Question

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

Answer 1

Answer:

The variance of the values is: 14.4

Step-by-step 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:

$Mean(x')=\dfrac{7+5+11+1+11}{5}\\\\i.e.\\\\Mean(x')=\dfrac{35}{5}\\\\i.e.\\\\Mean(x')=7$

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:

$\sigma^2=\dfrac{\sum (x-x')^2}{5}\\\\i.e.\\\\\sigma^2=\dfrac{4+16+36+16}{5}\\\\i.e.\\\\\sigma^2=\dfrac{72}{5}\\\\i.e.\\\\\sigma^2=14.4$

Hence, Variance=14.4

       

Answer 2

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