1, variance formula:

2. Standard variance formula (1):

3. Standard variance formula (2):

For example, their scores in five exams are as follows: x: 50, 100, 100, 60, 50, and the average e (x) = 72; Y: 73, 70, 75, 72, 70 Average E(Y)=72.

The average score is the same, but x is unstable and deviates greatly from the average. Variance describes the deviation between random variables and mathematical expectations. A single deviation is the average of the square deviation, that is, the variance without the influence of symbols, which is recorded as E(X): the direct calculation formula separates the discrete type from the continuous type.

A calculation formula is also derived: "variance is equal to the average of the sum of squares of deviations of each data and its arithmetic average". Among them, they are discrete and continuous calculation formulas respectively. It is called standard deviation or mean square deviation, and variance describes the degree of fluctuation.

The concept of variance:

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.

Variance is a measure of the difference between the source data and the expected value.