Question

Calculate Combined Mean:

Section	Mean Marks	No. of Students
A	75	50
B	60	60
C	55	50

Answer 1

$$\begin{gathered} N_{\mathrm{A}}=50,{\overline{\mathit{X}}}_{\mathrm{A}}=75 \\ {N}_{\mathrm{B}}=60,\mathit{}{\overline{\mathit{X}}}_{\mathrm{B}}=60 \\ {N}_{\mathrm{C}}=50,{\overline{\mathit{X}}}_{\mathrm{C}}=55 \\ {\overline{\mathit{X}}}_{\mathrm{A},\mathrm{B},\mathrm{C}}=\frac{N_{\mathrm{A}}{\overline{\mathit{X}}}_{\mathrm{A}}+N_{\mathrm{B}}{\overline{\mathit{X}}}_{\mathrm{B}}+N_{\mathrm{C}}{\overline{\mathit{X}}}_{\mathrm{C}}}{N_{\mathrm{A}}+N_{\mathrm{B}}+N_{\mathrm{C}}}=\frac{50\left(75\right)+60\left(60\right)+50\left(55\right)}{50+60+50} \\ =\frac{3750+3600+2750}{160}=\frac{10100}{160}=63.125 \end{gathered}$$
Thus, the combined mean marks is 63.125.