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

Question #143522
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 %
1
Expert's answer
2020-11-16T08:21:37-0500

Solution

Coefficient of Variation:

CV=Sxˉ100CV= {S \over \bar{x}} * 100

Systolic:

xˉ=xn=127710=127.7\bar{x} = {\sum x \over n} ={1277 \over 10} = 127.7

S=(xxˉ)2n1=3176.19=18.7856S= \sqrt{ \sum {(x-\bar{x})}^2 \over n-1} = \sqrt{3176.1 \over 9} = 18.7856


CV=18.7856127.7100=14.7107CV = {18.7856 \over 127.7} * 100 = 14.7107 %


CV of systolic is 14.7107 %

Diastolic:

yˉ=yn=74210=74.2\bar{y} = {\sum y \over n}={742 \over 10}=74.2

S=(yyˉ)2n1=1209.69=11.5931S = \sqrt{{(\sum y- \bar{y})}^2 \over n-1} = \sqrt{1209.6 \over 9} = 11.5931

CV=11.593174.2100=15.6241CV= {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


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