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The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5 then the average of the whole group

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The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5 then the average of the whole group is
A. `(15)/(4)`
B. `(1)/(5)`
C. 8
D. 4
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Correct Answer - A
We have,
`n_(1)=10,n_(2)=30,bar(X)_(1)=4.5, X_(2)=3.5`
Let `bar(X)` be the average of the whole group. Then,
`bar(X)=(n_(1)bar(X)_(1)+n_(2)bar(X)_(2))/(n_(1)+n_(2))=(10xx45+30xx35)/(40)=(45+105)/(40)=(15)/(4)`
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