17. The following data contains US arrest data published in McNeil (1977). The table shows arrests per 100,000 residents for “assault,” “murder,” and “rape” in each of the 50 US states in 1973. The variable “UP” indicates the percent of the urban population living in urban areas.

(a) Use this data to cluster US states using the single, complete, and the average linkage methods.

(b) Use this data to cluster US states using the Ward’s method.

State Murder Assault UP Rape State Murder Assualt UP Rape Alabama 13.2 236 58 21.2 Montana 6.0 109 53 16.4 Alaska 10.0 263 48 44.5 Nebraska 4.3 102 62 16.5 Arizona 8.1 294 80 31.0 Nevada 12.2 252 81 46.0 Arkansas 8.8 190 50 19.5 New Hampshire 2.1. 57 56 9.5 California 9.0 276 91 40.6 New Jersey 7.4 159 89 18.8 Colorado 7.9 204 78 38.7 New Mexico 11.4 285 70 32.1 Connecticut 3.3 110 77 11.1 New York 11.1 254 86 26.1 Delaware 5.9 238 72 15.8 North Carolina 13.0 337 45 16.1 Florida 15.4 335 80 31.9 North Dakota 0.8 45 44 7.3 Georgia 17.4 211 60 25.8 Ohio 7.3 120 75 21.4 Hawaii 5.3 46 83 20.2 Oklahoma 6.6 151 68 20.0 Idaho 2.6 120 54 14.2 Oregon 4.9 159 67 29.3 Illinois 10.4 249 83 24.0 Pennsylvania 6.3 106 72 14.9 Indiana 7.2 113 65 21.0 Rhode Island 3.4 174 87 8.3 Iowa 2.2 56 57 11.3 South Carolina 14.4 279 48 22.5 Kansas 6.0 115 66 18.0 South Dakota 3.8 86 45 12.8 Kentucky 9.7 109 52 16.3 Tennessee 13.2 188 59 26.9 Louisiana 15.4 249 66 22.2 Texas 12.7 201 80 25.5 Maine Maryland 11.3 300 Massachusetts 4.4 149 Michigan 12.1 255 Minnesota Mississippi 16.1 Missouri 2.1 83 51 7.8 Utah 3.2 120 80 22.9 67 27.8 Vermont 2.2 48 32 11.2 85 16.3 Virginia 8.5 156 63 20.7 74 35.1 Washington 4.0 145 73 26.2 2.7 72 66 14.9 West Virginia 5.7 81 39 9.3 9.0 178 259 44 17.1 70 28.2 Wisconsin 2.6 53 66 10.8 Wyoming 6.8 161 60 15.6