In: Statistics and Probability
2, 9, 15, 5, 11, 7, 11, 7, 5, 10 find the population mean, the population variance and the population standard deviation
Solution:
Given that,
x | x2 |
2 | 4 |
9 | 81 |
15 | 225 |
5 | 25 |
11 | 121 |
7 | 49 |
11 | 121 |
7 | 49 |
5 | 25 |
10 | 100 |
![]() |
![]() |
a ) The population mean is
=
(
x / n)
= (147 +( - 25 / 62 ) * 5
= (2+9+15+5+11+7+11+7+5+10 / 10 )
= 82 / 10
= 8.2
The population mean
= 8.2
b ) The population variance is 2
2
= (
x 2 ) - ((
x )2 / n ) / n )
= ( 800( (- 82 )2 / 10 ) / 10
= ( 800 - 672.4/ 10 )
= 127.6 / 10
= 12.76
The population variance is 2
= 12.76
c ) The population standard deviation is
=
The
population variance
=
12.76
= 3.5721
The population standard deviation
= 3.5721