SAT Math: Statistics and Data Practice Questions
Test yourself on Statistics and Data with 13 original SAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of SAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. The data set {4, 7, 9, 9, 11} has its largest value, 11, changed to 31. Which statistic changes the MOST?
Explanation. The mean is affected by every value, especially extreme ones. Original mean = 40/5 = 8; new mean = 60/5 = 12, a change of 4. The median (9) and mode (9) stay the same because the order of the middle and most-frequent values is unchanged, and the minimum stays 4.
2. A survey of 1,200 randomly selected city residents found that 60% support a new park. The margin of error is ±3%. Which is the best interpretation?
Explanation. A margin of error creates a confidence interval for the POPULATION parameter, not the sample. The plausible range for all city residents is 60% ± 3% = 57% to 63%. The sample's exact percentage is known (60%), so the interval is about the larger population, and conclusions only apply to the population sampled (city residents).
3. The mean of 6 numbers is 15. If a seventh number is added and the new mean becomes 16, what is the seventh number?
Explanation. Original sum = 6 × 15 = 90. New sum = 7 × 16 = 112. The seventh number = 112 − 90 = 22.
4. Two data sets each have 50 values and the same mean. Set A has a standard deviation of 2.5; Set B has a standard deviation of 8.1. Which statement is true?
Explanation. Standard deviation measures spread. A larger standard deviation (8.1 > 2.5) means values are more spread out from the mean. Standard deviation tells us nothing directly about the median, and we were told the means are equal.
5. A researcher wants to estimate the average daily screen time of high school students in a large district. Which sampling method best allows the result to be generalized to all students in the district?
Explanation. Only a random sample drawn from the entire population (all district students) allows generalization to that population. The other options are biased convenience samples that overrepresent particular subgroups (one class, volunteers, sports fans).
6. A list of test scores is: 82, 88, 90, 90, 75, 95. What is the range?
Explanation. Range = maximum − minimum = 95 − 75 = 20.
7. In a data set, the median is 50 and the mean is 65. This most strongly suggests:
Explanation. When the mean is greater than the median, high outliers or a long right tail pull the mean upward. This indicates a right (positive) skew. If skewed left, the mean would be less than the median.
8. A table shows that of 80 surveyed people, 30 prefer tea and the rest prefer coffee. Of those who prefer coffee, 20 are under age 30. What fraction of all surveyed people prefer coffee?
Explanation. Coffee preferers = 80 − 30 = 50. The fraction of all surveyed people who prefer coffee is 50/80. The 20-under-30 detail is extra information not needed for this question.
9. A data set of 9 values has a mean of 10. One value, 4, is removed. What is the new mean of the remaining 8 values?
Explanation. Original sum = 9 × 10 = 90. After removing 4, sum = 86 over 8 values: 86/8 = 10.75.
10. Which measure of center is LEAST affected by an extreme outlier in a data set?
Explanation. The median depends only on the order of values and the middle position, so a single extreme outlier has little effect. The mean, range, and standard deviation all incorporate the actual magnitude of every value, so they are sensitive to outliers.
11. A box plot shows a lower quartile of 25, median of 40, and upper quartile of 55. What is the interquartile range (IQR)?
Explanation. IQR = Q3 − Q1 = 55 − 25 = 30. The IQR measures the spread of the middle 50% of the data; the median value is not used in this calculation.
12. Two groups did an experiment. Group A was randomly assigned a new study app; Group B (also randomly assigned) used no app. Group A scored significantly higher. What conclusion is valid?
Explanation. Because subjects were RANDOMLY ASSIGNED to treatment groups in an experiment, a cause-and-effect conclusion is justified for the participants studied. However, causal claims cannot be generalized beyond the sample unless the participants were randomly selected from a broader population, so 'all students everywhere' is too strong.
13. A frequency table lists value 2 (frequency 3), value 5 (frequency 2), and value 8 (frequency 5). What is the mean of this data set?
Explanation. Sum = 2(3) + 5(2) + 8(5) = 6 + 10 + 40 = 56. Total count = 3 + 2 + 5 = 10. Mean = 56/10 = 5.6.
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FAQ
How do I decide whether to use mean or median?
Use the mean for roughly symmetric data with no extreme outliers. Use the median when data is skewed or contains outliers, since the median resists distortion from extreme values. On the SAT, watch for questions that change one extreme value—the mean will shift much more than the median.
What's the difference between random selection and random assignment?
Random selection (choosing subjects randomly from a population) lets you GENERALIZE results to that population. Random assignment (randomly placing subjects into treatment groups) lets you establish CAUSE AND EFFECT. The SAT loves questions where only one of these was done, limiting which conclusions are valid.
Do I need to calculate standard deviation by hand on the SAT?
No. The SAT never asks you to compute standard deviation. You only need to understand that it measures spread: a larger standard deviation means values are more spread out from the mean, and a smaller one means values cluster more tightly. Compare data sets conceptually rather than crunching numbers.