GMAT Quantitative: Statistics and Sets Problems 3

Question 1

A data set has standard deviation 0. What must be true?

Accepted Answer

All values are equal

Answer

A standard deviation of 0 means there is no spread, so every value is identical.

Question 2

If every value in a data set is increased by 10, what happens to the standard deviation?

Accepted Answer

Stays the same

Answer

Adding a constant shifts all values equally, leaving the spread unchanged.

Question 3

The set {x, 5, 8, 12} has a mean of 8. What is x?

Accepted Answer

7

Answer

The sum must be 32, so x = 32 − 25 = 7.

Question 4

How many subsets does a set with 4 elements have?

Accepted Answer

16

Answer

A set of n elements has 2^n subsets, and 2^4 = 16.

Question 5

The median of {4, 9, 11, 16} is which value?

Accepted Answer

10

Answer

With an even count, the median is the average of the two middle values: (9 + 11)/2 = 10.

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