Question

The mean marks of 100 students were found to be 40 . Later on it was discovered that a score of 53 was misread as 83. Find the corrected mean corresponding to the corrected score .

Answer 1

Given:
Incorrect Mean = 40
Number of students = 100
Correct value = 53
Incorrect value = 83

$$\begin{gathered} \mathrm{From}\mathrm{the}\mathrm{given}\mathrm{information}\mathrm{incorrect}\mathrm{summation}\mathrm{is}\mathrm{calculated}\mathrm{as}\mathrm{follows}: \\ {\overline{X}}_{\mathrm{I}}=\frac{\Sigma X_{\mathrm{I}}}{N} \\ 40=\frac{\Sigma X_{\mathrm{I}}}{100} \\ \Sigma X_I=4000 \\ \mathrm{Now}, \\ \mathrm{Correct}\Sigma X=\mathrm{Incorrect}\mathrm{summation}X\left(\Sigma X_I\right)-\mathrm{Incorrect}\mathrm{value}+\mathrm{Correct}\mathrm{value} \\ \mathrm{Correct}\Sigma X_{\mathrm{C}}=4000-83+53=3970 \\ {\overline{X}}_{\mathrm{C}}=\frac{\Sigma X_{\mathrm{C}}}{N}=\frac{3970}{100}=39.70 \end{gathered}$$
Thus, the corrected mean marks is 39.7.