Standard Deviation

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dhirajdas53: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Sat Apr 07, 2012 3:18 am

by dhirajdas53 » Wed Apr 17, 2013 6:13 pm

{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

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Source: Beat The GMAT — Data Sufficiency | Wed Apr 17, 2013 6:13 pm

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Wed Apr 17, 2013 7:02 pm

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.

Last edited by Anju@Gurome on Wed Apr 17, 2013 7:08 pm, edited 1 time in total.

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Wed Apr 17, 2013 7:07 pm

From St1, we can find SD of X and SD of Y Sufficient
diff between any 2 elements of X is 3. if we can visualise a number line with numbers at inteval of 3, we should be able to also compute the dispersion (or SD)
diff between any 2 elements of Y is 2. Same for Y
Hence sufficient.

From St2 also, we can deduce all the elements of both the sets.
Elements in SEt X are spaced at intervals of 32-8 / 8 = 3
so X = 8, 11, 14, 17, 20, 23, 26, 29, 32
Elements in SEt YX are spaced at intervals of 18-2 / 8 = 2
so X = 2, 4, 6, 8, 10, 12, 14, 16, 18
Hence Sufficient

Each statement alone is sufficient to answer the questions
Hence D

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dhirajdas53: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Sat Apr 07, 2012 3:18 am

by dhirajdas53 » Wed Apr 17, 2013 8:14 pm

Thanks!!!

I was using wrong formula

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J N: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Tue Mar 12, 2013 2:27 pm; Thanked: 3 times

by J N » Thu Apr 18, 2013 3:21 pm

what if given an even number of elements say 10 so mean/average is (5th +6th) /2

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Thu Apr 18, 2013 3:25 pm

As long as we can deduce each element of both the sets, we can calculate their individual means, medians, range, SD or any other parameter. Once we know the 2 comparable parameters in absolute terms, sure we can as well deduce the difference between the SD of 2 sets.

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