CHAPTER 22 KEY FORMULAS AND EQUATIONS

Mean	$\bar{x} = \frac{x_{1} f_{1} + x_{2} f_{2} + \dots + x_{n} f_{n}}{f_{1} + f_{2} + \dots + f_{n}}$ $\bar{x} = \frac{x_{1} f_{1} + x_{2} f_{2} + \dots + x_{n} f_{n}}{f_{1} + f_{2} + \dots + f_{n}}$ (22.1)
Standard deviation	$s = \sqrt{\frac{\sum {(x - \bar{x})}^{2}}{n - 1}}$ $s = \sqrt{\frac{\sum {(x - \bar{x})}^{2}}{n - 1}}$ (22.2) $s = \sqrt{\frac{n (\sum x^{2}) - {(\sum x)}^{2}}{n (n - 1)}}$ $s = \sqrt{\frac{n (\sum x^{2}) - {(\sum x)}^{2}}{n (n - 1)}}$ (22.3)
Normal distribution	$y = \frac{e^{- {(x - μ)}^{2} / 2 σ^{2}}}{σ \sqrt{2 π}}$ $y = \frac{e^{- {(x - μ)}^{2} / 2 σ^{2}}}{σ \sqrt{2 π}}$ (22.4)
Standard (`z`) score	$z = \frac{x - μ}{σ}$ $z = \frac{x - μ}{σ}$ (22.5)
Standard error of $\bar{x}$ $\bar{x}$	$σ_{\bar{x}} = \frac{σ}{\sqrt{n}}$ $σ_{\bar{x}} = \frac{σ}{\sqrt{n}}$ (22.6)
Least-squares lines	$y = m x + b$ $y = m x + b$ (22.7) $m = \frac{n \sum x y - (\sum x) (\sum y)}{n \sum x^{2} - {(\sum x)}^{2}}$ $m = \frac{n \sum x y - (\sum x) (\sum y)}{n \sum x^{2} - {(\sum x)}^{2}}$ (22.8) $b = \frac{(\sum x^{2}) (\sum y) - (\sum x y) (\sum x)}{n \sum x^{2} - {(\sum x)}^{2}}$ $b = \frac{(\sum x^{2}) (\sum y) - (\sum x y) (\sum x)}{n \sum x^{2} - {(\sum x)}^{2}}$ (22.9)

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