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# *********AVERAGES : Conceptual Question**********

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VP
Joined: 28 Mar 2006
Posts: 1384
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*********AVERAGES : Conceptual Question********** [#permalink]  02 Apr 2007, 16:56
Guys a basic conceptual question.

Suppose we have a set S = {10,20,30,40,50}

If we take individual values as 10,20 and take their av = 15

and the rest 3 values 30,40,50 and avg of these is = 40

So the group average of S {10,20,30,40,50} = 30 is not equal to the sum of individual averages 15+40 = 55 or even the av of the values 55/2 =27.5

Whats the deal here? Explanations needed please
Manager
Joined: 28 Aug 2006
Posts: 160
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This method works if there are even numbers.
Manager
Joined: 15 Dec 2005
Posts: 60
Followers: 1

Kudos [?]: 2 [0], given: 0

From wiki
In mathematics, an average, mean, or central tendency of a data set refers to a measure of the "middle" or "expected" value of the data set.

Average or i wud like to call it presently' central tendency' always refers to a set of data ...i.e average finds the central tendency of the set
So average of set will keep on changing if 'new ' elements are added.

When u take 10,20 its average is 15,then you added 30 to the set..it becomes 20..The central tendency of the set in this case increases...as new element is introduced.
In short,Average always refers to a set ...if you reduce/increase the number of elements definitely the value will change.

Director
Joined: 18 Jul 2006
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Re: *********AVERAGES : Conceptual Question********** [#permalink]  03 Apr 2007, 15:21
trivikram wrote:
Guys a basic conceptual question.

Suppose we have a set S = {10,20,30,40,50}

If we take individual values as 10,20 and take their av = 15

and the rest 3 values 30,40,50 and avg of these is = 40

So the group average of S {10,20,30,40,50} = 30 is not equal to the sum of individual averages 15+40 = 55 or even the av of the values 55/2 =27.5

Whats the deal here? Explanations needed please

If a1 is average of set of n1, a2 is average of set of n2, then total average a = (a1n1+a2n2)/(n1+n2)
in this case, a = (15*2+40*3)/(2+3) => 150/5 => 30

It is basically "weighted" average.
VP
Joined: 28 Mar 2006
Posts: 1384
Followers: 2

Kudos [?]: 19 [0], given: 0

Re: *********AVERAGES : Conceptual Question********** [#permalink]  03 Apr 2007, 17:53
Juaz wrote:
trivikram wrote:
Guys a basic conceptual question.

Suppose we have a set S = {10,20,30,40,50}

If we take individual values as 10,20 and take their av = 15

and the rest 3 values 30,40,50 and avg of these is = 40

So the group average of S {10,20,30,40,50} = 30 is not equal to the sum of individual averages 15+40 = 55 or even the av of the values 55/2 =27.5

Whats the deal here? Explanations needed please

If a1 is average of set of n1, a2 is average of set of n2, then total average a = (a1n1+a2n2)/(n1+n2)
in this case, a = (15*2+40*3)/(2+3) => 150/5 => 30

It is basically "weighted" average.

Thanks a bunch!
Re: *********AVERAGES : Conceptual Question**********   [#permalink] 03 Apr 2007, 17:53
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