For the following distribution,the mean devia | vedclass

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(B) First,we calculate the cumulative frequency $(cf)$ and the total frequency $(N)$:$x_i$$f_i$$cf$$6$$4$$4$$12$$7$$11$$18$$9$$20$$24$$18$$38$$30$$15$

Vedclass · Accepted Answer

$7.5$

Vedclass · Answer

(B) First,we calculate the cumulative frequency $(cf)$ and the total frequency $(N)$:$x_i$$f_i$$cf$$6$$4$$4$$12$$7$$11$$18$$9$$20$$24$$18$$38$$30$$15$$53$$36$$10$$63$$42$$5$$68$Here,$N = 68$,which is even. The median is the average of the $(\frac{N}{2})^{th}$ and $(\frac{N}{2} + 1)^{th}$ observations,i.e.,the $34^{th}$ and $35^{th}$ observations.Looking at the cumulative frequency,both the $34^{th}$ and $35^{th}$ observations fall in the class where $x_i = 24$.Therefore,$	ext{Median} = 24$.Now,we calculate the mean deviation about the median using the formula $	ext{MD}(	ext{Median}) = \frac{\sum f_i |x_i - 	ext{Median}|}{N}$:$\sum f_i |x_i - 24| = 4|6-24| + 7|12-24| + 9|18-24| + 18|24-24| + 15|30-24| + 10|36-24| + 5|42-24|$$= 4(18) + 7(12) + 9(6) + 18(0) + 15(6) + 10(12) + 5(18)$$= 72 + 84 + 54 + 0 + 90 + 120 + 90 = 510$$	ext{MD}(	ext{Median}) = \frac{510}{68} = 7.5$.

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

Similar Questions

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

If the mean deviation of the data $1, 1+d, 1+2d, \ldots, 1+100d$ $(d > 0)$ from their mean is $255$,then $d$ is equal to:

Find the mean deviation about the median for the following data: $3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21$ (in $.27$)

The mean deviation from the median for the following data is:
$x$ $10$ $11$ $12$ $13$
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The mean deviation about the mean of the set of first $n$ natural numbers,when $n$ is an even number,is equal to:

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

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$