Find the standard deviation for the observations 1, 2, 3, 4, 5. - Vidyadip

Question

Find the standard deviation for the observations $1, 2, 3, 4, 5.$

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Answer

Here,$n=5$
$X: 1,2,3,4,5$
$\therefore \bar{x}=\frac{1+2+3+4+5}{5}=\frac{15}{5}=3$
$(x-\bar{x}):-2,-1,0,1,2 \therefore \Sigma(x-\bar{x})=0$
$(x-\bar{x})^2: 4,1,0,1,4 \sum(x-\bar{x})^2=10$
Standard deviation :
$s=\sqrt{\frac{\sum(x-\bar{x})^2}{n}}=\sqrt{\frac{10}{5}}=\sqrt{2}=1.41$

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