

Subject:
determine a required future variation to achieve a goal
Category: Science > Math Asked by: baz229ga List Price: $20.00 
Posted:
19 May 2006 11:45 PDT
Expires: 18 Jun 2006 11:45 PDT Question ID: 730450 

There is no answer at this time. 

Subject:
Re: determine a required future variation to achieve a goal
From: berkeleychocolatega on 20 May 2006 12:11 PDT 
Let X(i) (i=1,2,...,20) be the numbers you already have and Y(i) (i=1,2,...,28) be the new numbers. So the mean of X is 22.4 and the standard deviation of X is 7.33. The sum of X and Y must be 48*25 = 1200 to make the overall mean 25. Since the sum of X is 20*22.4 = 448, the sum of Y must be 1200  448 = 752, which makes the mean of Y equal to 752/28 = 26.86. Also the standard deviation of X is given to be 7.33. This means 53.73 = 7.33^2 = the [sum of X^2  (mean of X)^2/20]/20 = [sum of X^2  22.4^2/20]/20 . (This is a common formula for the standard deviation. Here I'm assuming this is a "population mean". If it's a "sample mean" divide by 19 instead of 20.) So 1074.6 = 53.73*20 = sum of X^2  25.09 . So the sum of X^2 = 1099.7. We want the standard deviation of X and Y to be 5. So 25 = 5^2 = [sum of X^2 +sum of Y^2  27.5^2/48 ]/48 by the same formula. So 1200 = 25*48 = 1099.7 +sum of Y^2  15.76 . So the sum of Y^2 = 116.06 . Once more using the same standard deviation formula, we get the standard deviation of Y is sqrt[(sum of Y^2  (mean of Y)^2/28)/28 ]= sqrt [ (116.06  26.86^2/28 )/28 ] = 2.03 . 
Subject:
Re: determine a required future variation to achieve a goal
From: berkeleychocolatega on 06 Jun 2006 17:57 PDT 
I made a common error in the standard deviation formula. Sorry about that. The corrected formula for a standard deviation is sd^2 = (sum of squares  n*average^2)/n . The "n" in the formula was in the wrong place. Making these corrections, I get (check me): sum of X^2 = 11109.8 . This forces sum of Y^2 to be 20090.2 if the overall sd is to be 5. But then the sd of Y is imaginary since sum of Y^2 is less than 20200.87 which is 28*(26.86)^2. 
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