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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:
CV = Standard deviation/mean
For sample
CV = s/x̄
For population
CV = σ/µ
To calculate the coefficient of variation of a sample or a population data manually, you just need to follow the below steps:
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]
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
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
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
This report is generated by criticalvaluecalculator.com
Criticalvaluecalculator.com is a free online service for students, researchers, and statisticians to find the critical values of t and z for right-tailed, left tailed, and two-tailed probability.
