Standard deviation of sample = arithmetic square root of variance = s = sqrt ((x1-x) 2+(x2-x) 2+... (xn-x) 2)/n). The standard deviation formula is a mathematical formula. Standard deviation is also called standard deviation, or experimental standard deviation.

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.

Commonly used statistical formulas

The concept and calculation formula of variance, 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.

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: sample standard deviation = square root of arithmetic variance = s = sqrt ((x1-x) 2+(x2-x) 2+... (xn-x) 2)/n) population standard deviation = σ = sqrt ().

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.

Laplace formula

Laplace formula was put forward by German statistician Laspeyres in 1864. Also known as Laplace index formula and Laplace index formula, referred to as "Laplace" or "L", including Laplace price index formula and Laplace volume index formula.

Inferior formula

X=xmax-xmin(xmax is the largest and xmin is the smallest), and the distance formula is the most direct and simple method to calculate the distance. There are moving amplitude, sum of squares of deviation from the average, etc.

Relevant formulas of probability theory

The total probability formula is an important formula in probability theory, which transforms the probability solution of a complex event A into the probability summation of a simple event in different situations.

Variance formula

Variance formula is a mathematical formula and an important formula in mathematical statistics. It is applied to all kinds of things in life. The smaller the variance, the more stable the data set, and the larger the variance, the more unstable the data set.

Standard deviation can be used to measure uncertainty. For example, in physical science, when repeated measurements are made, the standard deviation of the set of measured values represents the accuracy of these measurements.

When determining whether the measured value conforms to the predicted value, the standard deviation of the measured value plays a decisive role: if the measured average value is too far from the predicted value (compared with the standard deviation value at the same time), it is considered that the measured value is contradictory to the predicted value. Very easy to understand. Therefore, if all the measured values fall outside a certain numerical range, it can be inferred that the predicted values are unreasonable.

Standard deviation is applied to investment and can be used as an index to measure the stability of return. The greater the standard difference, the higher the income, which means that the income is far from the past average, that is, the more unstable the income, the higher the risk. On the contrary, the smaller the standard deviation, the more stable the income and the lower the risk.