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# What is the standard deviation of Q, a set of consecutive

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Manager
Joined: 08 Aug 2008
Posts: 226
What is the standard deviation of Q, a set of consecutive [#permalink]

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12 Nov 2008, 04:27
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What is the standard deviation of Q, a set of consecutive integers?

(1) Q has 21 members.
(2) The median value of set Q is 20.

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CEO
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12 Nov 2008, 04:37
A

1) A constant shift of a set by any number doesn't influence on SD. Sufficient.
2) Let's consider the set M that has median value of 20. If we add two numbers at the beginning and the end of M, the new set will have the same median value but SD (average deviation from a mean) will increase. Insufficient.
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Manager
Joined: 08 Aug 2008
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12 Nov 2008, 04:42
OA is A.
but without the median, how can i conclude the shift is equal?
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12 Nov 2008, 04:54
1. Let's consider arbitrary set X (x1,x2,x3...xn) that has median Mx, Standart deviation SDx and mean Ax
2. Let's shift set X by d. We obtain a new set Y (x1+d, x2+d,x3+d...xn+d).
3. median of Y set will be My=Mx+d, mead - Ay=Ax+d
4. SDy=$$\sqrt{\frac{\sum{(yi-Ay)^2}}{n}}=\sqrt{\frac{\sum{(xi+d-Ax-d)^2}}{n}}=\sqrt{\frac{\sum{(xi-Ax)^2}}{n}}$$=SDx

When we shift set we doesn't shift distance between mean and set numbers. That is why SD doesn't change.
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12 Nov 2008, 11:05
i dont get why statement 2 is not sufficient..

we know that Q is Consecutive integers..so the difference is always a constant.. so why doest it matter if the median is 20 or not..we know the SD right?
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12 Nov 2008, 11:10
Think about SD as an average deviation from mean. It works in 95% cases.

For instance,

Set1={19,20,21} --> Mean=Median=20 ---> AvDev=1/n*sum(|xi-mean|)=(1+0+1)/3=2/3
Set2={18,19,20,21,22} --> Mean=Median=20 ---> AvDev=1/n*sum(|xi-mean|)=(2+1+0+1+2)/5=6/5
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VP
Joined: 17 Jun 2008
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13 Nov 2008, 03:39
fresinha12 wrote:
i dont get why statement 2 is not sufficient..

we know that Q is Consecutive integers..so the difference is always a constant.. so why doest it matter if the median is 20 or not..we know the SD right?

This is a typical "carry forward from stmt1" type question.
Stmt2 does not tell how many number of members is there in the set. Hence, it is insufficient. In order to find out the SD, individual members need to be known.

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Re: DS:SD   [#permalink] 13 Nov 2008, 03:39
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