Question

A sample of blood pressure measurements is taken for a group of​ adults, and those values​ (mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the two​ samples; then compare the variation.

Systolic
116
130
157
94
155
122
115
138
124
122

Diastolic
82
78
74
51
89
88
56
63
72
83

Answer 1

To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.

1. For the systolic sample:

•Find the mean:

mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130

•Find the standard deviation:

sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2

sum = 165.4

std = sqrt(sum/9) = 7.3

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%

2. For the diastolic sample:

•Find the mean:

mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5

•Find the standard deviation:

sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2

sum = 624.75

std = sqrt(sum/9) = 12.24

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%

So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.