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 90 70 64 69 69 53 64 55 84 71 61 61 99 58 64
female 65 83 82 70 75 84 90 84 87 89 90 71 90 79 77
the coefficient of variation for the male pulse rates is %
(type an integer or decimal rounded to one decimal place as needed)

Explanation:

Step1: Calculate the mean of male pulse rates

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
For male data: $n = 15$, $\sum x=90 + 70+64 + 69+69+53+64+55+84+71+61+61+99+58+64 = 1026$.
$\bar{x}_{male}=\frac{1026}{15}=68.4$.

Step2: Calculate the standard deviation of male pulse rates

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$.
$\sum(x_{i}-\bar{x})^{2}=(90 - 68.4)^{2}+(70 - 68.4)^{2}+(64 - 68.4)^{2}+(69 - 68.4)^{2}+(69 - 68.4)^{2}+(53 - 68.4)^{2}+(64 - 68.4)^{2}+(55 - 68.4)^{2}+(84 - 68.4)^{2}+(71 - 68.4)^{2}+(61 - 68.4)^{2}+(61 - 68.4)^{2}+(99 - 68.4)^{2}+(58 - 68.4)^{2}+(64 - 68.4)^{2}$
$=466.56+2.56 + 19.36+0.36+0.36+237.16+19.36+179.56+243.36+6.76+54.76+54.76+936.36+108.16+19.36=2349.6$.
$s_{male}=\sqrt{\frac{2349.6}{14}}\approx12.9$.

Step3: Calculate the coefficient of variation for male pulse rates

The formula for the coefficient of variation $CV=\frac{s}{\bar{x}}\times100\%$.
$CV_{male}=\frac{12.9}{68.4}\times 100\%\approx18.9\%$.

Answer:

$18.9$