Free SAT Data Analysis & Statistics Questions and Answers 2 — Questions and Answers
Question 1: A scatter plot shows the relationship between hours studied and test scores for 25 students. The line of best fit has a slope of 8.5. What does this slope represent?
- Each additional hour of study is associated with an 8.5-point increase in test score (Correct answer)
- The average test score is 8.5
- 85% of the variation is explained by study hours
- Students who studied scored 8.5 times higher
Correct answer: Each additional hour of study is associated with an 8.5-point increase in test score
The slope of a line of best fit represents the rate of change. A slope of 8.5 means that for each additional hour studied, the predicted test score increases by 8.5 points.
Question 2: A survey found that 60% of 500 respondents preferred Brand A. What is the margin of error at a 95% confidence level (approximately)?
- ±2.2%
- ±4.4% (Correct answer)
- ±6.0%
- ±10.0%
Correct answer: ±4.4%
The margin of error formula is approximately ±1.96 × √(p(1-p)/n) = 1.96 × √(0.6×0.4/500) ≈ 1.96 × 0.0219 ≈ ±4.3%, closest to ±4.4%.
Question 3: In a data set, the mean is 72 and the standard deviation is 5. Approximately what percentage of values fall between 62 and 82?
- 68%
- 95% (Correct answer)
- 99.7%
- 50%
Correct answer: 95%
The range 62 to 82 represents the mean ± 2 standard deviations (72-10 to 72+10). By the empirical rule, approximately 95% of data falls within 2 standard deviations of the mean.
Question 4: A two-way table shows the relationship between gender and preference for two activities. Which value would you calculate to determine if there is an association?
- The mean of each row
- The relative frequencies within each column (Correct answer)
- The sum of all cells
- The range of each row
Correct answer: The relative frequencies within each column
To determine association in a two-way table, you compare relative frequencies (proportions) across groups. If the proportions differ substantially between groups, an association likely exists.
Question 5: A box plot shows Q1 = 45, median = 55, Q3 = 70, with whiskers at 20 and 95. Which statement is true?
- The data is symmetric
- The data is skewed left
- The data is skewed right (Correct answer)
- Exactly 50% of the data falls between 20 and 55
Correct answer: The data is skewed right
The distance from Q3 to the upper whisker (95-70=25) is greater than Q1 to the lower whisker (45-20=25), but the median (55) is closer to Q1 (45) than Q3 (70), indicating right skew.
Question 6: A researcher collects data from 200 randomly selected households about income and education level. Which type of study is this?
- Experiment
- Observational study (Correct answer)
- Clinical trial
- Census
Correct answer: Observational study
Since the researcher only collects data without manipulating any variables, this is an observational study. Experiments require random assignment to treatment groups.
Free SAT Data Analysis & Statistics Questions and Answers 2
A scatter plot shows the relationship between hours studied and test scores for 25 students.
The line of best fit has a slope of 8.5.
What does this slope represent?