Data Sufficiency

Is the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?

(1) The variance for the set of measurements is 4.
(2) For each measurement, the difference between the mean and that measurement is 2.

What's the best way to determine which statement is sufficient? Can any experts assist?

ardz24 wrote:Is the standard deviation of the set of measurements x1, x2, x3, x4, ..., x20 less than 3 ?

(1) The variance for the set of measurements is 4.
(2) For each measurement, the difference between the mean and that measurement is 2.

What's the best way to determine which statement is sufficient? Can any experts assist?

Statement 1: All you need to know here is that there's a mathematical relationship between the variance and the standard deviation of a set. If you have the variance, you can find the standard deviation. (You may recall from Stat class that when you're computing standard deviation, the last step is to take the square root of the variance. If the variance is 4, the standard deviation is 2.) Sufficient.

Statement 2: A standard deviation is, a measure of the distance of the elements in a set from the mean. (Again, from stat class, you may recall that when calculating the standard deviation, you first find the mean, you then find the difference between each element in the set and the mean, before squaring those differences, etc.) If you can find the standard deviation, clearly, you can definitively answer the original question. Sufficient.

The answer is D