This coefficient is independent of the unit of measurement used for the variable. For example, if you recorded net daily earnings for a lemonade stand, there could be positive net earnings on some days and negative earnings on others. If net earnings were $5.00 on two days and -$5.00 on another two days, the mean would be 0 and the coefficient of variation would be infinity, which doesn’t make a lot of sense. This formula modifies Cᵥ to be larger when the sample size is small.

Variance treats all numbers in a set the same, regardless of whether they are positive or negative, which allows you to account for the most minute variability in data sets. Suppose an organization has 1,500 as the total of 15 variables in its research sample size. In the second case, we were told that 1, 2, 3, 4 and 5 was a sample, drawn from a bigger population. Sample variance, on the other hand, is denoted by s squared and is equal to the sum of squared differences between observed sample values and the sample mean, divided by the number of sample observations minus 1.

How To Calculate Variance In 4 Simple Steps

The sum of differences between the observations and the mean, squared. So, this means that the closer a number is to the mean, the lower the result we obtain will be. And the further away from the mean it lies, the larger this difference. The coefficient of variation’s ability to standardize measurements and facilitate cross-comparisons has made it an coefficient of variation meaning indispensable tool in the field of research and analysis. Examples of ratio scales include weight, length, and absolute temperature (Kelvin scale).

Learn from instructors who have worked at Meta, Spotify, Google, IKEA, Netflix, and Coca-Cola and master Python, SQL, Excel, machine learning, data analysis, AI fundamentals, and more. This exemplifies how the CV can be a powerful decision-making tool, enabling practitioners to cut through complexities and make informed choices based on standardized, objective measures of variability. The coefficient of variation’s versatility and applicability extend far beyond the realms of pure statistical analysis.

1. The new standard deviation would be 4.242 (the original standard 1.414 multiplied by 3).
2. A high Coefficient of variation interpretation will indicate that the group is more variable, while a low value of the coefficient of variation will suggest that the group is less variable.
3. The coefficient of variation plays a role in risk assessment and decision-making as it determines the variability of the particular data set and identifies the relative risk of using the data set.
4. By accounting for the differences in means, the CV enables investors to make informed decisions based on the relative volatility of their investments, rather than being misled by absolute measures of variability.
5. However, the low coefficient is not favorable when the average expected return is below zero.
6. It is how you can calculate and interpret the coefficient of variation as the standard deviation is a Statistics measuring, so it is estimated in terms of variance.

The coefficient of variation (CV)—also called the relative standard deviation (RSD)—is the ratio of the standard deviation to the mean. It is a parameter or statistic used to convey the variability of your data in relation to its mean. It is equal to the ratio of the standard deviation to the mean and can be expressed as a percentage. The sample standard deviations are still 15.81 and 28.46, respectively, because the standard deviation is not affected by a constant offset. The coefficients of variation, however, are now both equal to 5.39%. The problem here is that you have divided by a relative value rather than an absolute.

Dispersion

The coefficient of variation is a dimensionless relative measure of dispersion that is defined as the ratio of the standard deviation to the mean. If there are data sets that have different units then the best way to draw a comparison between them is by using the coefficient of variation. You will use a coefficient of variation in data analysis when you want to compare two or more data sets with each other.

Coefficient of Variation: Meaning, Formula and Examples

In finance, the coefficient of variation is important in investment selection. From a financial perspective, the financial metric represents the risk-to-reward ratio where the volatility shows the risk of an investment and the mean indicates the reward of an investment. To calculate the coefficient of variation, first find the mean, then the sum of squares, and then work out the standard deviation. With that information at hand, it is possible to calculate the coefficient of variation by dividing the standard deviation by the mean. Other than helping when using the risk/reward ratio to select investments, it is used by economists to measure economic inequality. Outside of finance, it is commonly applied to audit the precision of a particular process and arrive at a perfect balance.

To make sure you remember, here’s an example of a comparison between standard deviations. Let’s take the prices of pizza at 10 different places in New York. As you can see in the picture below, they range from 1 to 11 dollars. As you probably guessed, there is a population and sample formula once again. The last measure which we will introduce is the coefficient of variation.