In a group of 10 students, the mean of the lowest 9 scores is 46 while the mean of the highest 9 scores is 50. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by:
3.2
Let L be the lowest score, H the highest and S the sum of the middle 8 scores. Then L + S = 9 × 46 = 414 and S + H = 9 × 50 = 450, so H = L + 36.
Total of all 10 = 414 + H = 450 + L.
L can be at most the average of the middle 8: L ≤ (414 − L)/8, so L ≤ 46. H must be at least that average: H ≥ (450 − H)/8, so H ≥ 50 and L ≥ 14.
So the total lies between 450 + 14 = 464 and 450 + 46 = 496, and the mean lies between 46.4 and 49.6.
Difference = 49.6 − 46.4 = 3.2.
Hence, the answer is 3.2.
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