The variance sigma^2 of the data is . . . . | vedclass

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(B) First,calculate the mean $\overline{x}$:						$x_i$			$f_i$			$f_ix_i$			$f_ix_i^2$				$0$$3$$0$$0$		$1$$2$$2$$2$		$5$$3$$15$$75$		$6$$2$$12$$72$

Vedclass · Accepted Answer

$29$

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(B) First,calculate the mean $\overline{x}$:						$x_i$			$f_i$			$f_ix_i$			$f_ix_i^2$				$0$$3$$0$$0$		$1$$2$$2$$2$		$5$$3$$15$$75$		$6$$2$$12$$72$		$10$$6$$60$$600$		$12$$3$$36$$432$		$17$$3$$51$$867$		Total$\sum f_i = 22$$\sum f_ix_i = 176$$\sum f_ix_i^2 = 2048$	$\overline{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{176}{22} = 8$Variance $\sigma^2 = \frac{1}{N} \sum f_i x_i^2 - (\overline{x})^2$$\sigma^2 = \frac{2048}{22} - (8)^2$$\sigma^2 = 93.09 - 64 = 29.09$Rounding to the nearest integer,the correct option is $B$.

Marks of $A$	$30, 20, 40$
Marks of $B$	$70, 0, 5$

The variance $\sigma^2$ of the data is $ . . . . . .$

$x_i$ $0$ $1$ $5$ $6$ $10$ $12$ $17$

$f_i$ $3$ $2$ $3$ $2$ $6$ $3$ $3$

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The variance $\sigma^2$ of the data is $ . . . . . .$ $x_i$ $0$ $1$ $5$ $6$ $10$ $12$ $17$ $f_i$ $3$ $2$ $3$ $2$ $6$ $3$ $3$