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Part 1
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
70
64
68
71
53
62
54
84
72
63
63
100
56
62

Female
66
81
81
72
75
82
86
86
86
88
92
70
86
80
76
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Part 1
The coefficient of variation for the male pulse rates is

enter your response here​%.
​(Type an integer or decimal rounded to one decimal place as​ needed.)

To determine if there is a difference in variation between male and female pulse rates, we can calculate the coefficient of variation (CV) for each sample. The CV is calculated using the formula:

\[
\text{Coefficient of Variation (CV)} = \left(\frac{\text{Standard Deviation}}{\text{Mean}}\right) \times 100\%
\]

### Step 1: Calculate the mean and standard deviation for each group.

**Male Pulse Rates:**

**Data:** 86, 70, 64, 68, 71, 53, 62, 54, 84, 72, 63, 63, 100, 56, 62

**Female Pulse Rates:**

**Data:** 66, 81, 81, 72, 75, 82, 86, 86, 86, 88, 92, 70, 86, 80, 76

### Step 2: Calculate the CV for each sample.

Let’s calculate these values step-by-step.The coefficients of variation for the pulse rates are:

- **Male Pulse Rates:** \( 18.8\% \) (rounded to one decimal place)
- **Female Pulse Rates:** \( 9.1\% \) (rounded to one decimal place)

### Comparison:
The coefficient of variation is higher for males (\(18.8\%\)) compared to females (\(9.1\%\)), indicating that there is more variability in the pulse rates among males than females.

Would you like more details or have any questions?

### Related Questions:
1. How is the coefficient of variation used to compare data sets?
2. What other statistical measures can be used to compare variability between two groups?
3. Why is it important to use the sample standard deviation (ddof=1) instead of the population standard deviation?
4. How does the coefficient of variation differ from standard deviation?
5. What are the implications of high variability in pulse rates?

**Tip:** The coefficient of variation is particularly useful when comparing the degree of variation from one data set to another, even if the means are drastically different.

Explore the comparison of coefficient of variation (CV) in male and female pulse rates using statistical analysis. Calculate CV, mean, and standard deviation for each group. Understand how variability in pulse rates differs between genders.

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