Find the mean and variance for the data

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Question

${x_i}$
			${f_i}$
			${f_i}{x_i}$
			${{x_i} - \bar x}$
			${\left( {{x_i} - \bar x} \right)^2}$
			${f_i}{\left( {{x_i} - \bar x} \

Vedclass · Accepted Answer

$43.4$

Vedclass · Answer

${x_i}$
			${f_i}$
			${f_i}{x_i}$
			${{x_i} - \bar x}$
			${\left( {{x_i} - \bar x} ight)^2}$
			${f_i}{\left( {{x_i} - \bar x} ight)^2}$
		
		
			$6$
			$2$
			$12$
			$-13$
			$169$
			$338$
		
		
			$10$
			$4$
			$40$
			$-9$
			$81$
			$324$
		
		
			$14$
			$7$
			$98$
			$-5$
			$25$
			$175$
		
		
			$18$
			$12$
			$216$
			$-1$
			$1$
			$12$
		
		
			$24$
			$8$
			$192$
			$5$
			$25$
			$200$
		
		
			$28$
			$4$
			$112$
			$9$
			$81$
			$324$
		
		
			$30$
			$3$
			$90$
			$11$
			$121$
			$363$
		
		
			 
			$40$
			$760$
			 
			 
			$1736$
		
	


Here, $N = 40,\sum\limits_{i = 1}^7 {{f_1}{x_1}}  = 760$

$	herefore \bar x = \frac{{\sum\limits_{i = 1}^7 {{f_1}{x_1}} }}{N} = \frac{{760}}{{40}} = 19$

Variance $ = \left( {{\sigma ^2}} ight) = \frac{1}{N}\sum\limits_{i = 1}^7 {{f_1}{{\left( {{x_1} - \bar x} ight)}^2} = } \frac{1}{{40}} 	imes 1736 = 43.4$

Find the mean and variance for the data

${x_i}$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

${f_i}$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

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${x_i}$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
${f_i}$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

${x_i}$	${f_i}$	${f_i}{x_i}$	${{x_i} - \bar x}$	${\left( {{x_i} - \bar x} \right)^2}$	${f_i}{\left( {{x_i} - \bar x} \right)^2}$
$6$	$2$	$12$	$-13$	$169$	$338$
$10$	$4$	$40$	$-9$	$81$	$324$
$14$	$7$	$98$	$-5$	$25$	$175$
$18$	$12$	$216$	$-1$	$1$	$12$
$24$	$8$	$192$	$5$	$25$	$200$
$28$	$4$	$112$	$9$	$81$	$324$
$30$	$3$	$90$	$11$	$121$	$363$
	$40$	$760$			$1736$

Find the mean and variance for the data ${x_i}$ $6$ $10$ $14$ $18$ $24$ $28$ $30$ ${f_i}$ $2$ $4$ $7$ $12$ $8$ $4$ $3$