Question

The average marks for statistics in a class of 30 were 52. The top six students had an average of 31 marks . What were the average marks of the other students?

Answer 1

The given information can be summarised as follows:

Combined average marks = 52
$$\begin{gathered} N_1=6,{\overline{X}}_1=31 \\ {\overline{X}}_2=?,N_2=24 \\ {\overline{X}}_{1,2}=\frac{N_1{\overline{\mathrm{X}}}_1+N_2{\overline{\mathrm{X}}}_2}{N_1+N_2} \\ 52=\frac{6\left(31\right)+24\left({\overline{X}}_2\right)}{6+24} \\ 52\times 30=186+24{\overline{\mathit{X}}}_2 \\ 1560-186=24{\overline{\mathit{X}}}_2 \\ 24{\overline{\mathit{X}}}_2=1374 \\ {\overline{\mathit{X}}}_2=\frac{1374}{24}=57.25 \end{gathered}$$
So, average marks of the remaining 24 students is 57.25.