Respuesta :
Answer:
a.) Population mean, [tex]\mu[/tex] = 6.11
b.) Population Standard deviation, [tex]\sigma[/tex] = 1.67
Population Variance, [tex]\sigma^2[/tex] = 2.78
Step-by-step explanation:
Class Mid point Frequency [tex]x_i \times f_i[/tex] [tex](x_i - \mu)[/tex] [tex]f(x_i - \mu)^2[/tex]
2 - 4 3 20 60 -3.11 193.58
4 - 6 5 60 300 -1.11 73.93
6 - 8 7 80 560 0.889 63.23
8 - 10 9 20 180 2.89 167.04
total number of elements = 20 + 60 + 80 + 20 = 180
Population size, N = 180
a.) [tex]\sum_{i=1}^{4}[/tex] [tex]x_i \times f_i[/tex] = 60 + 300 + 560 + 180 = 1100
Population mean, [tex]\mu[/tex] = [tex]\frac{1100}{180} = 6.11[/tex]
b.) [tex]\sum_{i=1}^{4}f(x_i - \mu)^2[/tex] = 193.58 + 73.93 + 63.23 + 167.04 = 497.78
Population Standard deviation,
[tex]\sigma[/tex] = [tex]\sqrt{\frac{\sum_{i=1}^{4}f(x_i - \mu)^2}{N-1} } = \sqrt{\frac{497.78}{(180 - 1)} } = \sqrt{2.781} = 1.667[/tex]
Population Variance, [tex]\sigma^2[/tex] = 2.781
