Let x_1, x_2, dots, x_n be n observations suc | vedclass

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(C) The variance of a set of observations is always non-negative,which implies that the mean of the squares is greater than or equal to the square of

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$15$

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(C) The variance of a set of observations is always non-negative,which implies that the mean of the squares is greater than or equal to the square of the mean: $\frac{\sum x_i^2}{n} \geq \left(\frac{\sum x_i}{n}\right)^2$.Substituting the given values $\sum x_i^2 = 300$ and $\sum x_i = 60$:$\frac{300}{n} \geq \left(\frac{60}{n}\right)^2$$\frac{300}{n} \geq \frac{3600}{n^2}$Since $n > 0$,we can multiply both sides by $n^2$:$300n \geq 3600$$n \geq 12$.Among the given options,only $15$ satisfies the condition $n \geq 12$.

$x_i$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
$f_i$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

Let $x_1, x_2, \dots, x_n$ be $n$ observations such that $\sum x_i^2 = 300$ and $\sum x_i = 60$. Which of the following is a possible value for $n$?

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The data is obtained in tabular form as follows:
$x_i$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
$f_i$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

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