The coefficient of variation and the standard deviation are both used when the spread of the values in a dataset has to be measured. The main differences between the two measures are given in the table below. The coefficient of variation can be determined for both a sample as well as a population. In industries such as finance, the coefficient of variation is used to help investors assess the risk to reward ratio.
Common Applications for the Coefficient of Variation
The coefficient of variation values directly relates to data variability and relative risk as a high value will indicate that the data is highly variable and risk is low. A lower coefficient of variation will increase that the group is less variable, which coefficient of variation meaning means the risk is high. The standard deviation is in the numerator for both the population and sample formulas. The sample formula represents the entire population of the study, and the sample mean is the coefficient of variation with its standard deviation on top. Statisticians refer to mean as a measure of central tendency because it accounts for all the values in a data set, especially extreme variables. This makes it easy for you to identify the ideal midpoint of your research data.
Distribution
Now that you know what the coefficient of variation and standard deviation are, let’s work through two examples of calculating the CV. If the expected return in the denominator of the coefficient of variation formula is negative or zero, then the result could be misleading. The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population. Recall that CV% (coefficient of variance percentage) is equal to 100 times the ratio of the standard deviation to the mean. This means that we should start by finding the standard deviation. Using coefficient of variation formulas, find in which machine, A or B is there greater variability in individual wages.
When you are getting acquainted with statistics, it is hard to grasp everything right away. Therefore, let’s stop for a second to examine the formula for the population and try to clarify its meaning. The main part of the formula is its numerator, so that’s what we want to comprehend. Variance measures the dispersion of a set of data points around their mean value.
- For lab results, a good coefficient of variation should be lesser than 10%.
- In such cases, it’s advisable to complement the CV analysis with other statistical measures or subject matter expertise.
- Still, variance measures the dispersion of data in squared units that are hard to interpret.
- The coefficient of variation differs based on the composition of data points in your observation.
- The coefficient of variation can be useful when comparing data sets with different units or widely different means.
Importance in Statistics
Like the range, the IQR is a measure of variability, but you must find the quartiles in order to compute its value. The data on the left shows how the price of a carton of milk varied in a U.S. grocery store over the course of a year. The data on the right shows how the price of a carton of milk varied in a Japanese grocery store over the course of a year. As a dimensionless quantity, the coefficient of variation offers two main advantages. If you find a coefficient of variation of 0.10 or 10%, the standard deviation is one-tenth or 10% of the mean.
Dispersion
Researchers use coefficients of variation to compare outcomes of systematic investigations across different populations. For example, you can use COV to measure the variability of spending among high-income earners and low-income households. Financial analysts use coefficients of variation to evaluate investment risks for better decision-making. When presented with multiple investment options, coefficient of variation helps you compare both options in terms of risks and returns and choose the option with the highest ROI. First, variance gives results in squared units, while standard deviation in original units, as shown below. You must be asking yourself why there are unique formulas for the mean, median and mode.
Where σ is the standard deviation of a population, and μ is the mean. The result of your coefficient of variation will be in percentage, and if your answer is in decimal form, then you will use the two digits after your decimal and the follow-up rule to write your answer. If the coefficient of variation is given as 20.75 and the mean is 22.6 then find the standard deviation.
