In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

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Question :

Started 10 months ago by Shashank in

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A.
5
B.
3
C.
4
D.
6

Option C is the correct answer.

Explanatory Answer

Let a1, a2, a3, … , a10 be the 10 scores in ascending order (a1 – lowest, a10 – highest)
Mean of lowest 9 scores = 42
Sum of lowest 9 scores = 42*9 = 378 = a1+a2+ ….+ a9
Mean of highest 9 scores = 47
Sum of highest 9 scores = 47*9 = 423 = a2+a3+…+a10
Difference between highest and lowest score = 423-378 = 45 = a10-a1
Maximum possible mean when a1 is maximum
Hence a1=42, a10 = 87
Maximum mean = (378+87)/10 = 46.5
Minimum possible mean when a10 is minimum
Hence, a10=47, a1=2

Minimum mean = (423+2)/10 = 42.5
Difference = 46.5-42.5 = 4