Hi,
How do I find the coefficient of variation? I found the sample variance and the standard deviation for the problem I'm trying to solve, but I can't find the coefficient of the variation
see my earlier post to your question
To find the coefficient of variation (CV), you need to divide the standard deviation of a dataset by its mean, and then multiply the result by 100 to express it as a percentage. The formula for calculating CV is:
CV = (standard deviation / mean) * 100
Here are the steps to find the coefficient of variation:
1. Find the mean (average) of your dataset.
- Add up all the values in your dataset.
- Divide the sum by the total number of values.
2. Calculate the standard deviation of your dataset.
- Subtract the mean from each value in your dataset.
- Square each difference.
- Find the mean of the squared differences.
- Take the square root of the mean.
3. Divide the standard deviation by the mean.
4. Multiply the result by 100 to express it as a percentage.
Let's go through an example:
Example: Let's say you have the following dataset: {2, 4, 6, 8, 10}
Step 1:
- Calculate the mean:
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Step 2:
- Calculate the standard deviation:
Subtract the mean from each value: {2-6, 4-6, 6-6, 8-6, 10-6} = {-4, -2, 0, 2, 4}
Square each difference: {16, 4, 0, 4, 16}
Find the mean of the squared differences:
Mean of squared differences = (16 + 4 + 0 + 4 + 16) / 5 = 40 / 5 = 8
Take the square root of the mean: √8 ≈ 2.83
Step 3:
- Find the coefficient of variation:
CV = (2.83 / 6) * 100 ≈ 47.17%
Therefore, the coefficient of variation for this dataset is approximately 47.17%.