If Q is a set of consecutive integers, what is the standard

[VJesus12]

If \(Q\) is a set of consecutive integers, what is the standard deviation of \(Q?\)

(1) Set \(Q\) contains 21 terms.
(2) The median of set \(Q\) is 20.

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

[Brent@GMATPrepNow]

If \(Q\) is a set of consecutive integers, what is the standard deviation of \(Q?\)

(1) Set \(Q\) contains 21 terms.
(2) The median of set \(Q\) is 20.

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

Target question: What is the standard deviation of Q?

Given: Q is a set of CONSECUTIVE integers

Statement 1: Set Q contains 21 terms.
NOTE: Standard Deviation measures dispersion (spread-apart-ness). As such, the actual values mean nothing compared to RELATIVE values.
For example, the set {1,2,3,4} has the SAME STANDARD DEVIATION as the set {6,7,8,9}

So, knowing that set Q consists of 21 CONSECUTIVE integers is SUFFICIENT.
The Standard Deviation of Q will be the same as the Standard Deviation of {1,2,3,4...20,21}

Statement 2: The median of set Q is 20.
There are several different sets that satisfy this condition.
For example, set Q could equal {19, 20, 21} or set Q could equal {18, 19, 20, 21, 22}
These two sets have DIFFERENT standard deviations.
So, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent