Compute mean deviation from mean and coefficient of mean deviatio… - Vidyadip

Question

Compute mean deviation from mean and coefficient of mean deviation:

Weekly Wages (ₛ):	200-400	400-600	600-800	800-1000
No. of Workers:	20	40	30	10

✓

Answer

C.I.	f	M.V.(m)	fm	$\bar{\text{X}}=560\|\text{D}\|=\|\text{m}-\bar{\text{X}}\|$	f\|D\|
200-400	20	300	6,000	260	5,200
400-600	40	500	20,000	60	2,400
600-800	30	700	21,000	140	4,200
800-1000	10	900	9,000	340	3,400
	$\Sigma\text{f}=100$		$\Sigma\text{fm}=56,000$		$\Sigma\text{f\|D\|}=15,200$

$\bar{\text{X}}=\frac{\Sigma\text{fX}}{\Sigma\text{f}}$
$=\frac{56,000}{100}=500$
$\text{M.D.}_{\bar{\text{X}}}=\frac{\Sigma\text{f|D|}}{\Sigma\text{f}}$
$=\frac{15,200}{100}=152$
Coefficient of $\text{M.D.}_{\bar{\text{X}}}=\frac{\text{M.D.}_{\bar{\text{X}}}}{\bar{\text{X}}}$
$=\frac{152}{560}=0.27$

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