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The coefficient of variation is defined as
\(C.V = \frac{\sigma}{\overline x} \times 100 \%\)
Where \(\sigma\) is the standard deviation and \(\overline x\) is the mean of the given data.
The concept of coefficient of variation is proposed by the statistician Karl Pearson. He suggested that the measure of \(C.V\) is obtained by dividing the standard deviation by the arithmetic mean, and is expressed in terms of percentage.
The concept of coefficient of variation is useful in comparing the values of two or more data because the variables in the data may not have the same units of measurement.
If the data having lesser \(C.V\), then it is said to be more consistent or stable than the other.
Let us consider an example to understand the concept.
Example:
The height and marks of the students in a classroom are given below:
| Mean(\(\overline x\)) | Standard deviation(\(\sigma\)) | |
| Height | \(154 \ cm\) | \(96 \ cm\) |
| Marks | \(64\) | \(56\) |
Which is more consistent than the other?
Solution:
Let us compare the \(C.V\) of two data using the formula, \(C.V = \frac{\sigma}{\overline x} \times 100 \%\)
The coefficient of variation of heights, \(C.V_1 = \frac{96}{154} \times 100\% = 62.34\%\)
The coefficient of variation of marks, \(C.V_2 = \frac{56}{64} \times 100\% = 87.5\%\)
Since \(C.V_1 < C.V_2\), the height of the students is more consistent than the marks of the students.
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