Standard Deviation

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tejaswini0712: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Tue Jul 30, 2013 9:16 pm; Followed by:4 members

Standard Deviation

by tejaswini0712 » Thu Nov 21, 2013 2:03 am

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

Am confused about why B isn't enough to find the SD.. we are told the set consists of consecutive integers and that the median is 20. So doesn't that automatically imply that there are 39 terms in the set?[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Thu Nov 21, 2013 2:03 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pm; Thanked: 448 times; Followed by:34 members; GMAT Score:650

by theCodeToGMAT » Thu Nov 21, 2013 4:04 am

We are not told whether the sequence consist of negative integers.. So, we cannot assume that median 20 means 39 integers..
For example: -100, -99,........20,21.......138,139

Q is a set of consecutive integers = AP

To find: SD

Statement 1:
number of elements = 21
(x) + (x+1) .. (x+20) ==> Mean will have value in "x" + value
Formula = sqrt(n - mean)^2/N)
==> n will be "x" + value .. and mean wil be in "x" + some value..
So, "x" will be eliminated..So, we SD wil be some numeric value
SUFFICIENT

Statement 2:
Median = 20
We are not told whether the sequence consist of negative integers.
Since we don't know the number of terms.. we cannot comment on the value of MEAN
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]

R A H U L

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Thu Nov 21, 2013 4:26 am

tejaswini0712 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

SD describes how much a set of data DEVIATES from the mean.
For any set of of consecutive integers, the mean = the median.

Question rephrased: How do the integers in set Q deviate from the median?

Statement 1: Set Q contains 21 terms.
Any set of 21 consecutive integers will deviate from the median EXACTLY THE SAME WAY.
If M = the median, the set will look like this:
M-10, M-9...M-2, M-1, M, M+1, M+2...M+9, M+10.
Thus, the SD can be determined.
SUFFICIENT.

Statement 2: Median = 20.
If there are only 3 terms -- if Q = {19, 20, 21} -- then there is very little deviation from the median.
If there are 101 terms, then there will be quite a bit of deviation from the median.
Thus, the SD can be different values.
INSUFFICIENT.

The correct answer is A.

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