Compute Mean deviation about median for the following Frequency distribution.
Variable( $x$ ) $10$ $15$ $20$ $25$ $30$ $35$ $40$ 45
Frequency( $f$ ) $7$ $3$ $8$ $5$ $6$ $8$ $4$ 9

10.5

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Solution

The correct option is C $10.1$
$X i$ $f$ $c . f$ $| X i - M |$ $f i \times | X i - M |$
10 7 7 20 140
15 3 10 15 45
20 8 18 10 80
25 5 23 5 25
30 6 29 (Median Class) 0 0
35 8 37 5 40
40 4 41 10 40
45 9 50 15 135

$\sum f i | X i - M |$ $= 505$

Rank of median $=$ $\frac{N}{2}$ th observation $= 25 t h$

$(\frac{N}{2} + 1)$ th observation $= 26 t h$

Median = $\frac{30 + 30}{2}$ $= 30$

Mean Deviation about Median = $\frac{1}{N} \sum f i | X i - M |$ = $\frac{505}{50}$

Mean Deviation $= 10.1$

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Similar questions

CI	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
$f$	$9$	$13$	$6$	$12$	$9$	$6$	$10$	$15$	$6$	$4$

Marks	0-5	5-10	10-15	15-20	20-25	25-30	30-35	35-40	40-45	45-50
Frequency	3	5	7	8	10	11	14	19	15	13

$C I$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
$f$	$5$	$12$	$3$	$11$	$9$

$x$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f$	$5$	$8$	$15$	$16$	$6$

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Variable( $x$ )	$10$	$15$	$20$	$25$	$30$	$35$	$40$	45
Frequency( $f$ )	$7$	$3$	$8$	$5$	$6$	$8$	$4$	9