Question

Calcule o desvio padrão dos dados 8,6,6,12

Answer 1

$\delta={\sqrt {{\frac {1}{n}}\sum _{i=1}^{n}(X_{i}-{\overline {X}})^{2}}}}\\\\\overline X=\frac{8+6+6+12}{4} =8\\\\\delta={\sqrt {{\frac {1}{4}}\sum _{i=1}^{4}(X_{i}-{8})^{2}}}}\\=\sqrt{\frac{(8-8)^2}{4}+\frac{(6-8)^2}{4}+\frac{(6-8)^2}{4}+\frac{(12-8)^2}{4} } =\sqrt{6}$

segunda formula do desvio padrao:

$\delta={\sqrt {{\frac {1}{n-1}}\sum _{i=1}^{n}(X_{i}-{\overline {X}})^{2}}}}=\sqrt{\frac{(8-8)^2}{3}+\frac{(6-8)^2}{3}+\frac{(6-8)^2}{3}+\frac{(12-8)^2}{3} } =\sqrt{8}$