Question

Alguém poderia me dizer a variância dessa tabela?

Answer 1

$\left\begin{array}{ccccccc}\mathbf{Dados}&\mathbf{Frequ\hat{e}ncia}\\15&7\\18&4\\22&2\\29&9\\31&3\\\mathbf{Total}&25\end{array}\right$

$\mathrm{A\ vari\hat{a}ncia\ amostral}\ s^2\ \mathrm{\acute{e}\ dada}\ \text{por:}$

$\boxed{s^2=\dfrac{1}{n-1}\sum\limits^{n}_{i=1}{\left(x_i-\overline{x}\right)^2}}$

$\mathrm{A\ m\acute{e}dia\ amostral}\ \overline{x}\ \mathrm{ser\acute{a}\ igual}\ \text{a:}$

$\boxed{\overline{x}=\dfrac{1}{n}\sum\limits_{i=1}^{n}{x_i}}$

$\Longrightarrow \overline{x}=\dfrac{7(15)+4(18)+2(22)+9(29)+3(31)}{25}$

$\Longrightarrow\oveline{x}=\dfrac{575}{25}\Longrightarrow \overline{x}=23$

$\mathrm{Eis\ a\ tabela\ com\ os\ valores\ de}\ (x_i-\overline{x})^2:$

$\left\begin{array}{ccccccc}\mathbf{(x_i-\overline{x})}&\mathbf{(x_i-\overline{x})^2}&\mathbf{f_i}&\mathbf{(x_i-\overline{x})^2f_i}\\-8&64&7&448\\-5&25&4&100\\-1&1&2&2\\6&36&9&324\\8&64&3&192\\\mathbf{Total}&&25&1066\end{array}\right$

$\mathrm{Desse\ modo,\ a\ vari\hat{a}ncia\ \ser\acute{a}\ igual}\ \text{a:}$

$s^2=\dfrac{1}{25-1}\bigg[7(64)+4(25)+2(1)+9(36)+3(64)\bigg]$

$\Longrightarrow s^2=\dfrac{1}{24}\bigg[1066\bigg]\Longrightarrow \boxed{s^2=44.41\overline{6}}$