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2.3 Contoh Implementasi dengan R
## Menghasilkan dataset contoh
set.seed(123)
data <- data.frame(
id = 1:100,
nilai = c(rnorm(97, mean = 50, sd = 10), 150, -20, 200) # Menambahkan 3 outlier
)# Menampilkan data awal
print(head(data))
#> id nilai
#> 1 1 44.39524
#> 2 2 47.69823
#> 3 3 65.58708
#> 4 4 50.70508
#> 5 5 51.29288
#> 6 6 67.15065# Visualisasi data untuk melihat outlier
ggplot(data, aes(x = id, y = nilai)) +
geom_point() +
ggtitle("Visualisasi Data Awal") +
theme_minimal()
# Deteksi Outlier menggunakan Z-Score
data <- data %>%
mutate(z_score = (nilai - mean(nilai)) / sd(nilai),
outlier_z = abs(z_score) > 3)# Menampilkan data dengan Z-Score dan status outlier
print(data)
#> id nilai z_score outlier_z
#> 1 1 44.39524 -0.389888902 FALSE
#> 2 2 47.69823 -0.234391178 FALSE
#> 3 3 65.58708 0.607780249 FALSE
#> 4 4 50.70508 -0.092834318 FALSE
#> 5 5 51.29288 -0.065162186 FALSE
#> 6 6 67.15065 0.681389823 FALSE
#> 7 7 54.60916 0.090961823 FALSE
#> 8 8 37.34939 -0.721593614 FALSE
#> 9 9 43.13147 -0.449384746 FALSE
#> 10 10 45.54338 -0.335836934 FALSE
#> 11 11 62.24082 0.450244821 FALSE
#> 12 12 53.59814 0.043364858 FALSE
#> 13 13 54.00771 0.062646882 FALSE
#> 14 14 51.10683 -0.073921055 FALSE
#> 15 15 44.44159 -0.387707067 FALSE
#> 16 16 67.86913 0.715214486 FALSE
#> 17 17 54.97850 0.108349735 FALSE
#> 18 18 30.33383 -1.051872020 FALSE
#> 19 19 57.01356 0.204155991 FALSE
#> 20 20 45.27209 -0.348608927 FALSE
#> 21 21 39.32176 -0.628738155 FALSE
#> 22 22 47.82025 -0.228646451 FALSE
#> 23 23 39.73996 -0.609050491 FALSE
#> 24 24 42.71109 -0.469175568 FALSE
#> 25 25 43.74961 -0.420284155 FALSE
#> 26 26 33.13307 -0.920089508 FALSE
#> 27 27 58.37787 0.268385027 FALSE
#> 28 28 51.53373 -0.053823273 FALSE
#> 29 29 38.61863 -0.661840209 FALSE
#> 30 30 62.53815 0.464242577 FALSE
#> 31 31 54.26464 0.074742522 FALSE
#> 32 32 47.04929 -0.264941964 FALSE
#> 33 33 58.95126 0.295378894 FALSE
#> 34 34 58.78133 0.287379320 FALSE
#> 35 35 58.21581 0.260755586 FALSE
#> 36 36 56.88640 0.198169721 FALSE
#> 37 37 55.53918 0.134745032 FALSE
#> 38 38 49.38088 -0.155175036 FALSE
#> 39 39 46.94037 -0.270069312 FALSE
#> 40 40 46.19529 -0.305146338 FALSE
#> 41 41 43.05293 -0.453082311 FALSE
#> 42 42 47.92083 -0.223911518 FALSE
#> 43 43 37.34604 -0.721751380 FALSE
#> 44 44 71.68956 0.895072560 FALSE
#> 45 45 62.07962 0.442655944 FALSE
#> 46 46 38.76891 -0.654765163 FALSE
#> 47 47 45.97115 -0.315698320 FALSE
#> 48 48 45.33345 -0.345720196 FALSE
#> 49 49 57.79965 0.241163628 FALSE
#> 50 50 49.16631 -0.165276728 FALSE
#> 51 51 52.53319 -0.006770992 FALSE
#> 52 52 49.71453 -0.139467487 FALSE
#> 53 53 49.57130 -0.146210798 FALSE
#> 54 54 63.68602 0.518282157 FALSE
#> 55 55 47.74229 -0.232316685 FALSE
#> 56 56 65.16471 0.587895586 FALSE
#> 57 57 34.51247 -0.855149894 FALSE
#> 58 58 55.84614 0.149196136 FALSE
#> 59 59 51.23854 -0.067720164 FALSE
#> 60 60 52.15942 -0.024367305 FALSE
#> 61 61 53.79639 0.052698377 FALSE
#> 62 62 44.97677 -0.362512019 FALSE
#> 63 63 46.66793 -0.282895578 FALSE
#> 64 64 39.81425 -0.605553036 FALSE
#> 65 65 39.28209 -0.630605984 FALSE
#> 66 66 53.03529 0.016866925 FALSE
#> 67 67 54.48210 0.084979892 FALSE
#> 68 68 50.53004 -0.101074926 FALSE
#> 69 69 59.22267 0.308156710 FALSE
#> 70 70 70.50085 0.839110354 FALSE
#> 71 71 45.08969 -0.357195838 FALSE
#> 72 72 26.90831 -1.213138474 FALSE
#> 73 73 60.05739 0.347453203 FALSE
#> 74 74 42.90799 -0.459905692 FALSE
#> 75 75 43.11991 -0.449928857 FALSE
#> 76 76 60.25571 0.356790108 FALSE
#> 77 77 47.15227 -0.260093649 FALSE
#> 78 78 37.79282 -0.700717576 FALSE
#> 79 79 51.81303 -0.040674220 FALSE
#> 80 80 48.61109 -0.191415507 FALSE
#> 81 81 50.05764 -0.123314587 FALSE
#> 82 82 53.85280 0.055354008 FALSE
#> 83 83 46.29340 -0.300527531 FALSE
#> 84 84 56.44377 0.177331259 FALSE
#> 85 85 47.79513 -0.229828884 FALSE
#> 86 86 53.31782 0.030168021 FALSE
#> 87 87 60.96839 0.390341480 FALSE
#> 88 88 54.35181 0.078846437 FALSE
#> 89 89 46.74068 -0.279470279 FALSE
#> 90 90 61.48808 0.414807253 FALSE
#> 91 91 59.93504 0.341693368 FALSE
#> 92 92 55.48397 0.132146000 FALSE
#> 93 93 52.38732 -0.013638154 FALSE
#> 94 94 43.72094 -0.421633790 FALSE
#> 95 95 63.60652 0.514539535 FALSE
#> 96 96 43.99740 -0.408618380 FALSE
#> 97 97 71.87333 0.903724094 FALSE
#> 98 98 150.00000 4.581770457 TRUE
#> 99 99 -20.00000 -3.421487344 TRUE
#> 100 100 200.00000 6.935669811 TRUE# Deteksi Outlier menggunakan IQR
Q1 <- quantile(data$nilai, 0.25)
Q3 <- quantile(data$nilai, 0.75)
IQR <- Q3 - Q1
batas_bawah <- Q1 - 1.5 * IQR
batas_atas <- Q3 + 1.5 * IQR
data <- data %>%
mutate(outlier_iqr = nilai < batas_bawah | nilai > batas_atas)# Menampilkan data dengan status outlier berdasarkan IQR
print(data)
#> id nilai z_score outlier_z outlier_iqr
#> 1 1 44.39524 -0.389888902 FALSE FALSE
#> 2 2 47.69823 -0.234391178 FALSE FALSE
#> 3 3 65.58708 0.607780249 FALSE FALSE
#> 4 4 50.70508 -0.092834318 FALSE FALSE
#> 5 5 51.29288 -0.065162186 FALSE FALSE
#> 6 6 67.15065 0.681389823 FALSE FALSE
#> 7 7 54.60916 0.090961823 FALSE FALSE
#> 8 8 37.34939 -0.721593614 FALSE FALSE
#> 9 9 43.13147 -0.449384746 FALSE FALSE
#> 10 10 45.54338 -0.335836934 FALSE FALSE
#> 11 11 62.24082 0.450244821 FALSE FALSE
#> 12 12 53.59814 0.043364858 FALSE FALSE
#> 13 13 54.00771 0.062646882 FALSE FALSE
#> 14 14 51.10683 -0.073921055 FALSE FALSE
#> 15 15 44.44159 -0.387707067 FALSE FALSE
#> 16 16 67.86913 0.715214486 FALSE FALSE
#> 17 17 54.97850 0.108349735 FALSE FALSE
#> 18 18 30.33383 -1.051872020 FALSE FALSE
#> 19 19 57.01356 0.204155991 FALSE FALSE
#> 20 20 45.27209 -0.348608927 FALSE FALSE
#> 21 21 39.32176 -0.628738155 FALSE FALSE
#> 22 22 47.82025 -0.228646451 FALSE FALSE
#> 23 23 39.73996 -0.609050491 FALSE FALSE
#> 24 24 42.71109 -0.469175568 FALSE FALSE
#> 25 25 43.74961 -0.420284155 FALSE FALSE
#> 26 26 33.13307 -0.920089508 FALSE FALSE
#> 27 27 58.37787 0.268385027 FALSE FALSE
#> 28 28 51.53373 -0.053823273 FALSE FALSE
#> 29 29 38.61863 -0.661840209 FALSE FALSE
#> 30 30 62.53815 0.464242577 FALSE FALSE
#> 31 31 54.26464 0.074742522 FALSE FALSE
#> 32 32 47.04929 -0.264941964 FALSE FALSE
#> 33 33 58.95126 0.295378894 FALSE FALSE
#> 34 34 58.78133 0.287379320 FALSE FALSE
#> 35 35 58.21581 0.260755586 FALSE FALSE
#> 36 36 56.88640 0.198169721 FALSE FALSE
#> 37 37 55.53918 0.134745032 FALSE FALSE
#> 38 38 49.38088 -0.155175036 FALSE FALSE
#> 39 39 46.94037 -0.270069312 FALSE FALSE
#> 40 40 46.19529 -0.305146338 FALSE FALSE
#> 41 41 43.05293 -0.453082311 FALSE FALSE
#> 42 42 47.92083 -0.223911518 FALSE FALSE
#> 43 43 37.34604 -0.721751380 FALSE FALSE
#> 44 44 71.68956 0.895072560 FALSE FALSE
#> 45 45 62.07962 0.442655944 FALSE FALSE
#> 46 46 38.76891 -0.654765163 FALSE FALSE
#> 47 47 45.97115 -0.315698320 FALSE FALSE
#> 48 48 45.33345 -0.345720196 FALSE FALSE
#> 49 49 57.79965 0.241163628 FALSE FALSE
#> 50 50 49.16631 -0.165276728 FALSE FALSE
#> 51 51 52.53319 -0.006770992 FALSE FALSE
#> 52 52 49.71453 -0.139467487 FALSE FALSE
#> 53 53 49.57130 -0.146210798 FALSE FALSE
#> 54 54 63.68602 0.518282157 FALSE FALSE
#> 55 55 47.74229 -0.232316685 FALSE FALSE
#> 56 56 65.16471 0.587895586 FALSE FALSE
#> 57 57 34.51247 -0.855149894 FALSE FALSE
#> 58 58 55.84614 0.149196136 FALSE FALSE
#> 59 59 51.23854 -0.067720164 FALSE FALSE
#> 60 60 52.15942 -0.024367305 FALSE FALSE
#> 61 61 53.79639 0.052698377 FALSE FALSE
#> 62 62 44.97677 -0.362512019 FALSE FALSE
#> 63 63 46.66793 -0.282895578 FALSE FALSE
#> 64 64 39.81425 -0.605553036 FALSE FALSE
#> 65 65 39.28209 -0.630605984 FALSE FALSE
#> 66 66 53.03529 0.016866925 FALSE FALSE
#> 67 67 54.48210 0.084979892 FALSE FALSE
#> 68 68 50.53004 -0.101074926 FALSE FALSE
#> 69 69 59.22267 0.308156710 FALSE FALSE
#> 70 70 70.50085 0.839110354 FALSE FALSE
#> 71 71 45.08969 -0.357195838 FALSE FALSE
#> 72 72 26.90831 -1.213138474 FALSE FALSE
#> 73 73 60.05739 0.347453203 FALSE FALSE
#> 74 74 42.90799 -0.459905692 FALSE FALSE
#> 75 75 43.11991 -0.449928857 FALSE FALSE
#> 76 76 60.25571 0.356790108 FALSE FALSE
#> 77 77 47.15227 -0.260093649 FALSE FALSE
#> 78 78 37.79282 -0.700717576 FALSE FALSE
#> 79 79 51.81303 -0.040674220 FALSE FALSE
#> 80 80 48.61109 -0.191415507 FALSE FALSE
#> 81 81 50.05764 -0.123314587 FALSE FALSE
#> 82 82 53.85280 0.055354008 FALSE FALSE
#> 83 83 46.29340 -0.300527531 FALSE FALSE
#> 84 84 56.44377 0.177331259 FALSE FALSE
#> 85 85 47.79513 -0.229828884 FALSE FALSE
#> 86 86 53.31782 0.030168021 FALSE FALSE
#> 87 87 60.96839 0.390341480 FALSE FALSE
#> 88 88 54.35181 0.078846437 FALSE FALSE
#> 89 89 46.74068 -0.279470279 FALSE FALSE
#> 90 90 61.48808 0.414807253 FALSE FALSE
#> 91 91 59.93504 0.341693368 FALSE FALSE
#> 92 92 55.48397 0.132146000 FALSE FALSE
#> 93 93 52.38732 -0.013638154 FALSE FALSE
#> 94 94 43.72094 -0.421633790 FALSE FALSE
#> 95 95 63.60652 0.514539535 FALSE FALSE
#> 96 96 43.99740 -0.408618380 FALSE FALSE
#> 97 97 71.87333 0.903724094 FALSE FALSE
#> 98 98 150.00000 4.581770457 TRUE TRUE
#> 99 99 -20.00000 -3.421487344 TRUE TRUE
#> 100 100 200.00000 6.935669811 TRUE TRUE# Normalisasi Data menggunakan Min-Max Normalization
data <- data %>%
mutate(nilai_normalized = (nilai - min(nilai)) / (max(nilai) - min(nilai)))# Menampilkan data dengan nilai yang dinormalisasi
print(data)
#> id nilai z_score outlier_z outlier_iqr nilai_normalized
#> 1 1 44.39524 -0.389888902 FALSE FALSE 0.2927057
#> 2 2 47.69823 -0.234391178 FALSE FALSE 0.3077192
#> 3 3 65.58708 0.607780249 FALSE FALSE 0.3890322
#> 4 4 50.70508 -0.092834318 FALSE FALSE 0.3213867
#> 5 5 51.29288 -0.065162186 FALSE FALSE 0.3240585
#> 6 6 67.15065 0.681389823 FALSE FALSE 0.3961393
#> 7 7 54.60916 0.090961823 FALSE FALSE 0.3391326
#> 8 8 37.34939 -0.721593614 FALSE FALSE 0.2606790
#> 9 9 43.13147 -0.449384746 FALSE FALSE 0.2869612
#> 10 10 45.54338 -0.335836934 FALSE FALSE 0.2979245
#> 11 11 62.24082 0.450244821 FALSE FALSE 0.3738219
#> 12 12 53.59814 0.043364858 FALSE FALSE 0.3345370
#> 13 13 54.00771 0.062646882 FALSE FALSE 0.3363987
#> 14 14 51.10683 -0.073921055 FALSE FALSE 0.3232129
#> 15 15 44.44159 -0.387707067 FALSE FALSE 0.2929163
#> 16 16 67.86913 0.715214486 FALSE FALSE 0.3994051
#> 17 17 54.97850 0.108349735 FALSE FALSE 0.3408114
#> 18 18 30.33383 -1.051872020 FALSE FALSE 0.2287901
#> 19 19 57.01356 0.204155991 FALSE FALSE 0.3500616
#> 20 20 45.27209 -0.348608927 FALSE FALSE 0.2966913
#> 21 21 39.32176 -0.628738155 FALSE FALSE 0.2696444
#> 22 22 47.82025 -0.228646451 FALSE FALSE 0.3082739
#> 23 23 39.73996 -0.609050491 FALSE FALSE 0.2715453
#> 24 24 42.71109 -0.469175568 FALSE FALSE 0.2850504
#> 25 25 43.74961 -0.420284155 FALSE FALSE 0.2897709
#> 26 26 33.13307 -0.920089508 FALSE FALSE 0.2415139
#> 27 27 58.37787 0.268385027 FALSE FALSE 0.3562630
#> 28 28 51.53373 -0.053823273 FALSE FALSE 0.3251533
#> 29 29 38.61863 -0.661840209 FALSE FALSE 0.2664483
#> 30 30 62.53815 0.464242577 FALSE FALSE 0.3751734
#> 31 31 54.26464 0.074742522 FALSE FALSE 0.3375666
#> 32 32 47.04929 -0.264941964 FALSE FALSE 0.3047695
#> 33 33 58.95126 0.295378894 FALSE FALSE 0.3588693
#> 34 34 58.78133 0.287379320 FALSE FALSE 0.3580970
#> 35 35 58.21581 0.260755586 FALSE FALSE 0.3555264
#> 36 36 56.88640 0.198169721 FALSE FALSE 0.3494836
#> 37 37 55.53918 0.134745032 FALSE FALSE 0.3433599
#> 38 38 49.38088 -0.155175036 FALSE FALSE 0.3153676
#> 39 39 46.94037 -0.270069312 FALSE FALSE 0.3042744
#> 40 40 46.19529 -0.305146338 FALSE FALSE 0.3008877
#> 41 41 43.05293 -0.453082311 FALSE FALSE 0.2866042
#> 42 42 47.92083 -0.223911518 FALSE FALSE 0.3087310
#> 43 43 37.34604 -0.721751380 FALSE FALSE 0.2606638
#> 44 44 71.68956 0.895072560 FALSE FALSE 0.4167707
#> 45 45 62.07962 0.442655944 FALSE FALSE 0.3730892
#> 46 46 38.76891 -0.654765163 FALSE FALSE 0.2671314
#> 47 47 45.97115 -0.315698320 FALSE FALSE 0.2998689
#> 48 48 45.33345 -0.345720196 FALSE FALSE 0.2969702
#> 49 49 57.79965 0.241163628 FALSE FALSE 0.3536348
#> 50 50 49.16631 -0.165276728 FALSE FALSE 0.3143923
#> 51 51 52.53319 -0.006770992 FALSE FALSE 0.3296963
#> 52 52 49.71453 -0.139467487 FALSE FALSE 0.3168842
#> 53 53 49.57130 -0.146210798 FALSE FALSE 0.3162332
#> 54 54 63.68602 0.518282157 FALSE FALSE 0.3803910
#> 55 55 47.74229 -0.232316685 FALSE FALSE 0.3079195
#> 56 56 65.16471 0.587895586 FALSE FALSE 0.3871123
#> 57 57 34.51247 -0.855149894 FALSE FALSE 0.2477840
#> 58 58 55.84614 0.149196136 FALSE FALSE 0.3447552
#> 59 59 51.23854 -0.067720164 FALSE FALSE 0.3238116
#> 60 60 52.15942 -0.024367305 FALSE FALSE 0.3279973
#> 61 61 53.79639 0.052698377 FALSE FALSE 0.3354382
#> 62 62 44.97677 -0.362512019 FALSE FALSE 0.2953489
#> 63 63 46.66793 -0.282895578 FALSE FALSE 0.3030360
#> 64 64 39.81425 -0.605553036 FALSE FALSE 0.2718829
#> 65 65 39.28209 -0.630605984 FALSE FALSE 0.2694640
#> 66 66 53.03529 0.016866925 FALSE FALSE 0.3319786
#> 67 67 54.48210 0.084979892 FALSE FALSE 0.3385550
#> 68 68 50.53004 -0.101074926 FALSE FALSE 0.3205911
#> 69 69 59.22267 0.308156710 FALSE FALSE 0.3601031
#> 70 70 70.50085 0.839110354 FALSE FALSE 0.4113675
#> 71 71 45.08969 -0.357195838 FALSE FALSE 0.2958622
#> 72 72 26.90831 -1.213138474 FALSE FALSE 0.2132196
#> 73 73 60.05739 0.347453203 FALSE FALSE 0.3638972
#> 74 74 42.90799 -0.459905692 FALSE FALSE 0.2859454
#> 75 75 43.11991 -0.449928857 FALSE FALSE 0.2869087
#> 76 76 60.25571 0.356790108 FALSE FALSE 0.3647987
#> 77 77 47.15227 -0.260093649 FALSE FALSE 0.3052376
#> 78 78 37.79282 -0.700717576 FALSE FALSE 0.2626946
#> 79 79 51.81303 -0.040674220 FALSE FALSE 0.3264229
#> 80 80 48.61109 -0.191415507 FALSE FALSE 0.3118686
#> 81 81 50.05764 -0.123314587 FALSE FALSE 0.3184438
#> 82 82 53.85280 0.055354008 FALSE FALSE 0.3356946
#> 83 83 46.29340 -0.300527531 FALSE FALSE 0.3013336
#> 84 84 56.44377 0.177331259 FALSE FALSE 0.3474717
#> 85 85 47.79513 -0.229828884 FALSE FALSE 0.3081597
#> 86 86 53.31782 0.030168021 FALSE FALSE 0.3332628
#> 87 87 60.96839 0.390341480 FALSE FALSE 0.3680381
#> 88 88 54.35181 0.078846437 FALSE FALSE 0.3379628
#> 89 89 46.74068 -0.279470279 FALSE FALSE 0.3033667
#> 90 90 61.48808 0.414807253 FALSE FALSE 0.3704003
#> 91 91 59.93504 0.341693368 FALSE FALSE 0.3633411
#> 92 92 55.48397 0.132146000 FALSE FALSE 0.3431090
#> 93 93 52.38732 -0.013638154 FALSE FALSE 0.3290333
#> 94 94 43.72094 -0.421633790 FALSE FALSE 0.2896406
#> 95 95 63.60652 0.514539535 FALSE FALSE 0.3800297
#> 96 96 43.99740 -0.408618380 FALSE FALSE 0.2908973
#> 97 97 71.87333 0.903724094 FALSE FALSE 0.4176060
#> 98 98 150.00000 4.581770457 TRUE TRUE 0.7727273
#> 99 99 -20.00000 -3.421487344 TRUE TRUE 0.0000000
#> 100 100 200.00000 6.935669811 TRUE TRUE 1.0000000# Normalisasi Data menggunakan Z-Score Normalization
data <- data %>%
mutate(nilai_z_normalized = (nilai - mean(nilai)) / sd(nilai))# Menampilkan data dengan nilai yang dinormalisasi menggunakan Z-Score
print(data)
#> id nilai z_score outlier_z outlier_iqr nilai_normalized
#> 1 1 44.39524 -0.389888902 FALSE FALSE 0.2927057
#> 2 2 47.69823 -0.234391178 FALSE FALSE 0.3077192
#> 3 3 65.58708 0.607780249 FALSE FALSE 0.3890322
#> 4 4 50.70508 -0.092834318 FALSE FALSE 0.3213867
#> 5 5 51.29288 -0.065162186 FALSE FALSE 0.3240585
#> 6 6 67.15065 0.681389823 FALSE FALSE 0.3961393
#> 7 7 54.60916 0.090961823 FALSE FALSE 0.3391326
#> 8 8 37.34939 -0.721593614 FALSE FALSE 0.2606790
#> 9 9 43.13147 -0.449384746 FALSE FALSE 0.2869612
#> 10 10 45.54338 -0.335836934 FALSE FALSE 0.2979245
#> 11 11 62.24082 0.450244821 FALSE FALSE 0.3738219
#> 12 12 53.59814 0.043364858 FALSE FALSE 0.3345370
#> 13 13 54.00771 0.062646882 FALSE FALSE 0.3363987
#> 14 14 51.10683 -0.073921055 FALSE FALSE 0.3232129
#> 15 15 44.44159 -0.387707067 FALSE FALSE 0.2929163
#> 16 16 67.86913 0.715214486 FALSE FALSE 0.3994051
#> 17 17 54.97850 0.108349735 FALSE FALSE 0.3408114
#> 18 18 30.33383 -1.051872020 FALSE FALSE 0.2287901
#> 19 19 57.01356 0.204155991 FALSE FALSE 0.3500616
#> 20 20 45.27209 -0.348608927 FALSE FALSE 0.2966913
#> 21 21 39.32176 -0.628738155 FALSE FALSE 0.2696444
#> 22 22 47.82025 -0.228646451 FALSE FALSE 0.3082739
#> 23 23 39.73996 -0.609050491 FALSE FALSE 0.2715453
#> 24 24 42.71109 -0.469175568 FALSE FALSE 0.2850504
#> 25 25 43.74961 -0.420284155 FALSE FALSE 0.2897709
#> 26 26 33.13307 -0.920089508 FALSE FALSE 0.2415139
#> 27 27 58.37787 0.268385027 FALSE FALSE 0.3562630
#> 28 28 51.53373 -0.053823273 FALSE FALSE 0.3251533
#> 29 29 38.61863 -0.661840209 FALSE FALSE 0.2664483
#> 30 30 62.53815 0.464242577 FALSE FALSE 0.3751734
#> 31 31 54.26464 0.074742522 FALSE FALSE 0.3375666
#> 32 32 47.04929 -0.264941964 FALSE FALSE 0.3047695
#> 33 33 58.95126 0.295378894 FALSE FALSE 0.3588693
#> 34 34 58.78133 0.287379320 FALSE FALSE 0.3580970
#> 35 35 58.21581 0.260755586 FALSE FALSE 0.3555264
#> 36 36 56.88640 0.198169721 FALSE FALSE 0.3494836
#> 37 37 55.53918 0.134745032 FALSE FALSE 0.3433599
#> 38 38 49.38088 -0.155175036 FALSE FALSE 0.3153676
#> 39 39 46.94037 -0.270069312 FALSE FALSE 0.3042744
#> 40 40 46.19529 -0.305146338 FALSE FALSE 0.3008877
#> 41 41 43.05293 -0.453082311 FALSE FALSE 0.2866042
#> 42 42 47.92083 -0.223911518 FALSE FALSE 0.3087310
#> 43 43 37.34604 -0.721751380 FALSE FALSE 0.2606638
#> 44 44 71.68956 0.895072560 FALSE FALSE 0.4167707
#> 45 45 62.07962 0.442655944 FALSE FALSE 0.3730892
#> 46 46 38.76891 -0.654765163 FALSE FALSE 0.2671314
#> 47 47 45.97115 -0.315698320 FALSE FALSE 0.2998689
#> 48 48 45.33345 -0.345720196 FALSE FALSE 0.2969702
#> 49 49 57.79965 0.241163628 FALSE FALSE 0.3536348
#> 50 50 49.16631 -0.165276728 FALSE FALSE 0.3143923
#> 51 51 52.53319 -0.006770992 FALSE FALSE 0.3296963
#> 52 52 49.71453 -0.139467487 FALSE FALSE 0.3168842
#> 53 53 49.57130 -0.146210798 FALSE FALSE 0.3162332
#> 54 54 63.68602 0.518282157 FALSE FALSE 0.3803910
#> 55 55 47.74229 -0.232316685 FALSE FALSE 0.3079195
#> 56 56 65.16471 0.587895586 FALSE FALSE 0.3871123
#> 57 57 34.51247 -0.855149894 FALSE FALSE 0.2477840
#> 58 58 55.84614 0.149196136 FALSE FALSE 0.3447552
#> 59 59 51.23854 -0.067720164 FALSE FALSE 0.3238116
#> 60 60 52.15942 -0.024367305 FALSE FALSE 0.3279973
#> 61 61 53.79639 0.052698377 FALSE FALSE 0.3354382
#> 62 62 44.97677 -0.362512019 FALSE FALSE 0.2953489
#> 63 63 46.66793 -0.282895578 FALSE FALSE 0.3030360
#> 64 64 39.81425 -0.605553036 FALSE FALSE 0.2718829
#> 65 65 39.28209 -0.630605984 FALSE FALSE 0.2694640
#> 66 66 53.03529 0.016866925 FALSE FALSE 0.3319786
#> 67 67 54.48210 0.084979892 FALSE FALSE 0.3385550
#> 68 68 50.53004 -0.101074926 FALSE FALSE 0.3205911
#> 69 69 59.22267 0.308156710 FALSE FALSE 0.3601031
#> 70 70 70.50085 0.839110354 FALSE FALSE 0.4113675
#> 71 71 45.08969 -0.357195838 FALSE FALSE 0.2958622
#> 72 72 26.90831 -1.213138474 FALSE FALSE 0.2132196
#> 73 73 60.05739 0.347453203 FALSE FALSE 0.3638972
#> 74 74 42.90799 -0.459905692 FALSE FALSE 0.2859454
#> 75 75 43.11991 -0.449928857 FALSE FALSE 0.2869087
#> 76 76 60.25571 0.356790108 FALSE FALSE 0.3647987
#> 77 77 47.15227 -0.260093649 FALSE FALSE 0.3052376
#> 78 78 37.79282 -0.700717576 FALSE FALSE 0.2626946
#> 79 79 51.81303 -0.040674220 FALSE FALSE 0.3264229
#> 80 80 48.61109 -0.191415507 FALSE FALSE 0.3118686
#> 81 81 50.05764 -0.123314587 FALSE FALSE 0.3184438
#> 82 82 53.85280 0.055354008 FALSE FALSE 0.3356946
#> 83 83 46.29340 -0.300527531 FALSE FALSE 0.3013336
#> 84 84 56.44377 0.177331259 FALSE FALSE 0.3474717
#> 85 85 47.79513 -0.229828884 FALSE FALSE 0.3081597
#> 86 86 53.31782 0.030168021 FALSE FALSE 0.3332628
#> 87 87 60.96839 0.390341480 FALSE FALSE 0.3680381
#> 88 88 54.35181 0.078846437 FALSE FALSE 0.3379628
#> 89 89 46.74068 -0.279470279 FALSE FALSE 0.3033667
#> 90 90 61.48808 0.414807253 FALSE FALSE 0.3704003
#> 91 91 59.93504 0.341693368 FALSE FALSE 0.3633411
#> 92 92 55.48397 0.132146000 FALSE FALSE 0.3431090
#> 93 93 52.38732 -0.013638154 FALSE FALSE 0.3290333
#> 94 94 43.72094 -0.421633790 FALSE FALSE 0.2896406
#> 95 95 63.60652 0.514539535 FALSE FALSE 0.3800297
#> 96 96 43.99740 -0.408618380 FALSE FALSE 0.2908973
#> 97 97 71.87333 0.903724094 FALSE FALSE 0.4176060
#> 98 98 150.00000 4.581770457 TRUE TRUE 0.7727273
#> 99 99 -20.00000 -3.421487344 TRUE TRUE 0.0000000
#> 100 100 200.00000 6.935669811 TRUE TRUE 1.0000000
#> nilai_z_normalized
#> 1 -0.389888902
#> 2 -0.234391178
#> 3 0.607780249
#> 4 -0.092834318
#> 5 -0.065162186
#> 6 0.681389823
#> 7 0.090961823
#> 8 -0.721593614
#> 9 -0.449384746
#> 10 -0.335836934
#> 11 0.450244821
#> 12 0.043364858
#> 13 0.062646882
#> 14 -0.073921055
#> 15 -0.387707067
#> 16 0.715214486
#> 17 0.108349735
#> 18 -1.051872020
#> 19 0.204155991
#> 20 -0.348608927
#> 21 -0.628738155
#> 22 -0.228646451
#> 23 -0.609050491
#> 24 -0.469175568
#> 25 -0.420284155
#> 26 -0.920089508
#> 27 0.268385027
#> 28 -0.053823273
#> 29 -0.661840209
#> 30 0.464242577
#> 31 0.074742522
#> 32 -0.264941964
#> 33 0.295378894
#> 34 0.287379320
#> 35 0.260755586
#> 36 0.198169721
#> 37 0.134745032
#> 38 -0.155175036
#> 39 -0.270069312
#> 40 -0.305146338
#> 41 -0.453082311
#> 42 -0.223911518
#> 43 -0.721751380
#> 44 0.895072560
#> 45 0.442655944
#> 46 -0.654765163
#> 47 -0.315698320
#> 48 -0.345720196
#> 49 0.241163628
#> 50 -0.165276728
#> 51 -0.006770992
#> 52 -0.139467487
#> 53 -0.146210798
#> 54 0.518282157
#> 55 -0.232316685
#> 56 0.587895586
#> 57 -0.855149894
#> 58 0.149196136
#> 59 -0.067720164
#> 60 -0.024367305
#> 61 0.052698377
#> 62 -0.362512019
#> 63 -0.282895578
#> 64 -0.605553036
#> 65 -0.630605984
#> 66 0.016866925
#> 67 0.084979892
#> 68 -0.101074926
#> 69 0.308156710
#> 70 0.839110354
#> 71 -0.357195838
#> 72 -1.213138474
#> 73 0.347453203
#> 74 -0.459905692
#> 75 -0.449928857
#> 76 0.356790108
#> 77 -0.260093649
#> 78 -0.700717576
#> 79 -0.040674220
#> 80 -0.191415507
#> 81 -0.123314587
#> 82 0.055354008
#> 83 -0.300527531
#> 84 0.177331259
#> 85 -0.229828884
#> 86 0.030168021
#> 87 0.390341480
#> 88 0.078846437
#> 89 -0.279470279
#> 90 0.414807253
#> 91 0.341693368
#> 92 0.132146000
#> 93 -0.013638154
#> 94 -0.421633790
#> 95 0.514539535
#> 96 -0.408618380
#> 97 0.903724094
#> 98 4.581770457
#> 99 -3.421487344
#> 100 6.935669811# Visualisasi data setelah normalisasi
ggplot(data, aes(x = id)) +
geom_line(aes(y = nilai_normalized, color = "Min-Max Normalization")) +
geom_line(aes(y = nilai_z_normalized, color = "Z-Score Normalization")) +
ggtitle("Visualisasi Data Setelah Normalisasi") +
theme_minimal() +
scale_color_manual(values = c("blue", "red")) +
labs(color = "Metode Normalisasi")