Question

The mean of agroup of 100 observation is 50 and of another group of 150 observation is 100.what is the mean of all observation and show each step.

Answer 1

Answer:

Mean of all observation = 80 .

Step-by-step explanation:

We are given that the mean of a group of 100 observation is 50 and of another group of 150 observation is 100.

Let Mean of one group, $X_1bar$ = 50  and  No. of observation in one group,$n_1$ = 100

Similarly, Mean of another group, $X_2bar$ = 100  and  No. of observation in another group,$n_2$ = 150

So, Mean of all observations, X bar = $\frac{n_1*X_1bar + n_2*X_2bar}{n_1 + n_2}$

                                                           = $\frac{100*50 + 150*100}{100 + 150}$ = $\frac{20000}{250}$ = 80.

Therefore, the mean of all 250 observation = 80 .