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
71
64
72
70
54
66
55
82
70
60
63
97
56
66
 
Female
66
82
78
68
72
86
86
85
86
87
93
72
88
81
79


To determine if there is a difference in the variation of pulse rates between males and females, we can compute the **coefficient of variation (CV)** for each group. The coefficient of variation is a standardized measure of dispersion and is calculated as:

\[
\text{CV} = \left( \frac{\text{Standard Deviation (SD)}}{\text{Mean}} \right) \times 100
\]

### Step-by-step Solution:

1. **Calculate the mean and standard deviation for each sample.**
2. **Compute the coefficient of variation for each group.**
3. **Compare the coefficients of variation to determine which group has more relative variability.**

Let's calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the steps to calculate the coefficient of variation for each sample manually:

### Steps to Calculate the Coefficient of Variation (CV):

1. **Calculate the Mean:**
   - Add all the pulse rates together and divide by the number of observations.

2. **Calculate the Standard Deviation (SD):**
   - Find the square of the difference between each pulse rate and the mean.
   - Sum all these squared differences.
   - Divide by the number of observations minus one.
   - Take the square root of the result.

3. **Compute the Coefficient of Variation (CV):**
   - Use the formula \( \text{CV} = \left( \frac{\text{SD}}{\text{Mean}} \right) \times 100 \).

If you need more guidance or have any questions about the calculations, feel free to ask!

### Related Questions:
1. What is the purpose of the coefficient of variation in statistics?
2. How does the coefficient of variation differ from standard deviation?
3. How can we interpret the difference in CVs between two datasets?
4. What are some real-world applications of the coefficient of variation?
5. How would the CV change if we added an outlier to one of the datasets?

**Tip:** When comparing variability across different datasets, the coefficient of variation is especially useful because it is a relative measure of variability.

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.

Find the coefficient of variation for pulse rates in samples of adult males and females to compare the relative variability. This problem involves calculating mean, standard deviation, and coefficient of variation, with data from male and female pulse rates.

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