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 $83$.The corrected corresponding to the corrected score is ;

• A. $39.7$
• B. $40$
• C. $40.3$
• D. $39.3$

Answer 1

The correct option is A $39.7$

Total number of students $N=100$

Mean $\overline{x}=40$

$\overline{x}=\frac{\Sigma x_i}{N}$

$40=\frac{\Sigma x_i}{100}$

$\therefore \Sigma x_i=4000$

new Mean $\overline{x}=\frac{4000-(83-53)}{100}$

$\therefore \overline{x}=39.7$

hence, option $A$ is correct.