Question

The mean and standard deviation of $100$ observations were calculated as $40$ and $5.1$, respectively by a student who took by mistake $50$ instead of $40$ for one observation. Find the correct mean.

• A. $38.9$
• B. $37.9$
• C. $39.9$
• D. $36.9$

Answer 1

Answer: (C)

Given that number of observations $ \left(n\right) = 100 $
Incorrect mean $\left(\bar{x}\right) = 40$
We know that $\bar{x} =\frac{1}{n}\sum\limits_{i=1}^{n}x_{i}$
i.e. $40= \frac{1}{100}\sum \limits_{i=1}^{100} x_{i} $
or $\sum\limits_{i=1}^{100}x_{i} = 4000$
i.e. Incorrect sum of observations $= 4000$
Thus the correct sum of observations
$ = 4000 - 50 + 40 = 3990 $
Hence Correct Mean $= \frac{3990}{100}$
$= 39.9$