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 were recorded as $21,21$ and $18 .$ Find the mean and standard deviation if the incorrect observations are omitted.
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 were recorded as $21,21$ and $18 .$ Find the mean and standard deviation if the incorrect observations are omitted.
Number of observations $(n)=100$
Incorrect mean $(\bar{x})=20$
Incorrect standard deviation $(\sigma)=3$
$ \Rightarrow 20 = \frac{1}{{100}}\sum\limits_{i = 1}^{300} {{x_i}} $
$ \Rightarrow \sum\limits_{i = 1}^{100} {{x_i}} = 20 \times 100 = 2000$
Incorrect sum of observations $=2000$
$\Rightarrow$ Correct sum of observations $=2000-21-21-18=2000-60=1940$
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