How to average collection of different standard deviations

That's very helpful, thanks. I was hoping there would be a Function rather than having to write the whole thing out longhand but I guess the dumbing down of Numbers when it merged into iPad territory meant complex mathematical and statistical functions were removed or not added.

PS the Std Dev of a sample size of one is zero... but I know you just wanted to put some numbers there for the purposes of the example and I do appreciate your help doing that.

Thanks for adding your comment, I appreciate your help.

I want to calculate the average of the standard deviations in Column C. Statistically this is not a simple average such as a Mean or Median value. Anytime you calculate the average Standard Deviation (SD) you use one of two formulae. One (given above) is if the sample size is different for each SD value, the other is used when the sample sizes are identical for each SD value.

Standard Deviation is a measure of volatility that can be used in many situations where values are monitored from environmental monitoring, to engineering production, to stocks and bond returns, and many others. The formulae do not change, but sometimes you need to know the average of all the standard deviations to measure the effectiveness of a whole set of different values eg from different factories or machines measured the same day, or the volatility of a given portfolio given investment in different stocks and bonds. I am surprised it is not a built in function.

Thanks - although your graphic was a bit too small to read. I know these days there are useful stats packages such as R as well as one other popular one I can't remember the name of.

Back in 1978 my first year University Statistics course made us do all the work manually, F-Tests, Student's T test, Standard Deviation calculations, Chi-Squared, even Multiple Regression Analysis, and I don't think there were any dedicated stats programs available - at least, not for us Biologists. Heck, for computing we had to write code out one line at a time and send it in to be put onto punchcards to be fed into the mainframe and we'd get a result (or not) the next day.

So with Numbers I like the Functions, but am learning which ones to use all the time.

3 years has 36 months = 36 samples.

For this you use a different formula:

This needs no reference to sample size because the sample size is the same for every SD value. In the sample I posted k=14.

Haha! There were times when I thought doing just that would get me a better result for my programs.