Question

The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$, then the correct mean will be:

• A. $41$
• B. $49$
• C. $40.5$
• D. $42.5$

Answer 1

The correct option is A $41$

$Mean=\frac{S}{n}$

where S=sum of all observations

n=number of observations

hence, $40=\frac{S}{20}\Rightarrow S=800$

but Since, 53 is recorded as 33 so we need to add $(53-33=20)$ to get the correct mean which is

$Mea{n}_{correct}=\frac{800+20}{20}=41$