Problem

A sample of blood pressure measurements is taken for a group of adults, and those values $(\mathrm{mm} \mathrm{Hg})$ 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. The coefficient of variation for the systolic measurements is \%. (Type an integer or 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 coefficients of variation for each data set are Therefore, the systolic measurements vary the diastolic measurements.

Solution

Step 1 :Given the systolic measurements are [120, 130, 140, 150, 160, 170, 180, 190, 200, 210] and the diastolic measurements are [80, 85, 90, 95, 100, 105, 110, 115, 120, 125].

Step 2 :Calculate the mean and standard deviation for each set of measurements. The mean of systolic measurements is 165.0 and the standard deviation is 28.722813232690143. The mean of diastolic measurements is 102.5 and the standard deviation is 14.361406616345072.

Step 3 :The coefficient of variation (CV) is calculated by dividing the standard deviation by the mean and multiplying by 100 to get a percentage. The CV for systolic measurements is 17.40776559556978 and for diastolic measurements is 14.011128406190313.

Step 4 :Round the CV to one decimal place. The CV for systolic measurements is 17.4% and for diastolic measurements is 14.0%.

Step 5 :Compare the CVs. The systolic measurements have a higher CV, therefore they vary more than the diastolic measurements.

Step 6 :Final Answer: The coefficient of variation for the systolic measurements is \(\boxed{17.4\%}\). The coefficient of variation for the diastolic measurements is \(\boxed{14.0\%}\). Therefore, the systolic measurements vary more than the diastolic measurements.

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Source: https://solvelyapp.com/problems/19966/

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