Discussion

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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