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Discrete mathematics and continuous mathematics
If the average of x 1, x2, x3 ... xn is m, the variance formula can be expressed as:

Variance formula

Example 1 The five test results of two people are as follows:

X: 50, 100, 100, 60,50, with an average score of e (x) = 72;

Y: 73, 70, 75, 72, 70, with an average score of 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 variance, that is, the square of deviation, which eliminates the influence of symbols and is recorded as D(X):

The direct calculation formula separates the discrete type from the continuous type, specifically: here is a number.

Derive another calculation formula

Get: "variance is equal to the mean of the square minus the square of the mean".

Among them, they are discrete and continuous calculation formulas respectively. It is called standard deviation or mean square deviation, and variance describes fluctuation.