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.