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

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Nov 17, 2019 8:21 pm
BTGmoderatorDC wrote: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.

OA A

Source: Manhattan Prep
Computation of the standard deviation (SD) is not within the scope of the GMAT; however, its analysis and interpretation are. The standard deviation of a set of numbers is a measure of how far/close numbers are to their mean. Farther they are to the mean, greater is the SD and vice versa.

Let's take each statement one by one.

(1) Set Q contains 21 terms.

Say the terms are n, (n + 1), (n + 2), (n + 3), (n + 4), ... and (n + 20). Thus, the mean = (n + 10). Deviations (Difference of terms w.r.t. mean) of 21 terms w.r.t. (n + 10) are -9, -8, -7, -6, ... and 10. Since we have finite 21 values, SD can be computed. Sufficient.

There is no need to compute SD as this is a DS question; and in a DS question if we are satisfied that we would have a unique answer to the question asked, we need not calculate the answer.

(2) The median of set Q is 20.

Since Set Q is an even-spaced set, its median and mean would be equal. Thus, the mean of Set Q = 20. However, we cannot get the unique value of SD since we do not know the no. of terms. Insufficient.

Greater is the no. of terms of the set, greater is the SD and vice-versa.

The correct answer: A

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Mon Nov 18, 2019 5:32 am
BTGmoderatorDC wrote: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.

OA A

Source: Manhattan Prep
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
Brent Hanneson - Creator of GMATPrepNow.com
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