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Question 1 of 2
The height of a group of 55 dogs and a group of 55 cats are collected in centimetres. Compare the mean for dogs ˉx¯xD and the mean for cats ˉx¯xC.
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ˉx¯xD== dogs mean
ˉx¯xC== cats mean
Use the mean formula to find the average height of the dogs.
ˉx¯xD |
== |
sum of datanumber of datasum of datanumber of data |
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20+30+40+50+60520+30+40+50+605 |
Substitute values |
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20052005 |
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4040 cmcm |
Simplify |
Use the mean formula to find the average height of the cats.
ˉx¯xC |
== |
sum of datanumber of datasum of datanumber of data |
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38+39+40+41+42538+39+40+41+425 |
Substitute values |
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20052005 |
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4040 cmcm |
Simplify |
The mean of both groups is 4040 cm even though their heights are not the same.
This only means that both groups have their data centralized or averaged at 4040 cm.
ˉx¯xD=40=40 cmcm
ˉx¯xC=40=40 cmcm
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Question 2 of 2
The height of a group of 55 dogs and a group of 55 cats are collected in centimetres. Find and compare the standard deviation of both groups.
The mean of both groups is given: ˉX=40¯¯¯X=40
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To solve for the standard deviation for the height of the dogs, label the given values needed for the formula.
X values (heights)=20,30,40,50,60X values (heights)=20,30,40,50,60
Mean ˉX=40Mean ¯¯¯X=40
Number of dogs: n=5Number of dogs: n=5
Subsitute into the standard deviation formula
SS |
== |
√∑(X−¯X)2n√∑(X−¯X)2n |
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√(20−40)2+(30−40)2+(40−40)2+(50−40)2+(60−40)25√(20−40)2+(30−40)2+(40−40)2+(50−40)2+(60−40)25 |
Substitute values |
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√(-20)2+(-10)2+(0)2+(10)2+(20)25√(−20)2+(−10)2+(0)2+(10)2+(20)25 |
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√400+100+0+100+4005√400+100+0+100+4005 |
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√10005√10005 |
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√200√200 |
SdSd |
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14.114.1 |
To solve for the standard deviation for the height of the cats, label the given values needed for the formula.
X values (heights)=38,39,40,41,42X values (heights)=38,39,40,41,42
Mean ˉX=40Mean ¯¯¯X=40
Number of cats: n=5Number of cats: n=5
Subsitute into the standard deviation formula
SS |
== |
√∑(X−¯X)2n√∑(X−¯X)2n |
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√(38−40)2+(39−40)2+(40−40)2+(41−40)2+(42−40)2)5√(38−40)2+(39−40)2+(40−40)2+(41−40)2+(42−40)2)5 |
Substitute values |
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√(-2)2+(-1)2+(0)2+(1)2+(2)25√(−2)2+(−1)2+(0)2+(1)2+(2)25 |
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√4+1+0+1+45√4+1+0+1+45 |
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√105√105 |
Simplify |
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√2√2 |
ScSc |
== |
1.41.4 |
SdSd is greater than ScSc.
This means that the height of the dogs is more dispersed than the height of the cats.
Sd=14.1cmSd=14.1cm
Sc=1.4cmSc=1.4cm