Statistic

A Statistic is a scalar feature extracted from a Sample that represents it in some way. As opposed to Parameter.

$$T:X_{\mathrm{1..}n}\in \text{RV}\to \mathbb{R}$$

Sample Statistic

• Sample Mean $\overline{X}=\frac{\sum X}{n}$
• Sample Median: Middle entry in Sample
• Sample Mode: Most occurences in Sample
• Sample Variance $S^2=\frac{\sum (X-\overline{X}{)}^2}{n-1}$
• Sample Standard Deviation $S$
• Sample Proportion $\hat{p}=\frac{x}{n}$

Centrality Features

• Sample Mean, Median, Mode. Median is best.

Spread Features

• Sample Range $\max X-\min X$
• Sample Variance, Standard Deviation
• Percentile
• Quartile, Inter Quartile Range

Grouped Features

$$\overline{X}-\frac{1}{n}\sum _{j=1}^p{f}_j{x}_j{S}^2=\frac{1}{n-1}\left(\sum _{j=1}^p{f}_j{x}_j^2-n{x}^2\right)$$