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.

Systolic 116 128 156 95 155 124 118 135 124 121

Diastolic 82 76 73 51 91 87 57 62 71 82 1)

The coefficient of variation for the systolic measurements is __ % ?

2) The coefficient of variation for the diastolic measurements is __ %?

3) The coefficients of variation for each data set are [within 5 percentage points of each other OR more than 5% apart]. Therefore, the systolic measurements vary [signicantly more than, signifcantly less than, OR about the same]

Answer 1

1) Systolic:

X	(X - X̄)²
116	125.44
128	0.64
156	829.44
95	1036.84
155	772.84
124	10.24
118	84.640
135	60.840
124	10.240
121	38.440

	X	(X - X̄)²
total sum	1272	2969.60
n	10	10

mean =    ΣX/n =    1272.000   /   10   =   127.2000
                      
sample variance =    Σ(X - X̄)²/(n-1)=   2969.6000   /   9   =   329.956
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (2969.6/9)   =       18.1647

Coefficient of variation,CV=σ/µ=   14.28%

2) diastolic:

X	(X - X̄)²
82	77.44
76	7.84
73	0.04
51	492.84
91	316.84
87	190.44
57	262.440
62	125.440
71	4.840
82	77.440

	X	(X - X̄)²
total sum	732	1555.60
n	10	10

mean =    ΣX/n =    732.000   /   10   =   73.2000
                      
sample variance =    Σ(X - X̄)²/(n-1)=   1555.6000   /   9   =   172.844
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (1555.6/9)   =       13.1470

coefficient of variation,CV=σ/µ=   17.96%

3) The coefficient of variation are within 5 percentage points of each other.

Therefore, the systolic measurements vary significantly less than diastolic measurements.

Please revert for doubt.