The Coefficient of Variation (CV) measures the relative variability of a dataset, calculated as the ratio of the standard deviation ($\sigma$) to the mean ($\mu$) and typically expressed as a percentage:

$\text{Coefficient of Variation (CV)} = \frac{\sigma}{\mu} \times 100\%$

Step 1: Calculate the Mean ($\mu$)

Given the dataset: $2, 4, 6, 8, 10$.

$\mu = \frac{2 + 4 + 6 + 8 + 10}{5} = \frac{30}{5} = 6$

Step 2: Calculate the Standard Deviation ($\sigma$)

To find $\sigma$, we first calculate the squared differences from the mean, then take the square root of their average.

1. $(2 - 6)^2 = (-4)^2 = 16$
2. $(4 - 6)^2 = (-2)^2 = 4$
3. $(6 - 6)^2 = 0^2 = 0$
4. $(8 - 6)^2 = 2^2 = 4$
5. $(10 - 6)^2 = 4^2 = 16$

Average of squared differences: $\text{Variance} = \frac{16 + 4 + 0 + 4 + 16}{5} = \frac{40}{5} = 8$

Standard deviation: $\sigma = \sqrt{8} \approx 2.83$

Step 3: Calculate the Coefficient of Variation (CV)

$\text{CV} = \frac{2.83}{6} \times 100\% \approx 47.17\%$

Final Answer:

The Coefficient of Variation for the dataset $2, 4, 6, 8, 10$ is approximately 47.17%.

Would you like further details on any part of the calculation?

Here are five related questions to deepen understanding:

1. How does the Coefficient of Variation help in comparing datasets with different units?
2. What does a high Coefficient of Variation indicate about data consistency?
3. How would the CV change if all data points were increased by a constant value?
4. How does CV differ from standard deviation in terms of interpretation?
5. How is CV used in fields like finance or biology for data analysis?

Tip: CV is unitless, making it ideal for comparing variability across datasets of different scales.