Calculate the mean deviation about the mean for the following fre… - Vidyadip

Question

Calculate the mean deviation about the mean for the following frequency distribution:

Class interval	$0-4$	$4-8$	$8-12$	$12-16$	$16-20$
Frequency	$4$	$6$	$8$	$5$	$2$

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Answer

$\text{Class interval}$	$f_i$	$X_i$	$f_ix_i$	$\text{d}_\text{i}=\|\text{x}_\text{i}-\bar{\text{x}}\|$	$f_id_i$
$0-4$	$4$	$2$	$8$	$7.2$	$28.8$
$4-8$	$6$	$6$	$36$	$3.2$	$19.2$
$8-12$	$8$	$10$	$80$	$0.8$	$6.4$
$12-16$	$5$	$14$	$70$	$4.8$	$24.0$
$16-20$	$2$	$18$	$36$	$8.8$	$17.6$
	$N = 16$		$\sum\text{f}_\text{i}\text{x}_\text{i}=230$		$\sum\text{f}_\text{i}\text{d}_\text{i}=96.0$

Mean$=\frac{\sum\text{f}_\text{i}\text{x}_\text{i}}{\text{N}}=\frac{230}{25}=9.2$
And Mean deviation $ =\frac{\sum\text{f}_\text{i}\text{d}_\text{i}}{\text{N}}=\frac{96}{25}=3.84$
Hence$,$ the required $\text{MD} = 3.84$

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