Question

Twenty adult males between the ages of 30 and 40 participated in a study to evaluate the effect of a specific health regimen involving diet and exercise on the blood cholesterol. Ten were randomly selected to be a control​ group, and ten others were assigned to take part in the regimen as the treatment group for a period of 6 months. The accompanying table shows the reduction in cholesterol experienced for the time period for the 20 subjects. Compute the sample variance and sample standard deviation for both control and treatment groups.

Control
4, 5, -3, 13, 2, 6, 22, -7, 7, 6

Treatment
-8, 6, 7, 3, 3, 11, 31, 6 , 5, 5
  
  
  
  
  
  
  
  
  

Answer 1

(1)

For Control Group:

From the given data, the following Table is calculated:

n = 10

x	x -	(x - )2
4	- 1.5	2.25
5	- 0.5	0.25
- 3	- 8.5	72.25
13	7.5	56.25
2	- 3.5	12.25
6	0.5	0.25
22	16.5	272.25
- 7	- 12.5	156.25
7	1.5	2.25
6	0.5	0.25
Total =		574.5

Variance is given by:

Standard Deviation is given by:

(2)

For Treatment Group:

From the given data, the following Table is calculated:

n = 10

x	x -	(x - )2
-8	- 14.9	222.01
6	- 0.9	0.81
7	0.1	0.01
3	- 3.9	15.21
3	- 3.9	15.21
11	4.1	16.81
31	24.1	580.81
6	- 0.9	0.81
5	- 1.9	3.61
5	- 1.9	3.61
Total =		858.9

Variance is given by:

Standard Deviation is given by: