Calculate mean deviation using median and coefficient of mean deviation: Class: 5-15 15-25 25-35 35-45 45-55 Frequency: 5 4 5 4 2

C.I. f c.f. M.V.(m) M = 27* |D| = |m - M| f|D| 5-15 5 5 10 17 85 15-25 4 9 20 7 28 25-35 5 14 30 3 15 35-25 4 18 40 13 52 45-55 2 20 50 23 46 =20 |D|=226 Median = ( N 2 )^ th item= (20 2 )=10^thitem, which lies in the class 25-35. M=l_1+ N 2 -c.f. f =25+10-9 5 10 =25+1 5 10=27^* Mean Deviation M= |D| =226 20 =11.3 coefficient of M.D. M= M.D._ M M =11.3 27 =0.41

Calculate mean deviation using median and coefficient of mean dev…

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Question

Calculate mean deviation using median and coefficient of mean deviation:

Class:	5-15	15-25	25-35	35-45	45-55
Frequency:	5	4	5	4	2

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Answer

C.I.	f	c.f.	M.V.(m)	*M = 27 \|D\| = \|m - M\|**	f\|D\|
5-15	5	5	10	17	85
15-25	4	9	20	7	28
25-35	5	14	30	3	15
35-25	4	18	40	13	52
45-55	2	20	50	23	46
	$\Sigma\text{f}=20$				$\Sigma\text{f\|D\|}=226$

Median $=\Big(\frac{\text{N}}2{}\Big)^{\text{th}}\text{item}=\Big(\frac{20}{2}\Big)=10^\text{th}\text{item},$ which lies in the class 25-35.
$\text{M}=\text{l}_1+\frac{\frac{\text{N}}{2}-\text{c.f.}}{\text{f}}\times\text{i}$
$=25+\frac{10-9}{5}\times10$
$=25+\frac{1}{5}\times10=27^*$
Mean Deviation $M=\frac{\Sigma\text{f|D|}}{\Sigma\text{f}}=\frac{226}{20}=11.3$
coefficient of M.D. $M=\frac{\text{M.D.}_{\text{M}}}{\text{M}}$
$=\frac{11.3}{27}=0.41$

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