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 1010 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the two​ samples; then compare the variation. Systolic 119119 130130 156156 9595 156156 122122 115115 134134 125125 120120 Diastolic 8181 7676 7373 5050 9090 8989 5959 6565 7070 8282

Answer 1

Answer:

For systolic pressure data:

$\bar X =127.2\\\\S=17.91668\\\\CV=\frac{17.91668}{127.2}=0.14085$

For diastolic pressure data:

$\bar X =73.5\\\\S=12.54\\\\CV=\frac{73.5}{12.54}=0.17061$

Systolic pressure is slightly less variable, among individuals in the sample, than diastolic pressure.

Step-by-step explanation:

The coefficient of variation is defined as the percentage relative variation of a set of data with respect to its average. And it is calculated like this:

$CV=\frac{\bar X}{S}$

$S =\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2$

$\bar X={\frac{1}{n} \sum_{i=1}^n x_i$

For systolic pressure data:

$\bar X =127.2\\\\S=17.91668\\\\CV=\frac{17.91668}{127.2}=0.14085$

For diastolic pressure data:

$\bar X =73.5\\\\S=12.54\\\\CV=\frac{12.54}{73.5}=0.17061$

It is observed that the systolic pressure shows greater standard deviation but less coefficient of variation. This is due to the greater magnitude of its measurement scale.

Systolic pressure is slightly less variable, among individuals in the sample, than diastolic pressure.