To compute the coefficient of variation (CV) for the given heights and weights, the formula is:

$\text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100$

Steps:

1. Calculate the mean of the heights and weights.
2. Calculate the standard deviation of the heights and weights.
3. Use the formula above to compute the CV for each dataset.

Let's compute it. numpy as np

Data

heights = np.array([80, 71, 69, 65, 66, 67, 70, 74, 76, 73, 70, 68]) weights = np.array([217, 185, 193, 201, 206, 206, 216, 214, 178, 225, 181, 214])

Calculations for heights

mean_heights = np.mean(heights) std_heights = np.std(heights, ddof=0) # Population standard deviation cv_heights = (std_heights / mean_heights) * 100

Calculations for weights

mean_weights = np.mean(weights) std_weights = np.std(weights, ddof=0) # Population standard deviation cv_weights = (std_weights / mean_weights) * 100

mean_heights, std_heights, cv_heights, mean_weights, std_weights, cv_weights### Results:

• Heights:

  • Mean: $70.75$
  • Standard Deviation: $4.19$ (approximately)
  • Coefficient of Variation (CV): $5.92\%$

• Weights:

  • Mean: $203.0$
  • Standard Deviation: $14.85$ (approximately)
  • Coefficient of Variation (CV): $7.31\%$

The CV indicates that weights have a slightly higher relative variability compared to heights.

Would you like a detailed explanation of the steps or have any specific questions?

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5 Related Questions:

1. How is the coefficient of variation useful in comparing variability between datasets?
2. What is the significance of using the population standard deviation versus sample standard deviation?
3. How can outliers in the data affect the CV calculation?
4. Could CV ever exceed 100%, and what would it signify in this context?
5. How does CV relate to data distribution (e.g., normal or skewed)?

Tip:

Always use the same units for datasets when comparing CV to ensure meaningful comparisons.