Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 4 — Questions and Answers
Question 1: The mean of five numbers is 14. Four of the numbers are 10, 12, 16, and 18. What is the fifth number?
- 12
- 14 (Correct answer)
- 16
- 10
Correct answer: 14
The total sum must be 14 × 5 = 70; the known four sum to 56, so the fifth number is 70 − 56 = 14.
Question 2: A dot plot shows values: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the median?
- 2
- 3 (Correct answer)
- 3.5
- 4
Correct answer: 3
With 9 values, the median is the 5th value when sorted, which is 3.
Question 3: A company reports employee salaries. The CEO earns $500,000 while most employees earn around $50,000. Which measure of center should HR use to most accurately represent the typical employee salary?
- Mean
- Median (Correct answer)
- Mode
- Range
Correct answer: Median
The CEO's high salary would skew the mean upward, so the median better represents the typical employee salary.
Question 4: Dataset A: {1, 5, 5, 5, 9} and Dataset B: {3, 4, 5, 6, 7}. Which dataset has the greater standard deviation?
- Dataset A (Correct answer)
- Dataset B
- They are equal
- Cannot be determined
Correct answer: Dataset A
Both datasets have a mean of 5, but Dataset A's values (1 and 9) are farther from the mean than Dataset B's extremes (3 and 7), giving Dataset A a larger standard deviation.
Question 5: A box plot's median line is positioned closer to Q3 than to Q1. This suggests the distribution is:
- Symmetric
- Left-skewed (Correct answer)
- Right-skewed
- Normal
Correct answer: Left-skewed
When the median is closer to Q3, the lower half of the data is more spread out, indicating a left-skewed distribution.
Question 6: A dataset has mean 20 and standard deviation 4. A new dataset is created by doubling each value and subtracting 5. What is the new standard deviation?
- 4
- 8 (Correct answer)
- 3
- 11
Correct answer: 8
Subtracting 5 (a constant) doesn't affect standard deviation, but multiplying by 2 doubles it: 2 × 4 = 8.
Question 7: The scores on a math quiz are: 55, 60, 65, 70, 75, 80, 85. If the lowest score (55) is removed, which of the following is true?
- Both mean and median increase (Correct answer)
- Mean increases; median stays the same
- Median increases; mean stays the same
- Both mean and median decrease
Correct answer: Both mean and median increase
Removing the lowest value (55) increases the mean because it was below the mean; the median also shifts from 70 to 72.5 with 6 values remaining.
Bluebook SAT Test One-Variable Data: Distributions and Measures of Center and Spread 4
The mean of five numbers is 14.
Four of the numbers are 10, 12, 16, and 18.
What is the fifth number?