Question

Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?

Answer 1

To answer this question we need to remember the definition of the variance:

`s^2=(1)/(n-1)\sum_{i\mathop{=}1}^n(x-\bar{x})^2`

To helps us calculate it we have the table shown below:

From it we can calculate the mean:

`\bar{x}=(541)/(11)=49.181818`

Now, we have (on the table) the values x minus the mean and then the square of this. Adding we have:

`\sum_{i\mathop{=}1}^n(x-\bar{x})^2=7719.6364`

And hence the variance is:

`s^2=(7719.6364)/(11-1)=771.96364`

The standard deviation is the square root of the variance, then we have:

`\begin{gathered} s=√(771.96364) \\ s=27.784234 \end{gathered}`

Finally the range is the maximum value minus the minimum, then:

`range=81-1=80`

Therefore:

Range 80

Standard deviation 27.8

Variance 772

Now, jersey numbers don't represent any relation between the numbers they have which means that they are nominal data and therefore the last correct option is A.