DS. VARIANCE

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[email protected]: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Fri Sep 09, 2011 5:32 pm

Q: WHAT IS THE STANDARD DEVIATION OF INTEGERS IN THE SET X
(SET X : A, B, C, D, E )

A: VARIANCE OF THE NO. IN THE SET X IS 5
B: RANGE OF THE SET IS 1

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Source: Beat The GMAT — Data Sufficiency | Fri Sep 09, 2011 5:32 pm

n@resh: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Tue Apr 13, 2010 3:29 am; Thanked: 8 times

by n@resh » Fri Sep 09, 2011 8:42 pm

[email protected] wrote:Q: WHAT IS THE STANDARD DEVIATION OF INTEGERS IN THE SET X
(SET X : A, B, C, D, E )

A: VARIANCE OF THE NO. IN THE SET X IS 5
B: RANGE OF THE SET IS 1

Option: A

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Fri Sep 09, 2011 11:17 pm

Variance is the square of SD. Therefore SD = sqrt(5). Sufficient

Statement 2 is insufficient

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Sep 12, 2011 1:27 am

[email protected] wrote:Q: WHAT IS THE STANDARD DEVIATION OF INTEGERS IN THE SET X
(SET X : A, B, C, D, E )

A: VARIANCE OF THE NO. IN THE SET X IS 5
B: RANGE OF THE SET IS 1

Where is this question from? It is not mathematically possible for a set to have a variance of 5 and a range of 1, so the two statements are completely incompatible. That can never happen on a real GMAT question.

In any case, variance is just the square of standard deviation, so Statement 1 is sufficient. Statement 2 is actually almost sufficient - there are only two possible values for the standard deviation. Normally, knowing the range doesn't tell you much of anything about standard deviation, but here we have a set of five integers with a range of 1. There aren't many sets like that. If our elements are, say, 3 and 4, the only such sets would be:

A = 3, 3, 3, 3, 4
B = 3, 3, 3, 4, 4
C = 3, 3, 4, 4, 4
D = 3, 4, 4, 4, 4

Sets A and D are just 'mirror images' of each other, and so must have the same standard deviation (if you work out the distances from each element to the mean, they will be identical but in reverse order). The same is true of sets B and C. It is true that set A and set B have different standard deviations, though, so Statement 2 is not sufficient.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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