What are the formulas for calculating differences?
Variance is a measure of dispersion when probability theory and statistical variance measure random variables or a set of data. Variance describes the deviation between random variables and mathematical expectations.
The formula of variance is S2 = {(x1-m) 2+(x2-m) 2+(x3-m) 2+…+(xn-m) 2}/n, where m is the average value of data, n is the number of data and S2 is the variance. Text is expressed as an average, and its variance is equal to the sum of squares of the deviation of each data from 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.
When the data distribution is scattered, the sum of squares of the difference 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.
Extended reading: What is the standard deviation formula?
The standard deviation formula is a mathematical formula. Standard deviation is also called standard deviation or experimental standard deviation, and the formula is as follows:
The standard deviation of the portfolio formed by two securities = (w12σ12+w22σ 22+2w1w2ρ 1 2σ 1σ2), when the correlation coefficient ρ1,2 = When the correlation coefficient ρ 1, 2 =- 1, the standard deviation of the portfolio σp = w 1σ 1-w 2σ2.
Sample standard deviation = arithmetic square root of variance = s = sqrt ((x1-x) 2+(x2-x) 2+... (xn-x) 2)/(n-1))
Population standard deviation = σ = sqrt ((x1-x) 2+(x2-x) 2+... (xn-x) 2)/n)
Because the variance is the square of the data, which is too different from the detected value itself, it is difficult for people to measure it intuitively, so we often use the root sign of the variance to convert it back, that is, the standard deviation (SD).
In statistics, the average difference of samples is mostly divided by the degree of freedom (n- 1), which refers to the degree to which samples can be freely selected. When there is only one left, it can no longer be free, so the degree of freedom is (n- 1).
The standard deviation, also called mean square deviation in Chinese environment, is the square root of the arithmetic mean value deviating from the mean square, and is expressed by σ. It is most commonly used in probability statistics as a measure of statistical distribution. The standard deviation is the arithmetic square root of variance. The standard deviation can reflect the degree of dispersion of the data set. The standard deviation of two sets of data with the same average value may be different.
How to find variance
The variance is equal to the average of the sum of squares of deviation between each data and its arithmetic mean.
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).
In statistical description, variance is used to calculate the difference between each variable (observed value) and the population mean. In order to avoid the phenomenon that the average sum deviation is zero and the average square sum deviation is affected by the sample size, the average deviation of the average square sum is used to describe the variation degree of variables.