Question

VU U
If there are two groups containing 30 and 20 observations and having 50 and 60 as
arithmetic means, then the combined arithmetic mean is
(a) 55
(b) 56
(c) 54
(d) 52.​

Answer 1

Answer:

(c) 54 .

Step-by-step explanation:

We are given that there are two groups containing 30 and 20 observations and having 50 and 60 as  arithmetic means i.e.;

                  $n_1$   =  30                                $n_2$  =  20

              $X_1bar$ =   50                           $X_2bar$ =  60

Combined arithmetic mean formula = $\frac{n_1 *X_1bar + n_2*X_2bar}{n_1+n_2}$

                                                            = $\frac{30*50 + 20 * 60}{30+20}$ = $\frac{1500+1200}{50}$

                                                            = $\frac{2700}{50}$ = 54.

Therefore, combined arithmetic mean is 54.