What is power of mean in math?

Answer 1

The power mean, also known as the generalized mean, is a family of averages that includes various types of means as special cases. It is defined for a set of positive numbers and is determined by a parameter ( p ), where the power mean ( M_p ) is given by the formula ( M_p = \left( \frac{1}{n} \sum_{i=1}^{n} x_i^p \right)^{1/p} ) for ( p \neq 0 ). When ( p = 0 ), it converges to the geometric mean, and as ( p ) approaches negative infinity, it approaches the minimum value of the dataset, while approaching positive infinity yields the maximum. The power mean reflects how the average changes with different values of ( p ), providing insights into data distribution.