Listed below are pulse rates (beats per minute) from samples of aduft mafos 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 70 60 69 71 50 63 53 80 68 61 62 100 57 64 Female 67 80 81 69 74 86 88 89 88 90 69 79 78 

To determine if there appears to be a difference in pulse rates between adult males and females, we will calculate the coefficient of variation (CV) for each group. The coefficient of variation is defined as:

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

### Steps:
1. Calculate the mean and standard deviation for each sample (males and females).
2. Calculate the coefficient of variation for each sample.
3. Compare the coefficients of variation to analyze the difference in variation between the two groups.

#### 1. Male Pulse Rates:
- Data: 87, 70, 60, 69, 71, 50, 63, 53, 80, 68, 61, 62, 100, 57, 64

#### 2. Female Pulse Rates:
- Data: 67, 80, 81, 69, 74, 86, 88, 89, 88, 90, 69, 79, 78

Let's calculate these values step-by-step.### Results:

- **Male Pulse Rates:**
  - Mean: \( 67.67 \) beats per minute
  - Standard Deviation: \( 13.10 \) beats per minute
  - Coefficient of Variation: \( 19.35\% \)

- **Female Pulse Rates:**
  - Mean: \( 79.85 \) beats per minute
  - Standard Deviation: \( 8.15 \) beats per minute
  - Coefficient of Variation: \( 10.21\% \)

### Comparison:
The coefficient of variation for males (\(19.35\%\)) is significantly higher than that for females (\(10.21\%\)). This indicates that there is more variability in the pulse rates of males compared to females, despite females having a higher average pulse rate.

### Conclusion:
There appears to be a noticeable difference in the variation of pulse rates between males and females, with males showing greater variability.

Do you want more details or have any questions?

---

Here are 5 related questions for further exploration:
1. What is the impact of outliers on the coefficient of variation?
2. How would the comparison change if we used a larger sample size for both groups?
3. Can we apply hypothesis testing to check if the differences are statistically significant?
4. What are some biological reasons behind the difference in pulse rates between genders?
5. How does physical fitness level impact pulse rate variability?

**Tip:** When comparing data sets, the coefficient of variation is useful for comparing relative variability, especially when the means differ between groups.

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, 70, 60, 69, 71, 50, 63, 53, 80, 68, 61, 62, 100, 57, 64. Female: 67, 80, 81, 69, 74, 86, 88, 89, 88, 90, 69, 79, 78.

Analyze the difference in pulse rates between adult males and females by calculating the coefficient of variation. This detailed solution explains the steps to find the mean, standard deviation, and coefficient of variation for each group. Male pulse rate mean: 67.67 bpm, CV: 19.35%. Female pulse rate mean: 79.85 bpm, CV: 10.21%. Suitable for Grades 10-12.

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