Price Level Analysis
Justin Cowden
The purpose of this analysis is to cut down the amount of Price Codes we are currently using. I will be using a type of Unsupervised Machine Learning called K-Means Clustering. The goal of this algorithm is to find groups in the data, with the number of groups represented by the variable k. The algorithm works iteratively to assign each data point to one of k groups based on the features that are provided. Data points are clustered based on feature similarity.
We need to check if we have any missing data because this algorithm does not work with missing values.
I removed the missing values which did not count for much.
List of Average Price Per Section
| Section | Row | PerTix |
|---|---|---|
| 119CT | 1 | 1586.25 |
| 111CT | 1 | 1329.57 |
| 102CT | 1 | 1144.50 |
| 112CT | 1 | 981.75 |
| 101 | 7 | 735.00 |
| 101 | 8 | 735.00 |
| 101 | 9 | 735.00 |
| 111 | 8 | 735.00 |
| 102 | 3 | 728.00 |
| 119 | 2 | 728.00 |
| 102 | 1 | 702.00 |
| 110 | 1 | 702.00 |
| 102 | 8 | 679.50 |
| 119 | 5 | 679.50 |
| 119 | 6 | 679.50 |
| 119 | 7 | 679.50 |
| 119 | 8 | 679.50 |
| 102CT | A | 676.50 |
| 110 | 9 | 664.07 |
| 101 | 11 | 650.50 |
| 111 | 15 | 617.50 |
| 110 | 10 | 597.00 |
| 102 | 9 | 596.39 |
| 110 | 7 | 586.00 |
| 111CT | A | 579.57 |
| 119CT | A | 541.03 |
| 112 | 9 | 536.00 |
| 101CT | A | 512.25 |
| 110 | 16 | 507.00 |
| 102 | 18 | 500.00 |
| 110 | 15 | 500.00 |
| 110 | 18 | 498.60 |
| 110CT | A | 476.78 |
| 101 | 19 | 437.97 |
| 101CT | B | 426.45 |
| 111CT | B | 413.34 |
| 113 | 10 | 399.75 |
| 106 | C | 397.50 |
| 115 | E | 397.50 |
| 102 | 14 | 378.75 |
| 110 | 8 | 372.15 |
| 113 | 11 | 359.87 |
| 119 | 13 | 358.46 |
| 113 | 9 | 354.00 |
| 118 | 16 | 351.00 |
| 112 | 11 | 350.00 |
| 102 | 10 | 344.63 |
| 118 | 18 | 344.25 |
| 105 | G | 337.50 |
| 109 | 17 | 337.50 |
| 109 | 18 | 337.50 |
| 113 | 16 | 337.50 |
| 118 | 19 | 337.50 |
| 118 | 20 | 337.50 |
| 102CT | B | 337.44 |
| 107 | H | 322.00 |
| 107 | L | 322.00 |
| 115 | H | 322.00 |
| 115 | L | 322.00 |
| 106CT | 2 | 316.80 |
| 106 | J | 315.25 |
| 104 | 19 | 313.00 |
| 106 | M | 313.00 |
| 108 | 7 | 313.00 |
| 115 | M | 313.00 |
| 102 | 11 | 311.25 |
| 106 | E | 302.33 |
| 109 | 8 | 296.65 |
| 118 | 14 | 295.64 |
| 109 | 16 | 278.32 |
| 111 | 11 | 277.41 |
| 111 | 10 | 272.45 |
| 105 | 11 | 270.00 |
| 110 | 4 | 268.50 |
| 102 | 13 | 267.26 |
| 113 | 15 | 267.17 |
| 119CT | B | 265.72 |
| 117 | 11 | 263.67 |
| 119 | 11 | 262.53 |
| 105 | 16 | 260.75 |
| 108 | 11 | 260.50 |
| 108 | 9 | 260.50 |
| 114 | 12 | 260.50 |
| 110 | 11 | 259.86 |
| 108 | 19 | 259.42 |
| 112CT | B | 257.61 |
| 105 | 20 | 256.50 |
| 108 | 17 | 256.50 |
| 108 | 20 | 256.50 |
| 114 | 18 | 256.50 |
| 114 | 20 | 256.50 |
| 117 | 20 | 256.50 |
| 110 | 13 | 255.57 |
| 114 | 17 | 254.31 |
| 108 | 15 | 253.85 |
| 119 | 10 | 248.84 |
| 119 | 12 | 247.37 |
| 119 | 4 | 244.79 |
| 101 | 13 | 244.41 |
| 110 | 12 | 243.95 |
| 119 | 3 | 243.32 |
| 118 | 7 | 242.95 |
| 114 | 16 | 242.31 |
| 101 | 17 | 239.95 |
| 110CT | B | 238.41 |
| 101 | 15 | 237.16 |
| 105 | 15 | 236.75 |
| 110 | 14 | 236.61 |
| 117 | 14 | 231.46 |
| 102 | 4 | 229.40 |
| 107CT | 2 | 227.81 |
| 101 | 14 | 226.09 |
| 115 | 8 | 224.75 |
| 111 | 16 | 219.10 |
| 102 | 12 | 218.43 |
| 112 | 19 | 216.51 |
| 108 | 16 | 215.25 |
| 102 | 5 | 213.10 |
| 103 | 18 | 211.09 |
| 108 | 14 | 207.72 |
| 103 | 7 | 202.65 |
| 112 | 8 | 200.49 |
| 102 | 16 | 192.00 |
| 110 | 6 | 190.05 |
| 112 | 13 | 189.84 |
| 106 | 6 | 183.20 |
| 115 | 16 | 182.91 |
| 107 | 9 | 181.83 |
| 106 | 10 | 180.09 |
| 101 | 16 | 179.77 |
| 102 | 17 | 177.61 |
| 108 | 12 | 172.10 |
| 107 | 7 | 168.76 |
| 112 | 4 | 167.58 |
| 118 | 12 | 167.08 |
| 112 | 17 | 166.52 |
| 102 | 15 | 166.42 |
| 109 | 19 | 166.17 |
| 102 | 19 | 159.82 |
| 109 | 9 | 159.28 |
| 110 | 20 | 158.87 |
| 103 | 19 | 158.69 |
| 119 | 17 | 157.50 |
| 112 | 14 | 148.43 |
| 116 | G | 146.29 |
| 111 | 5 | 146.06 |
| 109 | 14 | 141.18 |
| 111 | 14 | 139.84 |
| 101 | 6 | 135.33 |
| 112 | 3 | 135.23 |
| 116 | 5 | 134.75 |
| 110 | 17 | 134.14 |
| 105 | 14 | 132.78 |
| 119 | 16 | 129.45 |
| 110 | 19 | 129.11 |
| 113 | 12 | 128.92 |
| 102 | 20 | 128.51 |
| 119 | 15 | 127.55 |
| 118 | 13 | 126.35 |
| 112 | 15 | 121.88 |
| 107 | F | 120.43 |
| 109 | 12 | 119.26 |
| 106 | D | 117.22 |
| 116 | 11 | 117.08 |
| 118 | 17 | 115.96 |
| 106 | 5 | 112.95 |
| 115 | 3 | 112.63 |
| 108 | 13 | 112.31 |
| 107 | 6 | 112.17 |
| 104 | 9 | 112.09 |
| 106 | H | 112.08 |
| 302 | 15 | 110.85 |
| 109 | 15 | 109.33 |
| 115 | J | 107.28 |
| 115 | 5 | 107.08 |
| 103 | 16 | 106.50 |
| 105 | F | 105.94 |
| 117 | J | 105.71 |
| 106 | F | 105.15 |
| 107 | 5 | 104.08 |
| 109 | 13 | 103.04 |
| 217 | 10 | 101.35 |
| 108 | 4 | 100.50 |
| 119 | 14 | 100.00 |
| 106 | 19 | 99.73 |
| 216 | 11 | 98.46 |
| 109 | 10 | 98.00 |
| 117 | 15 | 96.62 |
| 107 | 13 | 96.26 |
| 103 | 12 | 95.87 |
| 114 | 15 | 95.35 |
| 216 | 10 | 94.43 |
| 106 | 4 | 94.19 |
| 116 | 10 | 93.42 |
| 116 | 18 | 93.38 |
| 106 | 17 | 93.03 |
| 117 | E | 92.86 |
| 117 | 8 | 91.97 |
| 116 | 3 | 91.67 |
| 114 | 19 | 91.59 |
| 312 | 2 | 91.58 |
| 104 | 17 | 91.36 |
| 208 | 11 | 91.36 |
| 331 | 10 | 90.77 |
| 115 | 10 | 90.60 |
| 107 | K | 90.31 |
| 104 | 16 | 90.24 |
| 105 | 13 | 89.85 |
| 114 | 8 | 88.72 |
| 117 | 13 | 88.04 |
| 333 | 14 | 87.00 |
| 118 | 4 | 86.89 |
| 216 | 12 | 86.19 |
| 115 | 2 | 85.97 |
| 108 | 8 | 85.50 |
| 115 | 7 | 85.48 |
| 107 | 8 | 85.38 |
| 115 | 6 | 85.09 |
| 116 | 20 | 84.23 |
| 116 | 2 | 84.07 |
| 107 | D | 83.51 |
| 321 | 12 | 83.51 |
| 116 | 7 | 83.27 |
| 116 | 17 | 83.16 |
| 115 | K | 82.85 |
| 113 | 17 | 82.67 |
| 107 | 14 | 82.55 |
| 105 | 19 | 82.48 |
| 108 | 10 | 81.55 |
| 206 | 5 | 81.00 |
| 117 | 4 | 79.78 |
| 107 | 4 | 79.71 |
| 105 | 18 | 79.66 |
| 106 | 14 | 79.59 |
| 108 | 5 | 79.36 |
| 108 | 18 | 78.79 |
| 106 | 16 | 77.46 |
| 114 | 10 | 76.99 |
| 109 | 4 | 76.93 |
| 106 | 15 | 76.88 |
| 113 | 2 | 76.46 |
| 113 | 5 | 76.46 |
| 113 | 4 | 75.95 |
| 114 | 5 | 74.54 |
| 116 | 9 | 74.27 |
| 117 | 16 | 73.24 |
| 117 | 17 | 73.18 |
| 116 | 8 | 71.50 |
| 107 | 11 | 71.12 |
| 114 | 14 | 71.08 |
| 104 | 15 | 70.86 |
| 118 | 8 | 70.30 |
| 106 | 18 | 70.24 |
| 106 | 13 | 70.00 |
| 106 | 12 | 68.92 |
| 116 | 15 | 68.19 |
| 115 | 9 | 67.87 |
| 309 | 5 | 67.20 |
| 311 | 6 | 67.20 |
| 117 | 5 | 67.11 |
| 106 | 20 | 67.06 |
| 106 | 11 | 66.74 |
| 313 | 8 | 66.58 |
| 207 | 6 | 65.70 |
| 115 | 11 | 64.86 |
| 328 | 2 | 64.66 |
| 115 | 17 | 64.39 |
| 107 | 16 | 64.24 |
| 115 | 15 | 64.09 |
| 116 | 16 | 64.07 |
| 107 | 10 | 63.97 |
| 109 | 5 | 63.81 |
| 116 | 12 | 63.43 |
| 107 | 15 | 63.41 |
| 215 | 3 | 63.30 |
| 115 | 14 | 63.21 |
| 115 | 12 | 62.98 |
| 330 | 8 | 62.75 |
| 107 | 1 | 62.74 |
| 118 | 9 | 62.62 |
| 217 | 8 | 62.08 |
| 115 | 13 | 61.44 |
| 107 | 12 | 61.33 |
| 116 | 6 | 59.73 |
| 116 | 19 | 59.47 |
| 116 | 14 | 59.04 |
| 116 | 13 | 58.61 |
| 323 | 8 | 58.00 |
| 325 | 3 | 57.31 |
| 325 | 6 | 56.77 |
| 301 | 1 | 56.73 |
| 328 | 3 | 56.15 |
| 206 | 6 | 56.08 |
| 206 | 10 | 55.80 |
| 316 | 1 | 55.26 |
| 307 | 8 | 54.92 |
| 206 | 11 | 54.05 |
| 107 | 17 | 53.74 |
| 324 | 8 | 53.32 |
| 305 | 7 | 52.89 |
| 325 | 7 | 52.28 |
| 330 | 7 | 50.92 |
| 325 | 2 | 50.88 |
| 301 | 5 | 50.80 |
| 330 | 6 | 50.54 |
| 217 | 9 | 50.37 |
| 301 | 2 | 50.19 |
| 323 | 7 | 49.88 |
| 117 | 12 | 49.16 |
| 334 | 13 | 49.00 |
| 216 | 2 | 48.65 |
| 217 | 11 | 48.52 |
| 328 | 6 | 47.95 |
| 316 | 2 | 46.65 |
| 301 | 3 | 46.53 |
| 329 | 8 | 46.38 |
| 329 | 4 | 45.97 |
| 307 | 5 | 45.95 |
| 312 | 6 | 45.48 |
| 218 | 9 | 45.18 |
| 326 | 4 | 45.06 |
| 206 | 12 | 44.88 |
| 215 | 2 | 44.65 |
| 327 | 4 | 44.19 |
| 324 | 7 | 43.99 |
| 205 | 8 | 43.84 |
| 307 | 4 | 43.24 |
| 324 | 6 | 43.21 |
| 326 | 5 | 42.95 |
| 314 | 12 | 42.79 |
| 218 | 5 | 42.63 |
| 318 | 1 | 42.08 |
| 209 | 12 | 41.94 |
| 219 | 3 | 41.94 |
| 214 | 8 | 41.88 |
| 206 | 4 | 41.85 |
| 205 | 5 | 41.77 |
| 332 | 2 | 41.66 |
| 322 | 12 | 41.60 |
| 208 | 6 | 41.24 |
| 326 | 2 | 41.03 |
| 330 | 5 | 40.91 |
| 328 | 7 | 40.61 |
| 331 | 6 | 40.43 |
| 307 | 6 | 40.25 |
| 209 | 2 | 40.20 |
| 326 | 7 | 40.20 |
| 210 | 3 | 40.13 |
| 218 | 10 | 39.95 |
| 217 | 5 | 39.76 |
| 217 | 7 | 39.69 |
| 303 | 2 | 39.64 |
| 312 | 8 | 39.35 |
| 206 | 7 | 39.30 |
| 329 | 7 | 39.17 |
| 217 | 12 | 39.04 |
| 205 | 2 | 39.02 |
| 218 | 3 | 38.99 |
| 326 | 3 | 38.95 |
| 217 | 6 | 38.93 |
| 216 | 4 | 38.47 |
| 216 | 6 | 38.12 |
| 207 | 10 | 38.10 |
| 207 | 7 | 37.66 |
| 327 | 3 | 37.65 |
| 215 | 11 | 37.56 |
| 215 | 7 | 37.28 |
| 302 | 1 | 37.21 |
| 214 | 4 | 37.11 |
| 301 | 9 | 37.00 |
| 207 | 12 | 36.95 |
| 327 | 6 | 36.92 |
| 215 | 12 | 36.83 |
| 207 | 8 | 36.78 |
| 324 | 4 | 36.69 |
| 327 | 7 | 36.69 |
| 303 | 14 | 36.56 |
| 206 | 3 | 36.42 |
| 218 | 12 | 36.41 |
| 218 | 2 | 36.35 |
| 209 | 8 | 36.22 |
| 324 | 5 | 36.03 |
| 333 | 2 | 35.89 |
| 214 | 7 | 35.84 |
| 210 | 4 | 35.61 |
| 206 | 9 | 35.56 |
| 321 | 1 | 35.50 |
| 208 | 12 | 35.45 |
| 209 | 6 | 35.44 |
| 208 | 7 | 35.00 |
| 216 | 1 | 35.00 |
| 329 | 6 | 34.92 |
| 306 | 5 | 34.73 |
| 329 | 5 | 34.67 |
| 209 | 7 | 34.45 |
| 207 | 9 | 34.03 |
| 327 | 2 | 33.95 |
| 218 | 8 | 33.79 |
| 303 | 3 | 32.75 |
| 208 | 10 | 32.67 |
| 209 | 4 | 32.51 |
| 209 | 11 | 32.50 |
| 106 | 2 | 32.40 |
| 216 | 7 | 31.96 |
| 334 | 10 | 31.50 |
| 217 | 1 | 31.33 |
| 318 | 11 | 31.24 |
| 332 | 1 | 31.08 |
| 330 | 3 | 30.86 |
| 208 | 3 | 30.73 |
| 216 | 3 | 30.56 |
| 106CT | 19 | 30.40 |
| 317 | 8 | 30.35 |
| 207 | 5 | 30.28 |
| 320 | 1 | 30.13 |
| 320 | 5 | 30.00 |
| 333 | 3 | 30.00 |
| 333 | 4 | 30.00 |
| 317 | 3 | 29.70 |
| 319 | 1 | 29.19 |
| 331 | 3 | 29.16 |
| 329 | 2 | 29.06 |
| 334 | 14 | 28.71 |
| 306 | 7 | 28.63 |
| 302 | 13 | 28.50 |
| 331 | 5 | 28.45 |
| 301 | 7 | 28.16 |
| 301 | 6 | 28.10 |
| 333 | 1 | 28.02 |
| 304 | 10 | 27.95 |
| 318 | 8 | 27.88 |
| 322 | 5 | 27.67 |
| 310 | 7 | 27.65 |
| 330 | 2 | 27.64 |
| 301 | 14 | 27.38 |
| 324 | 3 | 27.28 |
| 316 | 10 | 27.00 |
| 322 | 8 | 26.84 |
| 329 | 3 | 26.65 |
| 324 | 2 | 26.60 |
| 305 | 4 | 26.50 |
| 318 | 7 | 26.34 |
| 314 | 3 | 26.32 |
| 305 | 10 | 26.26 |
| 309 | 6 | 26.23 |
| 301 | 12 | 26.21 |
| 331 | 4 | 26.04 |
| 301 | 10 | 25.80 |
| 304 | 1 | 25.78 |
| 305 | 8 | 25.75 |
| 318 | 12 | 25.61 |
| 334 | 11 | 25.25 |
| 305 | 1 | 25.20 |
| 309 | 4 | 25.00 |
| 318 | 10 | 25.00 |
| 313 | 6 | 24.94 |
| 302 | 12 | 24.93 |
| 314 | 8 | 24.85 |
| 305 | 2 | 24.81 |
| 315 | 1 | 24.32 |
| 317 | 1 | 24.31 |
| 321 | 8 | 24.29 |
| 314 | 1 | 24.20 |
| 301 | 13 | 24.14 |
| 313 | 1 | 24.14 |
| 306 | 1 | 24.08 |
| 322 | 7 | 23.98 |
| 307 | 3 | 23.88 |
| 312 | 3 | 23.63 |
| 334 | 7 | 23.46 |
| 302 | 7 | 23.43 |
| 304 | 12 | 23.33 |
| 333 | 9 | 22.69 |
| 320 | 3 | 22.56 |
| 305 | 9 | 22.43 |
| 302 | 14 | 22.34 |
| 302 | 9 | 22.34 |
| 334 | 6 | 22.09 |
| 312 | 5 | 22.00 |
| 315 | 8 | 22.00 |
| 332 | 7 | 22.00 |
| 320 | 8 | 21.89 |
| 303 | 13 | 21.83 |
| 303 | 8 | 21.72 |
| 334 | 8 | 21.72 |
| 322 | 1 | 21.47 |
| 312 | 7 | 21.45 |
| 317 | 4 | 21.45 |
| 315 | 11 | 21.40 |
| 303 | 5 | 21.32 |
| 314 | 6 | 21.23 |
| 317 | 2 | 21.16 |
| 306 | 4 | 21.13 |
| 316 | 7 | 20.86 |
| 303 | 7 | 20.85 |
| 302 | 6 | 20.72 |
| 333 | 10 | 20.70 |
| 306 | 2 | 20.68 |
| 306 | 6 | 20.61 |
| 303 | 6 | 20.55 |
| 316 | 8 | 20.23 |
| 303 | 9 | 20.21 |
| 332 | 11 | 20.16 |
| 333 | 8 | 20.15 |
| 323 | 1 | 20.07 |
| 313 | 10 | 20.00 |
| 314 | 10 | 19.93 |
| 303 | 10 | 19.88 |
| 333 | 12 | 19.70 |
| 304 | 11 | 19.55 |
| 322 | 4 | 19.50 |
| 333 | 11 | 19.35 |
| 320 | 9 | 19.25 |
| 316 | 9 | 18.76 |
| 310 | 6 | 18.73 |
| 333 | 6 | 18.52 |
| 309 | 7 | 18.47 |
| 305 | 3 | 18.45 |
| 324 | 1 | 18.34 |
| 308 | 6 | 18.23 |
| 308 | 1 | 18.12 |
| 310 | 5 | 18.06 |
| 304 | 8 | 17.79 |
| 332 | 12 | 17.65 |
| 332 | 10 | 17.58 |
| 314 | 7 | 17.50 |
| 306 | 3 | 17.41 |
| 312 | 1 | 17.29 |
| 321 | 11 | 17.29 |
| 322 | 3 | 17.26 |
| 319 | 10 | 17.23 |
| 320 | 10 | 17.11 |
| 303 | 12 | 16.98 |
| 304 | 7 | 16.90 |
| 315 | 10 | 16.79 |
| 304 | 13 | 16.68 |
| 305 | 5 | 16.65 |
| 332 | 6 | 16.55 |
| 321 | 6 | 16.52 |
| 320 | 7 | 16.51 |
| 314 | 11 | 16.39 |
| 313 | 7 | 16.38 |
| 313 | 9 | 16.21 |
| 322 | 10 | 16.11 |
| 306 | 9 | 16.08 |
| 332 | 8 | 16.04 |
| 303 | 4 | 15.95 |
| 306 | 8 | 15.92 |
| 311 | 7 | 15.76 |
| 334 | 12 | 15.46 |
| 314 | 5 | 15.45 |
| 308 | 7 | 15.37 |
| 321 | 7 | 15.32 |
| 310 | 4 | 15.14 |
| 304 | 9 | 15.06 |
| 305 | 6 | 14.99 |
| 321 | 10 | 14.61 |
| 314 | 4 | 14.58 |
| 312 | 4 | 14.55 |
| 322 | 6 | 14.44 |
| 314 | 9 | 13.66 |
| 304 | 6 | 12.27 |
| 315 | 2 | 10.47 |
| 310 | 1 | 8.83 |
Total Revenue by Price Code
K-Means Clustering
This is a distance Matrix showing which values are similar or dissimilar. If red then dissimilar and if blue then similar.
Which Sections are put into what Groups
102_10 102_11 102CT_B 104_19 105_G 106_E 106_J 106_M
1 1 1 1 1 1 1 1
106CT_2 107_H 107_L 108_7 109_17 109_18 109_8 112_11
1 1 1 1 1 1 1 1
113_11 113_16 113_9 115_H 115_L 115_M 118_14 118_16
1 1 1 1 1 1 1 1
118_18 118_19 118_20 119_13 107_12 115_13 116_13 116_14
1 1 1 1 2 2 2 2
116_19 116_6 217_8 323_8 102CT_1 111CT_1 119CT_1 101_6
2 2 2 2 3 3 3 4
102_19 102_20 103_19 105_14 109_14 109_9 110_17 110_19
4 4 4 4 4 4 4 4
110_20 111_14 111_5 112_14 112_3 113_12 116_5 116_G
4 4 4 4 4 4 4 4
119_15 119_16 119_17 104_15 106_13 106_15 106_16 106_18
4 4 4 5 5 5 5 5
107_11 109_4 113_2 113_4 113_5 114_10 114_14 114_5
5 5 5 5 5 5 5 5
116_8 116_9 117_16 117_17 118_8 101_16 102_12 102_15
5 5 5 5 5 6 6 6
102_16 102_17 102_5 103_18 103_7 106_10 106_6 107_7
6 6 6 6 6 6 6 6
107_9 108_12 108_14 108_16 109_19 110_6 111_16 112_13
6 6 6 6 6 6 6 6
112_17 112_19 112_4 112_8 115_16 118_12 106_11 106_12
6 6 6 6 6 6 7 7
106_20 107_1 107_10 107_15 107_16 109_5 115_11 115_12
7 7 7 7 7 7 7 7
115_14 115_15 115_17 115_9 116_12 116_15 116_16 117_5
7 7 7 7 7 7 7 7
118_9 207_6 215_3 309_5 311_6 313_8 328_2 330_8
7 7 7 7 7 7 7 7
103_12 104_16 104_17 105_13 106_17 106_19 106_4 107_13
8 8 8 8 8 8 8 8
107_K 108_4 109_10 109_13 114_15 114_19 115_10 116_10
8 8 8 8 8 8 8 8
116_18 116_3 117_15 117_8 117_E 119_14 208_11 216_10
8 8 8 8 8 8 8 8
216_11 217_10 312_2 331_10 303_12 303_4 304_13 304_6
8 8 8 8 9 9 9 9
304_7 304_8 304_9 305_5 305_6 306_3 306_8 306_9
9 9 9 9 9 9 9 9
308_1 308_6 308_7 310_1 310_4 310_5 311_7 312_1
9 9 9 9 9 9 9 9
312_4 313_7 313_9 314_11 314_4 314_5 314_7 314_9
9 9 9 9 9 9 9 9
315_10 315_2 319_10 320_10 320_7 321_10 321_11 321_6
9 9 9 9 9 9 9 9
321_7 322_10 322_3 322_6 332_10 332_12 332_6 332_8
9 9 9 9 9 9 9 9
334_12 205_2 205_5 206_4 206_7 208_6 209_12 209_2
9 10 10 10 10 10 10 10
210_3 214_8 216_4 217_12 217_5 217_6 217_7 218_10
10 10 10 10 10 10 10 10
218_3 219_3 303_2 307_6 312_8 318_1 322_12 326_2
10 10 10 10 10 10 10 10
326_3 326_7 328_7 329_7 330_5 331_6 332_2 101_13
10 10 10 10 10 10 10 11
101_14 101_15 101_17 102_13 102_4 105_11 105_15 105_16
11 11 11 11 11 11 11 11
105_20 107CT_2 108_11 108_15 108_17 108_19 108_20 108_9
11 11 11 11 11 11 11 11
109_16 110_11 110_12 110_13 110_14 110_4 110CT_B 111_10
11 11 11 11 11 11 11 11
111_11 112CT_B 113_15 114_12 114_16 114_17 114_18 114_20
11 11 11 11 11 11 11 11
115_8 117_11 117_14 117_20 118_7 119_10 119_11 119_12
11 11 11 11 11 11 11 11
119_3 119_4 119CT_B 105_18 105_19 106_14 107_14 107_4
11 11 11 12 12 12 12 12
107_8 107_D 108_10 108_18 108_5 108_8 113_17 114_8
12 12 12 12 12 12 12 12
115_2 115_6 115_7 115_K 116_17 116_2 116_20 116_7
12 12 12 12 12 12 12 12
117_13 117_4 118_4 206_5 216_12 321_12 333_14 117_12
12 12 12 12 12 12 12 13
216_2 217_11 217_9 301_2 301_5 323_7 325_2 325_7
13 13 13 13 13 13 13 13
328_6 330_6 330_7 334_13 107_17 206_10 206_11 206_6
13 13 13 13 14 14 14 14
301_1 305_7 307_8 316_1 324_8 325_3 325_6 328_3
14 14 14 14 14 14 14 14
101_11 101_7 101_8 101_9 102_1 102_3 102_8 102CT_A
15 15 15 15 15 15 15 15
110_1 110_9 111_8 112CT_1 119_2 119_5 119_6 119_7
15 15 15 15 15 15 15 15
119_8 106_2 106CT_19 207_5 208_10 208_3 209_11 209_4
15 16 16 16 16 16 16 16
216_3 216_7 217_1 301_6 301_7 302_13 303_3 304_10
16 16 16 16 16 16 16 16
306_7 310_7 317_3 317_8 318_11 318_8 319_1 320_1
16 16 16 16 16 16 16 16
320_5 322_5 329_2 330_2 330_3 331_3 331_5 332_1
16 16 16 16 16 16 16 16
333_1 333_3 333_4 334_10 334_14 101CT_A 102_18 102_9
16 16 16 16 16 17 17 17
110_10 110_15 110_16 110_18 110_7 110CT_A 111_15 111CT_A
17 17 17 17 17 17 17 17
112_9 119CT_A 302_14 302_6 302_9 303_10 303_13 303_5
17 17 18 18 18 18 18 18
303_6 303_7 303_8 303_9 304_11 305_3 305_9 306_2
18 18 18 18 18 18 18 18
306_4 306_6 309_7 310_6 312_5 312_7 313_10 314_10
18 18 18 18 18 18 18 18
314_6 315_11 315_8 316_7 316_8 316_9 317_2 317_4
18 18 18 18 18 18 18 18
320_3 320_8 320_9 322_1 322_4 323_1 324_1 332_11
18 18 18 18 18 18 18 18
332_7 333_10 333_11 333_12 333_6 333_8 333_9 334_6
18 18 18 18 18 18 18 18
334_8 301_10 301_12 301_13 301_14 302_12 302_7 304_1
18 19 19 19 19 19 19 19
304_12 305_1 305_10 305_2 305_4 305_8 306_1 307_3
19 19 19 19 19 19 19 19
309_4 309_6 312_3 313_1 313_6 314_1 314_3 314_8
19 19 19 19 19 19 19 19
315_1 316_10 317_1 318_10 318_12 318_7 321_8 322_7
19 19 19 19 19 19 19 19
322_8 324_2 324_3 329_3 331_4 334_11 334_7 101_19
19 19 19 19 19 19 19 20
101CT_B 102_14 106_C 110_8 111CT_B 113_10 115_E 103_16
20 20 20 20 20 20 20 21
104_9 105_F 106_5 106_D 106_F 106_H 107_5 107_6
21 21 21 21 21 21 21 21
107_F 108_13 109_12 109_15 112_15 115_3 115_5 115_J
21 21 21 21 21 21 21 21
116_11 117_J 118_13 118_17 302_15 206_3 206_9 207_10
21 21 21 21 21 22 22 22
207_12 207_7 207_8 207_9 208_12 208_7 209_6 209_7
22 22 22 22 22 22 22 22
209_8 210_4 214_4 214_7 215_11 215_12 215_7 216_1
22 22 22 22 22 22 22 22
216_6 218_12 218_2 218_8 301_9 302_1 303_14 306_5
22 22 22 22 22 22 22 22
321_1 324_4 324_5 327_2 327_3 327_6 327_7 329_5
22 22 22 22 22 22 22 22
329_6 333_2 205_8 206_12 215_2 218_5 218_9 301_3
22 22 23 23 23 23 23 23
307_4 307_5 312_6 314_12 316_2 324_6 324_7 326_4
23 23 23 23 23 23 23 23
326_5 327_4 329_4 329_8
23 23 23 23 K-Means Clustering Analysis
The first step is to define the number of Clusters (k). Then there are k centroids that are randomly generated from the data with each centroid defining a cluster. Each data point is then assigned to its nearest centroid based on Squared Euclidean Distance.
\[\sum_{x \neq y \in S_i} (x - \mu_i)(\mu_i - y)\]
The second step is recomputing the centroids by taking the mean of all the data points in the new clusters.
\[\ m_i^{(t+1)} = \frac{1}{\mid S_i^{(t)} \mid} \sum_{x_j \in S_i^{(t)}} x_j \]
The Algorithm for K-means iterates through these two steps until the sum of the squared distances is minimized or no data points change clusters.
K-means clustering with 23 clusters of sizes 28, 8, 3, 20, 18, 25, 26, 28, 45, 30, 44, 28, 13, 12, 17, 36, 13, 47, 38, 8, 22, 37, 18
Cluster means:
PerTix
1 1.09757030
2 -0.39225352
3 6.77949368
4 0.06031461
5 -0.31582040
6 0.32570048
7 -0.36408829
8 -0.20040426
9 -0.63635807
10 -0.50109206
11 0.67417463
12 -0.26214478
13 -0.44785787
14 -0.41837296
15 3.24462951
16 -0.55873318
17 2.28133039
18 -0.61000058
19 -0.58468068
20 1.50932522
21 -0.10112572
22 -0.52445988
23 -0.47719445
Clustering vector:
101_11 101_13 101_14 101_15 101_16 101_17 101_19 101_6
15 11 11 11 6 11 20 4
101_7 101_8 101_9 101CT_A 101CT_B 102_1 102_10 102_11
15 15 15 17 20 15 1 1
102_12 102_13 102_14 102_15 102_16 102_17 102_18 102_19
6 11 20 6 6 6 17 4
102_20 102_3 102_4 102_5 102_8 102_9 102CT_1 102CT_A
4 15 11 6 15 17 3 15
102CT_B 103_12 103_16 103_18 103_19 103_7 104_15 104_16
1 8 21 6 4 6 5 8
104_17 104_19 104_9 105_11 105_13 105_14 105_15 105_16
8 1 21 11 8 4 11 11
105_18 105_19 105_20 105_F 105_G 106_10 106_11 106_12
12 12 11 21 1 6 7 7
106_13 106_14 106_15 106_16 106_17 106_18 106_19 106_2
5 12 5 5 8 5 8 16
106_20 106_4 106_5 106_6 106_C 106_D 106_E 106_F
7 8 21 6 20 21 1 21
106_H 106_J 106_M 106CT_19 106CT_2 107_1 107_10 107_11
21 1 1 16 1 7 7 5
107_12 107_13 107_14 107_15 107_16 107_17 107_4 107_5
2 8 12 7 7 14 12 21
107_6 107_7 107_8 107_9 107_D 107_F 107_H 107_K
21 6 12 6 12 21 1 8
107_L 107CT_2 108_10 108_11 108_12 108_13 108_14 108_15
1 11 12 11 6 21 6 11
108_16 108_17 108_18 108_19 108_20 108_4 108_5 108_7
6 11 12 11 11 8 12 1
108_8 108_9 109_10 109_12 109_13 109_14 109_15 109_16
12 11 8 21 8 4 21 11
109_17 109_18 109_19 109_4 109_5 109_8 109_9 110_1
1 1 6 5 7 1 4 15
110_10 110_11 110_12 110_13 110_14 110_15 110_16 110_17
17 11 11 11 11 17 17 4
110_18 110_19 110_20 110_4 110_6 110_7 110_8 110_9
17 4 4 11 6 17 20 15
110CT_A 110CT_B 111_10 111_11 111_14 111_15 111_16 111_5
17 11 11 11 4 17 6 4
111_8 111CT_1 111CT_A 111CT_B 112_11 112_13 112_14 112_15
15 3 17 20 1 6 4 21
112_17 112_19 112_3 112_4 112_8 112_9 112CT_1 112CT_B
6 6 4 6 6 17 15 11
113_10 113_11 113_12 113_15 113_16 113_17 113_2 113_4
20 1 4 11 1 12 5 5
113_5 113_9 114_10 114_12 114_14 114_15 114_16 114_17
5 1 5 11 5 8 11 11
114_18 114_19 114_20 114_5 114_8 115_10 115_11 115_12
11 8 11 5 12 8 7 7
115_13 115_14 115_15 115_16 115_17 115_2 115_3 115_5
2 7 7 6 7 12 21 21
115_6 115_7 115_8 115_9 115_E 115_H 115_J 115_K
12 12 11 7 20 1 21 12
115_L 115_M 116_10 116_11 116_12 116_13 116_14 116_15
1 1 8 21 7 2 2 7
116_16 116_17 116_18 116_19 116_2 116_20 116_3 116_5
7 12 8 2 12 12 8 4
116_6 116_7 116_8 116_9 116_G 117_11 117_12 117_13
2 12 5 5 4 11 13 12
117_14 117_15 117_16 117_17 117_20 117_4 117_5 117_8
11 8 5 5 11 12 7 8
117_E 117_J 118_12 118_13 118_14 118_16 118_17 118_18
8 21 6 21 1 1 21 1
118_19 118_20 118_4 118_7 118_8 118_9 119_10 119_11
1 1 12 11 5 7 11 11
119_12 119_13 119_14 119_15 119_16 119_17 119_2 119_3
11 1 8 4 4 4 15 11
119_4 119_5 119_6 119_7 119_8 119CT_1 119CT_A 119CT_B
11 15 15 15 15 3 17 11
205_2 205_5 205_8 206_10 206_11 206_12 206_3 206_4
10 10 23 14 14 23 22 10
206_5 206_6 206_7 206_9 207_10 207_12 207_5 207_6
12 14 10 22 22 22 16 7
207_7 207_8 207_9 208_10 208_11 208_12 208_3 208_6
22 22 22 16 8 22 16 10
208_7 209_11 209_12 209_2 209_4 209_6 209_7 209_8
22 16 10 10 16 22 22 22
210_3 210_4 214_4 214_7 214_8 215_11 215_12 215_2
10 22 22 22 10 22 22 23
215_3 215_7 216_1 216_10 216_11 216_12 216_2 216_3
7 22 22 8 8 12 13 16
216_4 216_6 216_7 217_1 217_10 217_11 217_12 217_5
10 22 16 16 8 13 10 10
217_6 217_7 217_8 217_9 218_10 218_12 218_2 218_3
10 10 2 13 10 22 22 10
218_5 218_8 218_9 219_3 301_1 301_10 301_12 301_13
23 22 23 10 14 19 19 19
301_14 301_2 301_3 301_5 301_6 301_7 301_9 302_1
19 13 23 13 16 16 22 22
302_12 302_13 302_14 302_15 302_6 302_7 302_9 303_10
19 16 18 21 18 19 18 18
303_12 303_13 303_14 303_2 303_3 303_4 303_5 303_6
9 18 22 10 16 9 18 18
303_7 303_8 303_9 304_1 304_10 304_11 304_12 304_13
18 18 18 19 16 18 19 9
304_6 304_7 304_8 304_9 305_1 305_10 305_2 305_3
9 9 9 9 19 19 19 18
305_4 305_5 305_6 305_7 305_8 305_9 306_1 306_2
19 9 9 14 19 18 19 18
306_3 306_4 306_5 306_6 306_7 306_8 306_9 307_3
9 18 22 18 16 9 9 19
307_4 307_5 307_6 307_8 308_1 308_6 308_7 309_4
23 23 10 14 9 9 9 19
309_5 309_6 309_7 310_1 310_4 310_5 310_6 310_7
7 19 18 9 9 9 18 16
311_6 311_7 312_1 312_2 312_3 312_4 312_5 312_6
7 9 9 8 19 9 18 23
312_7 312_8 313_1 313_10 313_6 313_7 313_8 313_9
18 10 19 18 19 9 7 9
314_1 314_10 314_11 314_12 314_3 314_4 314_5 314_6
19 18 9 23 19 9 9 18
314_7 314_8 314_9 315_1 315_10 315_11 315_2 315_8
9 19 9 19 9 18 9 18
316_1 316_10 316_2 316_7 316_8 316_9 317_1 317_2
14 19 23 18 18 18 19 18
317_3 317_4 317_8 318_1 318_10 318_11 318_12 318_7
16 18 16 10 19 16 19 19
318_8 319_1 319_10 320_1 320_10 320_3 320_5 320_7
16 16 9 16 9 18 16 9
320_8 320_9 321_1 321_10 321_11 321_12 321_6 321_7
18 18 22 9 9 12 9 9
321_8 322_1 322_10 322_12 322_3 322_4 322_5 322_6
19 18 9 10 9 18 16 9
322_7 322_8 323_1 323_7 323_8 324_1 324_2 324_3
19 19 18 13 2 18 19 19
324_4 324_5 324_6 324_7 324_8 325_2 325_3 325_6
22 22 23 23 14 13 14 14
325_7 326_2 326_3 326_4 326_5 326_7 327_2 327_3
13 10 10 23 23 10 22 22
327_4 327_6 327_7 328_2 328_3 328_6 328_7 329_2
23 22 22 7 14 13 10 16
329_3 329_4 329_5 329_6 329_7 329_8 330_2 330_3
19 23 22 22 10 23 16 16
330_5 330_6 330_7 330_8 331_10 331_3 331_4 331_5
10 13 13 7 8 16 19 16
331_6 332_1 332_10 332_11 332_12 332_2 332_6 332_7
10 16 9 18 9 10 9 18
332_8 333_1 333_10 333_11 333_12 333_14 333_2 333_3
9 16 18 18 18 12 22 16
333_4 333_6 333_8 333_9 334_10 334_11 334_12 334_13
16 18 18 18 16 19 9 13
334_14 334_6 334_7 334_8
16 18 19 18
Within cluster sum of squares by cluster:
[1] 0.2795349487 0.0004723555 3.0258186242 0.0821703252 0.0040248697
[6] 0.2628048045 0.0029014139 0.0121864526 0.0046835516 0.0011515828
[11] 0.2533141541 0.0064703418 0.0005472786 0.0007276438 2.7039244632
[16] 0.0028297462 0.8252043521 0.0021460716 0.0015683409 0.1073056750
[21] 0.0234794244 0.0015257432 0.0009512979
(between_SS / total_SS = 98.6 %)
Available components:
[1] "cluster" "centers" "totss" "withinss"
[5] "tot.withinss" "betweenss" "size" "iter"
[9] "ifault" Here is a visualization of the Clusters and the Revenue in each Cluster. Each Cluster has its own color.
## Section Row PerTix Cluster
## 270 119CT 1 1586.25 3
## 154 111CT 1 1329.57 3
## 31 102CT 1 1144.50 3
## 167 112CT 1 981.75 15
## 9 101 7 735.00 15
## 10 101 8 735.00 15
## 11 101 9 735.00 15
## 153 111 8 735.00 15
## 26 102 3 728.00 15
## 263 119 2 728.00 15
## 14 102 1 702.00 15
## 128 110 1 702.00 15
## 29 102 8 679.50 15
## 266 119 5 679.50 15
## 267 119 6 679.50 15
## 268 119 7 679.50 15
## 269 119 8 679.50 15
## 32 102CT A 676.50 15
## 144 110 9 664.07 15
## 1 101 11 650.50 15
## 150 111 15 617.50 17
## 129 110 10 597.00 17
## 30 102 9 596.39 17
## 142 110 7 586.00 17
## 155 111CT A 579.57 17
## 271 119CT A 541.03 17
## 166 112 9 536.00 17
## 12 101CT A 512.25 17
## 135 110 16 507.00 17
## 23 102 18 500.00 17
## 134 110 15 500.00 17
## 137 110 18 498.60 17
## 145 110CT A 476.78 17
## 7 101 19 437.97 20
## 13 101CT B 426.45 20
## 156 111CT B 413.34 20
## 169 113 10 399.75 20
## 69 106 C 397.50 20
## 205 115 E 397.50 20
## 19 102 14 378.75 20
## 143 110 8 372.15 20
## 170 113 11 359.87 1
## 258 119 13 358.46 1
## 178 113 9 354.00 1
## 246 118 16 351.00 1
## 157 112 11 350.00 1
## 15 102 10 344.63 1
## 248 118 18 344.25 1
## 53 105 G 337.50 1
## 121 109 17 337.50 1
## 122 109 18 337.50 1
## 173 113 16 337.50 1
## 249 118 19 337.50 1
## 250 118 20 337.50 1
## 33 102CT B 337.44 1
## 95 107 H 322.00 1
## 97 107 L 322.00 1
## 206 115 H 322.00 1
## 209 115 L 322.00 1
## 77 106CT 2 316.80 1
## 74 106 J 315.25 1
## 42 104 19 313.00 1
## 75 106 M 313.00 1
## 112 108 7 313.00 1
## 210 115 M 313.00 1
## 16 102 11 311.25 1
## 71 106 E 302.33 1
## 126 109 8 296.65 1
## 245 118 14 295.64 1
## 120 109 16 278.32 11
## 148 111 11 277.41 11
## 147 111 10 272.45 11
## 44 105 11 270.00 11
## 140 110 4 268.50 11
## 18 102 13 267.26 11
## 172 113 15 267.17 11
## 272 119CT B 265.72 11
## 230 117 11 263.67 11
## 256 119 11 262.53 11
## 48 105 16 260.75 11
## 100 108 11 260.50 11
## 114 108 9 260.50 11
## 180 114 12 260.50 11
## 130 110 11 259.86 11
## 108 108 19 259.42 11
## 168 112CT B 257.61 11
## 51 105 20 256.50 11
## 106 108 17 256.50 11
## 109 108 20 256.50 11
## 185 114 18 256.50 11
## 187 114 20 256.50 11
## 237 117 20 256.50 11
## 132 110 13 255.57 11
## 184 114 17 254.31 11
## 104 108 15 253.85 11
## 255 119 10 248.84 11
## 257 119 12 247.37 11
## 265 119 4 244.79 11
## 2 101 13 244.41 11
## 131 110 12 243.95 11
## 264 119 3 243.32 11
## 252 118 7 242.95 11
## 183 114 16 242.31 11
## 6 101 17 239.95 11
## 146 110CT B 238.41 11
## 4 101 15 237.16 11
## 47 105 15 236.75 11
## 133 110 14 236.61 11
## 233 117 14 231.46 11
## 27 102 4 229.40 11
## 98 107CT 2 227.81 11
## 3 101 14 226.09 11
## 203 115 8 224.75 11
## 151 111 16 219.10 6
## 17 102 12 218.43 6
## 162 112 19 216.51 6
## 105 108 16 215.25 6
## 28 102 5 213.10 6
## 36 103 18 211.09 6
## 103 108 14 207.72 6
## 38 103 7 202.65 6
## 165 112 8 200.49 6
## 21 102 16 192.00 6
## 141 110 6 190.05 6
## 158 112 13 189.84 6
## 68 106 6 183.20 6
## 196 115 16 182.91 6
## 92 107 9 181.83 6
## 54 106 10 180.09 6
## 5 101 16 179.77 6
## 22 102 17 177.61 6
## 101 108 12 172.10 6
## 90 107 7 168.76 6
## 164 112 4 167.58 6
## 243 118 12 167.08 6
## 161 112 17 166.52 6
## 20 102 15 166.42 6
## 123 109 19 166.17 6
## 24 102 19 159.82 4
## 127 109 9 159.28 4
## 139 110 20 158.87 4
## 37 103 19 158.69 4
## 262 119 17 157.50 4
## 159 112 14 148.43 4
## 229 116 G 146.29 4
## 152 111 5 146.06 4
## 118 109 14 141.18 4
## 149 111 14 139.84 4
## 8 101 6 135.33 4
## 163 112 3 135.23 4
## 224 116 5 134.75 4
## 136 110 17 134.14 4
## 46 105 14 132.78 4
## 261 119 16 129.45 4
## 138 110 19 129.11 4
## 171 113 12 128.92 4
## 25 102 20 128.51 4
## 260 119 15 127.55 4
## 244 118 13 126.35 21
## 160 112 15 121.88 21
## 94 107 F 120.43 21
## 116 109 12 119.26 21
## 70 106 D 117.22 21
## 212 116 11 117.08 21
## 247 118 17 115.96 21
## 67 106 5 112.95 21
## 199 115 3 112.63 21
## 102 108 13 112.31 21
## 89 107 6 112.17 21
## 43 104 9 112.09 21
## 73 106 H 112.08 21
## 356 302 15 110.85 21
## 119 109 15 109.33 21
## 207 115 J 107.28 21
## 200 115 5 107.08 21
## 35 103 16 106.50 21
## 52 105 F 105.94 21
## 242 117 J 105.71 21
## 72 106 F 105.15 21
## 88 107 5 104.08 21
## 117 109 13 103.04 8
## 325 217 10 101.35 8
## 110 108 4 100.50 8
## 259 119 14 100.00 8
## 63 106 19 99.73 8
## 317 216 11 98.46 8
## 115 109 10 98.00 8
## 234 117 15 96.62 8
## 82 107 13 96.26 8
## 34 103 12 95.87 8
## 182 114 15 95.35 8
## 316 216 10 94.43 8
## 66 106 4 94.19 8
## 211 116 10 93.42 8
## 219 116 18 93.38 8
## 61 106 17 93.03 8
## 241 117 E 92.86 8
## 240 117 8 91.97 8
## 223 116 3 91.67 8
## 186 114 19 91.59 8
## 420 312 2 91.58 8
## 41 104 17 91.36 8
## 293 208 11 91.36 8
## 533 331 10 90.77 8
## 190 115 10 90.60 8
## 96 107 K 90.31 8
## 40 104 16 90.24 8
## 45 105 13 89.85 8
## 189 114 8 88.72 12
## 232 117 13 88.04 12
## 550 333 14 87.00 12
## 251 118 4 86.89 12
## 318 216 12 86.19 12
## 198 115 2 85.97 12
## 113 108 8 85.50 12
## 202 115 7 85.48 12
## 91 107 8 85.38 12
## 201 115 6 85.09 12
## 222 116 20 84.23 12
## 221 116 2 84.07 12
## 93 107 D 83.51 12
## 478 321 12 83.51 12
## 226 116 7 83.27 12
## 218 116 17 83.16 12
## 208 115 K 82.85 12
## 174 113 17 82.67 12
## 83 107 14 82.55 12
## 50 105 19 82.48 12
## 99 108 10 81.55 12
## 281 206 5 81.00 12
## 238 117 4 79.78 12
## 87 107 4 79.71 12
## 49 105 18 79.66 12
## 58 106 14 79.59 12
## 111 108 5 79.36 12
## 107 108 18 78.79 12
## 60 106 16 77.46 5
## 179 114 10 76.99 5
## 124 109 4 76.93 5
## 59 106 15 76.88 5
## 177 113 5 76.46 5
## 175 113 2 76.46 5
## 176 113 4 75.95 5
## 188 114 5 74.54 5
## 228 116 9 74.27 5
## 235 117 16 73.24 5
## 236 117 17 73.18 5
## 227 116 8 71.50 5
## 80 107 11 71.12 5
## 181 114 14 71.08 5
## 39 104 15 70.86 5
## 253 118 8 70.30 5
## 62 106 18 70.24 5
## 57 106 13 70.00 5
## 56 106 12 68.92 7
## 216 116 15 68.19 7
## 204 115 9 67.87 7
## 409 309 5 67.20 7
## 417 311 6 67.20 7
## 239 117 5 67.11 7
## 65 106 20 67.06 7
## 55 106 11 66.74 7
## 431 313 8 66.58 7
## 288 207 6 65.70 7
## 191 115 11 64.86 7
## 516 328 2 64.66 7
## 197 115 17 64.39 7
## 85 107 16 64.24 7
## 195 115 15 64.09 7
## 217 116 16 64.07 7
## 79 107 10 63.97 7
## 125 109 5 63.81 7
## 213 116 12 63.43 7
## 84 107 15 63.41 7
## 313 215 3 63.30 7
## 194 115 14 63.21 7
## 192 115 12 62.98 7
## 532 330 8 62.75 7
## 78 107 1 62.74 7
## 254 118 9 62.62 7
## 331 217 8 62.08 2
## 193 115 13 61.44 2
## 81 107 12 61.33 2
## 225 116 6 59.73 2
## 220 116 19 59.47 2
## 215 116 14 59.04 2
## 214 116 13 58.61 2
## 493 323 8 58.00 2
## 503 325 3 57.31 14
## 504 325 6 56.77 14
## 341 301 1 56.73 14
## 517 328 3 56.15 14
## 282 206 6 56.08 14
## 276 206 10 55.80 14
## 449 316 1 55.26 14
## 404 307 8 54.92 14
## 277 206 11 54.05 14
## 86 107 17 53.74 14
## 501 324 8 53.32 14
## 388 305 7 52.89 14
## 505 325 7 52.28 13
## 531 330 7 50.92 13
## 502 325 2 50.88 13
## 348 301 5 50.80 13
## 530 330 6 50.54 13
## 332 217 9 50.37 13
## 346 301 2 50.19 13
## 492 323 7 49.88 13
## 231 117 12 49.16 13
## 560 334 13 49.00 13
## 319 216 2 48.65 13
## 326 217 11 48.52 13
## 518 328 6 47.95 13
## 451 316 2 46.65 23
## 347 301 3 46.53 23
## 526 329 8 46.38 23
## 522 329 4 45.97 23
## 402 307 5 45.95 23
## 424 312 6 45.48 23
## 339 218 9 45.18 23
## 508 326 4 45.06 23
## 278 206 12 44.88 23
## 312 215 2 44.65 23
## 513 327 4 44.19 23
## 500 324 7 43.99 23
## 275 205 8 43.84 23
## 401 307 4 43.24 23
## 499 324 6 43.21 23
## 509 326 5 42.95 23
## 436 314 12 42.79 23
## 337 218 5 42.63 23
## 460 318 1 42.08 10
## 340 219 3 41.94 10
## 299 209 12 41.94 10
## 309 214 8 41.88 10
## 280 206 4 41.85 10
## 274 205 5 41.77 10
## 542 332 2 41.66 10
## 484 322 12 41.60 10
## 296 208 6 41.24 10
## 506 326 2 41.03 10
## 529 330 5 40.91 10
## 519 328 7 40.61 10
## 537 331 6 40.43 10
## 403 307 6 40.25 10
## 300 209 2 40.20 10
## 510 326 7 40.20 10
## 305 210 3 40.13 10
## 333 218 10 39.95 10
## 328 217 5 39.76 10
## 330 217 7 39.69 10
## 364 303 2 39.64 10
## 426 312 8 39.35 10
## 283 206 7 39.30 10
## 525 329 7 39.17 10
## 327 217 12 39.04 10
## 273 205 2 39.02 10
## 336 218 3 38.99 10
## 507 326 3 38.95 10
## 329 217 6 38.93 10
## 321 216 4 38.47 10
## 322 216 6 38.12 22
## 285 207 10 38.10 22
## 289 207 7 37.66 22
## 512 327 3 37.65 22
## 310 215 11 37.56 22
## 314 215 7 37.28 22
## 352 302 1 37.21 22
## 307 214 4 37.11 22
## 351 301 9 37.00 22
## 286 207 12 36.95 22
## 514 327 6 36.92 22
## 311 215 12 36.83 22
## 290 207 8 36.78 22
## 497 324 4 36.69 22
## 515 327 7 36.69 22
## 363 303 14 36.56 22
## 279 206 3 36.42 22
## 334 218 12 36.41 22
## 335 218 2 36.35 22
## 304 209 8 36.22 22
## 498 324 5 36.03 22
## 551 333 2 35.89 22
## 308 214 7 35.84 22
## 306 210 4 35.61 22
## 284 206 9 35.56 22
## 475 321 1 35.50 22
## 294 208 12 35.45 22
## 302 209 6 35.44 22
## 297 208 7 35.00 22
## 315 216 1 35.00 22
## 524 329 6 34.92 22
## 395 306 5 34.73 22
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