Standard deviation is spread, not size: the SAT math trap

Short answer: Look at the gaps, not the values. Shifting every number up doesn't change the spread.

The trap, in one question

Tempting answer: {110, 120, 130}  (bigger numbers)

Correct answer: They are equal  (same gaps of 10)

How to spot it in 3 seconds

Look at the gaps, not the values. Shifting every number up doesn't change the spread.

FAQ

What is the standard deviation is spread, not size trap on the SAT?

Example: Which data set has the larger standard deviation: {10, 20, 30} or {110, 120, 130}? The tempting answer is {110, 120, 130} (bigger numbers); the correct answer is They are equal (same gaps of 10).

How do you avoid the standard deviation is spread, not size trap?

Look at the gaps, not the values. Shifting every number up doesn't change the spread.

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