Answer to Question #94777 in Statistics and Probability for Ama

Question

A student calculated the mean of five numbers as 45.3. while checking his work he discovered that his total was short by 20.5. What is the correct mean of the numbers?

Answer 1

$$mean=\mu={Total \ sum \over n}$$

Given that

$n=5, mean=\mu= 45.3$

$New\ Total\ sum=Total\ sum+20.5$

$$new\ mean=\mu_{new}={New\ Total \ sum \over n}$$

$$new\ mean=\mu_{new}={Total\ sum+20.5 \over 5}=\mu+4.1=$$ $$=45.3+4.1=49.4$$

The correct mean of the numbers is $49.4$