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
Explanation:
Let the highest and lowest score be h and l respectively and total score of remaining 8 students be x.
The mean of the lowest 9 scores is 42
⇒ x + l = 9 × 42 = 378 …(1)
The mean of the highest 9 scores is 47
⇒ x + h = 9 × 47 = 423 …(2)
(2) – (1)
⇒ h – l = 423 – 378 = 45
Case 1: Least possible average is when we minimize the highest marks. The least highest marks can be 47.
∴ Lowest score = 47 – 45 = 2
∴ Least average = 9×47+210 = 42.5
Case 2: Highest possible average is when we maximize the lowest marks. The highest lowest marks can be 42.
∴ Highest score = 42 + 45 = 87
∴ Highest average = 9×42+8710 = 46.5
∴ The required difference = 46.5 – 42.5 = 4
Hence, option (a).
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