Find the mean deviation about the mean for th | vedclass

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(B) To find the mean deviation about the mean,we first calculate the mean $\bar{X}$.The midpoints $(x_i)$ of the classes are $5, 15, 25, 35, 45, 55, 6

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$10$

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(B) To find the mean deviation about the mean,we first calculate the mean $\bar{X}$.The midpoints $(x_i)$ of the classes are $5, 15, 25, 35, 45, 55, 65$.The sum of frequencies $N = \Sigma f_i = 4+6+16+28+16+6+4 = 80$.The sum $\Sigma f_i x_i = (4 	imes 5) + (6 	imes 15) + (16 	imes 25) + (28 	imes 35) + (16 	imes 45) + (6 	imes 55) + (4 	imes 65) = 20 + 90 + 400 + 980 + 720 + 330 + 260 = 2800$.Mean $\bar{X} = \frac{\Sigma f_i x_i}{N} = \frac{2800}{80} = 35$.Now,calculate $\Sigma f_i |x_i - \bar{X}| = \Sigma f_i |x_i - 35|$:$4|5-35| + 6|15-35| + 16|25-35| + 28|35-35| + 16|45-35| + 6|55-35| + 4|65-35|$$= 4(30) + 6(20) + 16(10) + 28(0) + 16(10) + 6(20) + 4(30)$$= 120 + 120 + 160 + 0 + 160 + 120 + 120 = 800$.Mean Deviation about the mean = $\frac{1}{N} \Sigma f_i |x_i - \bar{X}| = \frac{800}{80} = 10$.

Class interval	$0$-$10$	$10$-$20$	$20$-$30$	$30$-$40$	$40$-$50$	$50$-$60$	$60$-$70$
Frequency	$4$	$6$	$16$	$28$	$16$	$6$	$4$

$x_i$	$6$	$12$	$18$	$24$	$30$	$36$	$42$
$f_i$	$4$	$7$	$9$	$18$	$15$	$10$	$5$

$x_i$	$3$	$6$	$9$	$12$	$13$	$15$	$21$	$22$
$f_i$	$3$	$4$	$5$	$2$	$4$	$5$	$4$	$3$

Age (in years)	$16-20$	$21-25$	$26-30$	$31-35$	$36-40$	$41-45$	$46-50$	$51-55$
Number of persons	$5$	$6$	$12$	$14$	$26$	$12$	$16$	$9$

Find the mean deviation about the mean for the following data:
Class interval $0$-$10$ $10$-$20$ $20$-$30$ $30$-$40$ $40$-$50$ $50$-$60$ $60$-$70$
Frequency $4$ $6$ $16$ $28$ $16$ $6$ $4$

Similar Questions

For the following distribution,the mean deviation about the median is:
$x_i$ $6$ $12$ $18$ $24$ $30$ $36$ $42$
$f_i$ $4$ $7$ $9$ $18$ $15$ $10$ $5$

Find the mean deviation about the median for the following data:

$x_i$ $3$ $6$ $9$ $12$ $13$ $15$ $21$ $22$

$f_i$ $3$ $4$ $5$ $2$ $4$ $5$ $4$ $3$

Find the mean deviation of the numbers $3, 4, 5, 6, 7$.

$A$ batsman scores runs in $10$ innings: $38, 70, 48, 34, 42, 55, 63, 46, 54, 44$. The mean deviation about the median is:

Calculate the mean deviation about the median age for the age distribution of $100$ persons given below:

Age (in years) $16-20$ $21-25$ $26-30$ $31-35$ $36-40$ $41-45$ $46-50$ $51-55$

Number of persons $5$ $6$ $12$ $14$ $26$ $12$ $16$ $9$

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Find the mean deviation about the mean for the following data:Class interval$0$-$10$$10$-$20$$20$-$30$$30$-$40$$40$-$50$$50$-$60$$60$-$70$Frequency$4$$6$$16$$28$$16$$6$$4$