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

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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.

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.

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

C_{V} = Standard deviation/mean

**For sample**

**C _{V} = s/x̄**

- s = sample standard deviation
- x̄ = sample mean

**For population**

**C _{V} = σ/**

- σ = population standard deviation
- µ = population mean

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

- Check whether the data is sample data or population data.
- Calculate the total terms
- Calculate the mean or average value.
- Calculate the standard deviation of the particular data, this process is quite lengthy.
- 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 = **√** [****∑(x _{i} – x̄)/n-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

**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

**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

**C _{V} = s/x̄**

**C _{V}** = (26.26/21.2)

**C _{V}** =

- Hayes, A. (2022, October 20).
*Co-efficient of variation*. Investopedia. - Frost, J. (2020, October 26).
*Formulas of Coefficient of variation*. Statistics By Jim.

This report is generated by criticalvaluecalculator.com