Dr. Alok Dhaundiyal

I think this discussion on Talkstats will help you:

http://www.talkstats.com/showthread.php/14523-An-average-of-standard-deviations

By analogy to your treatment for the means, try:

{ [SD12*n1+SD22*n2+SD32*n3] / [n1+n2+n3] }0.5.

Probably the n's should be (n-1)'s instead of what I wrote, but I doubt the answer will change much, and it's much easier to write/read.

UPDATE: I do not have a reference for this, although I worked it out myself, and it's suggested in message #15 of Jan Antfolks's link. I'm wondering if Laura Stancampiano has a reference or a further explanation for why the means need to be explicitly considered in this calculation -- the chi-squared term (the sum of the squared residuals) implicitly incorporates each sample's mean.

SECOND UPDATE: As the variance is the square of the standard deviation, my answer is the same as the 'pooled variance' formula suggested by Behnam Sadeghirad.

You have to sum the deviance (sd^2*n) of each groups and then add also the deviance between the three groups mean (calculate the mean of the means and the deviance of the means wheighted). Therefore you have the total deviance of the whole group: divide it by (n1+n2+n3) and you got the total variance. Than square root. I attached the formula: g is the number of groups, in your case 3. If it is not clear and you provides the numbers I can calculate it for you

I also found out that it would be possible to use F formula to calculate combined variance for 3 groups:

Pooled Var = (DF1xV1+DF2xV2+DF3xV3)/(DF1+DF2+DF3)

(DF= N-1)

Hi,

This link might be usefull for you (Computer Program to Combine Means and Standard Deviations from Multiple Groups):

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

Hi,

I would like to extent the question above to the problem I´m facing:

If I have the monthly mean+-SD of body size for 6 consecutive months for a sample of individuals, and want to calculate the average growth rate (mean+-SD) for this period - how could I handle this? (Lets assume that growth is linear during this period)

Thank you so much!

you may be interested in a new methodology of calculation of deviation(s)

Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...

When calculating sample SD, you should correct the group sample size in the calculation of total deviance of the whole group. I added an adjusted version of the formula provided by Laura Stancampiano (g=number of groups). 

http://atozmath.com/CONM/Ch2_CombinedSD.aspx

This can be of help to you..

http://trendingsideways.com/index.php/combine-standard-deviations-with-this-free-spreadsheet/

Thank you very much! Hanna

Hi Joana

The link you provided doesn't work.

Thank you

Yes, I agree with Twan. If sample sizes are different you should use pooled formula:

Pooled SD: (N1-1)*M1+(N2-1)*M2/N1+N2-2

@Miguel Adriano Sánchez-Lastra

Are you sure about the formula?

I exerted on my data and it resulted on a negative output.

This calculator might help: https://www.statstodo.com/CombineMeansSDs_Pgm.php

Also, It includes explanation for the calculation.

http://www.math.hkbu.edu.hk/~tongt/papers/median2mean.html

I want to get the sum of 2 mean energy values of males and females in order to calculate the total mean energy intake from foods. But the problem is both mean energy values are with the SD values. Then how can I calculate the total mean energy with SD?

The two values are 2309 +- 365 kcal and 1829+- 383 kcal .no of males are 33 and females are 43 respectively. Can someone help me to calculate the total of these two values?

An stata module to perform this could be find here:

Article COMBINE: Stata module to combine n, mean, and SD from two gr...

Using the formula mentioned in chat and by using the online calculating websites, the mean value I obtained is the same but when I calculated in SPSS, the SD value differs. I'm not sure which value to report.