A problem with MEDIAN
in SPSS (computed with procesdure MEANS /cells GMEDIAN )
or in the matrix-program MatMate.

Different computation of medians - reason not clear:

Median of Age in sample:

Software	procedure	All	male	female
SPSS	Gruppierter Median	40.36	42.29	38.22
MatMate	Median	40.80	42.67	39.00

2) Median, documentation of frequencies

(only some categories around the median-category is documented)

Grey: median category, red: category-value; blue cumulated frequencies

All

male

female

Age (k)	freq (f)	Kum freq	Kum Freq %
...
38	6	86	45.50
39	4	90	47.62
40	5	95	50.26
41	6	101	53.44
42	6	107	56.61
43	6	113	59.79
44	6	119	62.96
...
N	189	189	100 %

Age	freq	Kum freq	Kum Freq %
...
40	1	42	44.21
41	3	45	47.37
42	3	48	50.53
43	4	52	54.74
44	3	55	57.89
45	3	58	61.05
47	1	59	62.11
...
N	95	95	100 %

Age	freq	Kum freq	Kum Freq %
...
36	3	40	42.55
37	4	44	46.81
38	5	49	52.13
40	4	53	56.38
41	3	56	59.57
42	3	59	62.77
...
...
N	94	94	100 %

n_0.5 = (189+1)/2 = 95

i=20 (the 20'th category cont. case n_0.5)

k_i = 40 k_i+1 = 41

f_i = 5 cf_i-1 = 90

n_0.5 = (95+1)/2 = 48

i=19 (the 19'th category cont. case n_0.5)

k_i = 42 k_i+1 = 43

f_i = 3 cf_i-1 = 45

n_0.5 = (94+1)/2 = 47.5

i=16 (the 16'th category cont. case n_0.5)

k_i = 38 k_i+1 = 40

f_i = 5 cf_i-1 = 44

x_0.5 =

x_0.5 = = 40.8

x_0.5 =

x_0.5 = = 42.667

x_0.5 =

x_0.5 = = 39.0

Median = 40.8

Median = 42.667

Median = 39.0

SPSS : 40.36

SPSS : 42.29

SPSS : 38.22

---

Legend:

n_0.5 : median-case

i : nr of category containing median-case

k_i : value for median-category

k_i+1 : value for next category

f_i : number of cases in i'th category

cf_i-1 : cumulated number of cases up to (i-1)'th category

Median-formula:= x_0.5 =

---

Data: agesex.txt

age	sex
32	2
29	2
45	2
42	1
52	1
41	1
20	2
44	2
52	2
48	1
79	1
25	2
20	2
22	2
34	2
37	2
54	2
26	1
31	1
44	2
41	2
45	2
42	2
62	1
49	2
61	2
29	2
30	2
29	2
41	2
36	2
42	2
57	2
59	2
29	2
29	2
20	2
64	1
39	1
28	1
21	1
43	1
64	1
33	1
33	2
23	1
57	2
40	1
30	2
33	2
41	1
20	2
78	2
37	2
45	1
34	1
21	1
43	2
44	2
56	2
38	2
43	1
44	1
22	2
61	2
40	2
38	1
53	1
41	1
63	1
45	2
28	2
28	2
30	1
29	1
61	1
29	1
44	1
27	1
64	1
20	2
51	2
29	2
25	1
34	1
28	1
44	1
34	1
28	2
36	2
30	1
23	1
24	1
33	1
61	1
34	1
42	1
31	1
42	2
40	2
20	1
28	1
45	1
23	1
28	2
24	2
51	1
25	1
43	1
21	1
83	1
41	2
56	2
54	2
38	2
27	1
84	1
58	2
30	2
45	2
45	2
56	1
34	1
37	1
61	1
51	2
33	2
38	2
24	2
85	2
25	1
47	1
38	2
79	2
31	2
82	2
40	2
34	2
73	1
53	1
38	2
32	2
42	1
72	1
62	1
84	1
48	2
32	2
22	1
21	2
71	2
36	2
28	2
77	2
50	1
82	1
27	1
45	1
57	1
49	1
70	1
37	2
56	1
56	1
39	1
34	2
33	1
43	1
22	1
62	1
39	1
24	1
40	2
37	2
61	1
39	1
69	2
33	2
43	2
65	1
50	1
60	1
66	2
32	2
78	2
49	2
71	1
77	1
73	1

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