Problem-Solving and Data AnalysisMediumComparing standard deviations by eye
Problem-Solving and Data Analysis practice question
Which of the following data sets has the greatest standard deviation?
- A. 1, 1, 9, 9Correct
- B. 4, 5, 5, 6
- C. 5, 5, 5, 5
- D. 3, 5, 5, 7
Answer: A. 1, 1, 9, 9
All four sets have mean 5. Standard deviation measures how far values sit from the mean: in set A every value is 4 away, which is more than any other set's spread.
Why the other answers are wrong
- B. 4, 5, 5, 6
- Values 1 or 0 away from the mean — a small spread.
- C. 5, 5, 5, 5
- All values equal the mean, so the standard deviation is 0.
- D. 3, 5, 5, 7
- Values 2 or 0 away from the mean — less spread than set A's 4.
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