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2.2 Metode Matematis 2.2.1 Hulu 1 (Kanan)
No
Jenis Butir
Diameter Phi (mm) (Ξ¦) 0.0625 4.0
1.0 Kerikil 0.125
3.0
0.25
2.0
0.5
1.0
1
0.0
2
1.0
Pasir Sangat 2.0 Kasar 3.0 Pasir Kasar 4.0 Pasir Sedang 5.0 Pasir Halus
Pasir Sangat 6.0 Halus 4
Sortasi:
Berat (gr)
Frekuensi (%)
m.f
m-x
(mx)^2
π.(πβ βπ)π πππ
ππ,π πππ
f(mx)^2
(mx)^3
f(mx)^3
(mx)^4
f(mx)^4
3.5
74.34
15.2
53.3
1.1
1.2
18.4
1.3
20.3
1.5
22.3
2.5
199.92
41.0
102.4
0.1
0.0
0.4
0.0
0.0
0.0
0.0
1.5
201.30
41.2
61.9
-0.9
0.8
33.4
-0.7
-30.1
0.7
27.1
0.5
11.83
2.4
1.2
-1.9
3.6
8.7
-6.9
-16.6
13.0
31.6
-0.5
0.21
0.0
0.0
-2.9
8.4
0.4
-24.4
-1.0
70.7
3.0
-1.5
0.56
0.1
-0.2
-3.9
15.2
1.7
-59.3
-6.8
231.3
26.5
488.16
100.0
218.6
-8.4
29.3
63.1
-90.0
-34.2
317.2
110.5
2.0
Skewness:
πΊπ = β πΊπ = β
Nilai tengah (m)
ππ = ππ =
= 0,794309489 (Moderately Sorted) ππ
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β34,2 100 .
(π,πππ)π
= -0.68297094 (Strongly Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 110,5 100 . (π,πππ)π
π = 2.77637335 (Very Lepto Kurtic)
2.2.2 Hulu 2 (Tengah)
No
Nilai Diameter Phi tengah (mm) (Ξ¦) (m) 0.0625 4.0
Jenis Butir
1.0 Kerikil 0.125
2
-1.0
4
-2.0
Pasir Sangat 6.0 Halus
πΊπ = β
π.(πβ βπ)π πππ
ππ,π πππ
f(m-x)^2
(m-x)^3
f(m-x)^3
(m-x)^4
f(m-x)^4
3.5
25.55
4.9
17.3
1.3
1.7
8.4
2.2
10.9
2.9
14.1
2.5
94.34
18.3
45.7
0.3
0.1
1.6
0.0
0.5
0.0
0.1
1.5
353.00
68.3
102.5
-0.7
0.5
33.5
-0.3
-23.4
0.2
16.4
0.5
42.37
8.2
4.1
-1.7
2.9
23.7
-4.9
-40.3
8.4
68.5
-0.5
1.00
0.2
-0.1
-2.7
7.3
1.4
-19.7
-3.8
53.1
10.3
-1.5
0.28
0.1
-0.1
-3.7
13.7
0.7
-50.7
-2.7
187.4
10.2
516.54
100.0
169.4
-7.2
26.1
69.3
-73.4
-58.9
252.0
119.6
Skewness:
πΊπ = β
(m-x)^2
0.0
5.0 Pasir Halus
Sortasi:
m-x
1.0
4.0 Pasir Sedang 1
m.f
2.0
3.0 Pasir Kasar 0.5
Frekuensi (%)
3.0
Pasir Sangat 2.0 Kasar 0.25
Berat (gr)
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β58,9 100 .
(π,ππ)π
So = 0.832757303 (Moderately Sorted) ππ = -1.020529 (Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 119,6 100 . (π,ππ)π
π = 2.4877 (Very Lepto Kurtic)
2.2.3 Hulu 3 (Kiri)
No
Nilai Diameter Phi tengah (mm) (Ξ¦) (m) 0.0625 4.0
Jenis Butir
1.0 Kerikil 0.125
πΊπ = β
(m-x)^3
f(m-x)^3
(m-x)^4
3.5
44.47
8.9
31.0
1.2
1.4
12.8
1.7
15.3
2.1
18.4
2.5
211.39
42.1
105.3
0.2
0.0
1.7
0.0
0.3
0.0
0.1
1.5
220.00
43.9
65.8
-0.8
0.6
28.1
-0.5
-22.5
0.4
18.0
0.5
25.00
5.0
2.5
-1.8
3.2
16.1
-5.8
-29.1
10.5
52.3
-0.5
0.66
0.1
-0.1
-2.8
7.8
1.0
-22.0
-2.9
61.5
8.1
-1.5
0.13
0.0
0.0
-3.8
14.4
0.4
-54.9
-1.4
208.5
5.4
501.65
100.0
204.5
-7.8
27.6
60.1
-81.4
-40.2
283.0
102.2
-2.0
Sortasi:
Skewness:
πΊπ = β
f(m-x)^2
-1.0
Pasir Sangat 6.0 Halus 4
(m-x)^2
0.0
5.0 Pasir Halus 2
m-x
1.0
4.0 Pasir Sedang 1
m.f
f(mx)^4
2.0
3.0 Pasir Kasar 0.5
Frekuensi (%)
3.0
Pasir Sangat 2.0 Kasar 0.25
Berat (gr)
π.(πβ βπ)π πππ
ππ,π πππ
= 0,775 (Moderately Sorted)
ππ = ππ =
Ξ£π.(πβ βπ)π 100 . πΊππ β40,2 100 . (π,πππ)π
ππ = -0.862856 (Strongly Coarsed Skewed)
Kurtosis: π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 102,2 100 . (π,πππ)π
π = 2.8327 (Very Lepto Kurtic)
2.2.4 Hilir 1 (Kanan)
No
Jenis Butir
Diameter (mm) 0.0625
1.0 Kerikil 0.125
Nilai Phi tengah Berat Frekuensi (Ξ¦) (m) (gr) (%) 4.0 3.5 125.00 25.2 3.0
Pasir Sangat 2.0 Kasar 0.25
1
0.0
2
-1.0
5.0 Pasir Halus Pasir Sangat 6.0 Halus
Sortasi:
πΊπ = β
π.(πβ βπ)π πππ
πππ,π πππ
= 1,019479 (Poorly Sorted)
f(m-x)^3
(m-x)^4
f(m-x)^4
88.1
1.1
1.2
30.5
1.3
33.5
1.5
36.9
2.5
120.76
24.3
60.8
0.1
0.0
0.2
0.0
0.0
0.0
0.0
1.5
196.07
39.5
59.3
-0.9
0.8
32.0
-0.7
-28.8
0.7
25.9
0.5
53.00
10.7
5.3
-1.9
3.6
38.5
-6.9
-73.2
13.0
139.2
-0.5
1.49
0.3
-0.2
-2.9
8.4
2.5
-24.4
-7.3
70.7
21.2
-1.5
0.05
0.0
0.0
-3.9
15.2
0.2
-59.3
-0.6
231.3
2.3
496.37
100.0
213.4
-8.4
29.3
103.9
-90.0
-76.4
317.2
225.5
-2.0
Skewness:
πΊπ = β
f(m-x)^2
1.0
4.0 Pasir Sedang
4
m-x
(mx)^3
2.0
3.0 Pasir Kasar 0.5
m.f
(mx)^2
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β76,4 100 .
(π,ππππ)π
ππ = -0,72112 (Strongly Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 102,2 100 . (π,πππ)π
π = 2.0875 (Very Lepto Kurtic)
2.2.5 Hilir 2 (Tengah)
No
Jenis Butir
1.0 Kerikil
Nilai Diameter Phi tengah Berat Frekuensi (mm) (Ξ¦) (m) (gr) (%) 0.0625 4.0 3.5 160.59 28.5 0.125 3.0
Pasir Sangat 2.0 Kasar 0.25
2.0
0.5
1.0
1
0.0
2
-1.0
3.0 Pasir Kasar 4.0 Pasir Sedang 5.0 Pasir Halus Pasir Sangat 6.0 Halus 4
Sortasi: π.(πβ βπ)π πππ
πππ,π πππ
= 1,066726 (Poorly Sorted)
m-x
f(m-x)^2
(mx)^3
f(m-x)^3
(m-x)^4
f(m-x)^4
99.8
1.3
1.7
48.2
2.2
62.6
2.9
81.4
2.5
126.10
22.4
56.0
0.3
0.1
2.0
0.0
0.6
0.0
0.2
1.5
190.31
33.8
50.7
-0.7
0.5
16.6
-0.3
-11.6
0.2
8.1
0.5
83.00
14.7
7.4
-1.7
2.9
42.6
-4.9
-72.4
8.4
123.1
-0.5
2.88
0.5
-0.3
-2.7
7.3
3.7
-19.7
-10.1
53.1
27.2
-1.5
0.29
0.1
-0.1
-3.7
13.7
0.7
-50.7
-2.6
187.4
9.7
563.17
100.0
213.5
-7.2
26.1
113.8
-73.4
-33.4
252.0
249.7
-2.0
Skewness:
πΊπ = β πΊπ = β
m.f
(mx)^2
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β33,4 100 .
(π,ππ)π
ππ = -0,27533 (Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 249,7 100 . (π,ππ)π
π = 1,928131(Very Lepto Kurtic)
2.2.6 Hilir 3 (Kiri)
No
Jenis Butir
Diameter (mm) 0.0625
1.0 Kerikil 0.125
Nilai Phi tengah Berat Frekuensi (Ξ¦) (m) (gr) (%) 4.0 3.5 122.36 24.5 3.0
Pasir Sangat 2.0 Kasar 0.25
1
0.0
2
-1.0
5.0 Pasir Halus Pasir Sangat 6.0 Halus
Sortasi:
πΊπ = β
π.(πβ βπ)π πππ
πππ,π πππ
= 1,172448 (Poorly Sorted)
f(mx)^3
(m-x)^4
f(mx)^4
85.7
1.2
1.4
35.3
1.7
42.3
2.1
50.8
2.5
93.12
18.6
46.6
0.2
0.0
0.7
0.0
0.1
0.0
0.0
1.5
172.45
34.5
51.8
-0.8
0.6
22.1
-0.5
-17.7
0.4
14.1
0.5
105.14
21.0
10.5
-1.8
3.2
68.2
-5.8
-122.7
10.5
220.9
-0.5
5.73
1.1
-0.6
-2.8
7.8
9.0
-22.0
-25.2
61.5
70.5
-1.5
0.75
0.2
-0.2
-3.8
14.4
2.2
-54.9
-8.2
208.5
31.3
499.55
100.0
193.8
-7.8
27.6
137.5
-81.4
-131.4
283.0
387.7
-2.0
Skewness:
πΊπ = β
(mx)^3
1.0
4.0 Pasir Sedang
4
m-x
f(mx)^2
2.0
3.0 Pasir Kasar 0.5
m.f
(mx)^2
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β131,4 100 .
(π,πππ)π
ππ = -0,81507 (Strongly Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 387,7 100 . (π,πππ)π
π = 2.051798 (Very Lepto Kurtic)
No
Jenis Butir
Diameter Phi (mm) (Ξ¦) 0.0625 4.0
1.0 Kerikil 0.125
3.0
0.25
2.0
0.5
1.0
1
0.0
2
1.0
Pasir Sangat 2.0 Kasar 3.0 Pasir Kasar 4.0 Pasir Sedang 5.0 Pasir Halus
Pasir Sangat 6.0 Halus 4
Sortasi:
Berat (gr)
Frekuensi (%)
m.f
m-x
(mx)^2
π.(πβ βπ)π πππ
ππ,π πππ
f(mx)^2
(mx)^3
f(mx)^3
(mx)^4
f(mx)^4
3.5
74.34
15.2
53.3
1.1
1.2
18.4
1.3
20.3
1.5
22.3
2.5
199.92
41.0
102.4
0.1
0.0
0.4
0.0
0.0
0.0
0.0
1.5
201.30
41.2
61.9
-0.9
0.8
33.4
-0.7
-30.1
0.7
27.1
0.5
11.83
2.4
1.2
-1.9
3.6
8.7
-6.9
-16.6
13.0
31.6
-0.5
0.21
0.0
0.0
-2.9
8.4
0.4
-24.4
-1.0
70.7
3.0
-1.5
0.56
0.1
-0.2
-3.9
15.2
1.7
-59.3
-6.8
231.3
26.5
488.16
100.0
218.6
-8.4
29.3
63.1
-90.0
-34.2
317.2
110.5
2.0
Skewness:
πΊπ = β πΊπ = β
Nilai tengah (m)
ππ = ππ =
= 0,794309489 (Moderately Sorted) ππ
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β34,2 100 .
(π,πππ)π
= -0.68297094 (Strongly Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 110,5 100 . (π,πππ)π
π = 2.77637335 (Very Lepto Kurtic)
2.2.2 Hulu 2 (Tengah)
No
Nilai Diameter Phi tengah (mm) (Ξ¦) (m) 0.0625 4.0
Jenis Butir
1.0 Kerikil 0.125
2
-1.0
4
-2.0
Pasir Sangat 6.0 Halus
πΊπ = β
π.(πβ βπ)π πππ
ππ,π πππ
f(m-x)^2
(m-x)^3
f(m-x)^3
(m-x)^4
f(m-x)^4
3.5
25.55
4.9
17.3
1.3
1.7
8.4
2.2
10.9
2.9
14.1
2.5
94.34
18.3
45.7
0.3
0.1
1.6
0.0
0.5
0.0
0.1
1.5
353.00
68.3
102.5
-0.7
0.5
33.5
-0.3
-23.4
0.2
16.4
0.5
42.37
8.2
4.1
-1.7
2.9
23.7
-4.9
-40.3
8.4
68.5
-0.5
1.00
0.2
-0.1
-2.7
7.3
1.4
-19.7
-3.8
53.1
10.3
-1.5
0.28
0.1
-0.1
-3.7
13.7
0.7
-50.7
-2.7
187.4
10.2
516.54
100.0
169.4
-7.2
26.1
69.3
-73.4
-58.9
252.0
119.6
Skewness:
πΊπ = β
(m-x)^2
0.0
5.0 Pasir Halus
Sortasi:
m-x
1.0
4.0 Pasir Sedang 1
m.f
2.0
3.0 Pasir Kasar 0.5
Frekuensi (%)
3.0
Pasir Sangat 2.0 Kasar 0.25
Berat (gr)
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β58,9 100 .
(π,ππ)π
So = 0.832757303 (Moderately Sorted) ππ = -1.020529 (Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 119,6 100 . (π,ππ)π
π = 2.4877 (Very Lepto Kurtic)
2.2.3 Hulu 3 (Kiri)
No
Nilai Diameter Phi tengah (mm) (Ξ¦) (m) 0.0625 4.0
Jenis Butir
1.0 Kerikil 0.125
πΊπ = β
(m-x)^3
f(m-x)^3
(m-x)^4
3.5
44.47
8.9
31.0
1.2
1.4
12.8
1.7
15.3
2.1
18.4
2.5
211.39
42.1
105.3
0.2
0.0
1.7
0.0
0.3
0.0
0.1
1.5
220.00
43.9
65.8
-0.8
0.6
28.1
-0.5
-22.5
0.4
18.0
0.5
25.00
5.0
2.5
-1.8
3.2
16.1
-5.8
-29.1
10.5
52.3
-0.5
0.66
0.1
-0.1
-2.8
7.8
1.0
-22.0
-2.9
61.5
8.1
-1.5
0.13
0.0
0.0
-3.8
14.4
0.4
-54.9
-1.4
208.5
5.4
501.65
100.0
204.5
-7.8
27.6
60.1
-81.4
-40.2
283.0
102.2
-2.0
Sortasi:
Skewness:
πΊπ = β
f(m-x)^2
-1.0
Pasir Sangat 6.0 Halus 4
(m-x)^2
0.0
5.0 Pasir Halus 2
m-x
1.0
4.0 Pasir Sedang 1
m.f
f(mx)^4
2.0
3.0 Pasir Kasar 0.5
Frekuensi (%)
3.0
Pasir Sangat 2.0 Kasar 0.25
Berat (gr)
π.(πβ βπ)π πππ
ππ,π πππ
= 0,775 (Moderately Sorted)
ππ = ππ =
Ξ£π.(πβ βπ)π 100 . πΊππ β40,2 100 . (π,πππ)π
ππ = -0.862856 (Strongly Coarsed Skewed)
Kurtosis: π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 102,2 100 . (π,πππ)π
π = 2.8327 (Very Lepto Kurtic)
2.2.4 Hilir 1 (Kanan)
No
Jenis Butir
Diameter (mm) 0.0625
1.0 Kerikil 0.125
Nilai Phi tengah Berat Frekuensi (Ξ¦) (m) (gr) (%) 4.0 3.5 125.00 25.2 3.0
Pasir Sangat 2.0 Kasar 0.25
1
0.0
2
-1.0
5.0 Pasir Halus Pasir Sangat 6.0 Halus
Sortasi:
πΊπ = β
π.(πβ βπ)π πππ
πππ,π πππ
= 1,019479 (Poorly Sorted)
f(m-x)^3
(m-x)^4
f(m-x)^4
88.1
1.1
1.2
30.5
1.3
33.5
1.5
36.9
2.5
120.76
24.3
60.8
0.1
0.0
0.2
0.0
0.0
0.0
0.0
1.5
196.07
39.5
59.3
-0.9
0.8
32.0
-0.7
-28.8
0.7
25.9
0.5
53.00
10.7
5.3
-1.9
3.6
38.5
-6.9
-73.2
13.0
139.2
-0.5
1.49
0.3
-0.2
-2.9
8.4
2.5
-24.4
-7.3
70.7
21.2
-1.5
0.05
0.0
0.0
-3.9
15.2
0.2
-59.3
-0.6
231.3
2.3
496.37
100.0
213.4
-8.4
29.3
103.9
-90.0
-76.4
317.2
225.5
-2.0
Skewness:
πΊπ = β
f(m-x)^2
1.0
4.0 Pasir Sedang
4
m-x
(mx)^3
2.0
3.0 Pasir Kasar 0.5
m.f
(mx)^2
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β76,4 100 .
(π,ππππ)π
ππ = -0,72112 (Strongly Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 102,2 100 . (π,πππ)π
π = 2.0875 (Very Lepto Kurtic)
2.2.5 Hilir 2 (Tengah)
No
Jenis Butir
1.0 Kerikil
Nilai Diameter Phi tengah Berat Frekuensi (mm) (Ξ¦) (m) (gr) (%) 0.0625 4.0 3.5 160.59 28.5 0.125 3.0
Pasir Sangat 2.0 Kasar 0.25
2.0
0.5
1.0
1
0.0
2
-1.0
3.0 Pasir Kasar 4.0 Pasir Sedang 5.0 Pasir Halus Pasir Sangat 6.0 Halus 4
Sortasi: π.(πβ βπ)π πππ
πππ,π πππ
= 1,066726 (Poorly Sorted)
m-x
f(m-x)^2
(mx)^3
f(m-x)^3
(m-x)^4
f(m-x)^4
99.8
1.3
1.7
48.2
2.2
62.6
2.9
81.4
2.5
126.10
22.4
56.0
0.3
0.1
2.0
0.0
0.6
0.0
0.2
1.5
190.31
33.8
50.7
-0.7
0.5
16.6
-0.3
-11.6
0.2
8.1
0.5
83.00
14.7
7.4
-1.7
2.9
42.6
-4.9
-72.4
8.4
123.1
-0.5
2.88
0.5
-0.3
-2.7
7.3
3.7
-19.7
-10.1
53.1
27.2
-1.5
0.29
0.1
-0.1
-3.7
13.7
0.7
-50.7
-2.6
187.4
9.7
563.17
100.0
213.5
-7.2
26.1
113.8
-73.4
-33.4
252.0
249.7
-2.0
Skewness:
πΊπ = β πΊπ = β
m.f
(mx)^2
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β33,4 100 .
(π,ππ)π
ππ = -0,27533 (Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 249,7 100 . (π,ππ)π
π = 1,928131(Very Lepto Kurtic)
2.2.6 Hilir 3 (Kiri)
No
Jenis Butir
Diameter (mm) 0.0625
1.0 Kerikil 0.125
Nilai Phi tengah Berat Frekuensi (Ξ¦) (m) (gr) (%) 4.0 3.5 122.36 24.5 3.0
Pasir Sangat 2.0 Kasar 0.25
1
0.0
2
-1.0
5.0 Pasir Halus Pasir Sangat 6.0 Halus
Sortasi:
πΊπ = β
π.(πβ βπ)π πππ
πππ,π πππ
= 1,172448 (Poorly Sorted)
f(mx)^3
(m-x)^4
f(mx)^4
85.7
1.2
1.4
35.3
1.7
42.3
2.1
50.8
2.5
93.12
18.6
46.6
0.2
0.0
0.7
0.0
0.1
0.0
0.0
1.5
172.45
34.5
51.8
-0.8
0.6
22.1
-0.5
-17.7
0.4
14.1
0.5
105.14
21.0
10.5
-1.8
3.2
68.2
-5.8
-122.7
10.5
220.9
-0.5
5.73
1.1
-0.6
-2.8
7.8
9.0
-22.0
-25.2
61.5
70.5
-1.5
0.75
0.2
-0.2
-3.8
14.4
2.2
-54.9
-8.2
208.5
31.3
499.55
100.0
193.8
-7.8
27.6
137.5
-81.4
-131.4
283.0
387.7
-2.0
Skewness:
πΊπ = β
(mx)^3
1.0
4.0 Pasir Sedang
4
m-x
f(mx)^2
2.0
3.0 Pasir Kasar 0.5
m.f
(mx)^2
ππ = ππ =
Kurtosis:
Ξ£π.(πβ βπ)π 100 . πΊππ β131,4 100 .
(π,πππ)π
ππ = -0,81507 (Strongly Coarsed Skewed)
π = π =
Ξ£π.(πβ βπ)π 100 . πΊππ 387,7 100 . (π,πππ)π
π = 2.051798 (Very Lepto Kurtic)
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