The coefficient of variation (CV) is calculated by dividing the standard deviation by the mean and then multiplying by 100 to express it as a percentage.
Here's a step-by-step guide:
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Calculate the Mean (Average): Sum all the values in your dataset and divide by the total number of values. The mean is often represented as μ (mu) for a population or x̄ (x-bar) for a sample.
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Calculate the Standard Deviation: The standard deviation measures the spread or dispersion of your data around the mean.
- Find the difference between each data point and the mean.
- Square each of these differences.
- Sum up all the squared differences.
- Divide this sum by the number of data points minus 1 (for a sample) or just the number of data points (for a population). This result is the variance.
- Take the square root of the variance to get the standard deviation. The standard deviation is often represented as σ (sigma) for a population or s for a sample.
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Calculate the Coefficient of Variation: Divide the standard deviation by the mean, and then multiply the result by 100 to express it as a percentage.
- Formula: CV = (Standard Deviation / Mean) * 100
- Symbolically: CV = (σ / μ) 100 (for a population) or CV = (s / x̄) 100 (for a sample)
Example:
Let's say you have the following data set representing the ages of five people: 25, 30, 35, 40, 45.
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Mean: (25 + 30 + 35 + 40 + 45) / 5 = 35
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Standard Deviation: (Using a calculator or spreadsheet software) ≈ 7.906
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Coefficient of Variation: (7.906 / 35) * 100 ≈ 22.59%
Why Use the Coefficient of Variation?
The coefficient of variation is useful because it's a relative measure of variability. This means you can use it to compare the dispersion of data sets that have different units or different means. For example, you can compare the variability in the weights of apples (measured in grams) to the variability in the heights of trees (measured in meters). You couldn't directly compare their standard deviations because of the different units and scales. A higher CV indicates greater variability relative to the mean.
In summary, the coefficient of variation allows you to compare the degree of variation from one data set to another, even if the means and units differ.
