Question

The standard deviation of the distribution 2, 2, 2, 2, 2 is​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Observations are 2,2,2,2,2}$

$\underline{\textsf{To find:}}$

$\textsf{Standard deviation of given  observations}$

$\underline{\textsf{Solution:}}$

$\textsf{First we find out mean of given observations}$

$\mathsf{Mean,\bar{x}=\dfrac{2+2+2+2+2}{5}=\dfrac{10}{5}=2}$

$\mathsf{Formula\;for\;Standard\;deviation:}$

$\boxed{\mathsf{S.D=\sqrt{\dfrac{\sum\,(x_i-\bar{x})^2}{n}}}}$

$\mathsf{S.D=\sqrt{\dfrac{(2-2)^2+(2-2)^2+(2-2)^2+(2-2)^2+(2-2)^2}{5}}}$

$\mathsf{S.D=\sqrt{\dfrac{0+0+0+0+0}{5}}}$

$\mathsf{S.D=\sqrt{\dfrac{0}{5}}}$

$\mathsf{S.D=\sqrt{0}}$

$\implies\boxed{\mathsf{S.D=0}}$

Find more:

Standard Deviation (S.D) for two observations 1 and 4 is​

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