Question

The numbers of regular season wins for 10 football teams in a given season are given below. Determine the​ range, mean,​ variance, and standard deviation of the population data set.

2​, 10​, 15​, 4​, 11​, 10​, 15​, 10​, 2​, 10

Answer 1

a

`R =13`

b

`\= x =8.9`

c

`var(x) = 16.57`

d

`\sigma = 4.1`

Explanation:

From the question we are given a data set

2​, 10​, 15​, 4​, 11​, 10​, 15​, 10​, 2​, 10

The sample size is n = 10

The range is

`R = maxNum - MinNum`

Where maxNum is the maximum number on the data set which is 15

and MinNum is the minimum number on the data set which is 2

So

`R = 15 - 2`

`R =13`

The mean is mathematically represented as

`\= x = (\sum x_i)/(N)`

substituting values

`\= x = (2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 )/(10)`

`\= x =8.9`

The variance is mathematically evaluated as

`var(x) = (\sum (x - \= x)^2)/(N)`

substituting values

`var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}`
`((2 - 8.9 )^2 +(10 - 8.9 )^2 )/(10)`

`var(x) = 16.57`

The standard deviation is
`\sigma = √(var(x))`

substituting values

`\sigma = √(16.57)`

`\sigma = 4.1`