The text in the image is asking to determine the mean of a data set given the coefficient of variation and the standard deviation:

• Coefficient of variation (CV) = 114.2%
• Standard deviation (σ) = 5.71

The formula for the coefficient of variation (CV) is:

$CV = \frac{\sigma}{\mu} \times 100$

Where:

• $CV$ is the coefficient of variation (in percentage),
• $\sigma$ is the standard deviation,
• $\mu$ is the mean.

To find the mean, $\mu$, we can rearrange the formula:

$\mu = \frac{\sigma}{CV} \times 100$

Now, let's calculate the mean.The mean ($\mu$) of the data set is 5.0.

Would you like more details or have any questions?

Here are five related questions for further exploration:

1. What is the relationship between the standard deviation and the mean in different data sets?
2. How is the coefficient of variation used to compare the variability between two different data sets?
3. What happens to the mean if the standard deviation is doubled while keeping the coefficient of variation the same?
4. Can the coefficient of variation be negative? Why or why not?
5. How would you interpret a coefficient of variation above 100%, like in this case?

Tip: A higher coefficient of variation indicates greater variability in relation to the mean, useful for comparing data sets with different units or scales.