# (weighted) mean of standard deviations

#### Kolin

##### New Member
Dear all,

I have the following problem. Suppose I have three results of temperature measurements:

10 +/- 2
2 +/- 6
9 +/- 3

Here the +/- are the standard deviations, or uncertainties on the measurements. The average here is 7. I do not want a weighted average because lower temperatures have a larger error bar, and a weighted average would obviously skew the mean towards higher temperatures.

Now, does anyone know a reasonable way to calculate the uncertainty on this average? I figure it is not simply the mean of the standard deviations, but unsure.

Any help very much appreciated!

#### BGM

##### TS Contributor
This depends on the information you have for your data.

If you have the complete raw data/all sufficient statistics, then you can recalculate the pooled mean and standard error again.

If you have the sample sizes for the three groups, there is also a nice discussion about this issue on how to work on the pooled sample variance. See