Answer to Question #274332 in Statistics and Probability for kunsu

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

126

158

96

156

122

117

134

125

118

Diastolic

79

77

76

53

88

89

58

66

72

84

The coefficient of variation for the systolic measurements is

enter your response here

​%.

Answer 1

The given data is as follows-

$\bar{x}=\dfrac{\sum x}{N}=\dfrac{1268}{10}=126.8$

$\bar{y}=\dfrac{\sum y}{N}=\dfrac{742}{10}=74.2$

Standard deviation

$\sigma_x=\sqrt{\dfrac{(x_i-\bar{x})^2}{N}}=\sqrt{\dfrac{3122.86}{10}}=\sqrt{312.86}=17.68$

$\sigma_y=\sqrt{\dfrac{(y_i-\bar{y})^2}{N}}=\sqrt{\dfrac{1323.57}{10}}=\sqrt{132.357}=11.50$

Coefficient of variation for systolic is-

$=\dfrac{\sigma_x}{\bar{x}}\times 1000=\dfrac{17.68}{126.8}\times 100=13.94$ %

Coefficient of variation for Diastolic is-

$=\dfrac{\sigma_y}{\bar{y}}\times 1000=\dfrac{11.5}{74.2}\times 100=15.49$ %