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Question
Find the mean and variance for each of the data in Exercise 1 to 5:
xi 6 10 14 18 24 28 30 fi 2 4 7 12 8 4 3
Find the mean and variance for each of the data in Exercise 1 to 5:
xi 6 10 14 18 24 28 30 fi 2 4 7 12 8 4 3
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Solution
xi fi fixi (xi−19) (xi−19)2 fi(xi)2 6 2 12 −13 169 338 10 4 40 −9 81 324 14 7 98 −5 25 175 18 12 216 −1 1 12 24 8 192 5 25 200 28 4 112 9 81 324 30 3 90 11 121 363 40 760 1736
Mean (¯¯¯x)=1N∑fixi=140×760=19
Variance σ2=1N∑ni=1fi(xi−¯¯¯x)2
= 140×1736=43.4
xi fi fixi (xi−19) (xi−19)2 fi(xi)2 6 2 12 −13 169 338 10 4 40 −9 81 324 14 7 98 −5 25 175 18 12 216 −1 1 12 24 8 192 5 25 200 28 4 112 9 81 324 30 3 90 11 121 363 40 760 1736
Mean (¯¯¯x)=1N∑fixi=140×760=19
Variance σ2=1N∑ni=1fi(xi−¯¯¯x)2
= 140×1736=43.4
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