Let x_1, x_2, , x_n be n observations such that x_i^2 = 400 and x_i = 80 . Then a possible value of n among the following is: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Let x_{1}, x_{2}, \dots, x_{n} be n observations such that \sum x_{i}^{2} = 400 and \sum x_{i} = 80 . Then a possible value of n among the following is:

Solution & Step-by-step Explanation

We know that variance σ^{2} \geq 0 : \frac{\sum x _{i}^{2}}{n} - (\frac{\sum x _{i}}{n})^{2} \geq 0 \frac{400}{n} - (\frac{80}{n})^{2} \geq 0 \frac{400}{n} - \frac{6400}{n ^{2}} \geq 0 Multiplying by n^{2} (which is positive): 400 n - 6400 \geq 0 400 n \geq 6400 ⟹ n \geq 16 .Among the given options, the only value of n that satisfies n \geq 16 is 18 .

Try it yourself before checking the explanation above.

Let x_{1}, x_{2}, \dots, x_{n} be n observations such that \sum x_{i}^{2} = 400 and \sum x_{i} = 80 . Then a possible value of n among the following is:

15

18

9

12

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