The mean of the following data is 16. Find th | vedclass

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(A) To find the mean,we use the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.First,calculate the class marks $(x_i)$ for each interval: $2, 6, 10

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$8$

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(A) To find the mean,we use the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.First,calculate the class marks $(x_i)$ for each interval: $2, 6, 10, 14, 18, 22, 26, 30, 34$.Next,calculate $f_i x_i$ for each class:$6 	imes 2 = 12$$8 	imes 6 = 48$$17 	imes 10 = 170$$23 	imes 14 = 322$$16 	imes 18 = 288$$15 	imes 22 = 330$$f 	imes 26 = 26f$$4 	imes 30 = 120$$3 	imes 34 = 102$Sum of frequencies $\sum f_i = 6+8+17+23+16+15+f+4+3 = 92+f$.Sum of $f_i x_i = 12+48+170+322+288+330+26f+120+102 = 1392+26f$.Given mean $\bar{x} = 16$,so $16 = \frac{1392+26f}{92+f}$.$16(92+f) = 1392+26f$$1472 + 16f = 1392 + 26f$$1472 - 1392 = 26f - 16f$$80 = 10f$$f = 8$.

Class	$0-4$	$4-8$	$8-12$	$12-16$	$16-20$	$20-24$	$24-28$	$28-32$	$32-36$
Frequency	$6$	$8$	$17$	$23$	$16$	$15$	$f$	$4$	$3$

Weekly income	Number of families
$0-1000$	$250$
$1000-2000$	$190$
$2000-3000$	$100$
$3000-4000$	$40$
$4000-5000$	$15$
$5000-6000$	$5$
Total	$600$

The mean of the following data is $16.$ Find the missing frequency $f.$

Class $0-4$ $4-8$ $8-12$ $12-16$ $16-20$ $20-24$ $24-28$ $28-32$ $32-36$

Frequency $6$ $8$ $17$ $23$ $16$ $15$ $f$ $4$ $3$

Similar Questions

If the mean of $12, 13, x, 17, 18$ and $20$ is $16,$ then $x = \ldots \ldots \ldots \ldots .$

Weekly income of $600$ families is tabulated below:

Weekly income Number of families

$0-1000$ $250$

$1000-2000$ $190$

$2000-3000$ $100$

$3000-4000$ $40$

$4000-5000$ $15$

$5000-6000$ $5$

Total $600$

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The mean of the following data is $16.$ Find the missing frequency $f.$ Class $0-4$ $4-8$ $8-12$ $12-16$ $16-20$ $20-24$ $24-28$ $28-32$ $32-36$ Frequency $6$ $8$ $17$ $23$ $16$ $15$ $f$ $4$ $3$