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Coefficient of Variation Calculator



How to use Coefficient of Variation Calculator?

  • Input the comma-separated values.
  • Select the data type “sample” or “population”
  • Click on the calculate button.




The coefficient of variation calculates the CV of a sample or a population data set and gives its step-by-step solution. Firstly, it calculates the average value (mean) and the standard deviation of the entered data, and also provides the steps of the calculation.


What is the coefficient of variation?


The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean. It is a statistical measure of the dispersion of data points in a data series around the mean.


Formulas of CV


The general formula for the coefficient of variation is as follows:

CV = Standard deviation/mean


For sample


CV = s/x̄

  • s = sample standard deviation
  • x̄ = sample mean

For population


CV = σ/µ

  • σ = population standard deviation
  • µ = population mean

Steps to calculate the coefficient of variation.


To calculate the coefficient of variation of a sample or a population data manually, you just need to follow the below steps:

  1. Check whether the data is sample data or population data.
  2. Calculate the total terms
  3. Calculate the mean or average value.
  4. Calculate the standard deviation of the particular data, this process is quite lengthy.
  5. Divide the SD by the average value to get the final result.

In the following examples, the procedure of calculating the coefficient of variation is completely described with steps.


Example


Calculate the CV of sample data 9, 3, 5, 8, 2, 64, 75, 23, 10, 13

Solution:

Step 1: Calculate the total terms

Total terms = n = 10

Step 2: Calculate the sample mean.

Mean = (9 + 3 + 5 + 8 + 2 + 64 + 75 + 23 + 10 + 13) / 10

Mean = 212 / 10

Mean = 21.2

Step 3: Calculate the standard deviation.

S = [∑(xi – x̄)/n-1]

  1. Calculating the deviation scores

Deviations = 9 – 21.2, 3 – 21.2, 5 – 21.2, 8 – 21.2, 2 – 21.2, 64 – 21.2, 75 – 21.2, 23 – 21.2, 10 – 21.2, 13 – 21.2

Deviations = -12.2, -18.2, -16.2, -13.2, -19.2, 42.8, 53.8, 1.8, -11.2, -8.2

  1. Calculating the squared deviations

Squared deviations = (-12.2)2, (-18.2)2, (-16.2)2, (-13.2)2, (-19.2)2, (42.8)2, (53.8)2, (1.8)2, (-11.2)2, (-8.2)2

Squared deviations = 148.84, 331.24, 262.44, 174.24, 368.64, 1831.84, 2894.44, 3.24, 125.44, 67.24

  1. Calculating the sum of squares

Sum of squares = 148.84 + 331.24 + 262.44 + 174.24 + 368.64 + 1831.84 + 2894.44 + 3.24 + 125.44 + 67.24

Sum of squares = 6207.6

Putting all values in the formula

S = √(6207.6/10-1)

S = √(6207.6/9)

S = √(689.733)

S = 26.26

Step 5: Calculating the final result

CV = s/x̄

CV = (26.26/21.2)

CV = 1.238


References