The mean deviation from the median for the fo | vedclass

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(C) First,we arrange the data in ascending order and calculate the cumulative frequency $(cf)$: $x_i: 2, 3, 5, 7, 9$ $f_i: 8, 6, 4, 2, 1$ $cf: 8, 14,

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$\frac{10}{7}$

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(C) First,we arrange the data in ascending order and calculate the cumulative frequency $(cf)$: $x_i: 2, 3, 5, 7, 9$ $f_i: 8, 6, 4, 2, 1$ $cf: 8, 14, 18, 20, 21$ Total frequency $N = \sum f_i = 21$. The median is the value corresponding to the $(\frac{N+1}{2})$-th observation,which is the $11$-th observation. From the $cf$ table,the $11$-th observation is $3$. So,$	ext{Median} (M) = 3$. Now,calculate the mean deviation about the median: $	ext{M.D.}(M) = \frac{\sum f_i |x_i - M|}{N}$ $|x_i - 3|: |2-3|=1, |3-3|=0, |5-3|=2, |7-3|=4, |9-3|=6$ $f_i |x_i - 3|: 8(1)=8, 6(0)=0, 4(2)=8, 2(4)=8, 1(6)=6$ $\sum f_i |x_i - 3| = 8 + 0 + 8 + 8 + 6 = 30$ $	ext{M.D.}(M) = \frac{30}{21} = \frac{10}{7}$.

Income per day	Number of persons
$0-100$	$4$
$100-200$	$8$
$200-300$	$9$
$300-400$	$10$
$400-500$	$7$
$500-600$	$5$
$600-700$	$4$
$700-800$	$3$

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

Class Interval	$0$–$2$	$2$–$4$	$4$–$6$	$6$–$8$	$8$–$10$
Frequency	$1$	$3$	$4$	$1$	$2$

The mean deviation from the median for the following data is
$x_i$ $2$ $3$ $5$ $7$ $9$
$f_i$ $8$ $6$ $4$ $2$ $1$

Similar Questions

If the mean deviation about the median for the numbers $3, 5, 7, 2k, 12, 16, 21, 24$ arranged in ascending order is $6$,then the median is:

Find the mean deviation about the mean for the following data:
Income per day Number of persons
$0-100$ $4$
$100-200$ $8$
$200-300$ $9$
$300-400$ $10$
$400-500$ $7$
$500-600$ $5$
$600-700$ $4$
$700-800$ $3$

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 $5$ $6$ $12$ $14$ $26$ $12$ $16$ $9$

The mean deviation about the mean for the following data is
Class Interval $0$–$2$ $2$–$4$ $4$–$6$ $6$–$8$ $8$–$10$
Frequency $1$ $3$ $4$ $1$ $2$

Find the mean deviation about the median for the data $36, 72, 46, 42, 60, 45, 53, 46, 51, 49$.

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The mean deviation from the median for the following data is $x_i$$2$$3$$5$$7$$9$$f_i$$8$$6$$4$$2$$1$