3.4: Chapter 3 Formulas

Mostly Harmless Statistics · LibreTexts

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    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)

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