Question

Calculate the Mean deviation about median of the following data.

Class interval:	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency:	6	7	15	16	4	2

Answer 1

x	f	Cumulative Frequency
0 - 10	6	6
10 - 20	7	13
20 - 30	15	28
30 - 40	16	44
40 - 50	4	48
50 - 60	2	50
	N = 50

`"N"/2 = 50/2` = 25

∴ Median lies in the interval (20 - 30) and its corresponding values are L = 20, f = 15, pcf = 13, C = 10

∴ Median = `"L" + (("N"/2 - "pcf")/"f") xx "C"`

= `20 + (25 - 13)/15 xx 10`

= `20 + 120/15`

= 20 + 8

= 28

x	f	Mid x	|D| = |X − 28|	f|D|
0 - 10	6	5	23	138
10 - 20	7	15	13	91
20 - 30	15	25	3	45
30 - 40	16	35	7	112
40 - 50	4	45	17	68
50 - 60	2	55	27	54
				∑f|D| = 508

Mean deviation about median = `(sum "f"|"D"|)/"N"`

= `508/50`

= 10.16