Question

What is the population variance of the data 16. 14, 15, 12. 14 and 13? (correct to two decimal places)​

Answer 1

Answer:

DATA VALUE FREQUENCY

40.0-41.9 2

5

8

;11

9

42.0-43.9

44.0-45.9

46.0-47.9

48.0-49.9

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

= 1.67

 

Additional Info:

Sample  Variance =  (1/(n-1))∑ (x-)²

= (1/5) 10

= 2

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