Coefficient of Variation Calculator

An online coefficient of variation calculator helps to calculate coefficient of variation corresponding to the given date set values. The coefficient of variance (CV) is the ratio of the standard deviation to the mean (average). For instance, the standard deviation (SD) is 17% of the mean, is a CV. Also, the coefficient of variance calculator allows you to calculate coefficient of variation (CV, RSD) of continuous data or binomial (rate, proportion) data.

What is Coefficient of Variation (CV)?

The (CV) indicate as a statistical measure of the dispersion of data points in a data series around the mean. According to probability theory and statistics, it is the ratio of the standard deviation to the mean, and also known as relative standard deviation (RSD). In other words, CV is the measure of relative variability.

What is Coefficient of Variation Formula:

As mentioned-above, CV is the ratio of the standard deviation to the mean, so:

CV = σ/ μ

Where;

CV = Coefficient of Variation

σ = Standard Deviation

μ = Mean

Formula to calculate Standard Deviation:

σ = √((∑▒〖(x- μ)^2 〗)/(n-1))

Formula to calculate Mean:

μ = (∑▒x)/n

How to Find the Coefficient of Variation with this Tool:

Calculation For Raw Data:

If you are going to enter raw data, then you ought to select ‘raw data’ option from this sample coefficient of variation calculator, and stick to these steps:

Inputs: Data for Means:

• First of all, you have to select the “Mean” option form the given drop-down menu
• Very next, you ought to choose the dataset type, it can be either “Population” or “Sample”
• Finally, enter the dataset numbers into the given box of this tool

Inputs: Data for Proportion:

• First of all, you need to choose the “Proportion” option form the designated drop-down menu
• Now, you have to select the dataset type, it either be in “Population” or “Sample”
• Very next, you have to add sample size (n) into the designated field
• Now, you have to choose proportions data from the drop-down menu, it can either ‘ Proportion e.g. 0.05’ or ‘Rate as Percentage e.g. 5%’ or ‘Number of Events e.g. 10’
• Then, you have to enter the “Event Proportions” or “Event Rate %” or “Number of events” for the selected proportions data
• Now, hit the calculate button of this COV calculator

Outputs:

The proportion of variance calculator calculates the same statistical values for both data for proportion and data for mean:

• No. of samples
• Mean (μ)
• Standard deviation (σ)
• Coefficient Of Variance
• Also, this percentage of variation calculator calculate the “Coefficient Of Variance %”

Calculation from Summary Data:

If you are going to enter summary data, then you ought to select a ‘summary data’ option. This coefficient of variation calculator with mean and standard deviation (mean sd cv calculator) shows you the accurate results for the summary data. Just stick to the given inputs:

Inputs:

• You have to select dataset type, choose whether your data represents a population or sample
• Now, you have to add the mean of the data set
• Very next, you have to add the standard deviation of the data set
• Finally, hit the calculate button of this calculator for covariation

Outputs:

Whether you make a calculation for data for raw and summary data set, the cv calculator will calculate the same statistical parameters for data set ranges:

Example Problem For Coefficient of Variation:

Problem:

Find the coefficient of variance for the samples 62.25, 60.36, 64.28, 61.24, and 66.24 of a population.

Solution:

First, calculate Mean:

Mean = (62.25 + 60.36 + 64.28 + 61.24 + 66.24)/5

= 314.37/5

=62.874

Second, calculate Standard Deviation:

SD =  √( (1/(5 – 1)) * 〖(62.25- 62.874)〗^2 + 〖(60.36- 62.874)〗^2 + 〖(64.28- 62.874)〗^2 + 〖(61.24 – 62.874)〗^2 + 〖(66.24- 62.874)〗^2)

= √( (1/(4) * 〖(-0.624)〗^2 + 〖(-2.514)〗^2 + 〖(1.406)〗^2 + 〖(-1.634)〗^2 + 〖(3.366)〗^2)

= √ ( (1/(4) * (0.389376) + (6.320196) + (1.976836) + (2.669956) + (11.329956)

= √5.67158

SD = 2.38150

Finally, Calculate (CV):

CV = Standard Deviation/ Mean

Put the values into the coefficient of variation equation:

= 2.38150/62.874

CV = 0.037877

References:

From Wikipedia, the free encyclopedia – According to The Theory And Statistics, The Coefficient of Variation (CV)

By ADAM HAYES – Reviewed By PETER WESTFALL – Financial Analysis – What does the coefficient of variation tell you!