A First Course in Statistics, 12th Edition

Selected Formulas

Chapter 2

$\text{Relative Frequency}=\left(\text{frequency}\right)/n$

$\overline{x}={\displaystyle \frac{\Sigma x}{n}}$

$s^2={\displaystyle \frac{\Sigma {\left(x-\overline{x}\right)}^2}{n-1}}={\displaystyle \frac{\Sigma x^2-{\displaystyle \frac{{\left(\Sigma x\right)}^2}{n}}}{n-1}}$

$s=\sqrt{s^2}$

$z={\displaystyle \frac{x-\mu }{\sigma }}={\displaystyle \frac{x-\overline{x}}{s}}$

$\text{Chebyshev}=\text{At least}\left(1-{\displaystyle \frac{1}{k^2}}\right)100\%$

$\text{IQR}\text{=}{Q}_{\text{U}}-Q_{\text{L}}$

Chapter 3

$P\left(A^c\right)=1-P\left(A\right)$

$\begin{array}{rrr}\hfill P\left(A\cup B\right)& \hfill =& P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\hfill \\ \hfill & \hfill =& P\left(A\right)+P\left(B\right)\text{if }A\text{and}B\text{mutually}\text{exclusive}\hfill \end{array}$

$\begin{array}{rrr}\hfill P\left(A\cap B\right)& \hfill =& P\left(A|B\right)\cdot P\left(B\right)=P\left(B|A\right)\cdot P\left(A\right)\hfill \\ \hfill & \hfill =& P\left(A\right)\cdot P\left(B\right)\text{if }A\text{and}B\text{independent}\hfill \end{array}$

$P\left(A|B\right)={\displaystyle \frac{P\left(A\cap B\right)}{P\left(B\right)}}$

$\left(\begin{array}{c}N\\ n\end{array}\right)={\displaystyle \frac{N!}{n!\left(N-n\right)!}}$

Chapter 4

Key Formulas

Random Variable	Prob. Dist’n	Mean	Variance
General Discrete:	Table, formula, or graph for ...