Question

The average marks in Mathematics for $5$ students was found to be $50$. Later is was discovered that in case of one student, the marks $48$ were misread as $84$. The correct average is

• A. $40.2$
• B. $40.8$
• C. $42.8$
• D. $48.2$

Answer 1

The correct option is C $42.8$

Average is the sum of the data values divided by the total number of data values.

Given that, average marks of the students with one of students incorrect mark is $50$

Number of students is $5$

One of the students incorrect mark is $84$ and

correct mark is $48$

Let the remaining four students marks be $x_1,x_2,x_3,x_4$

Therefore, incorrect average is $\frac{x_1+x_2+x_3+x_4+84}{5}=50$

$⟹x_1+x_2+x_3+x_4+84=50\times 5=250$

$⟹x_1+x_2+x_3+x_4=250-84=166$ -------(1)

Correct average $=\frac{x_1+x_2+x_3+x_4+48}{5}$ -------(2)

substituting (1) in (2) we get

Correct average $=\frac{166+48}{5}=\frac{214}{5}=42.8$