I'm trying to solve following type of combined date given question. Imagined that there's two factories. They are X and Y. "X" factory has 10 workers and "Y" has 20 workers. These two factory's production respectively given as Σx^2=2950 and ΣY^2=5000. Moreover, "X" factory mean is 18 and "Y" factory mean is 15.
If the whole population is considered as a one. How to calculate the mean and standard deviation in a situation like this one? I'm not expecting the final answer, I rather would like to know the procedure that how to solve such a question.
You have $\bar{x}=18$ and so $\Sigma x=18\times 10=180$
Similarly, $\bar{y}=15$ so $\Sigma y=15\times20=300$
So the pooled mean is $$\frac{180+300}{10+20}=16$$
For the standard deviation, the combined sum of squares is $2950+5000=7950$
Using the standard formula, the pooled standard deviation is $$\sqrt{\frac{7950}{30}-16^2}=3$$