1. There are 500 client records in the first sheet of the file Toy-Info which ha
ID: 3370085 • Letter: 1
Question
1. There are 500 client records in the first sheet of the file Toy-Info which have shopped many special toys from an e-Business website. Each record includes data on types of product purchased (between 1-5), purchase amount ($), age, gender, marital status, whether the client has a membership and whether the customer has a discount card. A business analyst has applied the k-means clustering method on all seven variables. The analyst increased the number of clusters to recommend a proper value of k. The resultant tests for k=5 and k=6 shown in the following sheets of the file revealed the best k as k=6. a) Explain how the analyst found that k=6 is a proper number of clusters. Refer the relevant sheet name, table name and the values you compared. b) Describe all 6 clusters by their average characteristics
Types of Products Perchase amount ($) Age Gender Marital Status Membership Discount card 2 666.0 30 0 0 0 1 2 1362.0 37 1 1 1 1 3 1406.0 37 0 0 1 0 4 884.0 23 1 1 1 1 5 1108.0 39 1 1 0 1 5 1491.0 55 0 0 0 1 5 587.0 77 0 1 0 0 4 844.0 25 1 1 0 1 3 1106.0 66 1 0 1 1 1 714.0 46 0 1 1 1 5 730.0 53 0 1 1 0 3 586.0 22 0 0 0 0 4 532.0 19 1 0 1 1 5 979.0 24 0 1 0 0 5 800.0 43 0 0 0 1 2 1301.0 49 0 1 0 1 3 1064.0 67 1 0 0 0 5 1012.0 60 0 0 0 1 5 837.0 58 0 0 0 1 4 709.0 72 1 1 0 0 4 512.0 42 1 1 1 0 3 966.0 66 0 0 0 0 4 1138.0 54 1 1 0 0 5 1142.0 43 0 1 0 0 2 706.0 33 0 0 1 1 3 1376.0 38 0 1 0 1 2 523.0 40 0 0 0 0 3 1380.0 60 0 1 1 1 3 1108.0 31 0 1 0 1 3 950.0 38 0 0 1 0 1 1077.0 57 0 1 1 0 4 1029.0 23 1 1 0 1 2 801.0 46 0 0 0 0 4 1232.0 76 1 0 1 0 1 1296.0 53 0 0 0 1 3 724.0 53 1 0 0 1 3 1010.0 33 1 1 1 0 1 662.0 54 1 1 1 0 2 1027.0 61 0 1 1 1 2 934.0 63 1 0 1 0 3 809.0 62 0 1 1 0 2 1067.0 40 1 0 1 0 5 1109.0 63 1 0 1 0 1 651.0 76 1 1 1 1 2 1185.0 72 1 1 1 0 3 1124.0 53 0 0 0 1 3 1137.0 27 1 0 1 0 2 742.0 28 1 0 0 0 3 1086.0 74 1 0 0 1 4 803.0 55 0 1 1 1 3 1227.0 54 0 0 1 0 2 1260.0 53 1 0 0 1 1 646.0 77 1 1 1 0 2 1348.0 21 1 0 0 1 5 1222.0 61 0 1 0 0 4 1467.0 33 0 1 0 0 5 1212.0 49 1 0 1 1 2 807.0 29 1 0 0 0 3 1213.0 69 0 0 0 1 2 881.0 38 1 1 0 0 5 1347.0 62 1 0 0 0 3 650.0 65 1 1 0 0 4 810.0 64 1 1 0 0 5 1104.0 72 1 1 1 0 3 1456.0 48 0 1 1 0 4 513.0 31 1 1 0 1 2 1043.0 24 0 0 0 0 1 731.0 49 0 1 0 1 5 1202.0 71 0 1 0 0 4 587.0 34 1 0 0 1 5 1321.0 70 1 1 0 0 2 1103.0 55 1 1 1 1 2 1352.0 46 0 0 0 1 2 685.0 19 0 1 1 1 5 1342.0 17 0 1 1 1 1 1202.0 60 1 1 0 1 4 1229.0 57 1 0 1 1 1 532.0 44 0 0 1 0 2 1366.0 37 1 1 1 0 4 1461.0 75 0 0 0 1 5 1408.0 73 0 1 1 0 2 1287.0 46 0 0 0 1 4 752.0 25 1 1 0 0 4 768.0 42 1 0 0 1 3 821.0 34 1 0 0 1 1 856.0 50 1 0 1 0 5 1174.0 70 0 1 1 1 4 1451.0 24 0 0 0 0 1 936.0 47 0 0 1 1 4 992.0 67 1 0 1 0 3 1414.0 46 0 1 1 1 3 523.0 31 0 0 0 0 3 1140.0 33 0 1 1 1 2 752.0 72 0 0 0 1 2 1141.0 48 1 1 1 1 2 966.0 62 0 1 1 1 4 1014.0 58 0 0 0 1 5 1309.0 35 0 0 1 1 2 585.0 64 1 0 0 1 2 1339.0 61 0 0 1 1 2 633.0 19 0 0 1 0 2 672.0 41 1 1 0 0 3 507.0 47 1 0 1 0 1 1490.0 66 1 1 1 0 4 562.0 29 1 0 1 0 5 1337.0 35 0 1 0 1 5 1376.0 77 0 1 1 1 4 651.0 60 1 1 1 0 5 685.0 51 1 1 1 0 3 1396.0 34 0 0 1 0 1 1157.0 40 1 1 1 1 1 701.0 47 1 0 1 1 3 553.0 72 1 0 1 1 2 1146.0 22 0 1 1 0 1 616.0 77 0 0 0 1 2 872.0 48 1 1 1 0 3 1379.0 28 1 0 1 1 2 721.0 71 1 0 0 0 4 548.0 32 0 0 1 1 1 690.0 53 0 0 1 1 4 1346.0 51 1 1 1 1 3 778.0 31 0 0 0 1 5 837.0 36 1 0 0 0 2 1421.0 50 0 1 0 0 2 1396.0 51 0 0 0 1 3 778.0 63 0 1 1 0 2 754.0 18 0 0 1 1 2 808.0 41 1 0 0 0 3 1136.0 69 0 0 1 0 2 878.0 60 1 0 1 0 3 1392.0 23 1 0 0 1 5 1387.0 55 1 1 1 0 1 1034.0 55 0 1 1 1 4 977.0 51 0 1 0 1 3 651.0 75 1 1 1 0 2 1142.0 44 0 1 1 0 1 546.0 49 1 1 0 0 3 946.0 44 0 1 1 1 5 688.0 21 0 1 0 0 1 815.0 75 0 1 1 0 5 1351.0 70 0 1 0 0 4 567.0 52 1 1 0 0 4 1210.0 26 0 0 1 0 2 610.0 60 1 1 1 0 5 1327.0 52 0 0 1 0 3 1218.0 61 1 0 1 1 4 554.0 54 1 0 1 0 5 614.0 59 1 1 1 1 3 1437.0 54 1 0 0 1 2 832.0 59 0 1 1 0 4 926.0 39 0 0 1 0 4 683.0 45 0 1 1 1 3 1190.0 56 0 0 0 1 2 1168.0 76 0 0 0 0 5 727.0 26 0 1 1 0 3 1093.0 21 1 1 1 1 5 806.0 40 1 0 1 1 5 908.0 32 0 0 0 1 3 1367.0 63 1 1 0 0 3 734.0 68 0 0 1 1 2 769.0 47 1 1 0 1 5 638.0 42 0 0 1 0 3 1465.0 50 1 0 0 0 4 1122.0 38 1 1 0 0 3 914.0 49 1 0 0 1 2 1219.0 37 0 1 1 1 3 854.0 70 1 0 1 0 5 1014.0 75 1 0 0 1 2 696.0 57 0 0 0 1 4 593.0 27 1 0 1 1 4 1287.0 47 1 1 0 0 3 915.0 22 0 0 1 0 4 810.0 69 1 1 1 1 4 551.0 60 1 1 0 1 4 1257.0 60 1 0 0 0 2 1243.0 53 0 0 0 0 5 813.0 24 1 0 0 0 1 1497.0 18 0 0 1 0 4 834.0 35 0 0 1 1 2 1443.0 38 0 1 1 1 1 900.0 43 1 0 1 1 4 736.0 45 1 0 1 1 5 923.0 78 1 0 0 1 3 836.0 57 0 0 1 1 4 501.0 28 1 1 1 0 5 1318.0 72 0 1 1 1 4 858.0 53 0 0 1 1 2 1466.0 37 1 1 0 0 3 842.0 50 1 1 0 1 3 974.0 33 1 0 0 0 4 726.0 42 1 1 0 0 4 752.0 25 0 1 1 1 5 1138.0 51 0 0 0 0 3 1161.0 65 1 1 1 1 5 1338.0 29 1 0 0 0 3 1197.0 58 1 0 1 0 1 567.0 60 1 0 0 0 3 772.0 26 0 1 0 0 3 1245.0 25 1 1 1 1 5 964.0 66 0 1 1 1 3 682.0 36 1 1 0 0 2 514.0 51 0 0 1 1 4 714.0 30 0 1 1 1 5 582.0 43 0 1 0 0 5 1424.0 68 1 0 0 0 5 509.0 77 0 1 0 1 5 1060.0 42 0 1 1 1 2 560.0 36 1 0 1 0 3 1378.0 32 0 0 1 0 3 1133.0 22 0 0 0 0 3 1252.0 23 0 0 0 0 3 1215.0 55 0 1 1 1 2 1448.0 55 1 1 0 0 3 632.0 54 1 1 1 1 2 1185.0 27 0 0 1 0 2 1462.0 33 1 0 0 1 3 588.0 29 0 0 1 1 4 545.0 35 0 0 0 0 3 536.0 77 1 1 1 1 1 873.0 44 1 0 0 1 2 756.0 71 0 1 1 0 1 1467.0 50 1 0 0 1 4 610.0 16 1 0 1 1 4 775.0 52 1 0 1 0 3 749.0 50 1 0 0 1 5 1176.0 53 0 1 1 0 2 1073.0 19 0 1 0 1 2 670.0 18 0 0 1 0 3 1065.0 22 0 0 0 1 5 664.0 39 0 0 0 1 4 985.0 16 1 1 1 1 5 759.0 58 1 1 0 1 2 1457.0 63 0 1 0 0 4 1102.0 22 1 1 1 1 4 1039.0 17 1 0 0 1 3 850.0 75 0 0 0 1 3 1336.0 27 0 1 1 1 2 1261.0 53 1 1 1 0 2 1415.0 71 0 1 1 1 5 1431.0 31 1 0 0 0 4 671.0 33 0 1 0 0 4 1435.0 39 0 1 0 1 4 1140.0 69 0 0 0 0 5 1193.0 33 0 0 1 0 3 547.0 27 1 1 0 1 2 1379.0 41 1 1 0 1 2 1388.0 32 1 0 1 1 3 781.0 50 0 1 1 1 2 1046.0 29 0 1 1 0 3 1320.0 71 1 1 1 1 5 597.0 47 0 0 1 0 4 1051.0 29 1 0 1 1 2 585.0 31 0 1 1 1 2 534.0 62 0 1 0 0 2 828.0 66 1 0 1 0 3 624.0 49 1 0 1 0 3 1392.0 44 1 1 1 0 1 567.0 17 0 1 1 0 2 1265.0 65 1 1 1 0 5 1007.0 47 0 0 0 0 4 1264.0 61 0 1 0 0 2 582.0 31 0 0 1 1 1 1267.0 71 0 1 0 0 3 1071.0 41 1 0 0 0 3 1254.0 63 1 1 1 1 1 906.0 59 1 1 1 1 5 867.0 42 0 1 0 1 2 1162.0 32 0 1 1 1 2 1472.0 31 0 1 1 0 5 1282.0 58 1 0 0 0 3 1145.0 21 0 1 0 0 5 628.0 67 1 1 1 1 4 619.0 73 1 0 0 1 4 864.0 63 1 1 1 0 2 1357.0 26 1 0 0 1 4 1044.0 58 1 0 1 0 5 1442.0 20 0 0 1 0 3 1491.0 21 0 1 1 1 1 1242.0 68 1 1 1 1 5 917.0 71 1 0 1 1 2 749.0 30 0 0 0 0 4 1268.0 64 0 0 0 0 5 1412.0 20 0 0 0 0 5 1145.0 21 1 1 0 0 5 1142.0 50 1 0 1 1 1 979.0 40 0 1 0 0 2 1222.0 39 0 1 0 0 3 1026.0 53 1 1 1 1 4 1136.0 70 0 0 1 0 5 1376.0 54 1 1 1 0 2 1042.0 74 0 1 1 0 3 1078.0 66 0 1 1 0 1 799.0 53 1 0 0 1 4 868.0 73 0 0 1 1 3 1314.0 52 0 1 1 0 3 1477.0 74 1 1 1 0 4 589.0 55 0 0 0 1 4 632.0 57 1 0 1 1 3 1330.0 63 0 1 0 0 3 1364.0 57 0 1 1 1 4 538.0 43 0 0 0 1 1 702.0 30 1 1 1 1 3 1108.0 27 0 0 1 0 5 831.0 60 1 0 0 1 3 1434.0 50 0 0 1 0 4 1040.0 48 1 0 1 1 5 1295.0 41 0 0 1 0 5 843.0 74 0 1 0 0 5 1159.0 39 1 1 0 0 5 1138.0 62 0 0 0 1 4 1485.0 68 0 0 1 0 5 902.0 68 0 1 0 1 3 851.0 68 1 1 1 0 2 1174.0 44 0 1 0 0 3 878.0 40 0 0 1 0 5 707.0 26 1 0 0 1 1 1026.0 59 1 1 0 1 2 1259.0 78 1 1 0 0 4 665.0 50 1 1 1 1 3 614.0 44 0 0 1 1 2 1332.0 69 0 1 1 1 2 801.0 41 0 0 0 0 2 1060.0 64 1 1 0 1 3 1162.0 39 0 1 0 1 2 1087.0 65 1 1 1 0 5 520.0 47 1 0 0 1 2 1383.0 23 0 0 0 1 4 1463.0 43 0 0 1 0 4 1257.0 29 0 1 1 1 3 1141.0 61 1 0 0 0 4 1095.0 24 1 1 0 0 3 713.0 19 0 1 0 0 2 1022.0 30 0 1 0 0 5 1310.0 26 0 0 0 0 2 1193.0 57 1 1 1 1 2 626.0 60 0 0 1 1 5 606.0 77 0 0 1 1 5 740.0 38 0 0 1 0 5 877.0 64 0 0 0 0 1 1071.0 63 0 1 0 0 2 507.0 26 1 1 0 0 3 1146.0 42 1 1 0 1 4 889.0 42 1 1 0 0 2 675.0 24 1 1 1 1 4 791.0 26 1 0 0 0 3 978.0 68 1 1 1 0 4 1427.0 77 1 0 0 0 4 694.0 29 0 0 1 0 4 614.0 58 0 0 1 0 3 1492.0 73 1 0 0 1 2 1058.0 45 1 0 0 1 5 927.0 17 1 0 1 0 5 611.0 19 0 0 1 0 5 1196.0 63 0 1 1 0 4 507.0 38 0 1 0 0 3 943.0 30 1 1 0 1 4 1328.0 39 1 0 0 0 4 1192.0 75 0 1 1 1 4 759.0 66 0 0 1 0 2 1420.0 27 1 0 1 0 4 1335.0 71 1 1 0 1 2 1451.0 77 0 1 1 1 4 1357.0 43 1 0 1 1 2 866.0 20 0 1 0 1 1 1191.0 20 0 0 1 1 3 547.0 36 0 1 1 1 3 1317.0 35 1 0 0 0 5 506.0 64 0 1 0 0 1 908.0 56 0 1 0 1 2 894.0 39 0 0 0 1 5 558.0 31 0 1 0 1 4 614.0 49 0 1 0 0 3 1073.0 49 0 1 0 1 3 998.0 18 1 0 0 1 3 1254.0 19 1 0 0 1 4 1077.0 55 0 1 0 0 4 1286.0 69 1 1 1 1 2 775.0 33 0 0 0 1 2 1022.0 22 1 0 1 0 4 1469.0 58 0 0 1 0 1 1066.0 44 1 0 0 1 4 1447.0 44 1 0 1 1 2 1339.0 49 1 1 1 0 1 1411.0 34 0 1 0 1 4 888.0 52 0 0 1 0 1 1069.0 47 1 0 0 0 4 1105.0 50 1 1 1 0 2 509.0 22 0 1 0 1 5 501.0 47 0 0 1 0 4 1196.0 25 0 0 1 0 2 760.0 31 1 0 0 0 4 644.0 54 1 1 0 0 4 1183.0 51 0 0 0 1 3 736.0 76 1 1 0 0 4 845.0 36 1 0 0 0 1 893.0 73 0 0 0 0 1 1097.0 45 1 0 1 0 4 515.0 44 0 0 1 1 2 1432.0 26 1 0 1 1 4 870.0 16 0 0 1 1 4 1395.0 42 1 1 0 1 5 591.0 20 1 1 0 1 1 1323.0 47 0 1 1 0 5 766.0 33 1 1 1 0 4 1230.0 55 0 1 0 0 4 833.0 43 0 0 0 1 5 1415.0 45 1 0 1 1 4 861.0 38 1 0 1 0 4 1335.0 21 0 1 1 0 5 817.0 47 0 1 1 0 2 1155.0 66 1 0 0 0 5 802.0 53 1 0 0 1 5 1322.0 19 0 1 1 1 3 554.0 63 1 1 1 1 2 1471.0 43 0 0 1 0 2 1418.0 47 1 1 0 1 1 1356.0 25 1 0 1 1 5 1088.0 67 1 1 0 0 3 1104.0 76 0 1 1 1 2 1359.0 38 0 1 1 1 1 1366.0 34 1 0 0 0 1 1498.0 71 1 1 0 0 5 735.0 37 1 1 0 1 4 1339.0 38 0 1 0 0 4 1440.0 58 0 0 0 0 3 1326.0 55 1 0 1 0 5 817.0 32 0 1 1 0 4 1264.0 49 1 1 0 0 1 571.0 77 0 1 1 1 5 970.0 26 0 1 1 0 4 519.0 49 1 1 0 1 1 1022.0 59 1 0 0 0 4 1401.0 64 1 0 1 0 5 1075.0 38 1 0 1 1 2 689.0 23 0 1 1 0 5 1226.0 60 1 0 1 0 1 1127.0 54 0 0 1 0 4 1446.0 39 0 0 0 1 5 1237.0 59 0 0 0 0 2 683.0 46 0 0 0 0 5 1218.0 48 1 0 0 1 5 514.0 55 1 0 1 0 4 852.0 75 1 1 0 1 5 869.0 61 1 1 1 1 5 1104.0 49 1 0 0 1 4 897.0 75 0 0 1 1 3 1454.0 24 1 0 0 1 5 1206.0 75 1 1 1 1 4 1492.0 76 1 0 1 1 4 1076.0 37 0 0 0 0 3 1287.0 18 0 0 1 0 4 1394.0 78 1 1 1 0 1 1467.0 76 0 1 0 1 2 722.0 69 0 1 0 1 5 1064.0 30 0 0 1 0 5 615.0 25 0 1 0 0 2 1028.0 29 1 0 1 1 4 708.0 35 0 1 0 1 5 1064.0 44 1 0 1 1 4 860.0 45 1 1 0 1 3 1225.0 25 1 0 0 1 1 1323.0 18 1 1 0 0 5 591.0 19 0 1 0 0 2 1174.0 31 0 0 0 1 4 543.0 58 0 0 0 0 3 748.0 50 1 0 0 1 5 704.0 39 1 1 1 0 4 1100.0 27 1 0 1 0 4 699.0 59 0 0 0 1 2 1289.0 45 0 0 0 0 3 614.0 19 1 0 1 1 4 1104.0 39 0 1 1 1 3 1498.0 43 1 1 0 1 1 1429.0 29 0 1 0 0 4 667.0 26 1 1 1 1 2 1253.0 44 1 0 1 1 2 915.0 77 0 0 0 0 5 1215.0 18 0 0 1 0 1 1314.0 70 0 1 0 0 5 938.0 27 0 1 0 0 3 1052.0 63 0 1 0 1 1 1010.0 20 1 0 1 1 5 967.0 73 0 0 1 0 4 923.0 60 0 0 0 0 4 1126.0 60 0 1 0 0 2 1148.0 57 0 1 1 0 3 1158.0 39 1 0 1 0 5 1487.0 73 1 1 1 0 3 1149.0 56 0 1 1 1 1 524.0 61 1 0 0 0 3 907.0 74 0 1 0 0 3 966.0 74 1 0 1 1 4 1453.0 52 1 1 0 0 2 644.0 46 0 1 1 0 3 693.0 53 1 1 0 0 3 1443.0 30 1 0 0 0 4 719.0 55 1 1 1 0 2 1165.0 38 0 0 0 0 4 948.0 36 1 0 0 1 2 900.0 58 0 0 0 0Explanation / Answer
a.)
There are basic 3 methods to decide optimal number of cluster:
-> Elbow method
-> Average Silhoutee
-> Gap Statistic Method
After trying all 3 methods to find optimal number of cluster, if any two methods give same number that will be the optimal number of cluster for data set.
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