SAT · Problem Solving & Data Analysis · Mean, median, and standard deviation
Question sat-q-00146
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The question
The five values in a data set are 56, 82, 20, 86, 30. What is the mean?
- 20
- 54.8
- 68.5
- 274
Show answer & worked solution
Answer: 54.8
Worked solution. Sum the values: 274. Divide by the number of values (5): 274 / 5 = 54.8.
Why each wrong choice is wrong. A distractor returns the median (middle value), which equals the mean only by coincidence. Another divides by the wrong count.
Test-day tactic. Mean is sum over count. Don't confuse it with median (middle value) or mode (most frequent value).
About this question type
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.
You will see a question shaped like this one on roughly every other official SAT form, typically at the back end of the section, where the score gradient is steepest. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.