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? 29 5 59 6 40 45 56 12 99 44 98

Answer 1

Range =94

σ² = 1,141.564

Standard Deviation = 33.78703

Explanation:

First off to find the range, we find the highest value and subtract it to the lowest value. In this situation the values are:

Highest = 99

Lowest = 5

Range = 99 - 5

Range = 94

Now to find the variance of the sample data set, we first need to find for the mean of the data.

The mean of the data with be the sum of all the numbers in the data set divided by the number of samples.

5 + 14 + 26 + 50 + 60 +72 + 79 + 88 + 93 +94 + 99

That would equal 680

Then you divide the number of samples and that is 11 so the next equation is 680 divided by 11

So the then-

Mean = 61.81818

Now to find the variance we simply use the formula:

Now to find the variance we simply use the formula:

σ²=
`((xi - Mean)^(2) )/(n-1)`

σ²=
`\frac{(5 - 61.818)^(2) + (14 - 61.818)^(2) + (26 - 61.818)^2 + (99 - 61.818)^2} {11-1}`

σ²=
`(11,415.64)/(10)`

σ²=
`1,141.564`

Now to find the standard deviation, we take the variance and get the square root of it.

Standard Deviation=
`√(1,141.564)`

Standard Deviation=
`33.78703`

HOPE THIS HELPS :)