- 算数平均值:$$\overset-x=\frac1n\overset n{\underset{i=1}{\sum x_i}}$$
- 总体方差:$$\sigma^2=\frac{1}{n}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}$$
- 样本方差:$$s^2=\frac{1}{n-1}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}$$
- 标准差,标准偏差,标准方差,总体标准偏差:$$\sigma=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}}$$
- 样本标准偏差(物理实验常用):$$s=\sqrt{\frac{1}{n-1}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}}$$
- 算术平均值的标准偏差:$${{\sigma
}_{{\bar{x}}}}={{s}_{{\bar{x}}}}=\sqrt{\frac{1}{n(n-1)}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}}$$
- 正态分布曲线函数:$$f({{{x}_{i}}-\bar{x}})=\frac{1}{\sigma \sqrt{2\pi
}}{{e}^{-\frac{{{({{x}_{i}}-\bar{x})}^{2}}}{2{{\sigma }^{2}}}}}$$
- A类不确定度:$$U_A=t_{\nu(p)}\sigma_{\bar{x}}= t_{\nu(p)}
\sqrt{\frac{1}{n(n-1)}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}}$$
- 间接测量量不确定度传递公式:$$U_F=
\sqrt{{(\frac{\partial f}{\partial x})}^{2}{U_x}^{2}+{(\frac{\partial f}{\partial
y})}^{2}{U_y}^{2}+{(\frac{\partial
f}{\partial z})}^{2}{U_z}^{2}+...}$$
- 间接测量量的相对不确定度:$$\frac{U_F}{F}=
\sqrt{{(\frac{\partial {\rm
ln}f}{\partial x})}^{2}{U_x}^{2}+{(\frac{\partial {\rm
ln}f}{\partial y})}^{2}{U_y}^{2}+{(\frac{\partial {\rm
ln}f}{\partial z})}^{2}{U_z}^{2}+...}$$