Question

The distribution of the number of hours spent at work in a year by 60 people is given below. Calculate the standard deviation using step deviation method.

$\begin{array}{cccccc}No.ofhours& 0-500& 500-1000& 1000-1500& 1500-2000& 2000-2500\\ No.ofpeople& 6& 12& 15& 18& 9\end{array}$

• A. 588
• B. 604
• C. 622
• D. 645

Answer 1

The correct option is B

604

Let the assumed mean be 1250 i.e. A = 1250 and the dividing factor (c) be 500.

$\begin{array}{cccccc}X& F& D& D^{\prime }=\frac{D}{c}& F{D}^{\prime }& F{D}^{\prime 2}\\ 250& 6& -1000& -2& -12& 24\\ 750& 12& -500& -1& -12& 12\\ 1250& 15& 0& 0& 0& 0\\ 1750& 18& 500& 1& 18& 18\\ 2250& 9& 1000& 2& 18& 36\\ & \sum F=60& & & \sum F{D}^{\prime }=12& \sum F{D}^{\prime 2}=90\end{array}$

$\sigma =\sqrt{\frac{\sum F{D}^{\prime 2}}{\sum F}-{\left(\frac{\sum F{D}^{\prime }}{\sum F}\right)}^2}\times c=\sqrt{\frac{90}{60}-{\left(\frac{-12}{60}\right)}^2}\times 500=\sqrt{1.5-0.04}\times 500=\sqrt{1.46}\times 500=1.208\times 500=604$