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 mean corresponding to the corrected score is

• A. $37.5$
• B. $35.6$
• C. $39.7$
• D. $38.7$

Answer 1

The correct option is C $39.7$

Let the $x_1,x_2,x_3........x_{100}$ be the marks of $100$ student
So,mean $\overline{x}=\frac{x_1+x_2+x_3+........+x_{100}}{100}=40x_1+x_2+x_3+........+x_{100}=4000$
As we have added $83$ instead of $53$ so corrected sum is
$x_1+x_2+x_3+........+x_{100}-83+53=4000-83+53=3970$
So,the corrected mean ${\overline{x}}_{corrected}=\frac{3970}{100}=39.7$