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Find the standard deviation of first ‘ten’ natural numbers.

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Here, 

The variable are 1,2, 3,…,9,10

n = 10

∴ Standard deviation,

\(σ=\sqrt\frac{\sum_{i=1}^{10} x_i^2}{10}\)-\((\frac{\sum_{i=1}^{10} x_i}{10})^2\)

=\(\sqrt\frac{1}{10}.\frac{10(10+1)(20+1)}{6}-\)\((\frac{10(10+1)}{2.10})^2\)

=\(\sqrt\frac{11.21}{6}-(\frac{11}{2})^2\)

=\(\sqrt\frac{77}{2}-\frac{121}{4}\)

\(\frac{1}{2}\sqrt {154-121}\)

\(\frac{1}{2}\sqrt {33}\)

= 2.83.

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