Call for help. Standard Deviation DS.

aman88 wrote:Set S consists of 7 integers. Is the range of set S less than 7?

(1) The mean of set S is 4.

(2) The standard deviation of set S is 0.


OA is B

Target question: Is the range of set S less than 7?

Statement 1: The mean of set S is 4.
There are several sets that meet this condition. Here are two:
Case a: Set S = {4, 4, 4, 4, 4, 4, 4} in which case the range of set S is less than 7
Case b: Set S = {0, 4, 4, 4, 4, 4, 8} in which case the range of set S is greater than 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The standard deviation of set S is 0.
If the standard deviation of any set is zero, then all of the numbers in that set are identical. In other words, the numbers have no deviation (they do not deviate).
If all of the numbers are identical, then the range equals zero.
This means that the range of set S must be less than 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Standard deviation (SD) is, at the most basic level, a measure of how much variation there is from the mean (or how far the data points are spread out). In statistics, it's somewhat complicated to calculate, but on the GMAT, thankfully, you won't need to calculate it. All you need to think about is the spread of the data - in other words, the range.

A set with a wide spread of data will have a high SD: [100, 150, 200, 250, 300]

A set with numbers very close to the mean will have a low SD: [198, 199, 200, 201, 202] (you'll notice that these sets have the same mean)

A set of all the same values will have a SD of 0, because there is no deviation from the mean: [200, 200, 200, 200, 200]

So, in statement (2) here, if the SD of the set is 0, it means that all values in the set are equal to the mean, so the range is definitely less than 7!