Question

A distribution consists of three components with total frequencies of 200, 250 and 300 having means of 25, 10 and 15 respectively . Find out the mean of combined distribution.

Answer 1

$$\begin{gathered} N_1=200,{\overline{X}}_1=25 \\ {N}_2=250,{\overline{\mathit{X}}}_2=10 \\ {N}_3=300,{\overline{\mathit{X}}}_3=15 \\ {\overline{X}}_{1,2,3}=\frac{{\overline{X}}_1{N}_1+\overline{X_2}\mathit{}{N}_2+{\overline{X}}_3\mathit{}{N}_3}{N_1+N_2+N_3} \\ =\frac{25\times 200+10\times 250+15\times 300}{200+250+300} \\ =\frac{5000+25000+45000}{750} \\ =\frac{12000}{750}=16 \end{gathered}$$
Thus, mean of combined distribution is 16.