Chapter 3

Q. 3.23

Sales of Automobiles

The mean of the number of sales of cars over a 3-month period is 87, and the standard deviation is 5. The mean of the commissions is $5225, and the standard deviation is $773. Compare the variations of the two.


Verified Solution

The coefficients of variation are

\begin{aligned}& \text { CVar }=\frac{s}{\bar{X}} \cdot 100=\frac{5}{87} \cdot 100 \approx 5.7 \% \quad \text { sales } \\& \text { CVar }=\frac{773}{5225} \cdot 100 \approx 14.8 \% \quad \text { commissions }\end{aligned}

Since the coefficient of variation is larger for commissions, the commissions are more variable than the sales.