Calculate Mean deviation from Median for the given data.
Wages(Rs) $20$ $18$ $16$ $14$ $12$ $10$ $8$ $6$
Frequency $2$ $4$ $9$ $18$ $27$ $25$ $14$ $1$

6.84

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4.44

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2.24

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3.21

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Solution

The correct option is C $2.24$
$x_{i}$ $f_{i}$ $f_{i} x_{i}$ $| x_{i} - Mean |$ $f_{i} | x_{i} - Mean |$
$20$ $2$ $40$ $8$ $16$
$18$ $4$ $72$ $6$ $24$
$16$ $9$ $144$ $4$ $36$
$14$ $18$ $252$ $2$ $36$
$12$ $27$ $324$ $0$ $0$
$10$ $25$ $250$ $2$ $50$
$8$ $14$ $112$ $4$ $56$
$6$ $1$ $6$ $6$ $6$

$n = 100$ $\sum f_{i} x_{i} = 1200$
$f_{i} | x_{i} - Mean | = 224$
Mean $= \frac{\sum f_{i} x_{i}}{n} = \frac{1200}{100} = 12$
Mean deviation from mean $= \frac{\sum f_{i} | x_{i} - Mean |}{n} = \frac{224}{100} = 2.24$

Suggest Corrections

Group	$6 - 8$	$8 - 10$	$10 - 12$	$12 - 14$	$14 - 16$	$16 - 18$	$18 - 20$
Frequencies	$12$	$20$	$16$	$15$	$17$	$8$	$12$

Wages(Rs)	$20$	$18$	$16$	$14$	$12$	$10$	$8$	$6$
Frequency	$2$	$4$	$9$	$18$	$27$	$25$	$14$	$1$

Score $(x)$	$6$	$20$	$8$	$18$	$16$	$12$	$14$	$10$
Frequency $(f)$	$2$	$7$	$11$	$27$	$18$	$13$	$17$	$5$