Fundamentals of Statistics: Tables and Formulas

This cheat sheet provides a comprehensive summary of key tables and formulas from Fundamentals of Statistics, covering various statistical concepts and calculations.

Core Principles

Understanding statistical formulas is crucial for data analysis and interpretation.
Different statistical distributions (Normal, t, Chi-square) are used for different types of data and analyses.
Hypothesis testing involves formulating null and alternative hypotheses and using sample data to assess their plausibility.
Confidence intervals provide a range of plausible values for population parameters.
Measures of central tendency (mean, median, mode) describe the center of a dataset.
Measures of dispersion (range, standard deviation, variance, IQR) describe the spread of a dataset.

Formulas

$ \sigma = \sqrt{\frac{\sum(x_i - \mu)^2}{N}} $
$ s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}} $
$ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} $
$ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} $
$ \chi^2 = \frac{(n-1)s^2}{\sigma^2} $
$ r = \frac{\sum \left( \frac{x_i - \bar{x}}{s_x} \right) \left( \frac{y_i - \bar{y}}{s_y} \right)}{n-1} $
$ P(E \text{ or } F) = P(E) + P(F) $
$ P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F) $
$ P(E^c) = 1 - P(E) $
$ P(E \text{ and } F) = P(E) \cdot P(F) $