Question

Calculate standard deviation by step-deviation method:

$\begin{array}{cccccc}\text{Class Interval}& 10-20& 20-30& 30-50& 50-70& 70-80\\ \text{Frequency}& 5& 8& 16& 8& 3\end{array}$

Answer 1

$\sigma =\sqrt{\frac{\sum f{d}^{{}^{\prime 2}}}{N}-{\left(\frac{\sum f{d}^{{}^{\prime }}}{N}\right)}^2}\times i$

$\sigma =\sqrt{\frac{33}{40}-{\left(\frac{27}{40}\right)}^2}\times 20=\sqrt{0.825-0.456}\times 20=\sqrt{0.37}\times 20=0.608\times 20=12.17$