Question

The hourly wages of 5 employees in a team (in Rs) are 250, 450, 600, 200 and 300. Find the standard deviation using step-deviation method.

• A. 123.45
• B. 146.25
• C. 162.65
• D. 105.5

Answer 1

The correct option is B 146.25

Here, all observations are divisible by 50. Choose the common factor(c) as 50.
$Mean,\overline{X}=\frac{250+450+600+200+300}{5}=\frac{1800}{5}=360$
$Factoredmean,\overline{x}=\frac{360}{50}=7.2$

$\begin{array}{cccc}X& X^{\prime }=\frac{X}{c}& d=x-\overline{x}& d^2\\ 250& 5& -2.2& 4.84\\ 450& 9& 1.8& 3.24\\ 600& 12& 4.8& 23.04\\ 200& 4& -3.2& 10.24\\ 300& 6& -1.2& 1.44\\ & & & \sum d^2=42.8\end{array}$

$\sigma =\sqrt{\frac{\sum d^2}{N}}\times c=\sqrt{\frac{42.8}{5}}\times 50=2.925\times 50=146.2$