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Merging two distributions

Merging two distributions

I have two lots and only N, mean and SD is reported. Now I would like to put them together to get a combined mean and SD. How do I do that? (My Mathcad is 8 Pro, if you are sending an example). Thanks in forward and Seasons Greetings.

Jarmo Kiiski
4 REPLIES 4

Merging two distributions

Please see the attached GIF image for the required formulas. I'm assuming that the two datasets are statistically independent.

Merging two distributions

Thanks!

Merging two distributions

If you only have exact distributional parameters, the formula Bonnie gave is correct. However, if you only have sample data, you should modify her formula for variance by using n1-1 everywhere in the formula instead of n1, and n2-1 instead of n2. (The attached file is supposed to be saved as version 8.)

Merging two distributions

Sorry,

but the formula given for the variance (sigma squared) of the merged distribution is only valid if the means of the two distributions are equal.
For the general case refer to formulae in attched picture.

Luc
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