To solve this problem and calculate the coefficient of variation (CV) for the given data set of heights, let’s break it down step by step:

Steps to Calculate CV:

1. Find the mean (average) of the dataset.
2. Find the standard deviation (SD) of the dataset.
3. Use the formula for the coefficient of variation: $CV = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100$
4. Round the CV to the nearest tenth as needed.

Let me extract the data from the image, calculate the necessary values, and provide the solution. numpy as np

Data extracted from the image

heights = [78, 67, 72, 78, 79, 67, 65, 67, 80, 75, 74, 77]

Step 1: Calculate the mean

mean_height = np.mean(heights)

Step 2: Calculate the standard deviation

std_dev_height = np.std(heights, ddof=1) # ddof=1 for sample standard deviation

Step 3: Calculate the coefficient of variation (CV)

cv_height = (std_dev_height / mean_height) * 100

mean_height, std_dev_height, cv_height### Calculations:

1. Mean (average) of heights: $73.25$
2. Standard deviation (SD): $5.46$ (rounded to two decimal places)
3. Coefficient of Variation (CV): $CV = \left( \frac{5.46}{73.25} \right) \times 100 = 7.46\%$

Final Answer:

The coefficient of variation (CV) for the given data set is approximately 7.5% (rounded to the nearest tenth).

Would you like further explanation of any step, or assistance comparing this data with another dataset?

Related Questions:

1. How do you calculate the standard deviation manually?
2. Why is the coefficient of variation a useful measure compared to standard deviation?
3. Can the CV be used to compare data from entirely different contexts?
4. How does changing a single value in the dataset affect the CV?
5. What does a lower or higher CV signify in real-world applications?

Tip:

Always ensure that the units in your data make sense if you're using the CV to compare different datasets!