Let n observations x_1, x_2, ....., x_n be su | vedclass

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

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$18$

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(C) We know that the variance $\sigma^2$ of a set of observations is always non-negative,i.e.,$\sigma^2 \ge 0$.The formula for variance is $\sigma^2 = \frac{\sum x_i^2}{n} - \left( \frac{\sum x_i}{n} \right)^2$.Substituting the given values $\sum x_i^2 = 400$ and $\sum x_i = 80$:$\frac{400}{n} - \left( \frac{80}{n} \right)^2 \ge 0$$\frac{400}{n} \ge \frac{6400}{n^2}$Since $n > 0$,we can multiply both sides by $n^2$:$400n \ge 6400$$n \ge \frac{6400}{400}$$n \ge 16$.Among the given options,only $18$ satisfies the condition $n \ge 16$.

Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Group $A$	$9$	$17$	$32$	$33$	$40$	$10$	$9$
Group $B$	$10$	$20$	$30$	$25$	$43$	$15$	$7$

Let $n$ observations $x_1, x_2, ....., x_n$ be such that $\sum {x_i}^2 = 400$ and $\sum x_i = 80$. Then,which of the following is a possible value for $n$?

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Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$

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