Calculation formula of standard deviation

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:

Standard deviation calculation formula: standard deviation σ = square root of variance.

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).

Note: X in the above two standard deviation formulas is the arithmetic average of a group of numbers (n data). When all numbers (number n) appear in probability (the sum of the corresponding n probability values is 1), then X is the mathematical expectation of this group of numbers.

What is the standard deviation?

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 groups of data with the same average value may be different; The reason is that its size depends not only on the deviation of the standard value, but also on the average level of the series.