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

Answer:

Systolic on right

$\hat{CV} =\frac{18.68}{127.5}=0.147$

Systolic on left

$\hat{CV} =\frac{12.65}{74.2}=0.170$

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.

Step-by-step 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:

$CV= \frac{\sigma}{\mu}$

And the best estimator is $\hat {CV} =\frac{s}{\bar x}$

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]

$s= \frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}$

For this case we have the following values:

$\bar x = 127.5, s= 18.68$

So then the coeffcient of variation is given by:

$\hat{CV} =\frac{18.68}{127.5}=0.147$

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:

$\hat{CV} =\frac{12.65}{74.2}=0.170$

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.