Problem-Solving and Data Analysis practice question

Answer: A. Set B has the larger standard deviation, because its values are more spread out from the mean.

Both sets have mean 10. Standard deviation measures how far values typically sit from the mean. Every value in A is exactly at the mean (deviation zero); B has values 9 below and 9 above. So B's standard deviation is larger.

Why the other answers are wrong

B. Set A has the larger standard deviation, because all its values are equal.

Identical values give a standard deviation of ZERO — the smallest possible, not the largest.

C. The two sets have the same standard deviation, because they have the same mean.

A shared mean says nothing about spread. Two sets can have the same centre and very different spreads, as these do.

D. The standard deviations cannot be compared without more data.

The values are all given, so the spread of each set is fully determined.

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