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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 -3.34575