SAT Math · Problem Solving & Data Analysis
Mean, median, and standard deviation
Measures of center and spread, and comparing data sets.
What's tested in this subtopic
Items test the mean and median of a small data set, the effect of adding or removing a value (especially an outlier) on the mean and median, and the conceptual meaning of standard deviation. The SAT does not ask you to compute standard deviation but does ask you to compare two data sets and judge which has a larger one.
Tactics that actually move your score
Mean is sensitive to outliers; median is not. Adding a value above the current mean raises the mean; adding one equal to the current median doesn't change the median. For standard deviation comparisons, the data set whose values are more spread out has the larger standard deviation — even if its mean is the same. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy The five values in a data set are 46, 29, 69, 78, 50. What is the mean?
- Easy The five values in a data set are 81, 11, 89, 25, 55. What is the mean?
- Medium The five values in a data set are 61, 58, 68, 64, 86. What is the mean?
- Medium The five values in a data set are 26, 34, 66, 88, 78. What is the mean?
- Medium The five values in a data set are 41, 52, 70, 81, 33. What is the mean?
- Hard The five values in a data set are 56, 82, 20, 86, 30. What is the mean?
- Easy The five values in a data set are 56, 79, 67, 16, 18. What is the mean?
- Easy The five values in a data set are 23, 85, 55, 58, 28. What is the mean?
- Medium The five values in a data set are 43, 55, 34, 80, 74. What is the mean?
- Medium The five values in a data set are 53, 16, 39, 25, 73. What is the mean?
- Medium The five values in a data set are 74, 21, 14, 25, 14. What is the mean?
- Hard The five values in a data set are 38, 55, 35, 14, 22. What is the mean?
- Easy The five values in a data set are 57, 79, 36, 73, 23. What is the mean?
- Easy The five values in a data set are 32, 72, 75, 19, 64. What is the mean?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.