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day4
Course: STAT 218, Fall 2009School: Cal Poly
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218 Stat - Day 4 Five-number summary, Boxplots Five-number summary (FNS): Minimum, Lower Quartile (Q1), Median, Upper Quartile (Q3), Maximum Quartiles are calculated as the median of the values below/above the location of the actual median Example: Natural selection (Bumpus) Humerus lengths (inches) of sparrows who survived storm (n=35): 0.687 0.728 0.739 0.752 0.659 0.726 0.744 0.703 0.728 0.741 0.755 0.689 0.729...
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218 Stat - Day 4 Five-number summary, Boxplots Five-number summary (FNS): Minimum, Lower Quartile (Q1), Median, Upper Quartile (Q3), Maximum Quartiles are calculated as the median of the values below/above the location of the actual median Example: Natural selection (Bumpus) Humerus lengths (inches) of sparrows who survived storm (n=35):
0.687 0.728 0.739 0.752 0.659 0.726 0.744 0.703 0.728 0.741 0.755 0.689 0.729 0.745 0.709 0.729 0.741 0.756 0.702 0.731 0.752 0.715 0.730 0.741 0.766 0.703 0.736 0.752 0.721 0.730 0.741 0.767 0.709 0.737 0.754 0.723 0.733 0.743 0.769 0.713 0.738 0.765 0.723 0.733 0.749 0.770 0.720 0.738 0.726 0.735 0.751 0.780 0.720 0.739 0.728 0.736 0.752
Humerus lengths of sparrows who perished in storm (n=24):
0.726 0.743
(a) Find FNS of humerus lengths for sparrows who survived the storm.
(b) Find FNS of humerus lengths for sparrows who did not survive the storm.
Boxplot: visual representation of FNS (c) Produce (unmodified) boxplots to compare these distributions.
(d) Compare and contrast the two distributions of humerus lengths.
Modified boxplot: indicates outliers separately, extends whisker to most extreme non-outlier. Outliers are values more than 1.5*(Q3-Q1) from nearer quartile (e) Check for outliers in both groups.
(f) Create modified boxplots of humerus lengths for the two groups.
(g) Use Minitab (bumpus.mtw) to reproduce this analysis. [Notes: The data are presented in unstacked format in c1 and c2, meaning that each group has its own column. The data are presented in stacked format in c4 and c5, meaning that all of the data are in one column with a separate column indicating the group variable. You can use Graph> Boxplot and then choose one Y, with groups with the stacked data or multiple Ys, simple with the unstacked data. Also, be aware that Minitab may calculate quartiles a bit differently.]
Example: Draft lottery The following data are the draft numbers (1-366) assigned to birthdates in the 1970 draft lottery. Men born on the date assigned a draft number of 1 were the first to be drafted, followed by those born on the date assigned draft number 2, and so on. Date 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Jan 305 159 251 215 101 224 306 199 194 325 329 221 318 238 17 121 235 140 58 280 186 337 118 59 52 92 355 77 349 164 211 Feb 86 144 297 210 214 347 91 181 338 216 150 68 152 4 89 212 189 292 25 302 363 290 57 236 179 365 205 299 285 Mar 108 29 267 275 293 139 122 213 317 323 136 300 259 354 169 166 33 332 200 239 334 265 256 258 343 170 268 223 362 217 30 Apr 32 271 83 81 269 253 147 312 219 218 14 346 124 231 273 148 260 90 336 345 62 316 252 2 351 340 74 262 191 208 May 330 298 40 276 364 155 35 321 197 65 37 133 295 178 130 55 112 278 75 183 250 326 319 31 361 357 296 308 226 103 313 Jun 249 228 301 20 28 110 85 366 335 206 134 272 69 356 180 274 73 341 104 360 60 247 358 109 137 22 64 222 353 209 Jul 93 350 115 279 188 327 50 13 277 284 248 15 42 331 322 120 98 190 227 187 27 153 172 23 67 303 289 88 270 287 193 Aug 111 45 261 145 54 114 168 48 106 21 324 142 307 198 102 44 154 141 311 344 291 339 116 36 286 245 352 167 61 333 11 Sep 225 161 49 232 82 6 8 184 263 71 158 242 175 1 113 207 255 246 177 63 204 160 119 195 149 18 233 257 151 315 Oct 359 125 244 202 24 87 234 283 342 220 237 72 138 294 171 254 288 5 241 192 243 117 201 196 176 7 264 94 229 38 79 Nov 19 34 348 266 310 76 51 97 80 282 46 66 126 127 131 107 143 146 203 185 156 9 182 230 132 309 47 281 99 174 Dec 129 328 157 165 56 10 12 105 43 41 39 314 163 26 320 96 304 128 240 135 70 53 162 95 84 173 78 123 16 3 100
(a) What draft number was assigned to your birthday? Is this draft number in the top third, middle third, or last third of the draft order?
The following table arranges in order the draft numbers for each month: Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Jan 17 52 58 59 77 92 101 118 121 140 159 164 186 194 199 211 215 221 224 235 238 251 280 305 306 318 325 329 337 349 355 Feb 4 25 57 68 86 89 91 144 150 152 179 181 189 205 210 212 214 216 236 285 290 292 297 299 302 338 347 363 365 Mar 29 30 33 108 122 136 139 166 169 170 200 213 217 223 239 256 258 259 265 267 268 275 293 300 317 323 332 334 343 354 362 Apr 2 14 32 62 74 81 83 90 124 147 148 191 208 218 219 231 252 253 260 262 269 271 273 312 316 336 340 345 346 351 May 31 35 37 40 55 65 75 103 112 130 133 155 178 183 197 226 250 276 278 295 296 298 308 313 319 321 326 330 357 361 364 Jun 20 22 28 60 64 69 73 85 104 109 110 134 137 180 206 209 222 228 247 249 272 274 301 335 341 353 356 358 360 366 Jul 13 15 ...
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