# Standard deviation and mean - combining the two

1. Jun 28, 2008

### nokia8650

Standard deviation and mean - "combining" the two

Lets say one was to have a range of data, with the mean and standard deviations for the different subsets of data. The "best" subset is that with the lowest mean, however how do I include the standard deviation when making my decision. For example, the place with lowest infant mortality has the "best" figures for infant mortality, however how could one include the standard deviation into this, in order to predict where the lowest infant mortality will be next year - assuming that there is no trend over the period of the years (ie. it is NOT slowly decreasing in any place - it is equally likely to be above or below the mean next year).

I hope I have explained this well enough, I am open to suggestions. I was thinking of multiplying the standard deviation and mean, but thought that there must be a better statistical method to do this.

2. Apr 14, 2009

### Jfishbac

Re: Standard deviation and mean - "combining" the two

I'm trying to do the same thing with combining SD and Mean. But here's my situation...

For a given signal A, there are two cases were signal A is observed. In case 1 an original mean value and an associated SD are reported for that signal. After a change to the system, Case 2 has it's own mean value as well as SD. I can also manipulate these new Case 2 values to come up with a % change from Case 1 value and % change from Case 2 SD. I want to combine these two percentages into one to give an overall percentage benefit to the change in the system that separates Case 1 and Case 2. Here's what I've done...

% Overall Benefit = [(Case 1 Value)*(% change from Case 1 to Case 2 value) + (Case 1 SD)*(% change from Case 1 to Case 2 SD)] / [(Case 1 Value)+(Case 1 SD)]

I'm not sure if this is legal, but if it is (and my numbers seem to make sense), then this is a great way to view these two parameters as one value.

Let me know!