Questions: 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 86 The coefficient of variation for the female pulse rates is 82.3 %. (Type an integer or decimal rounded to one decimal place as needed.) Compare the variation.

Solution Steps

To solve this problem, we need to calculate the coefficient of variation (CV) for the male pulse rates and compare it with the given CV for the female pulse rates. The coefficient of variation is calculated as the standard deviation divided by the mean, expressed as a percentage.

1. Calculate the mean of the male pulse rates.
2. Calculate the standard deviation of the male pulse rates.
3. Compute the coefficient of variation for the male pulse rates.
4. Compare the male CV with the given female CV.

The mean pulse rate for the male sample is calculated as follows: \[ \text{Mean} = \frac{\sum \text{pulse rates}}{n} = \frac{86}{1} = 86.0 \]

Since there is only one data point (86), the standard deviation is undefined (or \( \text{nan} \)). The formula for standard deviation is: \[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n-1}} \] In this case, \( n = 1 \), leading to division by zero.

The coefficient of variation (CV) is given by: \[ CV = \frac{\sigma}{\mu} \times 100 \] Since \( \sigma \) is \( \text{nan} \), the CV for the male pulse rates is also \( \text{nan} \).

The given coefficient of variation for female pulse rates is \( 82.3\% \). Since the male CV is \( \text{nan} \), we cannot make a valid comparison. However, it can be stated that: \[ CV_{\text{male}} \text{ is } \text{nan} \text{ and } CV_{\text{female}} = 82.3\% \] Thus, we conclude that the male pulse rates cannot be compared meaningfully to the female pulse rates.

Final Answer