Question

The following data values represent a population. What is the variance of the values? 7, 5, 11, 1, 11

Answer 1

The mean is 35/5=7

The variance is the average of the sum of squared differences of each element from the mean:

v=((7-7)^2+(5-7)^2+(11-7)^2+(1-7)^2+(11-7)^2)/5

v=(0+4+16+36+16)/5

v=14.4

Answer 2

The variance of the values is: 14.4

Explanation:

The data is given as follows:

7, 5, 11, 1, 11

The total number of data points are: 5

The mean of the data values is given by:

`Mean(x')=(7+5+11+1+11)/(5)\\\\i.e.\\\\Mean(x')=(35)/(5)\\\\i.e.\\\\Mean(x')=7`

Now,

x x-x' (x-x')²

7 7-7=0 0

5 5-7= -2 4

11 11-7=4 16

1 1-7= -6 36

11 11-7=4 16

The variance is given by:

`\sigma^2=(\sum (x-x')^2)/(5)\\\\i.e.\\\\\sigma^2=(4+16+36+16)/(5)\\\\i.e.\\\\\sigma^2=(72)/(5)\\\\i.e.\\\\\sigma^2=14.4`

Hence, Variance=14.4