I'm looking for a way to obtain the "composed" mean and standard deviation of two (related) datasets. So let's assume I have n = 25 recordings of one characteristic (x) and the same number of recordings for a distinct characteristic (y) with $$ \mu_x = 15, SD_x=2.5; \mu_y = 25, SD_y=3.5 $$
And furthermore let's assume that both characteristics may be added to a "composed" value with: $$\mu_{xy} = (15+25)/2 = 20$$
Is there any way to find out what the SD for both would be? I think neither the pooled SD as described somewhere else is correct nor (e.g., O'Neill 2014, p. 283) with
$$s_{\text{pooled}}^2 = \frac{n_1-1}{n_1+n_2-1} \cdot s_1^2 + \frac{n_2-1}{n_1+n_2-1} \cdot s_2^2 + \frac{n_1 n_2}{n_1 + n_2} \cdot (\bar{x}_1 - \bar{x}_2)^2.$$
seems right to me. Are there any suggestions? There is no way to find out what the correlation between both is.
Any help is appreciated.