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
coefficient of variation is the standard deviation divided by the mean.
http://en.wikipedia.org/wiki/Coefficient_of_variation
To find the coefficient of variation, you need to divide the standard deviation by the mean and then multiply it by 100. The formula for the coefficient of variation (CV) is:
CV = (Standard Deviation / Mean) * 100
Here are the steps to calculate the coefficient of variation:
1. Calculate the mean (average) of the data set.
2. Calculate the standard deviation of the data set.
3. Divide the standard deviation by the mean.
4. Multiply the result by 100 to convert it into a percentage.
Let's work through an example using a sample data set:
Data set: 5, 8, 12, 15, 20
Step 1: Calculate the mean:
Mean = (5 + 8 + 12 + 15 + 20) / 5 = 60 / 5 = 12
Step 2: Calculate the standard deviation:
First, find the squared difference between each data point and the mean:
(5 - 12)^2, (8 - 12)^2, (12 - 12)^2, (15 - 12)^2, (20 - 12)^2
= 49, 16, 0, 9, 64
Next, calculate the variance by finding the average of the squared differences:
Variance = (49 + 16 + 0 + 9 + 64) / 5 = 138 / 5 = 27.6
Finally, calculate the standard deviation by taking the square root of the variance:
Standard Deviation = sqrt(27.6) ≈ 5.25
Step 3: Calculate the coefficient of variation:
CV = (Standard Deviation / Mean) * 100 = (5.25 / 12) * 100 ≈ 43.75%
Therefore, the coefficient of variation for this data set is approximately 43.75%.