Question

the mean mark scored by 100 student was 40 .later on it was discoverd that a score of 53was misred as 83 find the correct mean mark

Answer 1

let the sum of all observation be x

x/100=40
x=40×100
x=4000

Incorrect value = 4000

Correct value = incorrect value - ( correct value - incorrect value)
                        = 4000- (83-53)
                        = 4000-30
                         = 3970

now the correct mean= 3970/100 = 39.7

Answer 2

We know that 
sum of observations = mean × no.of observations
                                 = 40 × 100
                                 = 4000
From the sum remove the wrong observation
⇒ 4000 - 83 = 3917
Add the correct observation 
⇒ 3917 + 53 = 3970
Correct sum of observations = 3970
Mean = 3970/100
=39.7