Fórmulas Médias

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Médias

1. Legenda

$x_{1}, x_{2}, x_{3}, ... , x_{n}$	$:$	termos
$n \, $	$:$	número de termos
$p_{1}, p_{2}, p_{3}, ... , p_{n}$	$:$	peso de cada termo

2. Média aritmética simples

$M.A.S=\dfrac{ x_{1}+x_{2}+x_{3}+ \hspace{0.1em} ... \hspace{0.1em} + \hspace{0.2em} x_{n} }{n}$

3. Média aritmética ponderada

$M.A.P=\dfrac{x_{1}p_{1}+x_{2}p_{2}+ \hspace{0.1em} ... \hspace{0.1em} + \hspace{0.2em} x_{n}p_{n}}{p_{1}+p_{2}+ \hspace{0.1em} ... \hspace{0.1em} + \hspace{0.2em} p_{n}}$

4. Média geométrica simples

$M.G.S = \sqrt[n]{x_{1}x_{2}x_{3} \hspace{0.2em} ... \hspace{0.2em} x_{n}}$

5. Média geométrica ponderada

$M.G.P= \, \, \sqrt[p_{1}+p_{2}+...+p_{n}]{x_{1}^{p_{1}}x_{2}^{p_{2}}x_{3}^{p_{3}} \hspace{0.1em} ... \hspace{0.1em} x_{n}^{p_{n}}}$

6. Média harmônica simples

$M.H.S = \dfrac{n}{\dfrac{1}{x_{1}}+\dfrac{1}{x_{2}}+ \hspace{0.2em} ... \hspace{0.1em} +\dfrac{1}{x_{n}}}$

7. Média harmônica ponderada

$M.H.P = \dfrac{p_{1}+p_{2}+ \hspace{0.2em} ... \hspace{0.1em} + \hspace{0.2em} p_{n}}{\dfrac{p_{1}}{x_{1}}+\dfrac{p_{2}}{x_{2}}+ \hspace{0.2em} ... \hspace{0.1em} +\dfrac{p_{n}}{x_{n}}}$

8. Média quadrática simples

$M.Q.S = \sqrt[]{\dfrac{x_{1}^{2}+x_{2}^{2}+ \hspace{0.2em} ... \hspace{0.1em} + \hspace{0.2em} x_{n}^{2}}{n}}$

9. Média quadrática ponderada

$M.Q.P = \sqrt[]{\dfrac{x_{1}^{2}p_{1}+x_{2}^{2}p_{2}+ \hspace{0.2em} ... \hspace{0.1em} + \hspace{0.2em} x_{n}^{2}p_{n}}{p_{1}+p_{2}+ \hspace{0.2em} ... \hspace{0.1em} + \hspace{0.2em} p_{n}}}$