Possible crude approaches: If the data is the same sample size, n1 = n2, why not combine the data of the two groups, but only for answering this question. Or if they are not the same sample size, n1 != n2, maybe take a random sample of the largest that is the same size as the smallest, combine the data and find the mean and standard deviation for that.

If you are combining test scores you might see

Stouffer, S.A., E.A. Suchman, L.C. DeVinney, S.A. Star, R.M. Jr. Williams 1949. The Am. Soldier, Vol.1: Adjustment During Army Life. Princeton University Press, Princeton.

which is referred to in

Whitlock, M.C. 2005. Combining probability from independent tests: the weighted Z-method is superior to Fisher’s approach. J. of Evolutionary Biology, 18:1368–1373.

You get the p values of K tests (any tests) and convert them to Z values then sum these Z values and divide the result by the square root of Z. The result is a Z-hat that estimates the combined p value.

The answer you may have been seeking might be found if you search for a similar question by Dr. @Lucy Whitehall. The researchers answering her might have more specific experience with this subject than do I.

There are some web-based programs that can combine mean and sd. Please double-check if that works:

https://www.statstodo.com/CombineMeansSDs.php

I agree with other colleagues Lewis Maccarter and Shin Murakami In addition, if you have access to original data sets (by requesting authors) then it is easy to calculate mean and standard deviation directly and cross-check with other web based method.

You can find a formula, however there are some softwares such as R and Stata that will calculate the mean and the SD for you.

Hi Baraa, Check Statstodo

It works perfect in combining means and standard deviation for more than one group. You will need to have mean and standard deviation for all your groups including the sample size in each group.

Check the link below

http://www.obg.cuhk.edu.hk

You can find a good explanation here: https://math.stackexchange.com/questions/2971315/how-do-i-combine-standard-deviations-of-two-groups - basically means can be combined by multiplying each by n_i/(n_1+n_2), and pooled SD by using similar approach (but here we use n_i-1 to have unbiased estimator - and we have a correction factor which is a function of the difference between means).