Question

Compute mean deviation about median from the following data:

Height in inches	No. of students
58	15
59	20
60	32
61	35
62	35
63	22
64	20
65	10
66	8

Answer 1

X	f	cf
58	15	15
59	20	35
60	32	67
61	35	102
62	35	137
63	22	159
64	20	179
65	10	189
66	8	197
	N = 197

Median = Size of `(("N" + 1)/2)^"th"` value

= Size of `((197 + 1)/2)^"th"` value

= Size of `(198/2)^"th"` value

= Size of 99^th value

= 99^th item

= 61

MD about median = `(sum"f" |"X" - "Median"|)/"N" = (sum"f" |"D"|)/"N"`

Mean deviation about median:

X	f	|D| = `|"X" - bar"X"|` = |X − 61|	f|D|
58	15	3	45
59	20	2	40
60	32	1	32
61	35	0	0
62	35	1	35
63	22	2	44
64	20	3	60
65	10	4	40
66	8	5	40
	N = 197		∑f|D| = 336

MD about median = `(sum"f" |"D"|)/"N" = 336/197` = 1.70558 = 1.71