To use this coefficient of variation calculator, follow the below steps:
As soon as you click the calculate button this coefficient of variation calculator gives the result of C_{v}, (COV) percentage %, standard deviation (S, σ) and arithmetic mean (μ, x̄) for the selected data set i-e sample or population with complete step by step solution.
Coefficient of Variation calculator can be used to calculate the coefficient of variation in the given data set by evaluating the ratio between standard deviation and mean of that set. After you insert your data set, it calculates the mean and standard deviation of data automatically in the background and delivers the very precise value for the coefficient of variation.
In this post, we will discuss the coefficient of variation, how to find coefficient of variation, CV formula, and how to use the coefficient of variation calculator.
The coefficient of variation is a normalized measure of the dispersion of a probability distribution in statistics and probability theory. It is calculated as the ratio of the standard deviation to the mean.
The formula for the coefficient of variation is given below:
\(c_v=\frac{\sigma }{\left|\mu \right|}\)
\(\sigma =\sqrt{\frac{1}{N}\sum _{i=1}^N\left(x_i-\mu \right)^2}\)
In the above equations:
Formula values | Refers to |
c_{v} | coefficient of variation |
σ | population standard deviation |
μ | mean of the population data set |
N | size of the population data set |
\(x_1,....,x_N\) | population data set |
To find the coefficient of variation using the above formula, follow the below steps:
We will use an example to understand how to calculate CV of population dataset by using the above steps and formula.
Suppose we have a,
Population dataset = (\(60.25, 62.38, 65.32, 61.41, 63.23).\)
Let’s calculate the coefficient of variation for this dataset.
Step 1: Calculate the population mean value of the data set in the first step.
Mean (μ) = \(= \dfrac{(60.25+62.38+65.32+61.41+63.23)}{5}\)
\(= \dfrac{312.59}{5}\)
\(= 62.51\)
Step 2: Calculate the population standard deviation for the same values by placing values in the above SD formula.
\(\sigma =\sqrt{\Big(\dfrac{1}{5-1}\Big)\times (60.25-62.51799)^2+(62.38-62.51799)^2+(65.32-62.51799)2+(61.41-62.51799)^2+(63.23-62.51799)^2)}\)
\(\sigma =\sqrt{\Big(\dfrac{1}{4}\Big)\times (-2.26799)^2+(-0.13798999)^2+(2.80201)^2+(-1.10799)^2+(0.71201)^2)}\)
\(= \sqrt{\dfrac{1}{4} \times (5.14377 + 0.01904 + 7.85126 + 1.22764 + 0.50695)}\)
\(= \sqrt{3.68716}\)
\(\sigma= 1.92\)
Step 3: Calculate the population coefficient of variation after getting mean (μ) and SD (σ).
\(CV = \dfrac{\text{Standard Deviation}\left(\sigma \right)}{\text{Mean}\left(\mu \right)}\)
\(= \dfrac{1.92}{62.51}\)
\(= 0.03071\)
Below are the various uses and applications of the coefficient of variation:
The coefficient of variation helps us to make an accurate comparison between the different data sets. If the data sets have the same population, the ideal method for calculating the variation should be the standard deviation. However, if the comparison is between two different data sets, a better picture is given in the CV.
The coefficient of variation measurement is a statistical figure. It helps us find out the repeatability and not its validity within a data set. In a way, knowing the degree of association, and not its agreement is more useful. The Variance Coefficient has its value when calculating data repeatability without needing to think too much about its validity.
The coefficient of variation is a useful concept for understanding data consistency. Data consistency means a sense of regularity inside the values in the data collection. The variance coefficient tests how stable the various values of the sample are from the mean. Consistency in a data set will be greater if the CV is low and smaller if the CV is higher.
The CV is the optimal tool for risk measurement in businesses. Risk managers like to use this tool more than anything else because it provides a better indicator of risk assessment at all levels.
If you learn how to measure the CV, it will be simple for you to select the right choices open to you. The coefficient of variation is helpful anytime a company wants to reduce its operations because of the high costs involved. Any of its workers will have to quit the organization. It allows us to determine which department will be facing the hard hit.
If the value of the coefficient of variation is less than 10, it is perceived as very good values. CV between 10 and 20 is also good value, but if this value gets greater than 30, it is not acceptable.
Yes. The coefficient of variation can be greater than 1. In this case, it is considered to be a high variance. If it is less than 1, it is considered as the low variance for the given data set.
Yes, a low coefficient of variation is good because it depicts the more accurate value. The greater value of CV is considered as a higher rate of dispersion around mean value.
The coefficient of variation less 1 is considered a low coefficient of variation in stats and probability theory.
If the value of the coefficient of variation is more than 1, it is considered a high coefficient of variation among the data set.
The most common usage of the CV is to test the technique accuracy. It is often used as a variation indicator where the standard deviation is proportional to the mean. It is also used as a way of measuring variation between measurements produced in various units.
The coefficient of variation has great importance when it comes to the variation in a data set. The coefficient of variance is important because the normal standard deviation must also be interpreted in light of the mean value.
The real value of the CV is not dependent on the unit in which measurements are taken in comparison. The coefficient of variance can be used instead of the SD for comparison between data sets of varying units.
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