Question

How do I find T score and Stanine when (Xbar = 66.73, σ = 5.77)

Height	Z-Score	T-Score	Stanine
64	-0.47
66	-0.13
69	0.39
63	-0.65
68	0.22
62	-0.82
63	-0.65
60	-1.17
66	-0.13
66	-0.13
63	-0.65
68	0.22
75	1.43
68	0.22
65	-0.3
64	-0.47
78	1.95
71	0.74
68	0.22
66	-0.13
53	-2.38
71	0.74
78	1.95
69	0.39
77	1.78
68	0.22
62	-0.82
69	0.39
55	-2.03
67	0.05

Answer 1

Step 1:

Arrange the data in increasing order:

Arrange in
Increasing order
53
55
60
62
62
63
63
63
64
64
65
66
66
66
66
67
68
68
68
68
68
69
69
69
71
71
75
77
78
78

Step 2:

Assign a Stanine score to the scores from Step 1:

Stanine score	Percentage of scores	No. of Scores
1	Bottom 4%	1
2	Next bottom 7%	2
3	Next bottom 12%	4
4	Next Bottom 17%	5
5	Middle 20%	6
6	Next top 17%	5
7	Next top 12%	4
8	Next top 7%	2
9	top 4%	1

Arrange in	Stanine
Increasing order
53	1
55	2
60	2
62	3
62	3
63	3
63	3
63	4
64	4
64	4
65	4
66	4
66	5
66	5
66	5
67	5
68	5
68	5
68	6
68	6
68	6
69	6
69	6
69	7
71	7
71	7
75	7
77	8
78	8
78	9

Height	t-score=	Stanine
x	(x-66.7333)/1.0537
64	-2.594	4
66	-0.6959	5
69	2.1512	7
63	-3.543	3
68	1.2021	5
62	-4.4921	3
63	-3.543	3
60	-6.3901	2
66	-0.6959	4
66	-0.6959	5
63	-3.543	4
68	1.2021	6
75	7.8454	7
68	1.2021	5
65	-1.645	4
64	-2.594	4
78	10.6925	8
71	4.0493	7
68	1.2021	6
66	-0.6959	5
53	-13.0334	1
71	4.0493	7
78	10.6925	9
69	2.1512	6
77	9.7435	8
68	1.2021	6
62	-4.4921	3
69	2.1512	6
55	-11.1353	2
67	0.2531	5