再论统计平均数大小关系的证明及其推广

On the Proving of the Magnitude of Averages and It's Generalization

调和平均数、几何平均数、算术平均数之间存在着单调上升的关系,并且可以将其归为“幂平均数”家族。文章利用不等式方法证明了幂平均数M(K)关于K在整个实数集上是单调上升的,并在此基础上将统计平均数加以推广。

There is a monotonous increasing relationship between harmonic mean, geometric mean and arithmetic mean. We can classify them to the family of power mean. This paper shows that the power mean is monotonic increasing about K on the set of real number using the inequation. Based on this the authors expand the concept of average.