Question

Find out standard deviation, given the following data:

8, 10, 12, 14, 16, 18, 20, 22, 24, 26

Answer 1

$\begin{array}{cccc}\text{S. No.}& \text{Size}& \text{Deviation from Assumed Average}& \text{Square of Deviation}\\ & \left(X\right)& (dx=X-A)& \left(d{x}^2\right)\\ & & A=20& \\ 1& 8& 8-20=-12& 144\\ 2& 10& 10-20=-10& 100\\ 3& 12& 12-20=-8& 64\\ 4& 14& 14-20=-6& 36\\ 5& 16& 16-20=-4& 16\\ 6& 18& 18-20=-2& 4\\ 7& 20\left(A\right)& 20-20=0& 0\\ 8& 22& 22-20=+2& 4\\ 9& 24& 24-20=+4& 16\\ 10& 26& 26-20=+6& 36\\ N=10& & \sum dx=-30& \sum d{x}^2=420\end{array}$

$\sigma =\sqrt{\frac{\sum d{x}^2}{N}-{\left(\frac{\sum dx}{N}\right)}^2}=\sqrt{\frac{420}{10}-{\left(\frac{-30}{10}\right)}^2}$

$=\sqrt{42-(-3{)}^2}=\sqrt{33}=5.74$

Standard Deviation = 5.74.