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# What is the standard deviation of the terms in Set S?

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Math Expert
Joined: 02 Sep 2009
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What is the standard deviation of the terms in Set S?  [#permalink]

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27 Nov 2014, 06:50
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Difficulty:

15% (low)

Question Stats:

69% (00:46) correct 31% (01:07) wrong based on 121 sessions

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Tough and Tricky questions: Statistics.

What is the standard deviation of the terms in Set S?

(1) Set S is composed of 7 consecutive even integers.
(2) The average (arithmetic mean) of the terms in Set S is 49.

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: What is the standard deviation of the terms in Set S?  [#permalink]

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27 Nov 2014, 07:32
1
1
statement 1 :- Set S is composed of 7 consecutive even integers.

let x,(x+1),(x+2),(x+3),(x+4),(x+5) and (x+6) be 7 consecutive numbers.
Mean = (x+3)
We can subtract mean (x+3) from each term. x will get cancelled out from each term and definite value of standard deviation can be found.

Statement is sufficient.

Statement 2 :- The average (arithmetic mean) of the terms in Set S is 49.
statement is insufficient.

Ans - A
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Re: What is the standard deviation of the terms in Set S?  [#permalink]

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27 Nov 2014, 09:18
1
To determine standard deviation, we need to know the number of values we're dealing with and the average (or difference between any value in the set and the average of the set).

Statement 1 tells us both these things. We know we have 7 points and since they're consecutive even integers, we can determine the sum of the differences. Sufficient.

Statement 2 only tells us the average. We don't know how many data points we have nor do we know what kinds of values are in the set. Insufficient.

Choice A

As an aside, aren't the two statements contradictory? If we have seven consecutive even integers, the mean value and the median will always be even, right? How can we have an odd value as the arithmetic mean? This doesn't take away from doing the problem... but maybe I'm just missing something?
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Re: What is the standard deviation of the terms in Set S?  [#permalink]

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27 Nov 2014, 19:42
1
Statement 1: Since we know number of terms and consecutive even integers are evenly distributed we can get the value of standard deviation. ---Sufficient.

Statement 2: So many combination of different terms produce Mean as 49 with different standard deviation. ---Insufficient.
e.g. (49,49) OR (48,49,50) etc.

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Re: What is the standard deviation of the terms in Set S?  [#permalink]

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28 Nov 2014, 07:48
Bunuel wrote:

Tough and Tricky questions: Statistics.

What is the standard deviation of the terms in Set S?

(1) Set S is composed of 7 consecutive even integers.
(2) The average (arithmetic mean) of the terms in Set S is 49.

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: What is the standard deviation of the terms in Set S?  [#permalink]

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03 Dec 2019, 08:01
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Re: What is the standard deviation of the terms in Set S?   [#permalink] 03 Dec 2019, 08:01
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