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(D) First,we calculate the mean $(\bar{x})$:$\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{(2 	imes 1) + (4 	imes 2) + (6 	imes 3) + (8 	imes 2)

Vedclass · Accepted Answer

$\frac{32}{9}$

Vedclass · Answer

(D) First,we calculate the mean $(\bar{x})$:$\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{(2 	imes 1) + (4 	imes 2) + (6 	imes 3) + (8 	imes 2) + (10 	imes 1)}{1 + 2 + 3 + 2 + 1} = \frac{2 + 8 + 18 + 16 + 10}{9} = \frac{54}{9} = 6$.Now,calculate the mean deviation about the mean $(MD_{\bar{x}})$:$MD_{\bar{x}} = \frac{\sum f_i |x_i - \bar{x}|}{\sum f_i} = \frac{1|2-6| + 2|4-6| + 3|6-6| + 2|8-6| + 1|10-6|}{9} = \frac{4 + 4 + 0 + 4 + 4}{9} = \frac{16}{9}$.Next,calculate the median $(M)$:Total frequency $N = 9$. The median is the value corresponding to the $\frac{N+1}{2}$-th observation,which is the $5$-th observation. Looking at the cumulative frequencies $(1, 3, 6, 8, 9)$,the $5$-th observation falls in the group where $x_i = 6$. Thus,$M = 6$.Calculate the mean deviation about the median $(MD_M)$:$MD_M = \frac{\sum f_i |x_i - M|}{\sum f_i} = \frac{1|2-6| + 2|4-6| + 3|6-6| + 2|8-6| + 1|10-6|}{9} = \frac{16}{9}$.The sum of the mean deviation from the mean and the mean deviation from the median is:$\frac{16}{9} + \frac{16}{9} = \frac{32}{9}$.

$x_i$	$2$	$4$	$6$	$8$	$10$
$f_i$	$1$	$2$	$3$	$2$	$1$

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
No of Girls	$6$	$8$	$14$	$16$	$4$	$2$

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

$x_i$	$3$	$9$	$17$	$23$	$27$
$f_i$	$8$	$10$	$12$	$9$	$5$

Consider the following distribution:
$x_i$ $2$ $4$ $6$ $8$ $10$
$f_i$ $1$ $2$ $3$ $2$ $1$

The sum of the mean deviation from the mean and the mean deviation from the median of this distribution is:

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The mean deviation from the median of the data $16, 22, 3, 14, 5, 10, 8, 6, 11, 4$ is

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

Marks $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

No of Girls $6$ $8$ $14$ $16$ $4$ $2$

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 $4$ $6$ $16$ $28$ $16$ $6$ $4$

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

$x_i$ $3$ $9$ $17$ $23$ $27$

$f_i$ $8$ $10$ $12$ $9$ $5$

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Consider the following distribution:$x_i$$2$$4$$6$$8$$10$$f_i$$1$$2$$3$$2$$1$The sum of the mean deviation from the mean and the mean deviation from the median of this distribution is: