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Q: determine a required future variation to achieve a goal ( No Answer,   2 Comments )
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 Subject: determine a required future variation to achieve a goal Category: Science > Math Asked by: baz229-ga List Price: \$20.00 Posted: 19 May 2006 11:45 PDT Expires: 18 Jun 2006 11:45 PDT Question ID: 730450
 ```how do i determine a required future variation given a to date mean & variation and a known number of future parts? for example .... say I have 20 parts with mean 22.4 units and standard deviation 7.33 units .... I need to achieve a total goal of better than a mean of 25 AND std dev of 5 .... I have the opportunity to achieve this with 28 more parts (ie overall 48 parts) ... I know their mean needs to be < 27.5 but what does their variation need to be & how is this calcualted? tia``` Clarification of Question by baz229-ga on 19 May 2006 11:51 PDT ```OK to assume my data is normally distributed to an acceptable confidence level ... the 20 parts ... and the 28 to come```
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 Subject: Re: determine a required future variation to achieve a goal From: berkeleychocolate-ga 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: berkeleychocolate-ga 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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