Calculate M.D about Mean for the given data
Size of item $4$ $6$ $8$ $10$ $12$ $14$ $16$
Frequency $2$ $1$ $3$ $6$ $4$ $3$ $1$

6.12

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5.12

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2.44

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3.44

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Solution

The correct option is C $2.44$
$x_{i}$ $f_{i}$ $f_{i} x_{i}$ $| x_{i} - Mean |$ $f_{i} | x_{i} - Mean |$
$4$ $2$ $8$ $6.2$ $12.4$
$6$ $1$ $6$ $4.2$ $4.2$
$8$ $3$ $24$ $2.2$ $6.6$
$10$ $6$ $60$ $0.2$ $1.2$
$12$ $4$ $48$ $1.8$ $7.2$
$14$ $3$ $42$ $3.8$ $11.4$
$16$ $1$ $16$ $5.8$ $5.8$
$n = 20$ $\sum f_{i} x_{i} = 204$ $\sum f_{i} | x_{i} - Mean | = 48.8$
Mean $= \frac{\sum f_{i} x_{i}}{n} = \frac{204}{20} = 10.2$
Mean deviation about Mean $= \frac{\sum f_{i} | x_{i} - Mean |}{n} = \frac{48.8}{20} = 2.44$

Suggest Corrections

$X$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$	$10 - 12$	$12 - 14$	$14 - 16$
$F$	$1$	$2$	$2$	$3$	$6$	$3$	$2$

Size of item	$4$	$6$	$8$	$10$	$12$	$14$	$16$
Frequency	$2$	$1$	$3$	$6$	$4$	$3$	$1$

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