Bluebook SAT Test SAT Data Analysis & Statistics 1 — Questions and Answers
Question 1: A researcher records the test scores of 30 students: the mean score is 74 and the median score is 81. What does this relationship between mean and median suggest about the distribution of scores?
- The distribution is symmetric around 77.5
- The distribution is skewed left, pulled down by a few very low scores (Correct answer)
- The distribution is skewed right, pulled up by a few very high scores
- The mean and median are too close to draw any conclusions
Correct answer: The distribution is skewed left, pulled down by a few very low scores
When the mean is lower than the median, a few unusually low values are pulling the mean down, creating a left (negative) skew. The median is resistant to outliers, so the gap reveals the direction of skew.
Question 2: A scatterplot of hours studied (x) vs. exam score (y) shows a strong positive linear association with r = 0.91. A student concludes that studying more causes higher scores. Which statement best evaluates this conclusion?
- The conclusion is valid because r = 0.91 is close to 1
- The conclusion is valid because the association is linear
- The conclusion is not valid; correlation does not establish causation (Correct answer)
- The conclusion is not valid because r must equal 1.0 to support any claim
Correct answer: The conclusion is not valid; correlation does not establish causation
Even a very strong correlation (r = 0.91) only shows that two variables move together — it does not prove that one causes the other. A lurking variable (e.g., student motivation) could explain both.
Question 3: The table below shows two data sets, each with 5 values: Set A: 10, 10, 10, 10, 10 Set B: 6, 8, 10, 12, 14 Which correctly compares their standard deviations?
- Set A has a larger standard deviation than Set B
- Set B has a larger standard deviation than Set A (Correct answer)
- Both sets have the same standard deviation because they have the same mean
- Standard deviation cannot be determined without a larger sample
Correct answer: Set B has a larger standard deviation than Set A
Standard deviation measures spread around the mean. Set A has zero spread (all values identical, SD = 0). Set B's values vary from the mean of 10 by 4, 2, 0, 2, and 4, giving a non-zero SD. Same mean does not imply same spread.
Question 4: A polling organization surveys 500 randomly selected voters and reports that 54% support a ballot measure, with a margin of error of ±3 percentage points. What is the best interpretation of this result?
- Exactly 54% of all voters support the measure
- The true population percentage is guaranteed to be between 51% and 57%
- It is plausible that the true population support is between 51% and 57% (Correct answer)
- The poll is unreliable because it did not survey all voters
Correct answer: It is plausible that the true population support is between 51% and 57%
A margin of error creates a confidence interval — a plausible range for the true parameter, not a guarantee. The interval 51%–57% is likely (typically 95% confident) to contain the true value, but not certain.
Question 5: A data set of 9 values has a median of 45. If the largest value in the set is increased from 90 to 200, what happens to the median and mean?
- Both the median and mean increase
- The median stays the same; the mean increases (Correct answer)
- The median increases; the mean stays the same
- Both the median and mean stay the same
Correct answer: The median stays the same; the mean increases
The median is the middle value (5th of 9 when ordered), so changing the largest value does not shift the middle value — median stays at 45. The mean includes all values in its calculation, so raising one value raises the sum and therefore the mean.
Question 6: Two classes each take the same 100-point exam. Class 1 has a mean of 78 and a standard deviation of 4. Class 2 has a mean of 78 and a standard deviation of 14. Which statement is most accurate?
- Class 1 performed better overall because its scores are more consistent
- Class 2 performed better overall because it has more variability
- Both classes performed equally overall, but Class 2's scores are more spread out (Correct answer)
- Class 1's scores are more spread out around the mean than Class 2's scores
Correct answer: Both classes performed equally overall, but Class 2's scores are more spread out
Both classes have the same mean (78), so overall performance is equal on average. Class 2's much larger standard deviation (14 vs. 4) means its scores are far more spread out — some students scored much higher or lower than the mean.
Bluebook SAT Test SAT Data Analysis & Statistics 1
A researcher records the test scores of 30 students: the mean score is 74 and the median score is 81.
What does this relationship between mean and median suggest about the distribution of scores?