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Raw Sc. (X): , Pop. Mean (μ): , St. Dev. (σ):
z = (X - μ) / σ = (100 - 50) / 75= 0.6667
 
St. Dev. (σ) - Population standard deviation. It is measurement, how much data is spread out. It is distance away from a mean.
Raw Sc. (X) - Raw score. The raw score is simply unchanged some test or tracking data. For example, it can be amount of answered questions from some test or some value from observation.
Pop. Mean (μ) - Population mean. In statistics, the population mean is the average of a set of data. Practically, in real life the average of data set and the mean are the same things.

Examples:

z scores for μ = 50 and σ = 75

Raw Sc. (X) Z score
81 0.4133
82 0.4267
83 0.44
84 0.4533
85 0.4667
86 0.48
87 0.4933
88 0.5067
89 0.52
90 0.5333
91 0.5467
92 0.56
93 0.5733
94 0.5867
95 0.6
96 0.6133
97 0.6267
98 0.64
99 0.6533
100 0.6667
101 0.68
102 0.6933
103 0.7067
104 0.72
105 0.7333
106 0.7467
107 0.76
108 0.7733
109 0.7867
110 0.8
111 0.8133
112 0.8267
113 0.84
114 0.8533
115 0.8667
116 0.88
117 0.8933
118 0.9067
119 0.92
120 0.9333

z scores for X = 100 and σ = 75

Pop. Mean (μ) Z score
31 0.92
32 0.9067
33 0.8933
34 0.88
35 0.8667
36 0.8533
37 0.84
38 0.8267
39 0.8133
40 0.8
41 0.7867
42 0.7733
43 0.76
44 0.7467
45 0.7333
46 0.72
47 0.7067
48 0.6933
49 0.68
50 0.6667
51 0.6533
52 0.64
53 0.6267
54 0.6133
55 0.6
56 0.5867
57 0.5733
58 0.56
59 0.5467
60 0.5333
61 0.52
62 0.5067
63 0.4933
64 0.48
65 0.4667
66 0.4533
67 0.44
68 0.4267
69 0.4133
70 0.4

z scores for X = 100 and μ = 50

St. Dev. (σ) Z score
55 0.9091
56 0.8929
57 0.8772
58 0.8621
59 0.8475
60 0.8333
61 0.8197
62 0.8065
63 0.7937
64 0.7813
65 0.7692
66 0.7576
67 0.7463
68 0.7353
69 0.7246
70 0.7143
71 0.7042
72 0.6944
73 0.6849
74 0.6757
75 0.6667
76 0.6579
77 0.6494
78 0.641
79 0.6329
80 0.625
81 0.6173
82 0.6098
83 0.6024
84 0.5952
85 0.5882
86 0.5814
87 0.5747
88 0.5682
89 0.5618
90 0.5556
91 0.5495
92 0.5435
93 0.5376
94 0.5319
 
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