Henry
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


On Mon, 04 Oct 1999 21:35:27 GMT, se16@btinternet.com (Henry) wrote:
>On Mon, 4 Oct 1999 14:29:17 0600, "Steve Schnick" ><sschnick@yahoo.com> 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 (Xik)^2 / n = (kM)^2 + sumof (XiM)^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.(MiM)^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."

