| - | 总体(Population) | 抽样(Sample) |
|---|---|---|
| 均值(mean) | μ = ∑ i = 1 N x i N \mu = \frac{\sum_{i=1}^{N}{x_i}}{N} μ=N∑i=1Nxi | x ‾ = ∑ i = 1 n x i n \overline{x}=\frac{\sum_{i=1}^{n}{x_i}}{n} x=n∑i=1nxi |
| 方差(variance) | σ 2 = ∑ i = 1 N ( x i − μ ) 2 N = ∑ i = 1 N x i 2 N − μ 2 \sigma^{2} = \frac{\sum_{i=1}^{N}({x_i-\mu})^2}{N}=\frac{\sum_{i=1}^{N}{x_{i}^{2}}}{N}-\mu^2 σ2=N∑i=1N(xi−μ)2=N∑i=1Nxi2−μ2 | S n 2 = ∑ i = 1 n ( x i − x ‾ ) 2 n S_{n}^{2} = \frac{\sum_{i=1}^{n}({x_i-\overline{x}})^2}{n} Sn2=n∑i=1n(xi−x)2 U n b a i s e d S a m p l e V a r i a n c e : S n 2 = ∑ i = 1 n ( x i − x ‾ ) 2 n − 1 Unbaised\ Sample\ Variance: S_{n}^{2} = \frac{\sum_{i=1}^{n}({x_i-\overline{x}})^2}{n-1} Unbaised Sample Variance:Sn2=n−1∑i=1n(xi−x)2 |
| 标准差 (standard deviation) | σ = σ 2 = ∑ i = 1 N ( x i − μ ) 2 N \sigma=\sqrt{\sigma^2}=\sqrt{\frac{\sum_{i=1}^{N}({x_i-\mu})^2}{N}} σ=σ2 =N∑i=1N(xi−μ)2 | S = S 2 = ∑ i = 1 n ( x i − x ‾ ) 2 n − 1 S=\sqrt{S^2}=\sqrt{\frac{\sum_{i=1}^{n}({x_i-\overline{x}})^2}{n-1}} S=S2 =n−1∑i=1n(xi−x)2 |
无偏样本方差（Unbaised Sample Variance）
用样本估计总体方差通常会导致数值偏低，无偏样本方差中分母减小使样本方差的值变大
标准差
方差的单位比原始数据多了一个平方，通过开方使这个衡量离散程度的数值与原始数据统一量纲，所以标准差的使用更为广泛。
