“Coefficient of Variation” (CV) is suitable for comparing the dispersion (Variation) of two groups of data collected with different measurement units. In this statistical index, the ratio of dispersion to a central criterion is measured. In fact, this index shows how much the standard deviation of the values ​​changes per unit of change in the average. The larger this index is, the greater the dispersion of the data.

Coefficient of Variation

To compare the dispersion of two groups of data collected with different measurement units, it is not correct to use standard deviation, variance, average absolute value of deviations from the mean, interquartile range and range of changes. Because we know that these sizes change as the data scale changes. To solve this problem, the coefficient of variation (CV) is used because it is a measure that shows the relative amount of dispersion.

Coefficient of Variation Calculation

To calculate it, it is enough to obtain the ratio of the standard deviation to the mean. Since the numerator and denominator of this fraction are the same, the result of the fraction is a unitless value that can also be expressed as a percentage. Therefore, it may be said for a data series that the coefficient of variation is 15%. This means that the standard deviation is 15% of the mean. The calculation of the coefficient of variation for the statistical population is as follows:

$$ CV = \frac{\sigma}{\mu}$$

And for sample, coefficient variation computer base on sample statistics:

$$ CV = \frac{s}{\bar{x} }$$

If we want to eliminate the effect of the difficulty or simplicity of the test (which lies in the average) and measure the dispersion according to the average of each class, it is enough to calculate the change coefficient for each one. A school with a lower coefficient of variation has uniform and homogeneous scores. In this way, the coefficient of variation for “Teacher A” is equal to 12.47% and for “Teacher B” is 30.55%. If it is assumed that these classes are a sample of the classes of these two teachers, the sample variation coefficient for “Teacher A” is equal to 13.33% and for “Teacher B” 32.66%. Note: If the data is multiplied or divided by a fixed value, the coefficient of variation will not change for them, so changing the scale in the data has no effect on the coefficient of variation. It should be noted that to calculate the coefficient of variation, it is necessary to have quantitative and relative data. Calculating coefficient of variation for interval data is not correct.