Statistikk formler

Her finner formler for statistikk både vanlige og mer avanserte formler. Disse formlene hjelper deg med å regne ut statistikk problemstillinger, f.eks. sannsynlighetsberegning.

Formel for Gjennomsnitt: `A = \frac{1}{n} \sum_{i=1}^{n} x_i`

Formel for Varians: `\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i – \bar{x})^2`

Formel for Standardavvik: `\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i – \bar{x})^2}`

Formel for Median: `Me = \begin{cases} x_{(n+1)/2} & \text{hvis n er odd} \\ \frac{1}{2} (x_{n/2} + x_{n/2 + 1}) & \text{hvis n er partall} \end{cases}`

Formel for Lineær regresjon: `y = mx + b`

Formel for Kovarians: ` Cov(X,Y) = \frac{1}{n} \sum_{i=1}^{n} (x_i – \bar{x})(y_i – \bar{y})`

Formel for Korrelasjon: ` \rho = \frac{Cov(X,Y)}{\sigma_X \sigma_Y}`

Formel for Binomialfordeling: `P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}`

Formel for Normalfordeling: `f(x|\mu,\sigma^2) = \frac{1}{\sigma \sqrt{2\pi}} \exp\left(-\frac{1}{2} \left(\frac{x-\mu}{\sigma}\right)^2\right)`

Formel for Chi-kvadratfordeling: `f(x;k) = \frac{1}{2^{k/2}\Gamma(k/2)} x^{k/2-1} e^{-x/2}`

Formel for T-fordeling: `f(x;n) = \frac{\Gamma\left(\frac{n+1}{2}\right)}{\sqrt{n\pi}\Gamma\left(\frac{n}{2}\right)\left(1+\frac{x^2}{n}\right)^{(n+1)/2}}`

Formel for F-fordeling: `f(x;m,n) = \frac{\Gamma\left(\frac{m+n}{2}\right)(\frac{m}{n})^{m/2}x^{m/2-1}}{\Gamma\left(\frac{m}{2}\right)\Gamma\left(\frac{n}{2}\right)(1+\frac{m}{n}x)^{(m+n)/2}}`

Formel for Nullhypotese: `H_0: \beta = 0`

Formel for Alternativ hypotese: `H_1: \beta \neq 0`

Formel for Konfidensintervall: `CI = \hat{\beta} \pm t_{\alpha/2, n-2} SE(\hat{\beta})`

Formel for Standardavvik i en utvalgsfordeling: `SE = \frac{\sigma}{\sqrt{n}}`

Formel for P-verdi: `p = P(\text{observasjon eller noe ekstremere}|\text{nullhypotese er sann})`

Formel for Regresjonslinje: `y = a + bx`

Formel for Korrelasjonskoeffisient: `r = \frac{n\sum xy – \sum x \sum y}{\sqrt{(n\sum x^2 – (\sum x)^2)(n\sum y^2 – (\sum y)^2)}}`

Formel for ANOVA: `F = \frac{MS_{\text{between}}}{MS_{\text{within}}}`

Formel for Konfidensnivå: `1 – \alpha`

Formel for Teststørrelse: `t = \frac{\hat{\beta} – \beta_0}{SE(\hat{\beta})}`

Formel for Skjevhet: `Skewness = \frac{\frac{1}{n} \sum_{i=1}^{n} (x_i – \bar{x})^3}{\left(\frac{1}{n} \sum_{i=1}^{n} (x_i – \bar{x})^2\right)^{3/2}}`

Formel for Sannsynlighet: `P(A) = \frac{n(A)}{n(S)}`

Formel for Komplementærsannsynlighet: `P(A’) = 1 – P(A)`

Formel for Uavhengige hendelser: `P(A \cap B) = P(A) \cdot P(B)`

Formel for Betinget sannsynlighet: `P(A|B) = \frac{P(A \cap B)}{P(B)}`

Formel for Total sannsynlighet: `P(A) = \sum_{i} P(A \cap B_i)`

Formel for Bayes’ teorem: `P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}`

Formel for Bernoulli fordeling: `P(X=k) = p^k (1-p)^{1-k}`

Formel for Poisson fordeling: `P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}`

Formel for Kumulativ fordeling: `F(x) = P(X \leq x)`

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