Coefficient of Variation Calculator

The coefficient of variation calculator 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:

C_V = Standard deviation/mean

For sample

C_V = s/x̄

• s = sample standard deviation
• x̄ = sample mean

For population

C_V = σ/µ

• σ = population standard deviation
• µ = population mean

How 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 = √ [∑(x_i – 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

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

3. 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 = 1.238

Frequently Asked Questions

1. What is a good coefficient of variation?

A good coefficient of variation depends on what you’re comparing and looking at. In general,

“A lower CV is usually better because it indicates that the data values are less spread out relative to the mean”.

For example, a low CV (0–20%) suggests that data points are close to the mean, which can indicate stability and consistency.

2. What is a high coefficient of variation?

 A coefficient of Variation greater than or above 1 is considered high. This indicates that the data set has a high level of variability relative to the mean.

3. When to use the coefficient of variation?

We use the coefficient of variation when we want to compare variability between two or more data sets:

1. For Groups that have means of very different magnitudes
2. For Characteristics that use different units of measurement.

References

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