QUESTION 34
We want to find the variance of [tex]82,44,67,52,120[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{82+44+67+52+120}{5}[/tex]
[tex]\bar X =\frac{365}{5}[/tex]
[tex]\Rightarrow \bar X =73[/tex]
This means that,
[tex]\sigma^2=\frac{(82-73)^2+(44-73)^2+(67-73)^2+(52-73)^2+(52-73)^2+(120-73)^2}{5}[/tex]
This gives us,
[tex]\sigma^2=\frac{(9)^2+(-29)^2+(-6)^2+(-21)^2+(47)^2}{5}[/tex]
[tex]\sigma^2=\frac{81+841+36+441+2209}{5}[/tex]
[tex]\sigma^2=\frac{3608}{5}[/tex]
[tex]\sigma^2=721.6[/tex]
QUESTION 35
We want to find the variance of [tex]10,12,15,18,11,13,14,16,19,20[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{10+12+15+18+11+13+14+16+19+20}{10}[/tex]
[tex]\bar X =\frac{148}{10}[/tex]
[tex]\fRightarrow \bar X =14.8[/tex]
This means that,
[tex]\sigma^2 =\frac{(10-14.8)^2+(12-14.8)^2+(15-14.8)^2+(18-14.8)^2+(11-14.8)^2+(13-14.8)^2+(14-14.8)^2+(16-14.8)^2+(19-14.8)^2+(20-14.8)^2}{10}[/tex]
This gives us,
[tex]\sigma^2=\frac{(-4.8)^2+(-2.8)^2+(0.2)^2+(3.2)^2+(-3.8)^2+(-1.8)^2+(-0.8)^2+(1.2)^2+(4.2)^2+(5.2)^2}{10}[/tex]
[tex]\sigma^2=\frac{23.04+7.84+0.04+10.24+14.44+3.24+0.64+1.44+17.64+27.04}{10}[/tex]
[tex]\sigma^2=\frac{105.6}{10}[/tex]
[tex]\sigma^2=10.56[/tex]
QUESTION 36
We want to find the variance of [tex]100,140,130,180,80,160[/tex].
The variance can be calculated using the formula,
[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]
where
[tex]\bar X =\frac{100+140+130+180+80+160}{6}[/tex]
[tex]\bar X =\frac{790}{6}[/tex]
[tex]\Rightarrow \bar X =131.67[/tex]
This means that,
[tex]\sigma^2=\frac{(100-131.6667)^2+(140-131.6667)^2+(130-131.6667)^2+(180-131.6667)^2+(80-131.6667)^2+(160-131.6667)^2}{6}[/tex]
This gives us,
[tex]\sigma^2=\frac{(-31.6667)^2+(8.3333)^2+(-0.6667)^2+(48.3333)^2+(-51.6667)^2+(28.3333)^2}{6}[/tex]
[tex]\sigma^2=\frac{10325}{9}[/tex]
[tex]\sigma^2=1147.22[/tex]
