UPSC NDA Math Model Paper 1

Given: Mean of 100 observations is 45 but later it was found that two observations 19 and 31 were recorded incorrectly as 91 and 13
As we know that, mean of n observations is given by:

n

∑

i=1

xi‌n
⇒

100

∑

i=1

xi=100×45=4500
⇒

100

∑

i=1

xi−(91+13)+(19+31) =4500−(91+13)+(19+31)=4446
So, the correct mean =4446∕100=44.46
Hence, option A is the correct answer.