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Set V consists of 2 distinct positive values. What is the

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Set V consists of 2 distinct positive values. What is the [#permalink]

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New post 05 May 2012, 08:47
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Set V consists of 2 distinct positive values. What is the standard deviation of set V?

(1) The mean of the set is 10.
(2) The range of the set is 10.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 31 May 2014, 16:05, edited 1 time in total.
Edited the OA.
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Re: Set V consists of 2 distinct positive values. What is the [#permalink]

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New post 06 May 2012, 02:30
The answer seems to be (B) here.

Statement (1) is insufficient: Just knowing the mean is not enough.
Statement (2):
Let the numbers be x and x+10
Then their mean = x+5
S.D. = sqrt (50/2) = 5
Sufficient.

(B) it is.
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Re: Set V consists of 2 distinct positive values. What is the [#permalink]

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New post 06 May 2012, 09:23
The answer has to be B.
After simplifying the question, we can arrive to below:
Let's assume the 2 distinct +ve numbers as x and y. Assuming y>x.
Mean= x+y/2
S.D = SQRT(((x+y/2) -x)^2 + (y-(x+y/2))^2)/2)
=SQRT(((x+y-2x)/2)^2 + ((2y-y-x)/2)^2/2)
=SQRT((y-x)^2/2)
=y-x/sqrt(2)...so we just need to know the diff between y and x and we get it from the 2nd statement which gives us the range.

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Re: Set V consists of 2 distinct positive values. What is the [#permalink]

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New post 31 May 2014, 11:53
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I also got B

Since the range is 10, in SD only the spread matters, hence 1 and 11 will have the same SD as 2 and 12, and as 3 and 13 etc...

Therefore B

Please clarify cause answer is given as E

Thanks!
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Re: Set V consists of 2 distinct positive values. What is the [#permalink]

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New post 31 May 2014, 16:06
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New post 02 Jun 2014, 01:43
We have two numbers. The question is about their standard deviation.

As the mean is ten, we have the following relationship for the two numbers(x1, x2): x1= 10-x, x2= 10+x. This does not help us to calculate the standard deviation. x could be 0, or extremely large.

Statement one is hence insufficient.

We're given the range, meaning that we now have the following relationship for x1 and x2: x1=x, x2=x(+ or -)10.

This helps us. We now know that one of the numbers is 5 above the mean and the other is 5 below the mean. We do not need the actual mean to calculate the deviation.

We get 5^2 and (-5)^2. Finding the variance = (25+25)/2 = 25 And the square root of 25=5 which is our standard deviation. However this was not asked of us.
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Re: Set V consists of 2 distinct positive values. What is the [#permalink]

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New post 01 Jan 2015, 20:38
Let x be one number so next n. is x+ 10. now x+x+10/2=x+5 is the mean. so std. deviation is s follows:sq root 50/2 Hence B.
Re: Set V consists of 2 distinct positive values. What is the   [#permalink] 01 Jan 2015, 20:38
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