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.

Answer 1

Systolic on right

`\hat{CV} =(18.68)/(127.5)=0.147`

Systolic on left

`\hat{CV} =(12.65)/(74.2)=0.170`

So for this case we have more variation for the data of systolic on left compared to the data systolic on right but the difference is not big since 0.170-0.147 = 0.023.

Explanation:

Assuming the following data:

Systolic (#'s on right) Diastolic (#'s on left)

117; 80

126; 77

158; 76

96; 51

157; 90

122; 89

116; 60

134; 64

127; 72

122; 83

The coefficient of variation is defined as " a statistical measure of the dispersion of data points in a data series around the mean" and is defined as:

`CV= (\sigma)/(\mu)`

And the best estimator is
`\hat {CV} =(s)/(\bar x)`

Systolic on right

We can calculate the mean and deviation with the following formulas:

[te]\bar x = \frac{\sum_{i=1}^n X_i}{n}[/tex]

`s= (\sum_(i=1)^n (x_i -\bar X)^2)/(n-1)`

For this case we have the following values:

`\bar x = 127.5, s= 18.68`

So then the coeffcient of variation is given by:

`\hat{CV} =(18.68)/(127.5)=0.147`

Systolic on left

For this case we have the following values:

`\bar x = 74.2 s= 12.65`

So then the coeffcient of variation is given by:

`\hat{CV} =(12.65)/(74.2)=0.170`

So for this case we have more variation for the data of systolic on left compared to the data systolic on right but the difference is not big since 0.170-0.147 = 0.023.