Answer to Question #143897 in Statistics and Probability for Vladimyr Lubin

Question

(3.2.23) Listed below are pulse rates​ (beats per​ minute) from samples of adult males and females. Does there appear to be a​ difference? Find the coefficient of variation for each of the two​ samples; then compare the variation.
Male 88,69,63,71,71,52,65,54,83,70,64,63,99,56,65
Female 67,84,82,70,76,85,86,85,87,88,94,72,86,79,80

Answer 1

Coefficient of variation:

$CV=\frac{s}{\bar x}\cdot100$

$\bar x=\frac{\sum x}{n}$

$s=\sqrt{\frac{\sum{(x-\bar x)^2}}{n-1}}$

$\bar x_{male}=\frac{88+69+63+71+71+52+65+54+83+70+64+63+99+56+65}{15}=68.867$

$s_{male}=\sqrt{\frac{(88-68.867)^2+...+(65-68.867)^2}{15-1}}=12.755$

$CV_{male}=\frac{12.755}{68.867}\cdot100=18.52$

$\bar x_{female}=\frac{67+84+82+70+76+85+86+85+87+88+94+72+86+79+80}{15}=81.4$

$s_{female}=\sqrt{\frac{(67-81.4)^2+...+(80-81.4)^2}{15-1}}=7.42$

$CV_{female}=\frac{7.42}{81.4}\cdot100=9.16$

$CV_{female}<CV_{male}$ therefore the variation for male pulse rates appears to be greater than the variation for female pulse rates.