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