Question

A sample of blood pressure measurements is taken for a group of adults, and those values (mm Hq) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient variation for each of the two samples; then compare the variation. 98 158 121 116 136 125 119 Systolic 120 128 160 Diastolic 80 78 76 52 91 86 58 63 74 83 The coefficient of variation for the systolic measurements is (Type an integer %. r decimal rounded to one decimal place as needed.) The coefficient of variation for the diastolic measurements is %. (Type an integer or decimal rounded to one decimal place as needed.) Compare the variation. the Therefore, the systolic measurements vary The coefficients of variation for each data set are diastolic measurements.

Answer 1

### Using Excel:

	Systolic(x)	Diastolic(y)	x^2	y^2
	120	80	14400	6400
	128	78	16384	6084
	160	76	25600	5776
	98	52	9604	2704
	150	91	22500	8281
	121	86	14641	7396
	116	58	13456	3364
	136	63	18496	3969
	125	74	15625	5476
	119	83	14161	6889
Total	1273	741	164867	56339

The coefficient of variation is

CV=(standard deviation/mean)*100

a) The mean of x is

10 i1i

1273 10

T= 127.3

standard deviation is:

(ΣΗ 10 2 i1 n n 1 Α

164867 1273)2 10 Sr 10 1

164867 16205 29 10

164867 162052.9 Sy

2814.1 Sr 9

V312.6778

S 17.6827

Hence coefficient of variation is:

$CV_x=\frac{s_x}{\bar{x}}*100$

$CV_x=\frac{17.6827}{127.3}*100$

CV 13.89

CV 13.9

b)

The mean of y is

$\bar{y}=\frac{\sum_{i=1}^{10}y_i}{n}$

$\bar{y}=\frac{741 }{10}$

$\bar{x}=74.1$

standard deviation is:

$s_y=\sqrt{\frac{\sum_{i=1}^{10}y_i^2-\frac{(\sum_{i=1}^{n}y_i)^2}{n}}{n-1}}$

$s_y=\sqrt{\frac{56339 -\frac{(741)^2}{10}}{10-1}}$

$s_y=\sqrt{\frac{56339 -\frac{549081}{10}}{9}}$

$s_y=\sqrt{\frac{56339 -54908.1}{9}}$

$s_y=\sqrt{\frac{1430.9}{9}}$

$s_y=\sqrt{158.8888}$

$s_y=12.61$

Hence coefficient of variation is:

$CV_y=\frac{s_y}{\bar{y}}*100$

$CV_y=\frac{12.61}{74.1}*100$

$CV_y=17.0175$

CV17.0

c) The coefficient of variation for systolic blood pressure is less than diastolic blood pressure.

Therefore, systolic measurements vary less than the diastolic measurements.