Question

The mean of 100 observations is 50. If one of the observations, 50 is replaced by 150, what is the resulting mean?

• A. 50.5
• B. 51
• C. 51.5
• D. 52

Answer 1

The correct option is B 51

Mean of 100 observations = 50
Sum of the 100 observations $=S=(50\times 100)=5000$
Replacing one observation value from 50 to 150, the total sum changes to,
S = (5000 - 50 +150) = 5100
So the new mean = $\left(\frac{\text{new sum of observations}}{\text{total no. of observations}}\right)$
$=\left(\frac{5100}{100}\right)$
= 51