What does the coefficient of variation mean?

Coefficient of variation, also known as deviation coefficient, is a normalized measure of deviation degree of probability distribution. The coefficient of variation is defined only when the average value is not zero, and it is generally applicable when the average value is greater than zero. Coefficient of variation is also called standard deviation rate or unit risk.

When it is necessary to compare the dispersion of two groups of data, if the measurement scales of the two groups of data are too different, or the data dimensions are different, it is not appropriate to measure them directly with standard deviation. The influence of measurement scale and dimension should be eliminated, and the coefficient of variation can eliminate these influences. It is the ratio of the standard deviation to its mean. CV (the ratio of standard deviation to average value is called coefficient of variation, and it is recorded as C.V), although there is no dimension, it is also standardized according to its average value, so that an objective comparison can be made. So it can be considered that the coefficient of variation, like range, standard deviation and variance, is an absolute value reflecting the degree of data dispersion. Its data size is not only affected by the discrete degree of variable values, but also by the average horizontal size of variable values.

What does the greater the coefficient of variation mean?

The greater the coefficient of variation, the greater the degree of variation based on the average. The coefficient of variation reflects the discrete trend, and the greater the coefficient of variation, the greater the degree of variation of the response based on the mean.

Calculation formula of coefficient of variation

Coefficient of variation c v = (standard deviation SD/ mean) × 100%.

In statistical analysis of data, if the coefficient of variation is greater than 15%, it should be considered that the data may be abnormal and should be excluded.

Advantages of coefficient of variation

Compared with the standard deviation, the coefficient of variation does not need the average value of reference data. Coefficient of variation is a dimensionless quantity, so when comparing two groups of data with different dimensions or different mean values, coefficient of variation should be used instead of standard deviation as a reference for comparison.

Disadvantages of coefficient of variation

When the average value is close to 0, small disturbance will also have a great influence on the coefficient of variation, resulting in insufficient accuracy. The coefficient of variation can not develop a tool similar to the confidence interval of the mean.