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

By the Cauchy-Schwarz inequality, the square of the sum of observations multiplied by n must be greater than or equal to the sum of their squares. Substituting the given values gives n multiplied by 400, which must be greater than or equal to 80 squared, or 6400. Solving for n gives n must be greater than or equal to 16. Among the provided choices, only 18 satisfies this condition, making it the correct value.

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