct answer)
- Increase the mean and decrease the median
Correct answer: Decrease the mean but leave the median relatively unchanged
The outlier 200 greatly inflates the mean; removing it brings the mean down significantly, while the median is resistant to outliers and changes little.
Question 2: The weights (in pounds) of five packages are 3, 7, 8, 8, and 9. What is the median weight?
- 7
- 8 (Correct answer)
- 8.5
- 9
Correct answer: 8
Arranged in order: 3, 7, 8, 8, 9. With 5 values, the median is the 3rd value, which is 8.
Question 3: Two datasets each have 5 values. Dataset P = {10, 10, 10, 10, 10} and Dataset Q = {6, 8, 10, 12, 14}. Which statement is correct?
- Dataset P has a larger standard deviation than Dataset Q.
- Both datasets have the same standard deviation.
- Dataset Q has a larger standard deviation than Dataset P. (Correct answer)
- The standard deviations cannot be compared without the variance.
Correct answer: Dataset Q has a larger standard deviation than Dataset P.
Dataset P has all identical values, so its standard deviation is 0. Dataset Q has spread around its mean of 10, giving a standard deviation greater than 0.
Question 4: The dot plot below shows the number of books read by students over the summer: 1, 2, 2, 3, 4, 4, 4, 5, 6. What is the mean number of books read?
- 3
- 3.4 (Correct answer)
- 4
- 3.67
Correct answer: 3.4
Sum = 1+2+2+3+4+4+4+5+6 = 31; count = 9; mean = 31 ÷ 9 ≈ 3.4.
Question 5: A dataset has a range of 40, a Q1 of 25, and a Q3 of 55. What is the interquartile range (IQR)?
- 15
- 30 (Correct answer)
- 40
- 55
Correct answer: 30
IQR = Q3 − Q1 = 55 − 25 = 30.
Question 6: A data set has a median of 30. If the two largest values are each increased by 50, what happens to the median?
- The median increases significantly.
- The median decreases.
- The median stays the same. (Correct answer)
- The median cannot be determined without more data.
Correct answer: The median stays the same.
The median depends only on the ordering and the middle value(s); changing extreme values does not move the middle value, so the median remains 30.
Question 7: A frequency distribution shows that in a class of 30 students, 10 scored 60, 15 scored 80, and 5 scored 100. What is the mean score?
- 75
- 76.7 (Correct answer)
- 78
- 80
Correct answer: 76.7
Weighted mean = (10×60 + 15×80 + 5×100) ÷ 30 = (600 + 1200 + 500) ÷ 30 = 2300 ÷ 30 ≈ 76.7.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 10
A dataset is: 5, 10, 15, 20, 25, 30, 200.
Removing the value 200 would most likely: