average

算术平均：

$$average = \frac{1}{4}(a+b+c+d)$$

几何平均：

$$average = \sqrt[4](abcd)$$

调和平均：更重视较小值

$$\begin{aligned} average = \frac{2ab}{a+b} \\ \frac{1}{average} = \frac{1}{2}(\frac{1}{a} + \frac{1}{b}) \end{aligned}$$

加权调和平均：

$$\begin{aligned} average_\beta = \frac{(1+\beta^2)\times a \times b}{(\beta^2 \times a) + b} \\ \frac{1}{average_\beta} = \frac{1}{1+\beta^2}(\frac{1}{a} + \frac{\beta^2}{b}) \end{aligned}$$

$\beta < 1$：更注重a $\beta = 1$：相当于调和平均 $\beta > 1$：更注重b