let (n1, x1), (n2,x2),.....(n10,x10) be the sample size and average respectively, of sample 1, sample 2 ,..... sample 10.

you can calculate the grand mean as X =(n1*x1 + n2*x2 +....+ n10*x10)/(n1+ n2 +...+ n10)

similarly, if s1^2, s2^2,.....s10^2 be the variances of samples 1, 2,...10 respectively, you can calculate the Pooled Variance S^2= [(n1-1)*s1^2 + (n2-1)*s2^2 +.... +(n10 -1)*s10^2)] / [(n1 - 1) +(n2 - 1) +.....+(n10 - 1)]

squared root of pooled variance gives the Pooled Std. Deviation.

Hi Carlos,

As Debopam already outlined, you can calculate a weighted average, where each mean's weigth is represented by its sample size.

Going from SPSS to NumPy, you always have the option for assigning a weights variable when computing means/averages.

Also, as a quick solution, here you have an online calculator with the formula: https://www.rapidtables.com/calc/math/weighted-average-calculator.html

Good luck!

weighted mean or geometric mean, depending how differnt the sample sizes are.

Matt