3.4: Chapter 3 Formulas
- Page ID
- 24031
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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) |