Question

"The average income of 100 persons is 20 while the average income of 150 persons is 25. Calculate the average income of 50 persons"

Answer 1

Here,
$$\begin{gathered} \mathrm{Combined}\mathrm{Average}\mathrm{Income}=\frac{N_1{\overline{X}}_1+N_2{\overline{X}}_2}{N_1+N_2} \\ \mathrm{or},25=\frac{100\times 20+50\times {\overline{X}}_2}{150} \\ \mathrm{or},3750=2000+50{\overline{X}}_2 \\ \mathrm{or},{\overline{X}}_2=\frac{1750}{50} \\ \therefore {\overline{X}}_2=35 \end{gathered}$$

Thus, the ​average income of 50 persons is Rs 35.