12.1 Expand your knowledge outliers some data sets include values so high or so
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12.1 Expand your knowledge outliers some data sets include values so high or so low that they seem vo stand apart from the rest of the data These data are ealed outliers outliers may represent data collection errors. data entry errors. or sim- ply valid but unusual daa values. is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits. Lower limit: Qu 15 x (IOR) Upper limit: e, 1.5 x (IOR) where IOR is the ile range. are suspected outliers. in the computer soft- ware package Minitab. values beyond these limits are plotted with asterisks Pick one of the youth commitment rat data sets for the 50 US states plus the District of Columbia (White, Black, be All) to give a five figure summary box and whisker plot. Determine whether any of the observations would and a considered outliers based on the 1.5 rule described above. would it be good to pay attention outliers lOR Boot Mead he in this specific situation? White min mln ap meol 65 mar 1206 ma Y N13 mar 302 TBR 222 TOR 53 xExplanation / Answer
Given,
All youth white black
20 7 0
34 10 77
36 12 83
41 14 108
41 14 116
44 14 156
52 16 159
54 26 160
66 31 169
68 33 171
72 34 173
73 39 180
78 42 193
79 42 206
84 43 227
87 45 240
90 47 241
95 50 241
99 53 243
99 54 249
105 57 250
106 58 261
107 62 276
108 63 277
108 64 296
109 65 297
119 66 308
120 71 324
122 72 336
126 72 337
127 72 342
128 78 351
131 80 365
133 80 381
134 84 396
134 89 413
135 87 451
136 91 463
142 95 475
145 96 524
146 98 548
168 98 595
170 105 631
178 112 649
186 120 682
186 149 688
231 154 697
245 155 727
264 167 739
302 200 818
302 213 1846
Data from MInitab
Descriptive Statistics: All youth, white, black
Variable Mean StDev Q1 Median Q3 IQR
All youth 120.88 64.18 78.00 109.00 142.00 64.00
white 72.53 47.35 42.00 65.00 95.00 53.00
black 375.2 289.1 193.0 297.0 475.0 282.0
lower limit = Q1 - 1.5* IQR
upper limit = Q3 + 1.5*IQR
for all youth ,
LL = -18
UL = 238
for white,
LL=-37.5
UL=174.5
for black
LL=-230
UL=616
This 1.5 rule is good for finding outliers above the range but not below
hence the formula can be modified for lower limit
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