If the average value of x 1, x2, x3 ... xn is m, the variance S2 =1/n [(x1-m) 2+(x2-m) 2+...+(xn-m) 2.

Variance is the average deviation from square, which is called standard deviation or mean square deviation. Variance describes the degree of fluctuation.

Variance is a measure of dispersion when probability theory and statistical variance measure random variables or a set of data. Variance in probability theory is used to measure the deviation between random variables and their mathematical expectations (that is, the mean value).

The variance (sample variance) in statistics is the average value of the square of the difference between each sample value and the average value of all sample values. In many practical problems, it is of great significance to study variance or deviation.

Statistical significance of variance

When the data distribution is scattered (that is, the data fluctuates greatly around the average value), the sum of squares of differences between each data and the average value is large, and the variance is large; When the data distribution is concentrated, the sum of squares of the differences between each data and the average value is very small. Therefore, the greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation.

The average value of the sum of squares of the difference between the data in the sample and the average value of the sample is called sample variance; The arithmetic square root of sample variance is called sample standard deviation. Sample variance and sample standard deviation are both measures of sample fluctuation. The greater the sample variance or standard deviation, the greater the fluctuation of sample data.