Answer to Question #143522 in Statistics and Probability for Vladimyr Lubin

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 119,128,157,94,157,121,118,136,125,122
Diastolic 79,76,75,54,89,88,60,65,73,83
The coefficient of variation for the systolic measurements is %

Answer 1

Solution

Coefficient of Variation:

$$CV= {S \over \bar{x}} * 100$$

Systolic:

$$\bar{x} = {\sum x \over n} ={1277 \over 10} = 127.7$$

$$S= \sqrt{ \sum {(x-\bar{x})}^2 \over n-1} = \sqrt{3176.1 \over 9} = 18.7856$$

$$CV = {18.7856 \over 127.7} * 100 = 14.7107$$

CV of systolic is 14.7107 %

Diastolic:

$$\bar{y} = {\sum y \over n}={742 \over 10}=74.2$$

$$S = \sqrt{{(\sum y- \bar{y})}^2 \over n-1} = \sqrt{1209.6 \over 9} = 11.5931$$

$$CV= {11.5931 \over 74.2} *100 = 15.6241$$

CV of diastolic is 15.6241 %

Comparison

The systolic sample gives a more precise estimate than the diastolic sample since it has a lower coefficient of variation.

The diastolic sample has a greater dispersion around its mean than the systolic sample since it has a higher coefficient of variation