If x_1, x_2, ..., x_n are n observations such | vedclass

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(D) We know that the variance $\sigma^2$ of a set of observations is always non-negative,i.e.,$\sigma^2 \geq 0$. The formula for variance is $\sigma^2

Vedclass · Accepted Answer

$27$

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(D) We know that the variance $\sigma^2$ of a set of observations is always non-negative,i.e.,$\sigma^2 \geq 0$. The formula for variance is $\sigma^2 = \frac{\sum_{i=1}^n x_i^2}{n} - \left(\frac{\sum_{i=1}^n x_i}{n}\right)^2$. Substituting the given values $\sum x_i^2 = 400$ and $\sum x_i = 100$: $\frac{400}{n} - \left(\frac{100}{n}\right)^2 \geq 0$ $\frac{400}{n} - \frac{10000}{n^2} \geq 0$ Multiplying by $n^2$ (since $n > 0$): $400n - 10000 \geq 0$ $400n \geq 10000$ $n \geq \frac{10000}{400}$ $n \geq 25$. Among the given options,only $27$ satisfies the condition $n \geq 25$.

If $x_1, x_2, ..., x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 100$,then which of the following is a possible value of $n$?

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