3.4 Chapter 3 Formulas

Sample Mean: $\bar{x} = \frac{\sum x}{n}$	Population Mean: $\mu = \frac{\sum x}{N}$
Weighted Mean: $\bar{x} = \frac{\Sigma(x w)}{\sum w}$	Range = Max – Min
Sample Standard Deviation: s = $\sqrt{\frac{\sum(x-\bar{x})^{2}}{n-1}}$	Population Standard Deviation = σ
Sample Variance: s² = $\frac{\Sigma(x-\bar{x})^{2}}{n-1}$	Population Variance = σ²
Coefficient of Variation: CVar = $\left(\frac{s}{\bar{x}} \cdot 100\right) \%$	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: $\left(\left(1-\frac{1}{(z)^{2}}\right) \cdot 100\right) \%$	Outlier Upper Limit: Q₃ + (1.5·IQR)

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University, https://mostlyharmlessstat.wixsite.com/webpage), © Rachel Webb, licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.