Question

Which of the following would be the variance of this population data set: 3, 9, 8, 9, 4, 5, 7, 11, 9, 7, 5, 4, 3, 1

Which of the following would be the standard deviation of this sample data set: 67, 54, 17, 77, 92, 41, 75, 81

Answer 1

Solution:

x	x2
3	9
9	81
8	64
9	81
4	16
5	25
7	49
11	121
9	81
7	49
5	25
4	16
3	9
1	1
∑x=85	∑x2=627

Population Variance σ2=∑x2-(∑x)2nn

=627-(85)214/14

=627-516.0714/14

=110.9286/14

=7.9235

Population Variance σ2=7.92

x	x2
67	4489
54	2916
17	289
77	5929
92	8464
41	1681
75	5625
81	6561
∑x=504	∑x2=35954

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√35954-(504)28/7

=√35954-31752/7

=√4202/7

=√600.2857

=24.5007

Sample Standard deviation S=24.50