The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which are recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

Answer

Correct S.D. `=sqrt{9.22}=3.036`

Explanation

$$ Here n=100, \bar{x}-20 and \sigma=3 $$

$$
\begin{aligned}
&\therefore \overline{\mathrm{x}}=\frac{1}{n} \sum \mathrm{x}_{\mathrm{i}} \\
&\Rightarrow \sum \mathrm{x}_{\mathrm{i}}=\mathrm{n} \times \overline{\mathrm{x}}=100 \times 20=2000 \\
...