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Topic: How to combine the standard deviations of multiple data subsets
Replies: 6   Last Post: Nov 23, 2012 1:26 PM

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Posts: 1,089
Registered: 12/6/04
Re: How to combine the standard deviations of multiple data subsets
Posted: Oct 5, 1999 6:02 PM
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On Mon, 04 Oct 1999 21:35:27 GMT, (Henry) wrote:

>On Mon, 4 Oct 1999 14:29:17 -0600, "Steve Schnick"
><> wrote:

>>If one has several subsets of a given data set, and the mean, count,
>>and standard deviations for each of these subsets, how can one
>>calculate the combined standard deviation of the data subsets? i.e.,
>>if the subsets were lumped together into one set, how does one
>>calculate this new standard deviation?

>Some clues:
>1. You need to calculate the new mean. (easy)
>2. You should work with variances not standard deviations
>3. If a set {Xi} i=1 to n has mean M
> then sumof (Xi-k)^2 / n = (k-M)^2 + sumof (Xi-M)^2 / n
>Ask again if this is not enough

He did and my reply was:
"Suppose data is Mi (the means) Ci (the counts) and Vi (the variances)
The overall count is C = sumof(Ci)
The overall mean is clearly M = sumof(Mi.Ci) / C
The overall variance is V = sumof(Ci.(Mi-M)^2) / C + sumof(Ci.Vi) / C
or equivalently V = sumof(Ci.[Vi+Mi^2]) / C - M^2
No guarantee on this, but I think it is right."

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