Question

Question 18
The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be:

A) 50.5
B) 51
C) 51.5
D) 52

Answer 1

The answer is B.
Given, mean of 100 observations is 50.
Here, n = 100 and $\overline{x}=50$
Then, $mean=\frac{{\sum }_{i=1}^n{x}_i}{n}$
$\therefore \frac{1}{100}\times {\sum }_{i=1}^{100}{x}_i=50\Rightarrow {\sum }_{i=1}^{100}{x}_i=5000\dots \dots \left(i\right)$
Now, the observation 50 is replaced by 150, then (i) becomes,
${\sum }_{i=1}^{100}{x}_i=5000-50+150=5100$
$\therefore$ Resulting mean $=\frac{{\sum }_{i=1}^{100}{x}_i}{100}=\frac{5100}{100}=51$
Hence, the resulting mean is 51.