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Let x1, x2,..., xₙ be n observations such that the sum of their squares is 200 and their sum is 40. Which among the following could be a possible value of n?

1. (A) 4
2. (B) 5
3. (C) 6
4. (D) 10

Correct answer: (D) 10

Solution

From the Cauchy-Schwarz or variance non-negativity condition: n * sum(x_i²) >= (sum x_i)² gives 200n >= 1600, so n >= 8. Among the options, only n = 10 satisfies this.

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