Question

The mean marks obtained in an examination by a group of 100 students were found to be 49.46. The mean marks obtained in the same examination by another group of 200 students were 52.32. Find out the mean of marks obtained by both the groups of students taken together.

Answer 1

The given information can be summarised as follows.
$$\begin{gathered} N_1=100,{\overline{X}}_1=49.46 \\ {N}_2=200,{\overline{X}}_2=52.32 \\ {\overline{\mathit{X}}}_{\mathit{1}\mathit{,}\mathit{2}}=\frac{N_1{\overline{X}}_1+N_2{\overline{X}}_2}{N_1+N_2} \\ =\frac{100\left(49.46\right)+200\left(52.32\right)}{100+200} \\ =\frac{4946+10464}{300}=\frac{15410}{300}=51.37 \\ \mathrm{Combined}\mathrm{Mean}\left({\overline{\mathit{X}}}_{1,2}\right)=51.37\mathrm{Marks} \end{gathered}$$

Thus, the mean marks of both the groups taken together is 51.37.