Question

Distance travelled by 100 cars in a month are tabulated below

$\begin{array}{cccccc}Distance\left(km\right)& 0-400& 400-800& 800-1200& 1200-1600& 1600-2000\\ No.ofcars& 25& 40& 20& 10& 5\end{array}$

Calculate the coefficient of variation.

• A. 30.5 %
• B. 45.5 %
• C. 61.1 %
• D. 72%

Answer 1

The correct option is C 61.1 %

Let the assumed mean be i.e. A = 1000 and the dividing factor (c) be 400.

$\begin{array}{cccccc}X& F& D=X-A& D^{\prime }=\frac{D}{c}& F{D}^{\prime }& F{D}^{\prime 2}\\ 200& 25& -800& -2& -50& 100\\ 600& 40& -400& -1& -40& 40\\ 1000& 20& 0& 0& 0& 0\\ 1400& 10& 400& 1& 10& 10\\ 1800& 5& 800& 2& 10& 20\\ & \sum F=100& & & \sum F{D}^{\prime }=-70& \sum F{D}^{\prime 2}=170\end{array}$

$\overline{X}=A+\frac{\sum FD}{\sum F}\times c=1000-\frac{70}{100}\times 400=720$

$\sigma =\sqrt{\frac{\sum F{D}^{\prime 2}}{\sum F}-{\left(\frac{\sum F{D}^{\prime }}{\sum F}\right)}^2}\times c=\sqrt{\frac{170}{100}-{\left(\frac{-70}{100}\right)}^2}\times 400=\sqrt{1.7-0.49}\times 400=\sqrt{1.21}\times 400=1.1\times 400=440$

$C.O.V=\frac{440}{720}\times 100$