Praktikum 11 APG
Lia Devita Malem Sembiring
2024-12-22
11.5 Penugasan
The admission officer of a business school has used an “index” of undergraduate grade point average (GPA) and graduate management aptitude test (GMAT) scores to help decide which applicants should be admitted to the school’s graduate programs.
Package
library(readxl) #Membaca data
library(dplyr) #Data processing##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(DT) #Menampilkan tabel agar mudah dilihat di browserImport Dataset
Observasi <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56,
57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85)
GPA <- c(2.96, 3.14, 3.22, 3.29, 3.69, 3.46, 3.03, 3.19, 3.63, 3.59, 3.3, 3.4, 3.5, 3.78, 3.44, 3.48, 3.47, 3.35, 3.39, 3.28, 3.21, 3.58, 3.33, 3.4, 3.38, 3.26, 3.6, 3.37, 3.8, 3.76, 3.24, 2.54, 2.43, 2.2, 2.36, 2.57, 2.35, 2.51, 2.51, 2.36, 2.36, 2.66, 2.68, 2.48, 2.46, 2.63, 2.44, 2.13, 2.41, 2.55, 2.31, 2.41, 2.19, 2.35, 2.6, 2.55, 2.72, 2.85, 2.9, 2.86, 2.85, 3.14, 3.28, 2.89, 3.15, 3.5, 2.89, 2.8, 3.13, 3.01, 2.79, 2.89, 2.91, 2.75, 2.73, 3.12, 3.08, 3.03, 3, 3.03, 3.05, 2.85, 3.01, 3.03, 3.04)
GMAT <- c(596, 473, 482, 527, 505, 693, 626, 663, 447, 588, 563, 553, 572, 591, 692, 528, 552, 520, 543, 523, 530, 564, 565, 431, 605, 664, 609, 559, 521, 646, 467, 446, 425, 474, 531, 542, 406, 412, 458, 399, 482, 420, 414, 533, 509, 504, 336, 408, 469, 538, 505, 489, 411, 321, 394, 528, 399, 381, 384, 494, 496, 419, 371, 447, 313, 402, 485, 444, 416, 471, 490, 431, 446, 546, 467, 463, 440, 419, 509, 438, 399, 483, 453, 414, 446)
Data_11 <- data.frame(cbind(Observasi,GPA,GMAT))
Data_11## Observasi GPA GMAT
## 1 1 2.96 596
## 2 2 3.14 473
## 3 3 3.22 482
## 4 4 3.29 527
## 5 5 3.69 505
## 6 6 3.46 693
## 7 7 3.03 626
## 8 8 3.19 663
## 9 9 3.63 447
## 10 10 3.59 588
## 11 11 3.30 563
## 12 12 3.40 553
## 13 13 3.50 572
## 14 14 3.78 591
## 15 15 3.44 692
## 16 16 3.48 528
## 17 17 3.47 552
## 18 18 3.35 520
## 19 19 3.39 543
## 20 20 3.28 523
## 21 21 3.21 530
## 22 22 3.58 564
## 23 23 3.33 565
## 24 24 3.40 431
## 25 25 3.38 605
## 26 26 3.26 664
## 27 27 3.60 609
## 28 28 3.37 559
## 29 29 3.80 521
## 30 30 3.76 646
## 31 31 3.24 467
## 32 32 2.54 446
## 33 33 2.43 425
## 34 34 2.20 474
## 35 35 2.36 531
## 36 36 2.57 542
## 37 37 2.35 406
## 38 38 2.51 412
## 39 39 2.51 458
## 40 40 2.36 399
## 41 41 2.36 482
## 42 42 2.66 420
## 43 43 2.68 414
## 44 44 2.48 533
## 45 45 2.46 509
## 46 46 2.63 504
## 47 47 2.44 336
## 48 48 2.13 408
## 49 49 2.41 469
## 50 50 2.55 538
## 51 51 2.31 505
## 52 52 2.41 489
## 53 53 2.19 411
## 54 54 2.35 321
## 55 55 2.60 394
## 56 56 2.55 528
## 57 57 2.72 399
## 58 58 2.85 381
## 59 59 2.90 384
## 60 60 2.86 494
## 61 61 2.85 496
## 62 62 3.14 419
## 63 63 3.28 371
## 64 64 2.89 447
## 65 65 3.15 313
## 66 66 3.50 402
## 67 67 2.89 485
## 68 68 2.80 444
## 69 69 3.13 416
## 70 70 3.01 471
## 71 71 2.79 490
## 72 72 2.89 431
## 73 73 2.91 446
## 74 74 2.75 546
## 75 75 2.73 467
## 76 76 3.12 463
## 77 77 3.08 440
## 78 78 3.03 419
## 79 79 3.00 509
## 80 80 3.03 438
## 81 81 3.05 399
## 82 82 2.85 483
## 83 83 3.01 453
## 84 84 3.03 414
## 85 85 3.04 446Metode Non Hirarki
Standarisasi Variabel
datatable(Data_11, caption = "Variabel")data_standardized <- round(scale(Data_11[,2:3]),4)
# Hanya memilih kolom/variabel yang berisikan indikator yang akan digunakan
# standarisasi data dilakukan untuk menyamakan semua satuan pengukuran variabel
# perlu dinormalisasi sebelum masuk ke analisis klaster
datatable(data_standardized, caption = "Data Hasil Standardisasi")data_standardized## GPA GMAT
## [1,] -0.0340 1.3193
## [2,] 0.3856 -0.1895
## [3,] 0.5721 -0.0791
## [4,] 0.7352 0.4729
## [5,] 1.6676 0.2030
## [6,] 1.1315 2.5092
## [7,] 0.1292 1.6873
## [8,] 0.5021 2.1412
## [9,] 1.5278 -0.5084
## [10,] 1.4345 1.2212
## [11,] 0.7585 0.9145
## [12,] 0.9916 0.7918
## [13,] 1.2247 1.0249
## [14,] 1.8774 1.2580
## [15,] 1.0849 2.4969
## [16,] 1.1781 0.4852
## [17,] 1.1548 0.7796
## [18,] 0.8751 0.3870
## [19,] 0.9683 0.6692
## [20,] 0.7119 0.4238
## [21,] 0.5488 0.5097
## [22,] 1.4112 0.9268
## [23,] 0.8285 0.9390
## [24,] 0.9916 -0.7047
## [25,] 0.9450 1.4297
## [26,] 0.6653 2.1534
## [27,] 1.4579 1.4788
## [28,] 0.9217 0.8654
## [29,] 1.9241 0.3993
## [30,] 1.8308 1.9326
## [31,] 0.6187 -0.2631
## [32,] -1.0130 -0.5207
## [33,] -1.2695 -0.7783
## [34,] -1.8056 -0.1772
## [35,] -1.4326 0.5220
## [36,] -0.9431 0.6569
## [37,] -1.4559 -1.0113
## [38,] -1.0830 -0.9377
## [39,] -1.0830 -0.3735
## [40,] -1.4326 -1.0972
## [41,] -1.4326 -0.0791
## [42,] -0.7333 -0.8396
## [43,] -0.6867 -0.9132
## [44,] -1.1529 0.5465
## [45,] -1.1995 0.2521
## [46,] -0.8032 0.1908
## [47,] -1.2461 -1.8700
## [48,] -1.9688 -0.9868
## [49,] -1.3161 -0.2385
## [50,] -0.9897 0.6078
## [51,] -1.5492 0.2030
## [52,] -1.3161 0.0068
## [53,] -1.8289 -0.9500
## [54,] -1.4559 -2.0540
## [55,] -0.8732 -1.1585
## [56,] -0.9897 0.4852
## [57,] -0.5935 -1.0972
## [58,] -0.2904 -1.3180
## [59,] -0.1739 -1.2812
## [60,] -0.2671 0.0681
## [61,] -0.2904 0.0926
## [62,] 0.3856 -0.8519
## [63,] 0.7119 -1.4407
## [64,] -0.1972 -0.5084
## [65,] 0.4089 -2.1521
## [66,] 1.2247 -1.0604
## [67,] -0.1972 -0.0423
## [68,] -0.4070 -0.5452
## [69,] 0.3623 -0.8887
## [70,] 0.0825 -0.2140
## [71,] -0.4303 0.0190
## [72,] -0.1972 -0.7047
## [73,] -0.1506 -0.5207
## [74,] -0.5235 0.7060
## [75,] -0.5701 -0.2631
## [76,] 0.3390 -0.3121
## [77,] 0.2457 -0.5943
## [78,] 0.1292 -0.8519
## [79,] 0.0592 0.2521
## [80,] 0.1292 -0.6188
## [81,] 0.1758 -1.0972
## [82,] -0.2904 -0.0668
## [83,] 0.0825 -0.4348
## [84,] 0.1292 -0.9132
## [85,] 0.1525 -0.5207
## attr(,"scaled:center")
## GPA GMAT
## 2.974588 488.447059
## attr(,"scaled:scale")
## GPA GMAT
## 0.4289954 81.5223466Menentukan Jumlah Cluster
jumlah_klaster <- c(1:10) # Vektor yang berisikan jumlah klaster yang ingin dilihat nilai dari total within-cluster sum of squares
within_ss <- c() #Vektor kosong yang akan diisi nilai total within-cluster sum of squares
for (i in jumlah_klaster) {
within_ss <- c(within_ss, kmeans(x = data_standardized, centers = i,
nstart = 25)$tot.withinss)
}
plot(x = jumlah_klaster, y = within_ss, type = "b",
xlab = "Number of Cluster",
ylab = "Total Within Sum of Squares",
main = "Elbow Plot")
abline(v = 6, col='red')
Dari Elbow Plot di atas, dapat dilihat bahwa pada titik ke enam nilai total WSS mulai menunjukkan penurunan yang kurang berarti, sehingga berdasarkan plot tersebut akan ditentukan jumlah klaster yang akan dibentuk adalah enam klaster.
Analisis Cluster
set.seed(123)
kmeans_clustering <- kmeans(x = data_standardized, centers = 6, nstart = 25) #parameter nstart digunakan untuk memberitahu fungsi berapa kali inisiasi centroid awal (secara acak) yang akan dibentuk.
kmeans_clustering## K-means clustering with 6 clusters of sizes 11, 18, 14, 9, 20, 13
##
## Cluster means:
## GPA GMAT
## 1 0.3686273 -1.1418182
## 2 1.1522111 0.6534944
## 3 -1.1812000 0.2363429
## 4 0.8569667 1.9053778
## 5 -0.0165250 -0.2722900
## 6 -1.2031077 -1.0934231
##
## Clustering vector:
## [1] 4 5 5 2 2 4 4 4 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 1 4 4 4 2 2 4 5 6 6 3 3 3 6 6
## [39] 3 6 3 6 6 3 3 3 6 6 3 3 3 3 6 6 6 3 6 1 1 5 5 1 1 5 1 1 5 5 1 5 5 5 5 3 5 5
## [77] 5 1 5 5 1 5 5 1 5
##
## Within cluster sum of squares by cluster:
## [1] 3.765827 5.815443 3.103552 4.562328 3.584926 4.300252
## (between_SS / total_SS = 85.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# X = miu + Z*sigmaDari output : K-means clustering with 6 clusters of sizes 20, 18, 13, 11, 10, 13
dapat di ketahui bahwa klaster pertama beranggotakan 20 observasi, klaster kedua 18 observasi, klaster ketiga 13 observasi, klaster ke empat 11 observasi, klaster kelima 10 observasi, dan klaster keenam 13 observasi.
Centroid
menghitung nilai rata-rata cluster dari setiap variabel
Data_11 %>%
mutate(Klaster = kmeans_clustering$cluster) %>%
group_by(Klaster) %>%
summarise(Mean_GPA= mean(GPA), Mean_GMAT = mean(GMAT))## # A tibble: 6 × 3
## Klaster Mean_GPA Mean_GMAT
## <int> <dbl> <dbl>
## 1 1 3.13 395.
## 2 2 3.47 542.
## 3 3 2.47 508.
## 4 4 3.34 644.
## 5 5 2.97 466.
## 6 6 2.46 399.Pengelompokkan objek ke dalam cluster
Kelompok<-Data_11 %>%
mutate(Klaster = kmeans_clustering$cluster) %>%
select(Observasi , Klaster) %>%
arrange(Klaster)
Kelompok## Observasi Klaster
## 1 24 1
## 2 58 1
## 3 59 1
## 4 62 1
## 5 63 1
## 6 65 1
## 7 66 1
## 8 69 1
## 9 78 1
## 10 81 1
## 11 84 1
## 12 4 2
## 13 5 2
## 14 9 2
## 15 10 2
## 16 11 2
## 17 12 2
## 18 13 2
## 19 14 2
## 20 16 2
## 21 17 2
## 22 18 2
## 23 19 2
## 24 20 2
## 25 21 2
## 26 22 2
## 27 23 2
## 28 28 2
## 29 29 2
## 30 34 3
## 31 35 3
## 32 36 3
## 33 39 3
## 34 41 3
## 35 44 3
## 36 45 3
## 37 46 3
## 38 49 3
## 39 50 3
## 40 51 3
## 41 52 3
## 42 56 3
## 43 74 3
## 44 1 4
## 45 6 4
## 46 7 4
## 47 8 4
## 48 15 4
## 49 25 4
## 50 26 4
## 51 27 4
## 52 30 4
## 53 2 5
## 54 3 5
## 55 31 5
## 56 60 5
## 57 61 5
## 58 64 5
## 59 67 5
## 60 68 5
## 61 70 5
## 62 71 5
## 63 72 5
## 64 73 5
## 65 75 5
## 66 76 5
## 67 77 5
## 68 79 5
## 69 80 5
## 70 82 5
## 71 83 5
## 72 85 5
## 73 32 6
## 74 33 6
## 75 37 6
## 76 38 6
## 77 40 6
## 78 42 6
## 79 43 6
## 80 47 6
## 81 48 6
## 82 53 6
## 83 54 6
## 84 55 6
## 85 57 6Metode Hirarki
library(factoextra)## Loading required package: ggplot2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(dendextend)##
## ---------------------
## Welcome to dendextend version 1.19.0
## Type citation('dendextend') for how to cite the package.
##
## Type browseVignettes(package = 'dendextend') for the package vignette.
## The github page is: https://github.com/talgalili/dendextend/
##
## Suggestions and bug-reports can be submitted at: https://github.com/talgalili/dendextend/issues
## You may ask questions at stackoverflow, use the r and dendextend tags:
## https://stackoverflow.com/questions/tagged/dendextend
##
## To suppress this message use: suppressPackageStartupMessages(library(dendextend))
## ---------------------##
## Attaching package: 'dendextend'## The following object is masked from 'package:stats':
##
## cutreedf2<-scale(Data_11)
fviz_nbclust(df2, FUN=hcut, method="gap_stat")
Dari grafik di atas diperoleh kesimpulan bahwa optimal jumlah cluster
adalah 3, karena gap statistics mencapai puncaknya pada k=3.Setelah k=3
nilai gap statistics mulai stabil atau tidak meningkat signifikan
Single Linkage
data11 <- data.matrix(Data_11)
a=dist(data11, method = "euclidean")
single <- hclust(a, method = "single")
plot(single,hang = -2, cex =0.55)
plot(color_branches(as.dendrogram(single), k = 3))
cluster_member<-cutree(single,k=3)
table(cluster_member)## cluster_member
## 1 2 3
## 77 5 3Pada klaster 1 sebanyak 31 observasi, klaster 2 sebanyak 28 observasi, dan klaster 3 sebanyak 26 observasi.
Menggabungkan data asli dengan data cluster
data_klaster <- data.frame( Data_11 ,Cluster= cluster_member)
klaster1 <- data_klaster[data_klaster$Cluster==1, ]
klaster1## Observasi GPA GMAT Cluster
## 1 1 2.96 596 1
## 2 2 3.14 473 1
## 3 3 3.22 482 1
## 4 4 3.29 527 1
## 5 5 3.69 505 1
## 7 7 3.03 626 1
## 9 9 3.63 447 1
## 10 10 3.59 588 1
## 11 11 3.30 563 1
## 12 12 3.40 553 1
## 13 13 3.50 572 1
## 14 14 3.78 591 1
## 16 16 3.48 528 1
## 17 17 3.47 552 1
## 18 18 3.35 520 1
## 19 19 3.39 543 1
## 20 20 3.28 523 1
## 21 21 3.21 530 1
## 22 22 3.58 564 1
## 23 23 3.33 565 1
## 24 24 3.40 431 1
## 25 25 3.38 605 1
## 27 27 3.60 609 1
## 28 28 3.37 559 1
## 29 29 3.80 521 1
## 31 31 3.24 467 1
## 32 32 2.54 446 1
## 33 33 2.43 425 1
## 34 34 2.20 474 1
## 35 35 2.36 531 1
## 36 36 2.57 542 1
## 37 37 2.35 406 1
## 38 38 2.51 412 1
## 39 39 2.51 458 1
## 40 40 2.36 399 1
## 41 41 2.36 482 1
## 42 42 2.66 420 1
## 43 43 2.68 414 1
## 44 44 2.48 533 1
## 45 45 2.46 509 1
## 46 46 2.63 504 1
## 48 48 2.13 408 1
## 49 49 2.41 469 1
## 50 50 2.55 538 1
## 51 51 2.31 505 1
## 52 52 2.41 489 1
## 53 53 2.19 411 1
## 55 55 2.60 394 1
## 56 56 2.55 528 1
## 57 57 2.72 399 1
## 58 58 2.85 381 1
## 59 59 2.90 384 1
## 60 60 2.86 494 1
## 61 61 2.85 496 1
## 62 62 3.14 419 1
## 63 63 3.28 371 1
## 64 64 2.89 447 1
## 66 66 3.50 402 1
## 67 67 2.89 485 1
## 68 68 2.80 444 1
## 69 69 3.13 416 1
## 70 70 3.01 471 1
## 71 71 2.79 490 1
## 72 72 2.89 431 1
## 73 73 2.91 446 1
## 74 74 2.75 546 1
## 75 75 2.73 467 1
## 76 76 3.12 463 1
## 77 77 3.08 440 1
## 78 78 3.03 419 1
## 79 79 3.00 509 1
## 80 80 3.03 438 1
## 81 81 3.05 399 1
## 82 82 2.85 483 1
## 83 83 3.01 453 1
## 84 84 3.03 414 1
## 85 85 3.04 446 1klaster2 <- data_klaster[data_klaster$Cluster==2, ]
klaster2## Observasi GPA GMAT Cluster
## 6 6 3.46 693 2
## 8 8 3.19 663 2
## 15 15 3.44 692 2
## 26 26 3.26 664 2
## 30 30 3.76 646 2klaster3 <- data_klaster[data_klaster$Cluster==3, ]
klaster3## Observasi GPA GMAT Cluster
## 47 47 2.44 336 3
## 54 54 2.35 321 3
## 65 65 3.15 313 3cluster_mean <- aggregate(. ~Cluster, data = data_klaster, FUN = mean)
cluster_mean## Cluster Observasi GPA GMAT
## 1 1 44.20779 2.958312 482.9870
## 2 2 17.00000 3.422000 671.6000
## 3 3 55.33333 2.646667 323.3333Dari tabel” diatas dapat dilihat observasi mana saja yang masuk ke dalam cluster 1,2,dan 3.Pada tabel cluster mean nilai rata-rata pelamar tertinggi GPA dan GMAT berada pada cluster 1 sedangkan cluster dengan rata-rata pelamar terendah GPA dan GMAT berada pada cluster 3. ketiga cluster dapat diberi nama cluster dengan pelamar GPA dan GMAT “Tinggi”, “Sedang”, dan “Rendah”.
Complete Linkage
b=dist(data11, method = "euclidean")
complete <- hclust(b, method = "complete")
plot(complete,hang = -2, cex =0.56)
plot(color_branches(as.dendrogram(complete), k = 3))
cluster_member2 <- cutree(complete,k=3)
table(cluster_member2)## cluster_member2
## 1 2 3
## 11 37 37Pada klaster 1 sebanyak 11 observasi, klaster 2 sebanyak 37 observasi, dan klaster 3 sebanyak 37 observasi.
Menggabungkan data asli dengan data cluster
data_klaster2 <- data.frame( Data_11 ,Cluster= cluster_member2)
klaster.1 <- data_klaster2[data_klaster2$Cluster==1, ]
klaster.1## Observasi GPA GMAT Cluster
## 1 1 2.96 596 1
## 6 6 3.46 693 1
## 7 7 3.03 626 1
## 8 8 3.19 663 1
## 10 10 3.59 588 1
## 14 14 3.78 591 1
## 15 15 3.44 692 1
## 25 25 3.38 605 1
## 26 26 3.26 664 1
## 27 27 3.60 609 1
## 30 30 3.76 646 1klaster.2 <- data_klaster2[data_klaster2$Cluster==2, ]
klaster.2## Observasi GPA GMAT Cluster
## 2 2 3.14 473 2
## 3 3 3.22 482 2
## 4 4 3.29 527 2
## 5 5 3.69 505 2
## 11 11 3.30 563 2
## 12 12 3.40 553 2
## 13 13 3.50 572 2
## 16 16 3.48 528 2
## 17 17 3.47 552 2
## 18 18 3.35 520 2
## 19 19 3.39 543 2
## 20 20 3.28 523 2
## 21 21 3.21 530 2
## 22 22 3.58 564 2
## 23 23 3.33 565 2
## 28 28 3.37 559 2
## 29 29 3.80 521 2
## 31 31 3.24 467 2
## 34 34 2.20 474 2
## 35 35 2.36 531 2
## 36 36 2.57 542 2
## 41 41 2.36 482 2
## 44 44 2.48 533 2
## 45 45 2.46 509 2
## 46 46 2.63 504 2
## 49 49 2.41 469 2
## 50 50 2.55 538 2
## 51 51 2.31 505 2
## 52 52 2.41 489 2
## 56 56 2.55 528 2
## 60 60 2.86 494 2
## 61 61 2.85 496 2
## 67 67 2.89 485 2
## 71 71 2.79 490 2
## 74 74 2.75 546 2
## 79 79 3.00 509 2
## 82 82 2.85 483 2klaster.3 <- data_klaster2[data_klaster2$Cluster==3, ]
klaster.3## Observasi GPA GMAT Cluster
## 9 9 3.63 447 3
## 24 24 3.40 431 3
## 32 32 2.54 446 3
## 33 33 2.43 425 3
## 37 37 2.35 406 3
## 38 38 2.51 412 3
## 39 39 2.51 458 3
## 40 40 2.36 399 3
## 42 42 2.66 420 3
## 43 43 2.68 414 3
## 47 47 2.44 336 3
## 48 48 2.13 408 3
## 53 53 2.19 411 3
## 54 54 2.35 321 3
## 55 55 2.60 394 3
## 57 57 2.72 399 3
## 58 58 2.85 381 3
## 59 59 2.90 384 3
## 62 62 3.14 419 3
## 63 63 3.28 371 3
## 64 64 2.89 447 3
## 65 65 3.15 313 3
## 66 66 3.50 402 3
## 68 68 2.80 444 3
## 69 69 3.13 416 3
## 70 70 3.01 471 3
## 72 72 2.89 431 3
## 73 73 2.91 446 3
## 75 75 2.73 467 3
## 76 76 3.12 463 3
## 77 77 3.08 440 3
## 78 78 3.03 419 3
## 80 80 3.03 438 3
## 81 81 3.05 399 3
## 83 83 3.01 453 3
## 84 84 3.03 414 3
## 85 85 3.04 446 3cluster_mean2 <- aggregate(. ~Cluster, data = data_klaster2, FUN = mean)
cluster_mean2## Cluster Observasi GPA GMAT
## 1 1 15.36364 3.404545 633.9091
## 2 2 35.86486 2.981622 517.6757
## 3 3 58.35135 2.839730 415.9730Dari tabel” diatas dapat dilihat observasi mana saja yang masuk ke dalam cluster 1,2,dan 3.Pada tabel cluster mean nilai rata-rata pelamar tertinggi GPA dan GMAT berada pada cluster 1 sedangkan cluster dengan rata-rata pelamar terendah GPA dan GMAT berada pada cluster 3. ketiga cluster dapat diberi nama cluster dengan pelamar GPA dan GMAT “Tinggi”, “Sedang”, dan “Rendah”.