Question

The data below show the number of hits on a website per week over a random sample of five weeks. Compute the followingstatistics.

Answer 1

We have a sample that is:

`115,39,160,240,176`

a) We can find the median by first sorting the sample:

`39,115,160,176,240`

The median is the value that has 50% of the values below its values.

In this case, this value is in the third place of the sorted sample and has a value of 160.

b) We have to find the mean.

We can calculate it as:

`\begin{gathered} \bar{x}=(1)/(n)\sum_{n\mathop{=}1}^5x_i \\ \\ \bar{x}=(1)/(5)(115+39+160+240+176) \\ \\ \bar{x}=(1)/(5)(730) \\ \\ \bar{x}=146 \end{gathered}`

c) We have to calculate the variance. To find its value we will use the mean value we have just calculated:

`\begin{gathered} s^2=(1)/(n)\sum_{n\mathop{=}1}^5(x_i-\bar{x})^2 \\ \\ s^2=(1)/(5)[(115-146)^2+(39-146)^2+(160-146)^2+(240-146)^2+(176-146)^2] \\ \\ s^2=(1)/(5)[(-31)^2+(-107)^2+(14)^2+(94)^2+(30)^2] \\ \\ s^2=(1)/(5)(961+11449+196+8836+900) \\ \\ s^2=(1)/(5)(22342) \\ \\ s^2=4468.4 \end{gathered}`

d) We have to calculate the standard deviation. As we have already calculated the variance, we can calculate it as:

`\begin{gathered} s=√(s^2) \\ s=√(4468.4) \\ s\approx66.85 \end{gathered}`

e) We now have to find the coefficient of variation:

`CV=\frac{s}{\bar{x}}=(66.85)/(146)\approx0.457876\cdot100\%\approx46\%`

Answer:

a) 160

b) 146

c) 4468.4

d) 66.85

e) 46%