As a starter - I am a newbie to this forum (and forums in general). Also, I have a very (very) basic understanding of stats/prob. Thank you in advance for your patience and please don't hesitate to provide feedback that will help me, help myself more efficiently!

I am trying to compute the expected standard deviation of a sum of sample means that are independent. Let me offer an example:

How would I compute the mean combined weight of the three and the std dev of the combined mean.

The combined mean seems trivial and I am assuming is L+C+M, but the std dev seems a little trickier. I've searched countless wiki articles, forums, etc and keep arriving at the square root of the sum of the variances:

Stotal = SQRT(Sl^2+Sc^2+Sm^2)

But I'm not convinced. For example, if I run through this exercise with Larry, Curly & Mo and 1) compute the std deviations Sl, Sc, Sm and combine them using the equation above, I get a different answer than if I 2) sum each (N) measurement of Larry, Curly, and Mo, then compute the std deviation.

Thanks in advance for the help!

David

I am trying to compute the expected standard deviation of a sum of sample means that are independent. Let me offer an example:

- Larry, Curly, & Mo are each weighed "N" times
- the mean weight is L (for Larry), C (for Curly), M (for Mo)
- The standard deviation for each is Sl, Sc, Sm

How would I compute the mean combined weight of the three and the std dev of the combined mean.

The combined mean seems trivial and I am assuming is L+C+M, but the std dev seems a little trickier. I've searched countless wiki articles, forums, etc and keep arriving at the square root of the sum of the variances:

Stotal = SQRT(Sl^2+Sc^2+Sm^2)

But I'm not convinced. For example, if I run through this exercise with Larry, Curly & Mo and 1) compute the std deviations Sl, Sc, Sm and combine them using the equation above, I get a different answer than if I 2) sum each (N) measurement of Larry, Curly, and Mo, then compute the std deviation.

Thanks in advance for the help!

David

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