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.

Extended data

Variance is the average of the square of the difference between the actual value and the expected value, while standard deviation is the arithmetic square root of variance. ? [5] In actual calculation, we use the following formula to calculate the variance.

Variance is the average of the sum of squares of the difference between each data and the average, that is

, where x represents the average number of samples, n represents the number of samples, xi represents individuals, and s 2 represents variance.

When in use

As an estimate of the variance of sample X, it is found that its mathematical expectation is not the variance of X, but the variance of X..

Second,

The mathematical expectation of X is the variance of X, and the variance of X is unbiased, so we always use it.

To estimate the variance of x, which is called "sample variance"

Variance is the degree of deviation from the center, which is used to measure the fluctuation of a batch of data (that is, the degree of deviation from the average value of this batch of data). It is called the variance of this group of data and is recorded as S2. In the case of the same sample size, the greater the variance, the greater the data fluctuation and the more unstable it is.

The formula can be further deduced as:

. Where x is the data in this set of data and n is an integer greater than 0.

Reference variance _ Baidu Encyclopedia