Arithmetic average refers to the sum of all data in a set of data divided by the number of data. It is an indicator reflecting the trend of data concentration.
The formula is:
Average value =(a 1+a2+…+an)/n
For example:
The average of 3, 4 and 5 is:
(3+4+5)/3=4
geometric mean
geometric mean
The nth arithmetic root of product of n positive real numbers. Given n positive real numbers a 1, a2, ... a2, ... an, its geometric average is (a1* a2 * ... * an) (1/n). In particular, the geometric average of two positive numbers A and B is c = (A * B). The geometric average of an is not greater than the arithmetic average of n numbers, that is, (a1* a2 * ... * an) (1/n) ≤ (a1+a2+...+an)/n. This inequality often plays a special role in studying other inequalities or extreme values.
Harmonic average
The harmonic average is an average. But statistical harmonic mean is different from mathematical harmonic mean. In mathematics, harmonic mean and arithmetic mean are independent and self-sufficient. The calculation results are different, and the former is always smaller than the latter. Therefore, the mathematical harmonic average is defined as the reciprocal of the average of reciprocal values. However, the statistical weighted harmonic mean is different. Is the deformation of the weighted arithmetic mean. Attached to the arithmetic average, the system cannot be established independently, and the calculation result is completely equal to the weighted arithmetic average. It is mainly used to solve the problem that the average value is required only by the variable value of each group and the corresponding total number of symbols when the overall unit number (frequency) cannot be mastered.
The formula is: 2/( 1/a+ 1/b)
weighted average
If n numbers x 1, x2, ... xn are w 1, w2, ... wn respectively, then the weighted average of these n numbers is (x1w1+x2w2+...+xnwn)/(w/kloc-0). ...
Note: 1) The English word "weight" means the importance of data, that is, the power of data reflects the relative "importance" of data.
2) Arithmetic average is a special case of weighted average, that is, when the weights of each item are equal, the weighted average is arithmetic average.
mean square value
The formula is: m = [(a 2+b 2+c 2+… n 2)/n] 1/2.