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[null,"https://en.wikipedia.org/wiki/K-means_clustering"]

{"sheet":"output_risolutore","index":1,"n_rows":38,"n_cols":28,"rows_kept":38,"cut":false,"hidden":false,"merged":[[3,25,4,27],[0,25,1,27],[3,30,4,32],[32,18,34,20],[4,1,4,3],[5,5,5,6],[5,7,5,8],[5,9,5,10],[9,6,9,7],[6,5,6,6],[6,7,6,8],[6,9,6,10],[3,13,4,15],[27,2,31,7]]}
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"IMPLEMENTAZIONE DELLE DISTANZE UTILIZZANDO I NOMI c_1 c_2 e c_3"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Quadrato delle distanze Euclidee da ciascun centroide",null,null,null,null,null,null,null,null,null,null,null,"Quadrato delle distanze Euclidee da ciascun centroide"]
[null,"test data"]
[null,"n","VAR1","VAR2",null,"cluster center 1",null,"cluster center 2",null,"cluster center 3",null,null,"index","dist c_1","dist c_2","dist c_3",null,null,"class","min distance",null,null,null,null,"index","dist c_1","dist c_2","dist c_3"]
[null,1,4,12,null,"c_1",null,"c_2",null,"c_3",null,null,1,{"$f":"(($C7-$F$8)^2+($D7-$G$8)^2)","v":3.3124999998144316},{"$f":"(($C7-$H$8)^2+($D7-$I$8)^2)","v":36.039999995395078},{"$f":"(($C7-$J$8)^2+($D7-$K$8)^2)","v":76.519999998046316},null,null,{"$f":"IF(MIN(N7:P7)=N7,\"CL1\",IF(MIN(N7:P7)=O7,\"CL2\",\"CL3\"))","v":"CL1"},{"$f":"MIN(N7:P7)","v":3.3124999998144316},{"$f":"IF(MIN(N7:P7)=N7,1,IF(MIN(N7:P7)=O7,2,3))","v":1},null,null,null,1,{"$f":"SUMSQ(C7:D7-c_1)","v":3.3124999998144316},{"$f":"SUMSQ(C7:D7-c_2)","v":36.039999995395078},{"$f":"SUMSQ(C7:D7-c_3)","v":76.519999998046316}]
[null,2,5,10,null,3.500000000067478,10.25000000003374,9.1999999998160256,9.0000000004485976,5.5999999999042318,3.4000000000957682,null,2,{"$f":"(($C8-$F$8)^2+($D8-$G$8)^2)","v":2.312499999814436},{"$f":"(($C8-$H$8)^2+($D8-$I$8)^2)","v":18.639999997557421},{"$f":"(($C8-$J$8)^2+($D8-$K$8)^2)","v":43.919999998620938},null,null,{"$f":"IF(MIN(N8:P8)=N8,\"CL1\",IF(MIN(N8:P8)=O8,\"CL2\",\"CL3\"))","v":"CL1"},{"$f":"MIN(N8:P8)","v":2.312499999814436},{"$f":"IF(MIN(N8:P8)=N8,1,IF(MIN(N8:P8)=O8,2,3))","v":1},null,null,null,2,{"$f":"SUMSQ(C8:D8-c_1)","v":2.312499999814436},{"$f":"SUMSQ(C8:D8-c_2)","v":18.639999997557421},{"$f":"SUMSQ(C8:D8-c_3)","v":43.919999998620938}]
[null,3,8,7,null,null,null,null,null,null,null,null,3,30.812499999612001,5.4400000013528516,18.719999999770156,null,null,"CL2",5.4400000013528516,2,null,null,null,3,{"$f":"SUMSQ(C9:D9-c_1)","v":30.812499999612001},{"$f":"SUMSQ(C9:D9-c_2)","v":5.4400000013528516},{"$f":"SUMSQ(C9:D9-c_3)","v":18.719999999770156}]
[null,4,5,3,null,null,null,null,null,null,null,null,4,54.812500000286796,53.640000003837784,0.51999999996169277,null,null,"CL3",0.51999999996169277,3,null,null,null,4,{"$f":"SUMSQ(C10:D10-c_1)","v":54.812500000286796},{"$f":"SUMSQ(C10:D10-c_2)","v":53.640000003837784},{"$f":"SUMSQ(C10:D10-c_3)","v":0.51999999996169277}]
[null,5,5,4,null,null,null,null,null,null,null,null,5,41.312500000219316,42.640000002940596,0.71999999977015638,null,null,"CL3",0.71999999977015638,3,null,null,null,5,{"$f":"SUMSQ(C11:D11-c_1)","v":41.312500000219316},{"$f":"SUMSQ(C11:D11-c_2)","v":42.640000002940596},{"$f":"SUMSQ(C11:D11-c_3)","v":0.71999999977015638}]
[null,6,2,11,null,3,10,9,8,5,4,"INI",6,2.8125000001518239,55.839999995556376,70.719999997854785,null,null,"CL1",2.8125000001518239,1,null,null,null,6,{"$f":"SUMSQ(C12:D12-c_1)","v":2.8125000001518239},{"$f":"SUMSQ(C12:D12-c_2)","v":55.839999995556376},{"$f":"SUMSQ(C12:D12-c_3)","v":70.719999997854785}]
[null,7,5,4,null,null,null,null,null,null,null,null,7,41.312500000219316,42.640000002940596,0.71999999977015638,null,null,"CL3",0.71999999977015638,3,null,null,null,7,{"$f":"SUMSQ(C13:D13-c_1)","v":41.312500000219316},{"$f":"SUMSQ(C13:D13-c_2)","v":42.640000002940596},{"$f":"SUMSQ(C13:D13-c_3)","v":0.71999999977015638}]
[null,8,3,8,null,null,null,null,null,null,null,null,8,5.312500000219309,39.43999999861591,27.919999998620938,null,null,"CL1",5.312500000219309,1,null,null,null,8,{"$f":"SUMSQ(C14:D14-c_1)","v":5.312500000219309},{"$f":"SUMSQ(C14:D14-c_2)","v":39.43999999861591},{"$f":"SUMSQ(C14:D14-c_3)","v":27.919999998620938}]
[null,9,6,2,null,null,null,null,null,null,null,null,9,74.312500000219316,59.240000005102928,2.1200000003447657,null,null,"CL3",2.1200000003447657,3,null,null,null,9,{"$f":"SUMSQ(C15:D15-c_1)","v":74.312500000219316},{"$f":"SUMSQ(C15:D15-c_2)","v":59.240000005102928},{"$f":"SUMSQ(C15:D15-c_3)","v":2.1200000003447657}]
[null,10,7,4,null,null,null,null,null,null,null,null,10,51.312499999949402,29.840000003676487,2.3200000001532293,null,null,"CL3",2.3200000001532293,3,null,null,null,10,{"$f":"SUMSQ(C16:D16-c_1)","v":51.312499999949402},{"$f":"SUMSQ(C16:D16-c_2)","v":29.840000003676487},{"$f":"SUMSQ(C16:D16-c_3)","v":2.3200000001532293}]
[null,11,10,8,null,null,null,null,null,null,null,null,11,47.312499999274607,1.6400000011915543,40.519999999961698,null,null,"CL2",1.6400000011915543,2,null,null,null,11,{"$f":"SUMSQ(C17:D17-c_1)","v":47.312499999274607},{"$f":"SUMSQ(C17:D17-c_2)","v":1.6400000011915543},{"$f":"SUMSQ(C17:D17-c_3)","v":40.519999999961698}]
[null,12,8,9,null,null,null,null,null,null,null,null,12,21.812499999477041,1.4399999995584614,37.119999999387083,null,null,"CL2",1.4399999995584614,2,null,null,null,12,{"$f":"SUMSQ(C18:D18-c_1)","v":21.812499999477041},{"$f":"SUMSQ(C18:D18-c_2)","v":1.4399999995584614},{"$f":"SUMSQ(C18:D18-c_3)","v":37.119999999387083}]
[null,13,10,9,null,null,null,null,null,null,null,null,13,43.812499999207127,0.64000000029435911,50.719999999770152,null,null,"CL2",0.64000000029435911,2,null,null,null,13,{"$f":"SUMSQ(C19:D19-c_1)","v":43.812499999207127},{"$f":"SUMSQ(C19:D19-c_2)","v":0.64000000029435911},{"$f":"SUMSQ(C19:D19-c_3)","v":50.719999999770152}]
[null,14,10,12,null,null,null,null,null,null,null,null,14,45.312499999004686,9.6399999976027733,93.319999999195531,null,null,"CL2",9.6399999976027733,2,null,null,null,14,{"$f":"SUMSQ(C20:D20-c_1)","v":45.312499999004686},{"$f":"SUMSQ(C20:D20-c_2)","v":9.6399999976027733},{"$f":"SUMSQ(C20:D20-c_3)","v":93.319999999195531}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(T7:T20)","v":38.950000000000003},null,null,null,"Funzione obiettivo"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Nella cella T20 si inserisce la funzione obiettivo che si vuole minimizzare"]
[null,null,"Osservazione: ",null,null,null,null,null,null,null,null,null,"In questo caso k=3, n=14"]
[null,null,null,null,null,null,null,null,null,null,null,null,"c_1=zona F8:G8"]
[null,null,null,null,null,null,null,null,null,null,null,null,"c_2=zona H8:I8"]
[null,null,null,null,null,null,null,null,null,null,null,null,"c_3=zona J8:K8"]
[null,null,"Verificare che i centroidi trovati dal risolutore corrispondano alle medie aritmetiche dei singoli gruppi (utilizzare per la verifica la funzione MEDIA.SE)"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Obiettivo: cercare i 6 numeri da inserire nella zona F8:K8 che minimizzano il numero contenuto nella cella obiettivo (T21)"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Vincolo",null,null,1,{"$f":"COUNTIF(U$7:U$20,V32)","v":4},"Numero di unità allocate al gruppo 1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Le celle W32, W33 e W34 devono essere strettamente maggiori di 0",null,null,2,{"$f":"COUNTIF(U$7:U$20,V33)","v":5},"Numero di unità allocate al gruppo 2"]
[null,null,"Verifica tramite la funzione MEDIA.SE",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,5,"Numero di unità allocate al gruppo 3"]
[null,null,"3.5 è la media delle unità che fanno parte del gruppo 1 per la variabile VAR1"]
[null,null,"10.25 è la media delle unità che fanno parte del gruppo 1 per la variabile VAR1"]
[null,null,{"$f":"AVERAGEIF($U$7:$U$20,1,C7:C20)","v":3.5},{"$f":"AVERAGEIF($U$7:$U$20,1,D7:D20)","v":10.25},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ossia il minimo di queste 3 celle deve essere >0"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MIN(W32:W34)","v":4}]

{"sheet":"Output_macro_KM","index":2,"n_rows":20,"n_cols":3,"rows_kept":20,"cut":false,"hidden":false,"merged":[]}
["Row Title","Centroid"]
[1,1]
[2,1]
[3,2]
[4,3]
[5,3]
[6,1]
[7,3]
[8,1]
[9,3]
[10,3]
[11,2]
[12,2]
[13,2]
[14,2]
[]
[null,"VAR1","VAR2"]
["Centroid 1",3.5,10.25]
["Centroid 2",9.1999999999999993,9]
["Centroid 3",5.6,3.4]