Question

what is the population variance of the data 16,14,15,12,14,13 is​

Answer 1

Given:

16,14,15,12,14,13

$\overline{\mathrm{X}}$=16+14+15+12+14+13/6

=84/6

=14

$\mathrm{V} \text { ariance }=\frac{\sum(\mathrm{x}-\overline{\mathrm{x}})^{2}}{10}$

=(16-14)²+(14-14)²+(15-14)²+(12-14)²+(14-14)²+(13-14)²/6

=2²+0+1²+(-2)²+0+(-1)²/6

=4+4+1+1/6

=10/6

=5/3

variance=5/3

Answer 2

Given : observation: 16,14,15,12,14,13

To Find : population variance of the data  

Solution:

$\overline{x}$ = (16 + 14 + 15 + 12 + 14 + 13) /6

= ( 84)/6

= 14

x       (x-  $\overline{x}$ )      (x-  $\overline{x}$ ) ²

16       2             4

14       0              0

15       1               1

12       -2             4

14         0            0

13        -1              1

                        10            

Population Variance =  (1/n)∑ (x- $\overline{x}$  )²

= (1/6)10

= 10/6

= 5/3

= 1.667

 

Additional Info:

Sample  Variance =  (1/(n-1))∑ (x-)²

= (1/5) 10

= 2

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