Use the 8 subject columns (every column except student_id, in their order), scale them with StandardScaler, and fit PCA() (all components) on the scaled data.
Store the smallest number of components whose explained variance adds up to at least 80% in result.
import io
import pandas as pd
marks = pd.read_csv(io.StringIO("""student_id,maths,physics,chemistry,computer,english,history,economics,geography
1,88,63,82,79,59,62,41,61
2,45,45,60,37,34,39,44,51
3,83,80,90,79,73,83,79,69
4,70,74,71,73,82,85,84,78
5,84,84,89,97,68,73,75,64
6,75,66,69,67,58,43,69,62
7,56,67,65,70,45,49,69,57
8,69,66,64,81,39,38,55,50
9,46,55,40,57,53,51,58,53
10,61,32,47,42,100,100,98,97
11,76,80,77,75,71,59,58,61
12,71,79,93,82,66,84,78,66
13,72,76,90,72,95,100,100,100
14,58,59,44,53,86,82,74,80
15,61,73,65,58,69,57,69,57
16,45,31,35,46,55,39,48,59
17,64,60,65,53,61,56,59,64
18,57,53,59,57,56,47,58,62
19,76,80,87,81,65,62,60,73
20,76,79,74,81,44,41,39,52
21,70,65,69,55,41,41,53,60
22,57,46,48,42,77,76,67,76
23,76,81,87,77,88,65,65,78
24,86,81,90,82,64,68,69,67
25,75,59,68,52,52,48,48,55
26,54,63,54,56,64,82,71,72
27,54,60,65,61,61,55,46,50
28,64,69,76,75,63,62,57,54
29,39,50,47,40,69,75,66,66
30,51,66,63,60,86,84,77,66
31,59,42,39,50,64,69,53,63
32,51,55,53,67,54,56,50,50
33,49,53,58,59,60,63,64,61
34,60,57,55,54,59,67,72,69
35,84,75,79,66,47,59,48,36
36,80,62,76,77,68,55,75,65
37,41,49,39,57,68,45,59,73
38,64,63,76,67,80,84,78,76
39,65,48,54,57,76,69,61,75
40,63,63,60,67,47,54,59,57
41,64,67,54,76,72,72,74,65
42,59,58,51,53,60,55,53,49
43,49,53,56,59,54,47,49,52
44,43,54,42,40,52,74,54,50
45,60,60,72,65,98,100,83,95
46,60,60,64,78,36,40,30,37
47,49,67,58,60,55,58,52,62
48,31,47,46,41,77,78,78,63
49,71,62,59,70,69,80,71,76
50,60,46,58,73,82,62,56,63
51,40,41,55,55,52,43,48,43
52,56,64,56,66,68,57,68,48
53,39,46,47,36,80,92,100,72
54,64,45,70,51,41,37,39,50
55,73,76,78,63,90,91,77,89
56,80,78,76,75,74,78,77,73
57,79,64,67,89,74,52,71,76
58,61,58,62,55,51,41,43,37
59,72,60,73,69,45,46,51,61
60,49,50,65,40,42,45,51,55
61,62,64,53,76,64,71,64,54
62,60,50,61,68,64,74,64,64
63,48,51,70,62,81,95,83,91
64,71,92,79,81,89,86,77,81
65,78,75,69,80,37,34,41,32
66,81,78,83,81,93,100,90,86
67,86,66,71,66,79,79,65,62
68,55,50,41,56,63,58,75,72
69,66,62,58,53,90,80,82,84
70,66,74,72,65,76,77,91,77
71,47,45,54,51,66,53,49,61
72,43,48,52,64,56,47,52,56
73,84,77,75,74,70,72,66,58
74,57,52,57,59,75,78,67,70
75,73,82,71,73,44,54,56,45
76,71,57,65,75,67,66,66,81
77,60,74,76,57,64,70,51,73
78,56,58,44,57,51,46,45,59
79,63,74,80,66,49,52,50,63
80,69,58,73,77,51,49,52,65
81,48,62,77,61,54,46,63,55
82,50,52,57,52,85,67,63,71
83,76,72,64,90,60,68,65,49
84,51,50,48,53,39,39,52,33
85,73,59,67,65,80,94,80,86
86,60,63,56,56,29,36,34,52
87,43,59,46,49,74,70,74,65
88,70,74,69,76,87,64,68,68
89,65,80,73,71,76,70,84,79
90,83,69,81,81,49,49,62,57
91,71,85,88,80,56,70,72,68
92,40,45,36,33,43,34,29,45
93,71,72,74,83,100,100,98,100
94,63,56,56,61,86,76,79,90
95,36,54,47,46,67,74,74,77
96,59,77,53,64,53,63,73,76
97,68,66,74,79,70,72,77,65
98,74,72,74,70,76,71,80,73
99,100,100,100,100,88,73,86,80
100,61,64,64,52,73,62,75,76
101,52,57,50,57,69,67,62,73
102,85,81,93,95,86,77,61,81
103,46,41,58,40,62,75,57,67
104,65,62,68,56,72,69,73,81
105,78,76,76,62,57,75,71,69
106,53,37,53,40,74,68,52,61
107,80,64,68,80,59,60,50,46
108,50,46,61,44,51,54,47,62
109,63,50,61,50,71,67,72,79
110,55,52,57,66,48,51,60,61
111,52,65,55,72,58,67,75,85
112,68,65,70,59,83,81,86,98
113,88,83,87,92,34,42,41,35
114,65,58,62,69,59,67,52,56
115,80,91,89,74,57,63,68,65
116,69,66,65,63,77,53,68,68
117,73,70,60,63,66,53,54,69
118,90,100,100,100,76,81,86,90
119,71,62,63,73,52,52,73,58
120,59,60,58,68,48,66,67,58
121,51,41,48,37,55,70,80,73
122,52,47,51,39,45,45,52,39
123,76,67,73,86,56,64,51,58
124,73,74,70,78,74,67,63,69
125,61,67,62,58,32,38,35,22
126,74,72,71,87,68,57,53,54
127,53,48,65,60,46,35,57,34
128,65,66,58,61,63,75,80,62
129,82,79,75,84,76,66,66,75
130,93,90,83,97,65,66,67,75
131,80,61,71,68,81,66,70,72
132,65,69,81,73,61,60,66,58
133,51,54,40,50,54,44,44,44
134,86,94,83,98,72,72,68,86
135,73,59,59,62,43,68,64,48
136,70,85,79,71,79,72,72,70
137,62,45,56,56,90,91,72,77
138,97,93,81,87,59,54,63,62
139,78,76,77,75,51,52,56,51
140,43,58,52,45,49,45,37,36
141,61,51,64,61,67,54,64,59
142,49,61,46,49,56,47,45,48
143,47,74,59,68,56,60,59,62
144,76,67,77,54,40,65,54,40
145,73,68,73,71,75,59,73,69
146,75,73,83,77,93,89,88,79
147,61,67,58,57,68,90,96,72
148,73,89,81,88,65,71,67,67
149,68,69,68,81,57,59,51,53
150,56,35,36,44,51,68,50,65
151,71,76,85,67,75,72,82,68
152,68,76,52,64,98,90,88,98
153,73,85,62,69,70,76,83,78
154,69,51,56,56,70,85,63,57
155,70,53,65,64,86,85,86,84
156,50,58,43,40,56,45,54,51
157,57,68,55,65,45,31,42,57
158,51,63,48,68,85,80,83,80
159,58,55,67,54,59,51,72,60
160,59,62,69,75,63,68,60,62
161,87,98,98,84,61,65,61,64
162,58,46,65,41,91,92,94,79
163,75,81,64,61,84,73,90,77
164,87,84,86,87,66,62,70,61
165,54,65,57,55,57,59,62,58
166,53,60,70,63,34,41,41,45
167,53,50,51,59,39,33,48,37
168,75,50,58,60,54,49,76,59
169,84,86,76,75,83,69,63,82
170,62,67,68,65,46,40,48,42
171,89,77,64,72,78,81,76,80
172,56,51,71,51,59,58,67,50
173,53,58,54,50,39,39,48,50
174,71,61,64,51,69,76,78,77
175,25,23,23,20,33,26,26,43
176,49,55,36,46,67,67,67,68
177,67,61,74,74,64,69,67,73
178,62,61,53,55,84,95,81,90
179,63,62,73,73,75,68,67,65
180,37,33,51,49,64,53,48,52
181,26,20,28,31,79,84,84,80
182,81,68,71,68,71,75,75,63
183,64,61,71,60,57,56,51,56
184,87,91,77,78,75,88,78,83
185,79,79,79,79,98,95,95,96
186,66,76,77,63,94,69,74,69
187,64,61,61,70,64,48,56,49
188,95,85,100,86,100,100,99,89
189,70,68,72,77,69,66,59,43
190,62,47,51,55,80,74,78,86
191,74,95,83,98,68,79,68,61
192,78,76,70,88,87,88,75,80
193,66,71,63,61,73,72,64,70
194,87,78,83,75,84,79,84,87
195,68,73,86,75,79,73,69,83
196,69,70,90,68,53,61,56,55
197,53,61,52,54,67,72,69,71
198,60,56,55,52,73,78,88,86
199,58,69,65,67,70,61,62,62
200,75,59,74,67,46,47,53,60
201,73,67,71,68,69,60,60,60
202,82,81,99,71,73,82,79,71
203,59,78,64,68,59,62,66,71
204,52,70,65,67,31,42,39,42
205,66,56,79,65,88,95,80,87
206,47,55,65,57,53,53,50,59
207,57,64,65,57,56,65,55,60
208,61,70,65,59,72,63,60,54
209,75,67,60,66,56,51,51,50
210,73,66,69,53,79,93,76,74
211,65,63,59,59,64,74,81,66
212,67,72,58,70,69,67,82,77
213,41,50,52,56,46,52,38,44
214,68,67,67,68,44,26,41,21
215,84,88,78,73,71,87,74,89
216,83,61,64,63,56,61,51,60
217,81,69,81,66,20,29,21,20
218,66,60,71,68,43,58,54,57
219,41,34,45,54,79,66,56,69
220,76,84,80,65,76,73,79,76"""))Store your final answer in a variable named result.
Each hint gives a little more help. Try on your own first.
Run your code to see the output here.