3.4 Chapter 3 Formulas

Sample Mean: $\bar{x} = \frac{\sum x}{n}$	Population Mean: $μ = \frac{\sum x}{N}$
Weighted Mean: $\bar{x} = \frac{Σ (x w)}{\sum w}$	Range = Max – Min
Sample Standard Deviation: s = $\sqrt{\frac{\sum (x - \bar{x})^{2}}{n - 1}}$	Population Standard Deviation = σ
Sample Variance: s² = $\frac{Σ (x - \bar{x})^{2}}{n - 1}$	Population Variance = σ²
Coefficient of Variation: CVar = $(\frac{s}{\bar{x}} \cdot 100)$	Z-Score: z = $\frac{x - \bar{x}}{s}$
Percentile Index: i = $\frac{(n + 1) \cdot p}{100}$	Interquartile Range: IQR = Q₃ – Q₁
Empirical Rule: z = 1, 2, 3 $\Rightarrow$ 68%, 95%, 99.7%	Outlier Lower Limit: Q₁ – (1.5·IQR)
Chebyshev’s Inequality: $((1 - \frac{1}{(z)^{2}}) \cdot 100)$	Outlier Upper Limit: Q₃ + (1.5·IQR)

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University), hosted on LibreTexts (stats.libretexts.org) and licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.