M(x) mediana D(x) dominanta R(x) = maxx_i − minx_i rozstep $S^{2}\left( x \right) = \frac{1}{n}\sum_{i = 1}^{N}{(x_{i} - \overset{\overline{}}{x})}^{2}\text{\ Wariancja}$

$d\left( x \right) = \frac{1}{N}\sum_{i = 1}^{N}\left| x_{i} - \overset{\overline{}}{x} \right|\ odchylenie\ przecietne$ $V\left( x \right) = \frac{S\left( x \right)d(x)}{\overset{\overline{}}{x}}\ wspolczynnik\ zmiennosci$

P=n! n/n permutacja $\hat{P}\left( n_{1},\ldots,n_{k} \right) = \frac{n!}{n_{1}!\ldots n_{2}!}\text{\ \ }\frac{n}{n}\ $ $V_{n}^{m} = \frac{n!}{\left( n - m \right)!}\frac{m}{n}\ {\hat{V}}_{n}^{m} = \ n^{m}\ \frac{m}{n}\text{\ wariancje}$

$C_{n}^{m} = \begin{pmatrix} n \\ m \\ \end{pmatrix} = \frac{n!}{m!\left( n - m \right)!}\ \frac{m}{n}\ {\hat{C}}_{n}^{m} = \begin{pmatrix} n + m - 1 \\ m \\ \end{pmatrix} = \begin{pmatrix} n + m - 1 \\ n - 1 \\ \end{pmatrix}\frac{m}{n}\ kombinacje\ bez\ kolejnosci$

$$P\left( A \right) = \frac{k}{n}\ \ k\ sprzyjajacych\ n\ mozliwych\ P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\ \ $$

$$P\left( B \middle| C \right) = \frac{P\left( B \cap C \right)}{P\left( C \right)}\text{\ BkiedyC\ P}\left( A \cap B \right) = P\left( A \right) \times \left( B \right)\text{\ \ }$$

$$\text{\ P}\left( B \right) = \sum_{i = 1}^{n}{P\left( C_{i} \right) \times P\left( B \middle| C \right)}prawdopodobienstwo\ calkowite\ P\left( C_{i} \middle| B \right) = \frac{P(C_{i}) \times P\left( B \middle| C_{i} \right)}{P\left( C_{1} \right) \times P\left( B \middle| C_{1} \right) + ... + P\left( C_{n} \right) \times P\left( B \middle| C_{n} \right)}\ \ \lbrack prawdopodobienstwo\ zajscia\ C_{i},\ zaszlo\ bo\ zaszlo\ B$$

$$r_{\text{xy}} = \frac{\sum_{i = 1}^{n}{\left( x_{i} - \overset{\overline{}}{x} \right)\left( y_{i} - \overset{\overline{}}{y} \right)}}{\sqrt{\sum_{i = 1}^{n}\left( x_{i} - \overset{\overline{}}{x} \right)^{2}\sum_{i = 1}^{n}\left( y_{i} - \overset{\overline{}}{y} \right)^{2}}} = \sqrt{a_{1}b_{1}} = \frac{\text{cov}\left( x,y \right)}{S\left( X \right)S\left( Y \right)}\text{\ liniowa\ }r_{s} = 1 - \frac{6\sum_{i = 1}^{n}d_{i}^{2}}{n\left( n^{2} - 1 \right)}$$

$$\text{co}v\left( x,y \right) = \frac{\sum_{i = 1}^{n}{\left( x_{i} - \overset{\overline{}}{x} \right)\left( y_{i} - \overset{\overline{}}{y} \right)}}{n} = \frac{1}{n}\sum_{i = 1}^{n}{x_{i}x_{i}} - \overset{\overline{}}{x}\overset{\overline{}}{y}$$

$$y_{i} = a_{0} + a_{1}x_{i},\frac{y}{x},\ \ x_{i} = b_{0} + b_{1}y_{i},\frac{x}{y},\ regresja\ liniowa\ a_{0} = \overset{\overline{}}{y} - a_{1}\overset{\overline{}}{x}\ b_{0} = \overset{\overline{}}{x} - b_{1}\overset{\overline{}}{y}$$

$$a_{1} = \frac{\sum_{i = 1}^{n}{\left( x_{i} - \overset{\overline{}}{x} \right)(y_{i} - \overset{\overline{}}{y})}}{\sum_{i = 1}^{n}{(x_{i} - \overset{\overline{}}{x})}^{2}}\ ,\ {}_{} = \frac{\sum_{i = 1}^{n}{\left( x_{i} - \overset{\overline{}}{x} \right)(y_{i} - \overset{\overline{}}{y})}}{\sum_{i = 1}^{n}{(y_{i} - \overset{\overline{}}{y})}^{2}}\ $$

$$\mathbf{u}_{\mathbf{i}}\mathbf{=}\mathbf{y}_{\mathbf{i}}\mathbf{-}\hat{\mathbf{y}_{\mathbf{i}}}\mathbf{\ }\text{reszta}\frac{y}{x},\ \ v_{i} = x_{i} - \hat{x_{i}},\ reszta\frac{x}{y},$$

$$\text{\ \ }S^{2}\left( u \right) = \frac{1}{n - 2}\sum_{i = 1}^{n}\left( y_{i} - \hat{y_{i}} \right)^{2},\ S^{2}\left( v \right) = \frac{1}{n - 2}\sum_{i = 1}^{n}\left( x_{i} - \hat{x_{i}} \right)^{2},\text{\ V}\left( u \right) = \frac{S\left( u \right)}{\overset{\overline{}}{Y}}100\%,\ V\left( v \right) = \frac{S\left( u \right)}{\overset{\overline{}}{X}}100\%,$$

$\ \varphi^{2} = \varphi_{x}^{2} = \varphi_{y}^{2},\ \ \varphi_{x}^{2} = \frac{\sum_{i = 1}^{n}\left( x_{i} - \hat{x_{i}} \right)^{2}}{\sum_{i = 1}^{n}{(x_{i} - \overset{\overline{}}{x})}^{2}}\ ,\varphi_{y}^{2} = \frac{\sum_{i = 1}^{n}\left( y_{i} - \hat{y_{i}} \right)^{2}}{\sum_{i = 1}^{n}{(y_{i} - \overset{\overline{}}{y})}^{2}}\ \ w.\ \ zbierznosci\ R^{2} = 1 - \varphi^{2}\text{\ w.\ \ determinacji}$

Parametryczne testy istotności

1. Dla wartości oczekiwanej (średniej)

$$N\left( m,\sigma \right)\ n > 30\ i\ \sigma\ nieznane\ \sigma \approx {S(x)}^{24}\ statystyka\ u\ u = \frac{\overset{\overline{}}{X} - m_{0}}{\sigma(X)}\ \ N \leq 30\ statystyka\ t\ t = \frac{\overset{\overline{}}{X} - m_{0}}{S(X)}$$

2. Na równość dwóch wartości przeciętnych

Rozklady N(m₁,σ(X₁)),  N(m₂,σ(X₂)),   obie proby sa niezalezne od siebie,   kiedy σ(X₁), σ(x₂)nieznane dla n₁, n₂ > 30 przyjmujemy σ(X₁) = S(X₁), σ(X₂) = S(X₂)

$$n_{1},n_{2} > 30\ \ u = \frac{\overset{\overline{}}{X_{1}} - \overset{\overline{}}{X_{2}}}{\sqrt{\frac{\sigma^{2}(X_{1})}{n_{1}} + \frac{\sigma^{2}(X_{2})}{n_{2}}}},\ \ n_{1},n_{2} \leq 30\ t = \frac{\overset{\overline{}}{X_{1}} - \overset{\overline{}}{X_{2}}}{\sqrt{\frac{n_{1}S^{2}\left( X_{1} \right) + n_{2}S^{2}\left( X_{2} \right)}{n_{1} + n_{2} - 1}\left( \frac{1}{n_{1}} + \frac{1}{n_{2}} \right)}}$$