Question

dado os numeros 5,8,7,9 e 3 calcule variância e o desvio padrão desses números.​

Answer 1

Calculemos a media:

$\bar{x}=\dfrac{5+8+7+9+3}{5}=\dfrac{32}{5}=6.4$

Agora apliquemos a formula de variancia:

$s^2=\dfrac{\sum(x_i-\bar{x})^2}{n-1}\\\\\\s^2=\dfrac{(5-6.4)^2+(8-6.4)^2+(7-6.4)^2+(9-6.4)^2+(3-6.4)^2}{5-1}=\\\\\\\dfrac{(-1.4)^2+(1.6)^2+(0.6)^2+(2.6)^2+(-3.4)^2}{4}=\\\\\\\dfrac{1.96+2.56+0.36+6.76+11.56}{4}=\\\\\\\dfrac{23.2}{4}=\boxed{5.8}$

Agora que temos a variancia soh precisamos tirar a raiz para achar o desvio padrao:

$s=\sqrt{s^2}=\sqrt{5.8}\approx2.4083$