Financial Calculators

## Calculate The Coefficient Of Variation

Calculate the coefficient of variation to compare two sets of data with different units of measurement

## Calculate the coefficient of variation

Dataset type
Mean (μ)
Standard deviation (σ)
Coefficient of variation
%

 ◦What is the coefficient of variation? ◦Can you tell me when I might need to use this as an adult?

## What is the coefficient of variation?

The coefficient of variation is a statistical measure that indicates the amount of variation or dispersion relative to the mean of a dataset. In other words, it is a way to compare the variability of two or more datasets that may have different units or scales.
To calculate the coefficient of variation, you first find the standard deviation of the dataset, then divide it by the mean of the dataset, and finally multiply by 100 to express the result as a percentage.
Here's an example: imagine you have two jars of jelly beans, one with 100 jelly beans and the other with 500 jelly beans. You count the jelly beans in each jar and find that the first jar has a mean of 50 jelly beans and a standard deviation of 10 jelly beans, while the second jar has a mean of 250 jelly beans and a standard deviation of 50 jelly beans.
To compare the variability of the two jars using the coefficient of variation, you would first calculate the coefficient of variation for the first jar as follows:
Coefficient of variation = (standard deviation / mean) x 100 Coefficient of variation = (10 / 50) x 100 Coefficient of variation = 20%
And then calculate the coefficient of variation for the second jar as follows:
Coefficient of variation = (standard deviation / mean) x 100 Coefficient of variation = (50 / 250) x 100 Coefficient of variation = 20%
Notice that both jars have the same coefficient of variation, even though the second jar has a much larger absolute variation than the first jar. This is because the coefficient of variation accounts for the variability relative to the mean, not the absolute variability.
Another example could be comparing the variability of the heights of two groups of people, such as professional basketball players and preschool children. In this case, you would first collect data on the heights of the two groups, calculate their means and standard deviations, and then use the coefficient of variation to compare their variability relative to their respective means.
Overall, the coefficient of variation is a useful measure for comparing the variability of two or more datasets that may have different scales or units.

## Can you tell me when I might need to use this as an adult?

It doesn't seem like I would ever use this
The coefficient of variation can be used in various fields and situations, including:
• Finance: The coefficient of variation can be used to measure the risk of an investment portfolio. A portfolio with a high coefficient of variation is considered to be riskier than one with a low coefficient of variation.
• Quality control: The coefficient of variation can be used to measure the variability of product quality. A manufacturing process with a low coefficient of variation produces consistent quality products, whereas a high coefficient of variation indicates that there is a lot of variation in the quality of the products.
• Biostatistics: The coefficient of variation is commonly used to compare the variation of different biological samples. For example, the coefficient of variation can be used to compare the variability of blood pressure measurements between different groups of people.
• Sports: The coefficient of variation can be used to compare the consistency of a player's performance in different games or seasons. For example, the coefficient of variation can be used to compare the consistency of a soccer player's goal-scoring ability in different seasons.
• So, while the coefficient of variation may not be used in everyday life, it can be useful in a wide range of professional and academic fields.
Article author
John Cruz
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.
###### Calculate The Coefficient Of Variation English
Published: Sun Apr 02 2023
In category Financial calculators

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