Question

Average income of 50 families is ₹3,000. Of these average income of 12 families is ₹1,800. Find out the average income of the remaining families.

Answer 1

The information given in the question can be summarised as follows.
Average income of all the 50 families = ${\overline{X}}_{12}$ = 3000

	Average income	Number of families
12 families	$\left({\overline{X}}_1\right)$ = 1800	N1 = 12
38 families	$\left({\overline{X}}_2\right)$ = ?	N1 = 38

Substituting the given values in the formula for combined mean
$$\begin{gathered} {\overline{X}}_{12}=\frac{N_1{\overline{X}}_1+N_2{\overline{X}}_2}{N_1+N_2} \\ 3000=\frac{12\times 1800+38\times {\overline{X}}_2}{50} \\ \mathrm{or},\mathrm{3000\; \times \; 50}=21600+38\overline{X} \end{gathered}$$₂or, 150000 − 21600 = 38X₂or, X₂ = 3378.95

Hence, the average income of remaining 38 families is Rs 3,378.95