Data Sufficiency

dhirajdas53 wrote:{x1,x2,x3...x9} and {y1,y2,y3...y9} are two evenly spaced sets having 9 elements each. What is the difference between their standard deviations?

(1) x2-x1=3 and y9-y8=2
(2)x1=8,x9=32 and y1=2,y9=18

First of all note that the elements of the both sets evenly spaced and contains 9 elements.
Hence, the means of the sets are the 5th element when they are arranged in ascending or descending order.

Also, if we know the difference between any two elements of the set, we can determine the distance of all the elements from their mean as all the elements are evenly spaced.

Statement 1: The distance between the elements of the 1st set is 3.
So, we can determine the distance of all the elements from their mean.
--> We can determine the standard deviation of the set as we know the distance of all the elements from the mean and the number of terms.

Same is the case with 2nd set.

And, as we can uniquely determine the standard deviations of the sets, we can easily compare them and answer the question.

Sufficient

Statement 2: This statement is essentially giving us the same information as statement 1 : the distance between the elements of the sets.

Sufficient

The correct answer is D.

Note : This is a very good DS problem as it seems that we have to do a lot of calculation but in reality we only need to determine whether we can do the calculation or not. Data sufficiency is all about whether we can do it, not actually doing it.