Question

Considerando a amostra {2, 3, 4, 5, 7, 10, 12} a variância e o desvio-padrão amostral são respectivamente:

 

Alternativas

1 - 10,50 e 3,24

2 - 8,40 e 2,89

3 - 13,81 e 3,71

4 - 10,00 e 3,00

5 - 9,45 e 3,07

Answer 1

(Variância) S^2=∑ (xi – Média)2 / (n – 1)

 

Média=(2+3+4+5+7+10+12)/7=6,143

 

S^2=((2 – 6,143)2 + (3 – 6,143)2 + (4 – 6,143)2+ (5 – 6,143)2+ (7 – 6,143)2+ (10 – 6,143)2f+ (12 – 6,143)2g)/6    = 13,81

 

e  o desvio padrão é:

 

S=Raiz de 13,81

 

S=3,716

 

Answer 2

media=2+3+4+5+7+10+12/7=43/7

media=6,14

 

Tabela  de frequencia:

X1                      x1-media                        x1-media                (x1-media)²            

2                         2-6,14=-4,14                    4,14                      17,1396

3                         3-6,14=-3,14                    3,14                         9,8596

4                         4-6,14=-2,14                    2,14                         4,5796

5                         5-6,14=-1,14                    1,14                         1,2996

7                         7-6,14=0,86                      0,86                         0,7396

10                      10-6,14=3,86                    3,86                       14,8996

12                       12-6,14=5,86                   5,86                        34,3396

Total                                                                                              82,8572

 

VAR= soma de (x1-media)²/numero de dados

VAR=82,8572/7

Var=11,83

 

Dp=√VAR

Dp=√11,836

Dp=3,44

 

Ai o valor mais aproximado ao resultado foi alternativa 1