标准差-方差一键在线计算器

标准差与方差计算公式

设数据为 $x_{1}, x_{2}, \dots, x_{n}$，平均值为 $\bar{x}$。下方计算器支持输入多组数据自动计算。

① 总体方差：$\sigma^{2} = \frac{\sum (x_{i} - \bar{x})^{2}}{n}$文章源自公式库网-https://www.gongshiku.com/html/202003/biaozhuncha-fangchayijianzaixianjisuanqi.html

② 总体标准差：$\sigma = \sqrt{ \frac{\sum (x_{i} - \bar{x})^{2}}{n} }$文章源自公式库网-https://www.gongshiku.com/html/202003/biaozhuncha-fangchayijianzaixianjisuanqi.html

③ 样本方差：$s^{2} = \frac{\sum (x_{i} - \bar{x})^{2}}{n-1}$文章源自公式库网-https://www.gongshiku.com/html/202003/biaozhuncha-fangchayijianzaixianjisuanqi.html

④ 样本标准差：$s = \sqrt{ \frac{\sum (x_{i} - \bar{x})^{2}}{n-1} }$文章源自公式库网-https://www.gongshiku.com/html/202003/biaozhuncha-fangchayijianzaixianjisuanqi.html

已知全部数据用总体公式；用样本估计整体时用样本公式（分母 $n-1$ 为贝塞尔校正，使估计无偏）。文章源自公式库网-https://www.gongshiku.com/html/202003/biaozhuncha-fangchayijianzaixianjisuanqi.html 文章源自公式库网-https://www.gongshiku.com/html/202003/biaozhuncha-fangchayijianzaixianjisuanqi.html文章源自公式库网-https://www.gongshiku.com/html/202003/biaozhuncha-fangchayijianzaixianjisuanqi.html