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The average of 75 scores is 45. The average of the first 50 scores is 42 and that of the last 26 scores is 52. What is the $$50^{th}$$ score?
The average of 75 scores is 45.
Total of first 75 scores = $$45\times75$$ = 3375 Eq.(i)
The average of the first 50 scores is 42.
Total of first 50 scores = $$42\times50$$ = 2100 Eq.(ii)
average of last 26 scores is 52.
total of last 26 scores = $$52\times26$$ = 1352 Eq.(iii)
$$50^{th}$$ score = Eq.(ii)+Eq.(iii)-Eq.(i)
= 2100+1352-3375
= 3452-3375
= 77
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