Josephine Mater works for a market research firm that specializes in the food industry She currently is analyzing Trader Joe's, a national chain of specialty grocery stores Specifically, Josephine would like to gain insight on Trader Joe's future expansion plans (which are closely guarded by the company) Josephine knows that Trader Joe's replenishes its inventory at its retail stores with frequent trucking shipments from its distribution centers The file TraderJoes contains data on the location of Trader Joe's retail stores To keep costs low, retail stores are typically located near a distribution center Josephine would like to use k means clustering to estimate the location and number of Trader Joe's distribution centers (information on Trader Joe's distribution centers is not publicly disclosed) Store Longitude Latitude 1 123 79 46 19343 2 123 26 44 58258 3 122 99 45 52289 4 122 876 42 32652 5 122 803 45 49238 6 122 72 45 41391 7 122 695 47 64454 8 122 643 45 48075 9 122 637 38 23242 10 122 636 45 54438 11 122 62 45 53463 12 122 572 45 41981 13 122 554 45 61973 14 122 55 47 23565 15 122 513 45 44331 16 122 503 37 96506 17 122 489 48 75622 18 122 486 37 68 19 122 482 37 97716 20 122 418 37 65319 21 122 41 37 77264 22 122 405 47 57458 23 122 387 37 59855 24 122 344 47 7393 25 122 339 37 5246 26 122 322 47 3165 27 122 305 37 53499 28 122 302 38 31705 29 122 298 47 39707 30 122 296 47 60876 31 122 294 37 83701 32 122 294 37 99631 33 122 282 37 77122 34 122 274 37 85247 35 122 261 37 50716 36 122 185 47 89622 37 122 158 37 4458 38 122 142 47 61054 39 122 118 37 88576 40 122 087 37 37854 41 122 073 37 68527 42 122 033 37 34921 43 122 027 38 0349 44 122 024 36 97445 45 122 021 37 94612 46 122 002 37 82312 47 121 987 37 30523 48 121 97 36 97865 49 121 962 37 23581 50 121 953 37 277 51 121 894 36 59656 52 121 878 37 25177 53 121 862 37 2994 54 121 761 38 54663 55 121 696 37 93187 56 121 654 37 1305 57 121 492 38 57759 58 121 44 38 56786 59 121 388 38 62586 60 121 32 37 99837 61 121 315 44 05817 62 121 272 38 64463 63 121 176 38 67796 64 121 022 37 72087 65 120 706 35 54969 66 120 597 35 2455 67 120 591 35 11859 68 120 436 34 95303 69 119 828 34 43583 70 119 817 39 5329 71 119 784 36 73704 72 119 776 39 11271 73 119 76 36 81793 74 119 729 34 44025 75 119 728 36 84926 76 119 682 34 43309 77 119 038 34 21639 78 119 024 35 38484 79 119 019 35 37329 80 118 91 34 18422 81 118 869 34 21898 82 118 807 34 14665 83 118 762 34 15334 84 118 644 34 19731 85 118 591 34 15447 86 118 516 34 43382 87 118 502 34 27936 88 118 422 34 03867 89 118 39 34 02369 90 118 387 33 97568 91 118 387 34 13956 92 118 387 33 74446 93 118 378 34 09316 94 118 373 33 8278 95 118 373 34 15038 96 118 373 33 81512 97 118 372 34 07415 98 118 359 34 05512 99 118 359 34 18126 100 118 352 33 84097 101 118 352 34 1519 102 118 326 34 10122 103 118 318 34 11227 104 118 31 33 75528 105 118 308 34 17724 106 118 27 34 1893 107 118 225 34 20655 108 118 207 34 53603 109 118 2 34 13949 110 118 2 34 20682 111 118 188 33 83035 112 118 168 34 14061 113 118 149 34 60032 114 118 139 34 14276 115 118 13 33 7523 116 118 118 33 79633 117 118 083 34 16424 118 118 048 33 72105 119 118 002 34 14426 120 117 966 33 65877 121 117 919 33 64963 122 117 907 33 72463 123 117 9 33 91668 124 117 831 33 60382 125 117 815 33 81556 126 117 807 34 10668 127 117 792 33 8896 128 117 72 34 09668 129 117 708 33 52253 130 117 694 34 04745 131 117 638 33 61478 132 117 632 33 46629 133 117 59 33 9089 134 117 585 34 17876 135 117 409 47 70885 136 117 327 47 5888 137 117 271 32 83281 138 117 269 32 82081 139 117 26 33 04687 140 117 25 33 09544 141 117 234 32 78682 142 117 232 32 86561 143 117 217 32 73607 144 117 168 32 74979 145 117 115 33 52734 146 117 097 32 7349 147 117 075 33 10019 148 117 074 33 00139 149 117 068 32 89321 150 116 397 33 72751 151 116 225 33 71304 152 116 163 43 66244 153 115 336 36 14631 154 115 258 36 18053 155 115 21 36 14866 156 115 053 36 06332 157 112 469 34 54002 158 112 465 33 6573 159 112 258 33 63819 160 112 099 33 85854 161 112 063 33 58324 162 112 03 33 51067 163 111 994 33 43542 164 111 979 33 58337 165 111 964 33 53885 166 111 899 33 37847 167 111 893 33 61603 168 111 791 33 30634 169 110 966 32 39091 170 110 945 32 25465 171 110 885 32 25409 172 106 57 35 10099 173 106 519 35 18081 174 105 853 35 61607 175 104 983 39 73121 176 104 951 39 61179 177 104 764 38 90436 178 98 4513 29 48541 179 98 4093 29 40233 180 97 7623 30 44073 181 97 7525 30 40136 182 97 7444 30 27292 183 97 3841 32 73762 184 97 3783 32 70787 185 97 1342 32 94124 186 96 9518 32 63058 187 96 7869 32 90051 188 96 7579 32 77713 189 96 6478 40 74222 190 96 4983 32 82626 191 96 052 41 26742 192 95 8777 36 1756 193 95 7754 29 7407 194 95 6328 29 89655 195 95 583 29 73648 196 95 5092 30 17049 197 95 4935 29 7504 198 94 8407 39 03608 199 93 4558 45 07246 200 93 4308 44 95794 201 93 3439 44 94652 202 93 1629 44 93301 203 93 1472 45 07913 204 92 9476 44 91542 205 91 1449 30 41925 206 90 7521 41 92332 207 90 5771 38 66337 208 90 4329 38 60089 209 88 3382 41 8639 210 88 2942 42 16558 211 88 1438 41 76063 212 88 0445 42 05053 213 88 0216 41 81329 214 88 013 41 86359 215 87 9825 42 10995 216 87 9531 42 28308 217 87 8406 42 01114 218 87 8326 42 01281 219 87 829 42 12753 220 87 8255 41 63057 221 87 8206 42 0724 222 87 7979 41 88806 223 87 658 41 89622 224 87 6424 41 92673 225 87 6236 41 87033 226 86 7316 33 45148 227 86 2208 41 73677 228 86 2118 39 91254 229 86 0759 39 90505 230 85 6486 38 26247 231 85 6307 38 24999 232 85 5766 42 91203 233 84 5885 42 69237 234 84 5327 38 01034 235 84 4965 33 85753 236 84 4015 39 21231 237 84 3857 33 9253 238 84 3726 33 7717 239 84 2807 30 43826 240 84 2384 33 98519 241 84 1558 39 84581 242 84 1541 39 68016 243 84 0062 35 90739 244 83 4833 42 43115 245 83 1327 42 49229 246 83 1141 40 09923 247 83 111 42 69812 248 82 9179 40 04152 249 82 6321 27 79292 250 82 5132 27 26128 251 82 5105 27 94076 252 82 3659 29 61567 253 82 3343 34 80839 254 82 2729 28 33298 255 81 9179 41 45532 256 81 8115 26 2448 257 81 4807 41 46228 258 81 4609 28 46305 259 81 4114 30 27459 260 81 3659 28 59825 261 80 8508 35 16029 262 80 2935 26 02727 263 80 2879 25 658 264 80 2433 26 63748 265 80 1193 26 14728 266 80 087 26 85989 267 80 0775 26 55034 268 80 0591 26 46708 269 80 02 40 55691 270 79 8521 32 82348 271 79 0907 40 36484 272 79 0039 35 93247 273 78 7816 43 03781 274 78 4748 38 07687 275 77 86 40 79339 276 77 5945 43 08836 277 77 5064 37 66598 278 77 4289 38 84039 279 77 3497 38 97708 280 77 1888 38 77422 281 77 1311 38 85023 282 77 0737 38 98751 283 77 0507 38 79997 284 77 0206 38 89612 285 77 0046 39 02077 286 76 7955 39 18831 287 76 736 39 38867 288 76 5373 37 11208 289 76 0798 43 03851 290 76 0508 36 86532 291 75 4329 40 07347 292 75 2855 40 00678 293 75 2535 40 23401 294 74 9218 39 89122 295 74 6127 40 35442 296 74 3882 40 78788 297 74 2972 40 72755 298 74 1534 40 84334 299 74 0754 40 94454 300 74 0326 40 99121 301 74 0034 40 7171 302 73 9874 40 73225 303 73 9859 40 69868 304 73 9815 40 73883 305 73 9801 40 77691 306 73 9757 40 82704 307 73 8335 42 71786 308 73 7982 41 01899 309 73 7477 40 77337 310 73 6957 40 64316 311 73 6401 40 63871 312 73 5831 40 74875 313 73 4673 40 77649 314 73 4615 41 08376 315 73 4313 41 21417 316 73 3591 41 12701 317 73 3114 40 84014 318 73 2451 41 19096 319 73 1151 40 85288 320 72 7274 41 7371 321 72 5884 42 34176 322 71 7128 42 29593 323 71 5481 32 9299 324 71 4537 42 324 325 71 4135 42 48284 326 71 232 42 29315 327 71 1956 42 50472 328 71 1241 42 34216 329 71 1033 42 36476 330 70 9408 42 45928 331 70 9287 42 52787 332 70 2881 41 65249 333 70 2569 43 663 334 50 12118 26 46036 How large must k be so that the average distance to each cluster centroid is less than 8 distance units as measured in the original (nonnormalized) coordinates Be sure to Normalize Input Data and specify 50 iterations and 10 random starts in Step 2 of the XLMiner k Means Clustering procedure

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Josephine Mater works for a market research firm that specializes in the food industry. She currently is analyzing Trader Joe's, a national chain of specialty

Josephine Mater works for a market research firm that specializes in the food industry. She currently is analyzing Trader Joe's, a national chain of specialty grocery stores. Specifically, Josephine would like to gain insight on Trader Joe's future expansion plans (which are closely guarded by the company). Josephine knows that Trader Joe's replenishes its inventory at its retail stores with frequent trucking shipments from its distribution centers. The file TraderJoes contains data on the location of Trader Joe's retail stores. To keep costs low, retail stores are typically located near a distribution center. Josephine would like to use k-means clustering to estimate the location and number of Trader Joe's distribution centers (information on Trader Joe's distribution centers is not publicly disclosed).

Store	Longitude	Latitude
1	-123.79	46.19343
2	-123.26	44.58258
3	-122.99	45.52289
4	-122.876	42.32652
5	-122.803	45.49238
6	-122.72	45.41391
7	-122.695	47.64454
8	-122.643	45.48075
9	-122.637	38.23242
10	-122.636	45.54438
11	-122.62	45.53463
12	-122.572	45.41981
13	-122.554	45.61973
14	-122.55	47.23565
15	-122.513	45.44331
16	-122.503	37.96506
17	-122.489	48.75622
18	-122.486	37.68
19	-122.482	37.97716
20	-122.418	37.65319
21	-122.41	37.77264
22	-122.405	47.57458
23	-122.387	37.59855
24	-122.344	47.7393
25	-122.339	37.5246
26	-122.322	47.3165
27	-122.305	37.53499
28	-122.302	38.31705
29	-122.298	47.39707
30	-122.296	47.60876
31	-122.294	37.83701
32	-122.294	37.99631
33	-122.282	37.77122
34	-122.274	37.85247
35	-122.261	37.50716
36	-122.185	47.89622
37	-122.158	37.4458
38	-122.142	47.61054
39	-122.118	37.88576
40	-122.087	37.37854
41	-122.073	37.68527
42	-122.033	37.34921
43	-122.027	38.0349
44	-122.024	36.97445
45	-122.021	37.94612
46	-122.002	37.82312
47	-121.987	37.30523
48	-121.97	36.97865
49	-121.962	37.23581
50	-121.953	37.277
51	-121.894	36.59656
52	-121.878	37.25177
53	-121.862	37.2994
54	-121.761	38.54663
55	-121.696	37.93187
56	-121.654	37.1305
57	-121.492	38.57759
58	-121.44	38.56786
59	-121.388	38.62586
60	-121.32	37.99837
61	-121.315	44.05817
62	-121.272	38.64463
63	-121.176	38.67796
64	-121.022	37.72087
65	-120.706	35.54969
66	-120.597	35.2455
67	-120.591	35.11859
68	-120.436	34.95303
69	-119.828	34.43583
70	-119.817	39.5329
71	-119.784	36.73704
72	-119.776	39.11271
73	-119.76	36.81793
74	-119.729	34.44025
75	-119.728	36.84926
76	-119.682	34.43309
77	-119.038	34.21639
78	-119.024	35.38484
79	-119.019	35.37329
80	-118.91	34.18422
81	-118.869	34.21898
82	-118.807	34.14665
83	-118.762	34.15334
84	-118.644	34.19731
85	-118.591	34.15447
86	-118.516	34.43382
87	-118.502	34.27936
88	-118.422	34.03867
89	-118.39	34.02369
90	-118.387	33.97568
91	-118.387	34.13956
92	-118.387	33.74446
93	-118.378	34.09316
94	-118.373	33.8278
95	-118.373	34.15038
96	-118.373	33.81512
97	-118.372	34.07415
98	-118.359	34.05512
99	-118.359	34.18126
100	-118.352	33.84097
101	-118.352	34.1519
102	-118.326	34.10122
103	-118.318	34.11227
104	-118.31	33.75528
105	-118.308	34.17724
106	-118.27	34.1893
107	-118.225	34.20655
108	-118.207	34.53603
109	-118.2	34.13949
110	-118.2	34.20682
111	-118.188	33.83035
112	-118.168	34.14061
113	-118.149	34.60032
114	-118.139	34.14276
115	-118.13	33.7523
116	-118.118	33.79633
117	-118.083	34.16424
118	-118.048	33.72105
119	-118.002	34.14426
120	-117.966	33.65877
121	-117.919	33.64963
122	-117.907	33.72463
123	-117.9	33.91668
124	-117.831	33.60382
125	-117.815	33.81556
126	-117.807	34.10668
127	-117.792	33.8896
128	-117.72	34.09668
129	-117.708	33.52253
130	-117.694	34.04745
131	-117.638	33.61478
132	-117.632	33.46629
133	-117.59	33.9089
134	-117.585	34.17876
135	-117.409	47.70885
136	-117.327	47.5888
137	-117.271	32.83281
138	-117.269	32.82081
139	-117.26	33.04687
140	-117.25	33.09544
141	-117.234	32.78682
142	-117.232	32.86561
143	-117.217	32.73607
144	-117.168	32.74979
145	-117.115	33.52734
146	-117.097	32.7349
147	-117.075	33.10019
148	-117.074	33.00139
149	-117.068	32.89321
150	-116.397	33.72751
151	-116.225	33.71304
152	-116.163	43.66244
153	-115.336	36.14631
154	-115.258	36.18053
155	-115.21	36.14866
156	-115.053	36.06332
157	-112.469	34.54002
158	-112.465	33.6573
159	-112.258	33.63819
160	-112.099	33.85854
161	-112.063	33.58324
162	-112.03	33.51067
163	-111.994	33.43542
164	-111.979	33.58337
165	-111.964	33.53885
166	-111.899	33.37847
167	-111.893	33.61603
168	-111.791	33.30634
169	-110.966	32.39091
170	-110.945	32.25465
171	-110.885	32.25409
172	-106.57	35.10099
173	-106.519	35.18081
174	-105.853	35.61607
175	-104.983	39.73121
176	-104.951	39.61179
177	-104.764	38.90436
178	-98.4513	29.48541
179	-98.4093	29.40233
180	-97.7623	30.44073
181	-97.7525	30.40136
182	-97.7444	30.27292
183	-97.3841	32.73762
184	-97.3783	32.70787
185	-97.1342	32.94124
186	-96.9518	32.63058
187	-96.7869	32.90051
188	-96.7579	32.77713
189	-96.6478	40.74222
190	-96.4983	32.82626
191	-96.052	41.26742
192	-95.8777	36.1756
193	-95.7754	29.7407
194	-95.6328	29.89655
195	-95.583	29.73648
196	-95.5092	30.17049
197	-95.4935	29.7504
198	-94.8407	39.03608
199	-93.4558	45.07246
200	-93.4308	44.95794
201	-93.3439	44.94652
202	-93.1629	44.93301
203	-93.1472	45.07913
204	-92.9476	44.91542
205	-91.1449	30.41925
206	-90.7521	41.92332
207	-90.5771	38.66337
208	-90.4329	38.60089
209	-88.3382	41.8639
210	-88.2942	42.16558
211	-88.1438	41.76063
212	-88.0445	42.05053
213	-88.0216	41.81329
214	-88.013	41.86359
215	-87.9825	42.10995
216	-87.9531	42.28308
217	-87.8406	42.01114
218	-87.8326	42.01281
219	-87.829	42.12753
220	-87.8255	41.63057
221	-87.8206	42.0724
222	-87.7979	41.88806
223	-87.658	41.89622
224	-87.6424	41.92673
225	-87.6236	41.87033
226	-86.7316	33.45148
227	-86.2208	41.73677
228	-86.2118	39.91254
229	-86.0759	39.90505
230	-85.6486	38.26247
231	-85.6307	38.24999
232	-85.5766	42.91203
233	-84.5885	42.69237
234	-84.5327	38.01034
235	-84.4965	33.85753
236	-84.4015	39.21231
237	-84.3857	33.9253
238	-84.3726	33.7717
239	-84.2807	30.43826
240	-84.2384	33.98519
241	-84.1558	39.84581
242	-84.1541	39.68016
243	-84.0062	35.90739
244	-83.4833	42.43115
245	-83.1327	42.49229
246	-83.1141	40.09923
247	-83.111	42.69812
248	-82.9179	40.04152
249	-82.6321	27.79292
250	-82.5132	27.26128
251	-82.5105	27.94076
252	-82.3659	29.61567
253	-82.3343	34.80839
254	-82.2729	28.33298
255	-81.9179	41.45532
256	-81.8115	26.2448
257	-81.4807	41.46228
258	-81.4609	28.46305
259	-81.4114	30.27459
260	-81.3659	28.59825
261	-80.8508	35.16029
262	-80.2935	26.02727
263	-80.2879	25.658
264	-80.2433	26.63748
265	-80.1193	26.14728
266	-80.087	26.85989
267	-80.0775	26.55034
268	-80.0591	26.46708
269	-80.02	40.55691
270	-79.8521	32.82348
271	-79.0907	40.36484
272	-79.0039	35.93247
273	-78.7816	43.03781
274	-78.4748	38.07687
275	-77.86	40.79339
276	-77.5945	43.08836
277	-77.5064	37.66598
278	-77.4289	38.84039
279	-77.3497	38.97708
280	-77.1888	38.77422
281	-77.1311	38.85023
282	-77.0737	38.98751
283	-77.0507	38.79997
284	-77.0206	38.89612
285	-77.0046	39.02077
286	-76.7955	39.18831
287	-76.736	39.38867
288	-76.5373	37.11208
289	-76.0798	43.03851
290	-76.0508	36.86532
291	-75.4329	40.07347
292	-75.2855	40.00678
293	-75.2535	40.23401
294	-74.9218	39.89122
295	-74.6127	40.35442
296	-74.3882	40.78788
297	-74.2972	40.72755
298	-74.1534	40.84334
299	-74.0754	40.94454
300	-74.0326	40.99121
301	-74.0034	40.7171
302	-73.9874	40.73225
303	-73.9859	40.69868
304	-73.9815	40.73883
305	-73.9801	40.77691
306	-73.9757	40.82704
307	-73.8335	42.71786
308	-73.7982	41.01899
309	-73.7477	40.77337
310	-73.6957	40.64316
311	-73.6401	40.63871
312	-73.5831	40.74875
313	-73.4673	40.77649
314	-73.4615	41.08376
315	-73.4313	41.21417
316	-73.3591	41.12701
317	-73.3114	40.84014
318	-73.2451	41.19096
319	-73.1151	40.85288
320	-72.7274	41.7371
321	-72.5884	42.34176
322	-71.7128	42.29593
323	-71.5481	-32.9299
324	-71.4537	42.324
325	-71.4135	42.48284
326	-71.232	42.29315
327	-71.1956	42.50472
328	-71.1241	42.34216
329	-71.1033	42.36476
330	-70.9408	42.45928
331	-70.9287	42.52787
332	-70.2881	41.65249
333	-70.2569	43.663
334	50.12118	26.46036

How large must k be so that the average distance to each cluster centroid is less than 8 distance units as measured in the original (nonnormalized) coordinates? Be sure to Normalize Input Data and specify 50 iterations and 10 random starts in Step 2 of the XLMiner k-Means Clustering procedure.