Answer to Question #143523 in Statistics and Probability for Vladimyr Lubin

Question

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

Solution

$$CV = {S \over \bar{x} } *100$$

Male:

$$\bar{x}= {\sum x \over n} = {1033 \over 15} = 68.8667$$

$$S= \sqrt{\sum {(x-\bar{x})}^2 \over n-1} = \sqrt{2277.7333 \over 14} =12.7552$$ $$CV= {12.7552 \over 68.8667} *100 = 18.5216$$

CV of male is 18.5216%

Female:

$$\bar {y} = {\sum y \over n} = {1221 \over 15} = 81.4$$

$$S= \sqrt{\sum {(y-\bar{y})}^2 \over n-1}= \sqrt{771.6 \over 14} = 7.4239$$

$$CV = {7.4239 \over 81.4}*100 = 9.1203$$

CV of female is 9.1203 %

Comparison

The female sample gives a more precise estimate than the male sample since it has a lower coefficient of variation.

The male sample has a greater dispersion around the mean than the female sample since it has a greater coefficient of variation.