Question

There are two branches of an establishment employing 100 and 80 persons respectively. If the Arithmetic Means of the monthly salaries by the two branches are ₹ 275 and ₹ 225 respectively, find out the arithmetic mean of the salaries of the employees of the establishment as a whole.

Answer 1

The given information can be summarised as follows.

$$\begin{gathered} N_1=100,{\overline{\mathit{X}}}_1=275 \\ {N}_2=80,{\overline{X}}_2=225 \\ {\overline{\mathit{X}}}_{1,2}=\frac{N_1\mathit{}{\overline{\mathit{X}}}_1+N_2{\overline{X}}_2}{{\mathrm{N}}_1+{\mathrm{N}}_2} \\ =\frac{100\left(275\right)+80\left(225\right)}{100+80} \\ =\frac{27500+18000}{180}=\frac{45500}{180} \\ =252.8 \end{gathered}$$
Thus, the combined mean salary is Rs 252.8