Question

Listed below are amounts (in millions of dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service company's employees?The coefficient of variation for the amount collected by the security service company is __%.The coefficient of variation for the amount collected by other companies is __%.

Answer 1

The coefficient of variation of a dataset is given by the ratio between the standard deviation to the mean.

`CV=(\sigma)/(\mu)`

The mean and the standard deviation of a dataset with N elements are given by the following formulas:

`\begin{gathered} \mu=(\sum_i^Nx_i)/(N) \\ \\ \sigma=\sqrt{(1)/(N-1)\sum_{n\mathop{=}0}^(\infty)(x_i-\mu)^2} \end{gathered}`

Then, using those formula for the security service company, we have the following coefficient of variation:

`\begin{gathered} \mu=1.53 \\ \sigma=0.15670212364724... \\ CV=0.102419689...\approx10.2\% \end{gathered}`

Then, using those formula for the other companies, we have the following coefficient of variation:

`\begin{gathered} \mu=1.72 \\ \sigma=0.11352924243951... \\ CV=0.0660053735...\approx6.6\% \end{gathered}`