参考网址:
http://baike.baidu.com/view/441784.htm
调和平均数:
${{H}_{n}}=frac{n}{sumlimits_{i=1}^{n}{frac{1}{{{x}_{i}}}}}=frac{n}{frac{1}{{{x}_{1}}}+frac{1}{{{x}_{2}}}+cdots +frac{1}{{{x}_{n}}}}$
几何平均数:
${{G}_{n}}=sqrt[n]{prodlimits_{i=1}^{n}{{{x}_{i}}}}=sqrt[n]{{{x}_{1}}{{x}_{2}}cdots {{x}_{n}}}$
算数平均数:
${{A}_{n}}=frac{sumlimits_{i=1}^{n}{{{x}_{i}}}}{n}=frac{{{x}_{1}}+{{x}_{2}}+cdots +{{x}_{n}}}{n}$
平方平均数:
${{Q}_{n}}=sqrt{frac{sumlimits_{i=1}^{n}{x_{i}^{2}}}{n}}=sqrt{frac{x_{1}^{2}+x_{2}^{2}+cdots +x_{n}^{2}}{n}}$
关系为:
${{H}_{n}}le {{G}_{n}}le {{A}_{n}}le {{Q}_{n}}$
简记为“调几算方”
当为两个数时:
$frac{2}{frac{1}{a}+frac{1}{b}}le sqrt{ab}le frac{a+b}{2}le sqrt{frac{{{a}^{2}}+{{b}^{2}}}{2}}$