Student Name: Mira Khairunnisa Binti Muhammad Amin
Certification of Originality
I hereby confirm and understand that:
Plagiarism (copying / cheating) is not permitted, and if caught and found guilty, I will
receive an F grade for this extended assignment and will be subjected to the Academic
Disciplinary Committee.
All answers submitted for this extended assignment is my own original work.
Signature:
Students’s Name:
Question 1
ID
Gender
Background
English
Mathematics
Class
1
Female
M40
84
76
Arts
2
Male
T20
73
78
Science
3
Male
T20
43
98
Science
4
Female
T20
21
99
Science
5
Male
B40
33
40
Engineering
6
Female
M40
77
55
Engineering
7
Male
M40
90
67
Engineering
8
Male
B40
100
54
Others
9
Male
T20
22
33
Engineering
10
Female
T20
42
100
Science
11
Female
M40
12
23
Science
12
Male
M40
98
19
Others
13
Female
B40
78
60
Arts
14
Female
B40
98
69
Arts
15
Female
B40
93
90
Arts
16
Male
M40
94
99
Arts
17
Male
M40
65
11
Engineering
18
Male
M40
47
45
Arts
19
Female
B40
68
65
Science
20
Male
T20
79
78
Engineering
21
Male
T20
30
90
Science
22
Female
T20
89
87
Science
23
Female
B40
70
89
Engineering
24
Female
B40
81
76
Others
25
Female
B40
91
79
Others
26
Male
B40
60
68
Others
27
Male
M40
50
54
Others
28
Female
M40
44
98
Arts
29
Male
M40
32
94
Engineering
30
Male
T20
12
93
Engineering
31
Male
T20
45
90
Engineering
32
Male
T20
76
95
Engineering
Based on the training data furnished, compute the Entropy for each of the following cases:
I. The overall collection of the training data
Class
Total
Arts
7
Engineering
8
Science
11
Others
6
Total
32
= – [7/32 log2 (7/32) + 8/32 log2 (8/32) + 11/32 log2 (11/32) + 6/32 log2 (6/32)]
= – [(-0.4796) + (-0.5) + (-0.5296) + (-0.4528)]
= – (-1.962)
= 1.962
II. Gender attribute
Class/Gender
Male
Female
Arts
2
5
Engineering
9
2
Science
3
5
Others
4
2
Total
18
14
Overall Calculation
= – [18/32 log2 (18/32) + 14/32 log2 (14/32)
= – [ -0.4669 + (-0.5218)]
= – (-0.9887)
= 0.9887
Male
= – [2/18 log2 (2/18) + 9/18 log2 (9/18) + 3/18 log2 (3/18) + 4/18 log 2 (4/18)]
= – [(-0.3552) + (-0.5) + (-0.4308) + (-0.4822)]
= 1.7652
Female
= – [5/14 log (5/14) + 2/14 log2 (2/14) + 5/14 log (5/14) + 2/14 log2 (2/14)]
= – [-0.5305 + (-0.0363) + (-0.5305) + (-0.0363)]
= 1.1336
Weighted Average
= (18/32 x 1.7652) + (14/32 x 1.1336)
= 0.99 + 0.50
= 1.49
III. Background attribute using multiway split
Class/Background
B40
M40
T20
Arts
3
4
0
Engineering
2
4
2
Science
0
1
9
Others
5
2
0
Total
10
11
11
Overall
= – [10/32 log (10/32)] + 11/32 log2 (11/32) + 11/32 log2 (11/32)
= – [-0.5244 + (-0.5296) + (-0.5296)]
= 1.5836
B40
= – [3/10 log2 (3/10) + 2/10 log2 (2/10) + 0 + 5/10 log2 (5/10)]
= – [-0.5211 + (-0.042) + (-0.5)]
= 1.0631
M40
= – [4/11 log (4/11) + 4/11 log (4/11) + 1/11 log2 (1/11) + 2/11 log2 (2/11)]
= – [ -0.5307 + (-0.5307) + (-0.3145) + (-0.4472)
= 1.8231
T20
= – [2/11 log2 (2/11) + 9/11 log2 (9/11)
= – (-0.4472 + (-0.2369))
= 0.6841
Weighted Average
= (10/32 x 1.0631) + (11/32 x 1.8231) + (11/32 x 0.6841)
= 0.3322 + 0.6267 + 0.2352
= 1.194
IV. English attribute using multiway splits (<= 64, >= 65 and < 80, and >= 80)
Class/Marks
<= 64
>= 65 and < 80
>= 80
Arts
2
1
4
Engineering
5
5
1
Science
5
2
1
Others
2
0
4
Total
14
8
10
Split <= 64
= – [(2/14 log2 (2/14) + 5/14 log2 (5/14) + 2/14 log2 (2/14) + 5/14 log2 (5/14)]
= – [-0.4011 + (-0.4011) + (-0.5305) + (-0.5305)
= 1.8632
Split >= 65 and <80
= – [1/8 log2 (1/8) + 5/18 log2 (5/18) + 2/8 log2 (2/8)]
= – [ -0.375 + (-0.4238) + (-0.5)]
= 1.2988
Split >= 80
= – [4/10 log2 (4/10) + (1/10 log2 (1/10) + 4/10 log2 (4/10) + (1/10 log2 (1/10)]
= – (-0.5288 + (-0.5288) + (-0.3322) + (-0.3322)
= 1.722
Weighted Average
= (14/32 x 1.8632) + (8/32 x 1.2988) + (10/32 x 1.722)
= 0.8152 + 0.3247 + 0.5381
= 1.678
V. Mathematics attribute using multiway splits (<= 64, >= 65 and < 80, and >= 80)
Class/Marks
<= 64
>= 65 and < 80
>= 80
Arts
2
2
3
Engineering
4
2
5
Science
1
2
5
Others
3
3
0
Total
10
9
13
Split <= 64
= – [2/10 log2 (2/10) + 4/10 log2 (4/10) + 1/10 log2 (1/10) + 3/10 log2 (3/10)]
= – [ -0.4644 + (-0.5288) + (-0.3322) + (-0.5211)
= 1.8465
Split >=65 and <80
= – [2/9 log2 (2/9) + 2/9 log2 (2/9) + 2/9 log2 (2/9) + 3/9 log2 (3/9)
= -(-0.4822) + (-0.4822) + (-0.4822) + (-0.5211)
=1.9749
Split >= 80
= – [3/13 log2 (3/13) + 5/13 log2 (5/13) + 5/13 log2 (5/13)]
= – [ -0.4882 + (-0.5302) + (-0.5302)]
= 1.5486
Weighted Average
= (10/32 x 1.8465) + (9/32 x 1.9749) + (13/32 x 1.5486)
= 0.5770 + 0.5554 + 0.6291
