Question

Assume the following three samples of data:

Sample A: 4, 5, 6, 7, 8

Sample B: 3, 5, 6, 7, 9

Sample C: 2, 5, 6, 7, 10

Which of the above samples (A, B, or C) will have the smallest variance (s²)?

		Sample A
		Sample B
		Sample C
		The variance of the three samples will be the same

Answer 1

Following is the formula used for calculating variance:

Calculating variance for sample A:

The mean value can be calculated as follows:

Mean value = (4+5+6+7+8)/5 = 6

x	x-mean value	(x-mean value)2
4	-2	4
5	-1	1
6	0	0
7	1	1
8	2	4
Total	10

Variance = 10/(5-1) = 10/4 = 2.5

Calculating the variance for sample B:

The mean value can be calculated as follows:

Mean value = (3+5+6+7+9)/5 = 6

x	x-mean value	(x-mean value)2
3	-3	9
5	-1	1
6	0	0
7	1	1
9	3	9
Total	20

Variance = 20/(5-1) = 20/4 = 5

Calculating the variance for the sample C:

The mean value can be calculated as follows:

Mean value = (2+5+6+7+10)/5 = 6

x	x-mean value	(x-mean value)2
2	-4	16
5	-1	1
6	0	0
7	1	1
10	4	16
Total	34

Variance = 34/(5-1) = 34/4 = 8.5

The variance for the three samples is as follows:

Sample A: 2.5

Sample B: 5

Sample C: 8.5

Sample A has the smallest variance