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.
Let c be a constant, then D(C) = 0 (constant has no fluctuation); D(CX )=C2D(X) (constant square extraction, C is constant, X is random variable).
Syndrome: especially D(-X) = D(X), D(-2X) = 4D(X) (variance is not negative).
If x and y are independent of each other, then the first two items are only D(X) and D(Y), and the third item is expanded as follows.
When x and y are independent of each other, the third term is zero. In particular, the item-by-item summation of independent premises can be extended to finite terms.
Average variance formula: (n represents the number of this group of data, x 1, x2, x3...xn represents the specific value of this group of data).