The variance and standard deviation are a direct function of the size of the results in the sample, and the coefficient of variation is expressed in relation to the size of the arithmetic mean of the sample.
The coefficient of variation allows us to compare the variability from two different samples, in which different units of measurement were used or have different arithmetic means.
The coefficient of variation is the ratio of the standard deviation to the arithmetic mean. If the population parameters are known, s can be replaced by σ, and 
with μ.
The formula for calculating the coefficient of variation is
The formula shows that the variability of a given variable is greater the higher the value of the standard deviation.
Unlike the variance and standard deviation, the coefficient of variation is not expressed in units of measure.
Sometimes the value of the coefficient of variation is multiplied by 100 to express the variability in percentages.
Example: Coefficient of variation of height of girls in 52 class
In the example of the height of girls (in cm) in 52 class of the "X" primary school, which we used as an example of calculating the arithmetic mean, median, mode, rank, variance and standard deviation, we obtained the following data: 140, 141, 138, 140, 122, 160, 154, 132, 148, 135, 140. We calculated that the arithmetic mean value is 140.91 cm, and the standard deviation is 10.34. CVA= 10.34/140.91=0.07.
Let's assume that we measured the height of a boy in the same class and got =152.36cm, with a standard deviation s=7.25. The coefficient of variation would be CVB=7.25/152.36=0.05.
By comparing the coefficients of variation, we can see that the variability in height is 1.4 times greater in girls (CVA/ CVB=0.07/0.05=1.4). Expressed as a percentage, the variability in girls' height is 40% (1.4*100%-100%=40%) greater than the variability in boys' height.
It can be said that the variability in girls' height is almost 1.5 times greater than the variability in boys' height.
coefficient of variation
Comments (0)