Coefficient of Variation
Comparison of two data in terms of measures of central tendencies and dispersions in some cases will not be meaningful, because the variables in the data may not have same units of measurement.
For example consider the two data
Here we cannot compare the standard deviations 1. 5kg and ₹21.60. For comparing two or more data for corresponding changes the relative measure of standard deviation, called “Coefficient of variation” is used.
Coefficient of variation of a data is obtained by dividing the standard deviation by the arithmetic mean. It is usually expressed in terms of percentage. This concept is suggested by one of the most prominent Statistician Karl Pearson.
Thus, coefficient of variation of first data (C.V1) = σ1/x1 ×100%
and coefficient of variation of second data (C.V2) = σ2/ x2 × 100%
The data with lesser coefficient of variation is more consistent or stable than the other data. Consider the two data
If we compare the mean and standard deviation of the two data, we think that the two datas are entirely different. But mean and standard deviation of B are 60% of that of A. Because of the smaller mean the smaller standard deviation led to the misinterpretation.
To compare the dispersion of two data, coefficient of variation = σ/x ×100%
The coefficient of variation of A = 191. 5/700 ×100% = 27. 4%
The coefficient of variation of B = 114. 9/420 ×100% = 27. 4%
Thus the two data have equal coefficient of variation. Since the data have equal coefficient of variation values, we can conclude that one data depends on the other. But the data values of B are exactly 60% of the corresponding data values of A. So they are very much related. Thus, we get a confusing situation.
To get clear picture of the given data, we can find their coefficient of variation. This is why we need coefficient of variation.
The mean of a data is 25.6 and its coefficient of variation is 18.75. Find the standard deviation.
Mean = 25. 6 , Coefficient of variation, C.V. = 18.75
Coefficient of variation, C.V. = σ/ ×100%
The following table gives the values of mean and variance of heights and weights of the 10th standard students of a school.
Which is more varying than the other?
For comparing two data, first we have to find their coefficient of variations
Mean 1= 155cm, variance σ12 = 72. 25 cm2
Therefore standard deviation σ1 = 8. 5
Coefficient of variation
Mean 2 = 46.50 kg, Variance σ22 = 28.09 kg2
Standard deviation σ2 = 5. 3kg
Coefficient of variation
= 11. 40% (for weights)
C .V1 = 5.48% and C .V2 = 11.40%
Since C .V2 > C .V1 , the weight of the students is more varying than the height.
The consumption of number of guava and orange on a particular week by a family are given below.
Which fruit is consistently consumed by the family?
First we find the coefficient of variation for guavas and oranges separately.
C .V1 = 23.54% , C .V2 = 65.50% Since, C .V1<C .V2 , we can conclude that the consumption of guavas is more consistent than oranges.