Data: SampleID Zip Code Ward Pb Bottle 1 (ppb) - First Draw Pb Bottle 2 (ppb) -
ID: 3375129 • Letter: D
Question
Data:
SampleID Zip Code Ward Pb Bottle 1 (ppb) - First Draw Pb Bottle 2 (ppb) - 45 secs flu Pb Bottle 3 (ppb) - 2 mins flus
1 48504 6 0.344 0.226 0.145
2 48507 9 8.133 10.77 2.761
4 48504 1 1.111 0.11 0.123
5 48507 8 8.007 7.446 3.384
6 48505 3 1.951 0.048 0.035
7 48507 9 7.2 1.4 0.2
8 48507 9 40.63 9.726 6.132
9 48503 5 1.1 2.5 0.1
12 48507 9 10.6 1.038 1.294
13 48505 3 6.2 4.2 2.3
15 48507 9 4.358 0.822 0.147
16 48505 5 24.37 8.796 4.347
17 48505 2 6.609 5.752 1.433
18 48503 7 4.062 1.099 1.085
19 48507 9 2.484 0.72 0.565
20 48507 9 0.438 1.046 0.511
21 48503 5 1.29 0.243 0.225
22 48504 6 0.548 0.622 0.361
23 48504 2 3.131 0.674 0.683
24 48504 6 120 239.7 29.71
25 48505 1 2.911 0.406 0.237
26 48505 5 16.52 10.26 2.762
27 48505 1 1.984 1.13 0.712
28 48503 7 5.367 2.474 1.616
29 48504 2 5.5 8.4 2.4
30 48506 4 0.639 0.223 0.194
31 48503 7 6.087 28.87 2.13
31 48503 7 10.32 13.47 18.19
33 48503 6 66.88 2.662 2.082
34 48505 1 20.41 3.543 2.344
35 48504 6 109.6 80.47 94.52
36 48503 8 5.06 3.406 4.088
37 48504 2 2.774 0.21 0.264
38 48505 3 4.453 3.679 3.523
39 48505 1 0.4 0.3 0.7
40 48529 9 0.974 0.142 0.118
41 48505 5 3.228 2.534 2.222
42 48505 2 12.55 4.132 0.12
43 48505 3 0.501 0.156 15.14
44 48504 2 2.448 0.373 0.288
45 48505 3 5.508 5.157 2.621
46 48504 6 1.293 0.441 0.281
47 48505 1 4.699 1.395 0.329
48 48504 6 6.093 2.682 1.458
49 48504 2 0.8 0.8 0.5
50 48503 5 1.626 1.332 0.327
51 48507 8 2.576 2.852 1.48
52 48504 1 2.362 0.467 0.339
53 48503 5 1.585 0.494 1.232
54 48506 4 3.058 1.808 1.169
55 48506 4 2.423 0.393 0.373
56 48503 8 30.91 42.58 44.6
57 48503 8 4.47 3.649 1
58 48505 1 2.172 1.76 1.44
59 48505 3 1.8 0.5 0.2
63 48503 5 0.965 0.166 0.319
65 48505 1 7.636 5.206 9.239
66 48506 3 3.158 1.948 2.802
67 48503 7 105.3 12.84 4.534
68 48506 3 4.476 0.355 0.334
69 48504 1 2.828 6.694 20.99
71 48503 5 2.481 3.86 24.64
72 48507 5 11.52 0.288 0.215
73 48507 8 3.784 0.292 0.258
74 48503 5 1.344 0.729 1.226
75 48504 6 11.93 9.645 3.514
76 48507 9 10.96 7.744 4.16
77 48504 6 3.341 0.555 0.917
78 48503 5 1.229 1.192 0.218
79 48503 6 6.3 1.1 0.3
79 48503 6 5.153 0.385 0.322
80 48504 6 6.054 0.927 0.676
82 48504 2 31.14 4.73 3.188
83 48504 6 102.7 9.894 3.133
84 48504 2 1.38 3.734 0.524
85 48505 3 1.132 2.17 0.465
87 48507 9 3.232 2.989 1.927
88 48532 8 0.507 2.315 0.231
90 48506 4 8.561 5.141 4.724
91 48505 3 9.997 0.983 0.611
92 48504 1 4.152 0.758 0.433
93 48504 2 75.82 11.65 3.942
95 48506 4 138.8 2.745 0.797
96 48507 9 0.8 0.2 0.2
97 48504 2 7.244 1051 1.328
98 48506 3 1.621 0.3 0.238
99 48505 1 1.032 0.363 0.216
100 48504 2 0.866 0.292 0.269
101 48504 2 2.525 0.59 0.438
102 48505 5 9.408 4.444 3.935
103 48505 0 0.739 4.883 0.953
104 48505 1 0.9 0.2 0.1
105 48504 2 1.403 0.142 0.121
106 48503 8 5.655 5.882 10.66
107 48505 2 31.06 8.578 3.176
108 48506 4 1.469 0.291 0.25
109 48505 1 23.85 2.301 1.62
110 48505 2 9.766 11.13 7.144
111 48505 1 4.69 0.953 0.929
112 48505 3 4.066 5.894 4.76
113 48505 1 0.846 0.455 0.366
114 48505 1 2.054 3.978 0.355
115 48506 7 3.744 5.592 2.476
116 48507 9 12.9 2.202 1.667
117 48505 1 0.543 0.183 0.162
118 48503 7 6.877 2.984 2.201
119 48505 1 0.552 0.19 0.205
121 48506 3 59 2.9 0.5
122 48506 4 0.349 0.13 0.131
123 48506 4 4.764 1.388 1.06
124 48506 4 0.832 0.284 0.214
125 48506 4 1.224 0.568 0.465
126 48507 9 15.9 3.7 2.2
127 48506 4 5.667 1.405 0.896
128 48506 4 3.564 2.767 2.127
129 48506 4 0.475 0.2 0.268
130 48507 9 5.3 0.5 0.2
131 48506 4 1.166 0.736 0.269
132 48506 4 0.684 0.306 0.094
133 48503 8 6.347 1.724 0.678
134 48507 9 10.56 5.672 4.813
135 48502 5 2.273 2.808 3.048
136 48505 1 1.571 1.265 0.316
137 48503 8 5.402 4.196 1.945
138 48504 6 43.19 7.688 4.39
139 48503 8 1.492 1.409 0.378
140 48503 5 66.24 17.75 8.815
141 48505 1 1.799 0.032 0.031
142 48503 8 1.861 1.355 0.64
143 48503 8 2.672 2.001 1.094
144 48505 1 3.741 1.211 0.258
145 48506 4 1.934 0.374 0.424
146 48506 4 27.05 0.902 0.61
147 48506 4 1.174 0.291 4.055
148 48507 9 2.325 1.099 0.466
149 48506 4 1.966 0.253 0.201
150 48506 4 1.959 0.438 0.448
151 48506 4 0.823 1.881 0.412
152 48506 4 11.2 7.553 12.21
153 48504 2 5.668 3.341 3.268
154 48506 4 6.261 1.316 0.5
155 48506 4 4.797 1.594 1.264
156 48506 4 0.64 0.905 0.151
158 48507 9 8.713 2.799 50.97
159 48507 9 2.544 1.099 0.498
161 48507 9 0.41 0.096 0.116
162 48503 7 32.85 35.76 9.103
163 48503 7 12.87 14.87 6.326
164 48503 8 38.02 38.7 38.94
165 48507 9 2.435 8.183 1.296
166 48507 9 2.997 1.867 1.512
167 48507 9 11 10.53 8.688
168 48507 9 6.219 12.33 4.202
169 48503 8 8.8 3.1 4.5
170 48504 6 8.071 0.947 0.839
171 48507 9 3.262 0.453 0.252
172 48503 8 2.267 0.541 0.391
173 48505 3 0.922 0.878 0.491
174 48504 6 27.02 31.25 11.37
176 48503 8 0.906 0.961 1.052
177 48507 9 2.85 6.862 0.951
178 48504 2 1.852 0.472 0.422
179 48506 4 5.35 1.328 0.595
180 48503 7 25.21 4.337 1.019
182 48504 6 15.55 3.962 1.861
183 48506 4 0.793 0.533 0.391
184 48506 4 5.068 0.683 0.489
185 48507 8 26.64 8.878 6.619
186 48506 4 1.867 0.165 0.175
189 48506 4 19.16 12.54 7.719
191 48503 5 28.7 12.7 8.6
192 48507 9 20.22 8.908 6.677
193 48507 8 2.9 0.6 0.7
194 48503 7 18.86 5.051 2.548
195 48507 9 2.816 0.324 0.362
196 48506 3 118.4 40.78 39.99
197 48506 3 27.45 0.939 0.533
198 48503 7 1.2 0.1 0.1
200 48506 4 4.681 0.755 0.456
201 48506 3 11.57 6.08 1.782
202 48532 8 6.557 0.289 0.371
203 48505 3 3.4 9.6 1.7
204 48504 6 0.7 0.2 0.2
205 48507 8 158 90.83 91.69
206 48506 4 0.977 0.47 0.381
207 48503 8 8.471 4.692 1.48
208 48507 9 11.47 23.15 7.129
209 48503 7 5.228 2.477 1.014
210 48507 9 0.956 0.196 0.157
211 48504 6 1.671 0.405 4.721
212 48507 9 1.152 0.708 0.282
213 48507 9 0.5 0.1 0.1
214 48503 5 10.74 2.331 1.628
215 48507 9 3.9 0.4 0.2
216 48507 9 2.149 0.368 0.333
217 48506 4 1.1 0.4 0.2
218 48507 9 7.087 9.467 1.28
219 48505 1 1.329 0.609 0.527
220 48507 9 6.2 0.7 0.6
221 48505 3 0.8 0.26 0.255
222 48503 8 9.3 9.7 5
223 48504 2 2.1 1.2 0.5
224 48505 1 4.563 3.106 2.997
225 48504 2 4.808 6.196 1.523
226 48504 2 0.753 2.526 0.549
227 48505 1 1.862 1.213 0.898
228 48503 7 1.183 0.366 0.201
229 48503 7 8.2 3.2 2.6
230 48504 6 3.679 0.498 0.288
231 48505 1 2.37 7.333 3.797
234 48504 2 0.828 1.318 0.233
235 48503 7 0.719 0.254 0.058
236 48504 1 2.822 1.221 0.258
237 48504 8 2.867 0.723 0.744
238 48503 7 2.332 3.588 1.221
240 48503 8 4.401 2.111 1.572
241 48504 6 2.708 2.238 0.809
242 48504 6 34.13 6.002 1.71
243 48503 7 5.218 2.614 0.831
244 48503 7 15.73 13.95 3.584
245 48504 6 3.045 2.744 0.299
246 48503 7 1.1 0.5 0.3
247 48503 7 1.386 0.288 0.432
248 48504 6 0.915 0.354 0.306
249 48504 6 2.145 0.345 3.738
250 48507 8 4.056 0.547 0.378
251 48503 7 1.668 1.508 2.72
252 48503 7 7.575 1.362 1.094
253 48507 8 5.59 4.306 2.019
254 48503 5 0.708 0.326 0.303
255 48504 6 1.701 4.397 1.287
256 48504 6 1.467 0.149 0.137
258 48504 2 2.582 259.8 61.96
259 48505 2 22.08 15.86 9.262
260 48507 8 16.51 2.024 7.068
262 48507 8 56.26 4.692 1.243
263 48504 6 2.433 1.334 1.376
264 48503 7 0.5 0.2 0.5
265 48504 6 29.13 11.57 6.388
266 48505 1 12.3 0.5 0.4
267 48504 6 3.445 0.29 0.167
268 48507 9 16.49 12.83 9.018
269 48503 7 3.365 2.45 1.675
270 48503 7 1.154 0.176 0.12
271 48507 9 13.53 21.91 4.675
272 48504 6 2.229 1.573 0.84
273 48503 7 28.91 5.471 3.056
274 48503 7 6.601 1.929 0.417
275 48507 9 0.948 0.27 0.207
276 48505 3 3.484 0.434 0.306
278 48503 7 1.888 0.359 0.322
279 48503 7 13.95 12.2 8.251
280 48504 6 6.27 4.036 1.182
281 48506 7 19.12 22.02 7.968
282 48507 9 1.633 0.465 0.238
283 48503 7 1.114 0.605 0.255
284 48503 7 3.9 0.558 0.504
285 48504 1 3.521 0.45 0.321
286 48507 9 3.832 0.794 0.339
287 48505 3 3.243 0.738 0.27
289 48503 7 0.99 0.25 0.263
290 48507 9 1.203 19.26 1.626
291 48506 3 2.261 0.102 0.407
292 48503 4 16.99 6.32 3.585
293 48503 7 3.322 2.559 1.512
294 48506 4 14.33 1.284 0.323
295 48503 7 18.11 20.21 4.263
296 48503 7 12.81 7.874 1.78
298 48503 7 1.083 0.322 0.26
299 48503 7 29.59 3.258 1.843
300 48505 1 4.287 4.345 4.905
CASE STUDY: LEAD LEVELS IN WATER Suppose you were asked by the Michigan Dept of Environmental Quality to analyze these data to determine if there are any concerns with the water's lead levels. A high lead level is generally anything min of flushing) determine if there are any outliers using one or more methods of your choice. Comment on the implications of your findings- what do the results suggest about the water quality? If your supervisor suggested you "throw out" the outliers because they are unusual, what might your response be?Explanation / Answer
Method used to calculate outliers in excel:
1. Calculating quartiles: Formula for Q1 quartile(array,1) and for Q3 is quartile(array,3). Same process has been repeated for all three samples.
2. Calculating upper and lower bound: Upper bound = Q3+ (1.5*IQR) and Lower bound = Q1 - (1.5*IQR) where IQR = Q3 - Q1. Same process repeated for the three samples
3. Outliers would be values greater than upper bound and lower than lower bound for each of the three samples.
Hence outliers for:
S1 (immediate sample):
Outliers for S2 (45sec):
Outliers for S3 (2 min)
The outliers for immediate sample are much higher than the outliers for 45 sec which are in turn higher than outliers for 2 min sample.
All the outliers of the immediate sample are greater than upper bound of 20.258 which is higher than 15 i.e a high lead level.Outliers can be error in measurements or could also mean useful information. Discarding them would not be a good idea and further analysis should be done on them. Throwing them out can introduce bias in subsequent analysis. Usually only the extreme obervations which are four or more standard deviations from the mean can be excluded unless any good reason comes up to include them.
The high upper bound of around 20 for immediate sample does point towards high lead level in the sample. There are around 30 odd outliers each for all the three samples. We can't simply throw them away.
Q1 Q3 IQR Upper bound Lower bound S1 1.578 9.05 7.472 20.258 -9.63 S2 0.46 4.8065 4.3465 11.32625 -6.05975 S3 0.306 2.7405 2.4345 6.39225 -3.34575Related Questions
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