What is the coefficient of variation？

Implementing the new development concept is the only way for China’s development and growth in the new era, in which coordinated development plays an important role in China’s overall development. We must adhere to overall planning and comprehensive balance, and actively promote all-round development in various regions and fields. The coefficient of variation can be used to measure the level gap and its changing trend of economic and social development in different regions and fields in China, and provide statistical basis for formulating regional coordinated development strategies. The coefficient of variation plays an important role in analyzing the differences and heterogeneity of observed values.

I. What is the coefficient of variation?

Coefficient of variation is a relative statistic to measure the degree of variation of data, which is used to compare the degree of variation of two or more sample data with different average values, and is the ratio of standard deviation to its average value. It can also be called dispersion coefficient and standard deviation coefficient.

Second, what is the function of coefficient of variation?

The coefficient of variation is mainly used to compare the dispersion degree of different groups of data. When comparing the variation degree of two or more sample data, if the unit of measurement is the same as the average, the standard deviation can be directly used for comparison; If the measurement units or averages are different, the standard deviation cannot be used to compare the degree of variation, but the coefficient of variation (relative value) should be used for comparison. The coefficient of variation is a dimensionless quantity, which can eliminate the influence of data value or measurement unit on the comparison of dispersion degree of two or more sample data. The smaller the coefficient of variation, the smaller the degree of variation of sample data; Conversely, the greater the coefficient of variation, the greater the degree of variation of the sample data. When observing the variation trend of coefficient of variation, we should also analyze it together with the average value and standard deviation.

Third, how to calculate the coefficient of variation

The coefficient of variation is the ratio of the standard deviation of a set of sample data to its mean value, and the calculation formula is:

Among them,Is the coefficient of variation,Is the standard deviation,Is the mathematical expectation or average. Usually, the coefficient of variation is meaningful only when the average value is not zero, and it is generally applicable to the case where the average value is greater than zero; When the average value is close to zero, the value of the coefficient of variation tends to infinity, which must be carefully explained at this time.

Fourth, data interpretation

Taking the per capita GDP of different regions in China as an example, this paper analyzes the changes of regional economic development level differences in China. Table 1 shows the coefficient of variation of per capita GDP of 31 provinces in China from 2013 to 2022.

Table 1 Coefficient of variation of GDP per capita in 31 provinces (2013-2022)

Figure 1 Coefficient of variation of GDP per capita in 31 provinces (2013-2022)

Since the 18th National Congress of the Communist Party of China, the CPC Central Committee has put forward new development concepts, promoted high-quality development, and formulated a series of major strategies with overall significance, and China’s economic strength has achieved a historic leap. As shown in Figure 1, from 2013 to 2022, the average level of per capita GDP of 31 provinces in China has been rising, and the coefficient of variation and range ratio (measured by the ratio of maximum to minimum) have shown a trend of first expanding and then decreasing, indicating that the differences in development levels among regions fluctuated during the painful period of economic development, but the overall decreasing trend remained unchanged. The ratio of maximum value to minimum value decreased from 4.55 times in 2013 to 4.23 times in 2022, and the coefficient of variation decreased from 44.82% in 2013 to 42.73% in 2022. Generally speaking, in the past 10 years, the regional economic development gap in China has narrowed, and the overall regional economic development has become more coordinated.