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A class of 7 students has an average score of 62 and a variance of 20 in a mathematics examination. A student fails if they score below 50 marks. In the worst case, what is the maximum number of students who could have failed?

1. 0
2. 1
3. 2
4. 3

Correct answer: 0

Solution

Mean = 62, variance = 20, so sum of (xi - 62)² = 7*20 = 140. If one student scores x < 50, then (x-62)² > (50-62)² = 144 > 140. This means a single student scoring below 50 would already require sum of squared deviations > 144, which exceeds the total 140. Hence no student can score below 50 while maintaining variance = 20. Maximum number of failing students = 0.

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