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 87 68 60 71 68 50 66 56 81 70 60 63 99 57 63
female 64 81 78 68 74 84 88 85 89 90 92 68 86 82 78
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

First, find the sum of male pulse rates: \(87 + 68+60 + 71+68+50+66+56+81+70+63+99+57+63\)
\(=899\)
There are \(n = 14\) data points.
The mean \(\bar{x}=\frac{899}{14}\approx64.2\)

Step2: Calculate the standard deviation of male pulse rates

The formula for the sample standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}\)
\(\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}=(87 - 64.2)^{2}+(68 - 64.2)^{2}+(60 - 64.2)^{2}+(71 - 64.2)^{2}+(68 - 64.2)^{2}+(50 - 64.2)^{2}+(66 - 64.2)^{2}+(56 - 64.2)^{2}+(81 - 64.2)^{2}+(70 - 64.2)^{2}+(63 - 64.2)^{2}+(99 - 64.2)^{2}+(57 - 64.2)^{2}+(63 - 64.2)^{2}\)
\(=(22.8)^{2}+(3.8)^{2}+(- 4.2)^{2}+(6.8)^{2}+(3.8)^{2}+(-14.2)^{2}+(1.8)^{2}+(-8.2)^{2}+(16.8)^{2}+(5.8)^{2}+(-1.2)^{2}+(34.8)^{2}+(-7.2)^{2}+(-1.2)^{2}\)
\(=519.84+14.44 + 17.64+46.24+14.44+201.64+3.24+67.24+282.24+33.64+1.44+1211.04+51.84+1.44\)
\(=2456.6\)
\(s=\sqrt{\frac{2456.6}{13}}\approx13.7\)

Step3: Calculate the coefficient of variation for male pulse rates

The formula for the coefficient of variation \(CV=\frac{s}{\bar{x}}\times100\%\)
\(CV=\frac{13.7}{64.2}\times100\%\approx21.3\%\)

Answer:

\(21.3\)