11.	Compute the Coefficient of Variation for:
o	Data set: 2, 4, 6, 8, 10.


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.

Compute the Coefficient of Variation for:
Data set: 2, 4, 6, 8, 10.

Find the Coefficient of Variation for the data set 2, 4, 6, 8, 10 with a step-by-step solution. This statistical problem explains calculating the mean and standard deviation, leading to the final CV, which is approximately 47.17%. Ideal for students in Grades 10-12.

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