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Find the mean deviation from mean of the following distribution.

written 5.2 years ago by teamques10 ★ 68k

•   modified 5.2 years ago

C.I	0-10	10-20	20-30	30-40	40-50
$F_{i}$	5	8	15	16	6

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written 5.2 years ago by teamques10 ★ 68k

Solution:

C.I	$f_{i}$	$x_{i}$	$f_{I}x_{i}$	$d_{I}=|x_{I}-\bar{x}|$	$f_{I}d_{i}$
0-10	5	5	25	22	110
10-20	8	15	120	12	96
20-30	15	25	375	2	30
30-40	16	35	560	8	128
40-50	6	45	270	18	108
	$\sum f_{I}=50$		$\sum f_{i} x_{I}=1350$		$\sum f_{i} d_{i}=472$

$\operatorname{Mean} \overline{x}=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$\therefore \overline{x}=\frac{1350}{50}$

$\therefore \overline{x}=27$

$M \cdot D=\frac{\sum f_{i} d_{i}}{f_{i}}$

$\therefore M \cdot D=\frac{472}{50}$

$\therefore M \cdot D .=9.44$

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