Question

Shack Homebuilders Limited is evaluating a new promotional campaign that could increase home sales. Possible outcomes and probabilities of the outcomes are shown next. Compute the coefficient of variation.

Possible Outcomes

Additional Sales

in Units Probabilities

Ineffective campaign ........................ 40 0.30

Normal response .............................. 100 0.30

Extremely effective ........................... 120 0.40

Short answer

Cofficient of variaence is 0.3752.

Step-by-step solution

Compute expected value-

$\begin{array}{c}\mathrm{Expected}\mathrm{value}=\mathrm{Respective}\mathrm{sales}\times \mathrm{Respective}\mathrm{probability}\\ \mathbf{=}(\mathbf{40}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{30})\mathbf{+}(\mathbf{100}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{30})\mathbf{+}(\mathbf{120}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{40})\\ =12+30+48\\ =90\mathrm{units}\end{array}$

Computation of total probability-

Probability	Sales	Probability*(sales-Expected sales)2	Total
0.30	40	0.30*(40-90)2	750
0.30	100	0.30*(100-90)2	30
0.40	120	0.40*(120-90)2	360
			1140

Computation of Standard deviation ( approx )- 

$\begin{array}{c}\mathbf{Standard}\mathbf{}\mathbf{deviation}\mathbf{=}\sqrt{\begin{array}{c}\mathbf{Probability}\mathbf{\times }{(\mathbf{sales}\mathbf{-}\mathbf{Expectedsales})}^2\end{array}}\\ \mathbf{=}\sqrt{1140}\\ \mathbf{=}\mathbf{33}\mathbf{.}\mathbf{7639}\mathbf{units}\end{array}$

Computation of co-efficient of variation ( approx.)-

$\begin{array}{c}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{variation}\mathbf{=}\frac{\mathrm{Standard}\mathrm{deviation}}{\mathrm{Expected}\mathrm{sales}}\\ \mathbf{=}\frac{\mathbf{33}\mathbf{.}\mathbf{7639}}{90}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{3752}\end{array}$