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.