Question

The monthly power consumption (in units) of 50 households is given below. Calculate the standard deviation using step deviation method.

$\begin{array}{cccccc}No.ofunits& 0-100& 100-200& 200-300& 300-400& 400-500\\ No.ofhouseholds& 10& 20& 9& 8& 3\end{array}$

• A. 98.4
• B. 106.9
• C. 115.3
• D. 121.4

Answer 1

The correct option is C 115.3

Let the assumed mean be 250 i.e. A = 250 and the dividing factor (c) be 100.

$\begin{array}{cccccc}X& F& D& D^{\prime }=\frac{D}{c}& F{D}^{\prime }& F{D}^{\prime 2}\\ 50& 10& -200& -2& -20& 40\\ 150& 20& -100& -1& -20& 20\\ 250& 9& 0& 0& 0& 0\\ 350& 8& 100& 1& 8& 8\\ 450& 3& 200& 2& 6& 12\\ & \sum F=50& & & \sum F{D}^{\prime }=-26& \sum F{D}^{\prime 2}=80\end{array}$

$\sigma =\sqrt{\frac{\sum F{D}^{\prime 2}}{\sum F}-{\left(\frac{\sum F{D}^{\prime }}{\sum F}\right)}^2}\times c=\sqrt{\frac{80}{50}-{\left(\frac{-26}{50}\right)}^2}\times 100=\sqrt{1.6-0.2704}\times 100=\sqrt{1.3296}\times 100=1.153\times 100=115.3$