Question

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

Answer 1

Given:

N= 30
$$\begin{gathered} Mean,{\overline{X}}_{30}=52 \\ \Sigma X_{30}={\overline{X}}_{30}\times N \\ or,\Sigma X_{30}=30\times 52 \\ \Rightarrow \Sigma X_{30}=1560 \end{gathered}$$

Average of top 6 students = 31

ΣX of top 6 students, $\Sigma X_6$= 31 × 6 = 186

ΣX of remaining 24 (30-6) students, $\Sigma X_{24}$ = $\Sigma X_{30}-\Sigma X_6$= 1560 − 186 = 1374

Now, we will calculate the average marks of the other students by using the direct method:

$$\begin{gathered} \overline{X}\mathrm{of}24\mathrm{students}=\frac{\Sigma X_{24}}{N} \\ or,{\overline{X}}_{24}=\frac{1374}{24} \\ \Rightarrow {\overline{X}}_{24}=57.25\mathrm{marks} \end{gathered}$$