What is a weighted inequality?

Weighted inequality is a mathematical term published in 1993.

People's Education Press High School Mathematics Mean Inequality Grade Two, that is, Grade Eight.

As an important formula in mathematics. The content of the formula is Hn≤Gn≤An≤Qn, that is, the harmonic average does not exceed the geometric average, the geometric average does not exceed the arithmetic average, and the arithmetic average does not exceed the square average.

Harmonic average is a kind of average. But statistical harmonic mean is different from mathematical harmonic mean. In mathematics, harmonic average and arithmetic average 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. But the statistical weighted harmonic average is different. It is a deformation of weighted arithmetic average, attached to arithmetic average, and the calculation result is completely equal to weighted arithmetic average.

It is mainly used to solve the problem that only the variable value of each group and the corresponding total number of symbols are needed and the average value is required when the overall unit number (frequency) cannot be mastered.

General form of weighted inequality:

If both a and b are real numbers, then a 2+b 2 ≥ 2ab, and the equal sign holds if and only if a = b.

Proved as follows:

∵(a-b)^2≥0；

∴a^2+b^2-2ab≥0；

∴a^2+b^2≥2ab。