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 (#'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
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

Answer:

1. coefficient of variation(systolic) = 13.88%

2. coefficient of variation(diastolic)  = 16.2%

3. The coefficients of variation for each data set are within 5 percentage points of each other Therefore  the systolic measurements vary signifcantly less than the diastolic

Step-by-step explanation:

1.  Mean of systolic = ( 117+126+158+96+157+122+116+134+127+122)÷10

      = 127.5

Standard Deviation of systolic = (((117-127.5)^2 +(126-127.5)^2+(158-127.5)^2+ (96-127.5)^2 + (157-127.5)^2 + (122-127.5)^2 + (116-127.5)^2 +(134-127.5)^2 +(127-127.5)^2 +( 122-127.5)^2) ÷ 10)^(0.5)

 SD = 17.7

coefficient of variation(systolic)

= Standard Deviation of systolic /mean of systolic

= $\frac{17.7}{127.5} * 100$

coefficient of variation(systolic) = 13.88%

2. Mean of diastolic = ( 80+77+76+51+90+89+60+64+72+83) ÷ 10

   = 74.2

Standard Deviation of diastolic  = (((80-74.2)^2 +(77-74.2)^2+(76-74.2)^2+ (51-74.2)^2 + (90-74.2)^2 + (89-74.2)^2 + (60-74.2)^2 +(64-74.2)^2 +(72-74.2)^2 +(83-74.2)^2) ÷ 10)^(0.5)

 SD = 12

coefficient of variation(diastolic)

= Standard Deviation of diastolic /mean of diastolic

 = $\frac{12}{74.2} *100$

coefficient of variation(diastolic)  = 16.2%

3. The coefficients of variation for each data set are within 5 percentage points of each other Therefore  the systolic measurements vary signifcantly less than the diastolic