Question

The mean marks of 100 students were found to be 40 later it was discovered score of 53 was misread as 83 find the correct mean corresponding to the correct score find the mean after correcting wrong score.

Answer 1

Given :

• Mean marks of 100 students were found to be 40. Later it was discovered score of 53 misread as 83.

To calculate :

• The mean after correcting the wrong score.

Calculation :

For calculating the sum of observations, formula is given by :-

$\underline{\boxed{\sf{Sum \: of \: observations = Mean \times No. \: of \: observations}}}$

Plugging the values,

$: \implies \rm 40 \times 100 = 4000$

$\underline{ \underline{ \boldsymbol{According \: to \: the \: Question : }}}$

Let's calculate the correct mean!

$: \implies \rm 4000 - 83 + 53$

Simplifying,

$: \implies \underline{ \boxed{3970}}$

Now, we need to divide 3970 by 100 to get our final answer.

$: \implies \rm Correct \: mean = \dfrac{3970}{100}$

Cancelling the numbers,

$: \implies \underline{ \boxed{\rm{Correct \: mean = 39.7}}} \blue{\bigstar}$

Therefore,

• The correct mean is 39.7