What to Do if You Have Missing Data in Bayseing Netowkrs

Tutorial 7 - Missing data

In this tutorial we volition build a unproblematic Bayesian network (shown below) using data that is incomplete, i.due east. certain values in the data are missing (unobserved). We will then testify how predictions can be performed with missing data. Finally we will demonstrate how to fill-in missing values using the Bayesian network.

Missing data network

To demonstrate learning with missing data, we will apply data sampled from the multivariate Gaussian distribution tabulated below. Ane m samples were taken, following which 5% of the data was randomly ready to missing.

X Y Z
Mean 6.5 ii.9 5.five
Covariance (Ten) 0.four 0.i 0.3
Covariance (Y) 0.ane 0.11 0.08
Covariance (Z) 0.3 0.08 0.3

The information in this example is very simplistic, but allows u.s. to keep the example uncomplicated. Typically a more circuitous network would be used, and the network might include latent variables as used in the mixture model tutorial, allowing us to model more circuitous and hidden patterns (automatic feature applied science).

All the examples in this tutorial use continuous variables, however the aforementioned techniques can be used with discrete variables, and Dynamic Bayesian networks (time serial).

The following concepts will be covered:

  • Continuous variables
  • Nodes with multiple variables
  • Creating a Data Connectedness
  • Parameter learning
  • Batch queries

Bayes Server must be installed, before starting this tutorial. An evaluation version tin can be downloaded from the Downloads page

Companion video (No Audio)

Create the model construction

  • Click New on the File tab to create a new empty network.

  • To add together a new node, click Node on the Network tab, Editing grouping, to create a new node. This volition launch the New node window.

  • Enter Multivariate Gaussian in the Name text box.

  • This node will contain three continuous variables, so in the Variable department, click the Multiple tab.

  • Click the Add Continuous toolbar push button iii times, to add 3 new continuous variables to the node.

  • Rename the new variables to the following, by clicking on the name of each new variable, and typing the new name.

    • Ten
    • Y
    • Z

    The New Node window should look similar this:

    Missing data - new node

  • Click the OK button to create the new node.

    The network structure is now complete.

Learning with missing data

In this section nosotros will learn the parameters of the multivariate Gaussian with data that contains missing values.

For convenience, we will utilize Microsoft Excel as the information source, however another database can be substituted.

Although Microsoft Excel is a convenient mode of storing data, in practice we recommend using a database every bit the data source.

Adding a information connection

Annotation: You can skip this step, and instead use the pre-installed Tutorial information connection (Walkthrough Data in before versions).

  • Select the data (including the header) in the data section and copy it to the clipboard (Ctrl+C).

    If yous utilize a database to store your information, missing data is usually denoted by (null) values, and columns will take an option to allow or disallow (nada) values.

  • Open Microsoft Excel and paste the data into a new Microsoft Excel spreadsheet (Ctrl+V).

  • Save the new spreadsheet.

  • In Bayes Server, click the Data Connections button on the Information tab, Data Sources group. This will launch the Data connection manager.

  • Click the New button on the toolbar. This will launch the Data connection editor.

  • In the list of data providers, select the appropriate Excel Driver for the version of Microsoft Excel yous are using.

  • Next to the File Name text box, click the Ellipsis (...) button, and select the Microsoft Excel spreadsheet created in an before step.

  • Click the Test Connectedness button, to ensure the new information connection is working.

  • Click OK to add together the new Data Connection.

Parameter learning

  • Click the Parameter Learning button, on the Data tab. This will launch the Data tables window.

  • In the Data Connexion drop down, select the new Data Connection created in an earlier step, or the Tutorial data connection if y'all skipped that step. This should enable the Information drop down.

  • In the Data drib downward, select the worksheet that contains the data. (If the data is on the first worksheet, select Sheet1$). If you lot are using the pre-installed Tutorial data connection, select Tutorial 7 - Missing information.

  • Click the OK push button. This will launch the Information map window.

  • In the Data map window, ensure that variable X has automatically been mapped to column 10, variable Y has automatically been mapped to column Y, and variable Z has automatically been mapped to column Z.

    The window should look like this:

    Missing data - data map

  • Click the OK button. This will launch the Parameter learning wizard.

  • Click Next in the wizard, accepting all the default settings, until you reach the Run page. Click the Run button to kickoff learning.

    Since we are learning with missing information, the learning procedure volition require a number of iterations.

  • When learning has completed, click the Finish button on the sorcerer. This will launch the Candidate Networks window.

  • Click the OK push in the Candidate Networks window.

  • The distribution for the node Multivariate Gaussian has now been learned. Select the node, and click the Distribution push on the Network tab, Editing group. This will launch the Distribution editor window.

    The window should look like this:

    Missing data - distribution editor

  • Now compare the mean, variance and covariance parameters in the Distribution editor window, with those from the original sampling distribution tabulated in the introduction. The values are sufficiently shut to indicate that we have successfully approximated the original distribution even though 5% of the data was discarded.

  • Click OK to close the Distribution Editor window.

Perform predictions with missing information

In this section we will predict the variable Z, using values for 10 and Y which might exist missing. This demonstrates that nosotros tin still predict Z, even if have incomplete information. We will re-apply the information nosotros setup in the previous department.

Since nosotros are predicting a continuous variable, the job is known as regression.

Batch query - predictions

  • Click the Batch query button, on the Data tab. This will launch the Data tables window.

  • In the Information Connection drib down, select the new Data Connection created in an earlier stride, or the Tutorial information connection if y'all skipped that step. This should enable the Data drib down.

  • In the Data drop downward, select the worksheet that contains the information. (If the data is on the get-go worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial vii - Missing data.

  • Click the OK button. This volition launch the Data map window.

  • In the Information map window, ensure that variable X has automatically been mapped to column Ten, and variable Y has automatically been mapped to column Y.

Because we are predicting Z, we do not want the Z variable to be mapped.

  • Click the Un-map column button at the terminate of the Z row.

In order to test how well our model tin predict Z, nosotros desire to take access to the Z data cavalcade, simply we practise not desire to map it to the variable we are predicting.

  • Click on the Information tab, and click the bank check box next to Z.

Another way of performing the aforementioned prediction, would be to exit the default mappings (including Z) and use the Retract evidence feature which assumes the variable y'all are predicting is missing, fifty-fifty if it mapped to non missing data.

The data map windows should look like this:

Missing data - prediction data map

Missing data - prediction data map information

  • Click the OK button. This will launch the Batch query window.

  • In the query pane on the left hand side, ensure the following queries/information columns are checked.

    • Predict(Z)
    • Variance(Z)
    • X
    • Y
    • Z
  • Click the Showtime push button on the Batch Query tab, Batch Query group. This outputs the predictions to the window.

    Instead of outputting to the window, you tin also output the predictions to a database. This is useful if y'all are working with large datasets.

    The window should wait similar this:

    Missing data - batch query

    Note that nosotros get a prediction for Z, even if the value for 10 or Y is missing, based on the data bachelor. In fact, we yet go a prediction if both X and Y are missing (see case 997).

    Along with the predicted value for Z, we also get a variance indicating the spread for the prediction.

  • Close the Batch query window.

Filling in missing data

In this department we volition demonstrate how a Bayesian network can exist used to backup missing values.

This is different from the prediction performed above, firstly because we are too predicting X and Y, only as well because if any values are known, nosotros retain their values.

Batch query - fill-in missing values

  • Click the Batch query button, on the Data tab. This will launch the Data tables window.

  • In the Data Connection drop down, select the new Information Connection created in an earlier pace, or the Tutorial data connection if you skipped that stride. This should enable the Information drib down.

  • In the Data drib downwardly, select the worksheet that contains the information. (If the data is on the first worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial 7 - Missing information.

  • Click the OK button. This will launch the Data map window.

  • In the Data map window, ensure that variable Ten has automatically been mapped to column X, and variable Y has automatically been mapped to column Y and variable Z has automatically been mapped to column Z.

    Different the previous section nosotros include the mapping for Z.

    The data map window should look like this:

    Missing data - fill missing data map

  • Click the OK button. This will launch the Batch query window.

  • On the Batch query tab, Batch query grouping, ensure that the Retract option is turned OFF. This ensures that existing values will be output, and missing values volition be replaced by predicted values.

  • In the query pane on the left hand side, ensure the following queries/information columns are checked.

    • Predict(10)
    • Predict(Y)
    • Predict(Z)
    • X
    • Y
    • Z

    It is the columns Predict(Ten), Predict(Y) and Predict(Z) that volition contain our original data with missing values filled in. Although not required, we accept included the columns Ten, Y and Z for comparison.

  • Click the First button on the Batch Query tab, Batch Query grouping. This outputs the predictions to the window.

    Instead of outputting to the window, you can also output the predictions to a database. This is useful if you lot are working with large datasets.

    The window should await similar this:

    Missing data - batch query fill missing

  • Notation that the original data is retained, nonetheless missing values are replaced with predicted values.

Data

Case X Y Z
0 vii.361322367 3.643201047 half-dozen.588605476
one 5.922611866 5.177020763
two 6.734592687 ii.540409254 5.735911197
3 half dozen.214891612 three.098860437 five.212103279
4 7.245333106 3.737858898 half-dozen.246807317
5 6.187227835 2.809222957 5.154439521
6 vi.127841245 v.257808701
7 5.420549855 ii.789983186 3.824171095
8 7.636637234 2.822159507 six.0035082
9 6.865330437 2.707942279 5.560468267
10 7.026775618 3.18926625 5.544403824
11 eight.241347584 3.667843081 7.136554568
12 half dozen.862291101 iii.384921933
thirteen 6.382521691 2.616473832 5.686374713
xiv vii.741580895 three.649089818 6.209658017
fifteen seven.35690619 5.858972228
16 half dozen.283815662 3.102976165 v.383477518
17 8.1692888 3.393410808 7.410928557
18 6.415122356 iii.37686942 5.360733995
19 7.319021079 two.888678131 six.32623456
twenty five.487696 4.761963138
21 5.537592284 2.641392062
22 v.549138903 two.687142009 four.946209321
23 two.915170336 5.926632454
24 6.814135318 2.860260755 v.840769372
25 v.969226118 ii.557137533 4.962035067
26 7.328855174 iii.424848988 5.699110923
27 5.992640112 2.821734388 5.39441374
28 3.30077682 v.597015287
29 6.125132829 two.994691325 5.021193115
30 two.91047831 5.123655817
31 6.437989569 3.124747556 five.841610558
32 6.534085647 two.855246834 5.120398352
33 3.019425824 5.72764605
34 half dozen.563657499 3.07146835 5.695404153
35 7.14056442 two.941180993 6.042606067
36 vi.30789806 2.458248557 5.30204915
37 6.879490735 3.475622606 5.742896246
38 six.407409625 three.127032583 5.514673104
39 v.88065558 3.351495179 5.148263324
40 2.994561306 5.174832252
41 6.353335182 2.854178844 5.315722038
42 6.976010328 3.3518604
43 7.46693531 3.648246109 6.615507994
44 6.244280149 2.869164132 5.08913155
45 6.085534082 ii.64720529 v.200212027
46 5.9713148 ii.913353784 v.037540821
47 2.977520081 5.937204306
48 six.057136532 four.951382998
49 6.882216192 iii.240281267 five.743295966
50 five.640954857 three.015062939 4.75385882
51 7.321360904 six.305422628
52 6.455554432 ii.818199177 5.850607894
53 6.268045882 3.038089256 5.129929448
54 six.345488741 three.136579476 5.695596935
55 7.060588272 2.988998422 5.69256609
56 6.501012554 2.830530268 5.321441873
57 half dozen.382532128 3.120994255 5.660898431
58 5.662831617 2.697172784
59 vii.048640482 2.828555842 five.645351624
60 6.805833875 ii.490609499 6.097848922
61 6.607422216 two.982227352 5.509822749
62 7.186044038 2.971533988 6.067915739
63 half-dozen.358017453 2.893218043 5.4341287
64 7.518403921 iii.318224851 6.461504966
65 six.020192143 2.139412397 5.488469128
66 5.825310702 ii.167001882 v.199221927
67 6.853488349 3.20644835 six.055716077
68 5.802990108 ii.431395262 four.951872716
69 six.347060776 2.59097972 5.275174484
70 2.867355123 4.53991452
71 7.551006666 2.930814592 6.252212258
72 6.956474922 2.946300113 5.684037963
73 vi.576540302 3.241121899 v.396611449
74 three.421800591
75 6.086830191 three.043787569 5.348294414
76 six.240607142 2.210123178 four.897220562
77 6.605607336 iii.346278478 v.750291587
78 3.030177481 5.266824964
79 5.490461783 2.249058077 4.380099178
80 6.31461542 2.949349575 v.689228517
81 5.931297807 2.868347476 4.939817685
82 2.69959019 4.296612051
83 six.689073094 2.683420306 v.945552455
84 seven.00757263 two.971770331 half dozen.04460193
85 6.149398359 ii.540029993 five.302082457
86 half dozen.465218078 ii.803324551 6.113201536
87 6.637031623 2.910439685 v.285953636
88 7.077141159 iii.927992996 5.687541369
89 6.28687294 3.026804266 5.062739577
90 6.028051908 2.363302372 5.27109251
91 half-dozen.402809092 two.904332673 v.016257518
92 6.775156922 2.97920289 5.969680585
93 five.987869675 2.821823643 5.289889639
94 six.333704604 3.052481508 5.122340327
95 six.308542175 2.913524776 five.510700359
96 six.032685882 two.355387057 five.052397241
97 half-dozen.570714516 five.602559121
98 5.878432738 2.604579845 iv.96776982
99 6.556585753 2.686323245 5.595305408
100 vi.487414818 3.036945011 5.447483183
101 6.184605404 2.978941104 5.5573754
102 7.630436437 half dozen.267985493
103 7.492649134 iii.57768332 5.952459046
104 six.059613772 two.723297138 5.309575852
105 7.016809185 3.303013279 5.675482494
106 5.353811728 ii.199801987 4.635987666
107 v.735329006 iii.001137479 4.411810395
108 six.614689885 ii.734556349
109 six.134413542 3.20116548 5.425713252
110 6.676398064 2.90098181 5.717644583
111 v.907583177 2.726105676 5.259474915
112 4.895193617 2.674765559 4.1694444
113 seven.218781954 three.057266354 6.624032652
114 2.862572558 5.714951145
115 6.753359476 two.873792528
116 vii.363700426 ii.568008828 6.053455074
117 7.100027953 2.874574307 half dozen.117414783
118 6.007840116 2.341920886 5.123433543
119 6.659391721 two.952358938 5.852424552
120 6.502406223 2.662795828
121 6.684169599 3.336343763 v.30299905
122 half-dozen.96896762 3.23246908 half-dozen.090332869
123 5.916009156 two.752365768 5.126880456
124 6.61792677 v.177048925
125 7.194942641 ii.63576156 half dozen.175994666
126 3.931668721
127 6.918439527 3.052689784 five.982199991
128 7.550337227 two.476160292 six.817891974
129 6.144706782 ii.521898648 v.320753668
130 6.65632187 2.611218013 5.797190702
131 six.527684824 ii.847870383 iv.971596694
132 5.895315478 two.832152111 five.078776905
133 6.806538025 2.877300436 6.061073965
134 3.089530712 5.295367399
135 6.804589737 3.049129925 5.55281585
136 5.622716653 2.537849724 4.554709924
137 half-dozen.708489801 2.606386902 5.728295962
138 5.8207204 ii.598661969 v.194597464
139 5.708823368 2.871966811 iv.895632787
140 seven.074762068 iii.124964175 5.971105588
141 5.613388619 2.243767581 4.813146675
142 7.904074888 3.597291299 6.245908958
143 6.836083109 two.791231488 5.971413994
144 half dozen.230064831 3.212994667 4.650919116
145 6.407247247 3.026649985 5.3961284
146 half dozen.406918863 2.334885183 5.424689734
147 6.896141251 six.223953765
148 7.084181012 iii.265680002 6.13185279
149 7.296952683 3.276935815 5.5306946
150 6.682895844 2.700447218 5.297744203
151 7.518296677 three.182496741 5.904263233
152 6.91625288 2.85600896 5.760381359
153 6.633209915 3.201560441 v.639482636
154 seven.0211199 three.073996556 6.261321843
155 9.042261327 3.396359008 7.467300747
156 7.340466132 3.28017227 six.072604745
157 7.116118021 ii.924143917 v.847241518
158 6.738063099 three.032361028 5.860911661
159 5.661035287 2.598830681 five.098418561
160 5.467996357 ii.130209122 4.979502813
161 vi.810160147 3.158106994 5.890262741
162 half dozen.458575035 five.275777978
163 6.684370778 2.706043352 6.024105122
164 4.716045252 2.190078374 three.953523841
165 5.663167389 2.269116781 4.938256185
166 6.773706218 2.941131718 5.379892249
167 5.765264396 2.703574481 five.06304299
168 half dozen.682023872 three.171587498 5.721538225
169 half dozen.647114191 3.043006859 5.819118688
170 5.857453521 iii.103367816 5.044418451
171 6.362953926 ii.779090487 5.496660196
172 2.750106448 5.620231942
173 6.620380813 2.815381747 5.656687971
174 vi.562366738 2.845120077 4.904661668
175 5.911450816 2.69524639 iv.907616019
176 half-dozen.382663563 3.10714041 5.351039152
177 6.320558523 2.558464132 v.51372535
178 vi.833375657 3.409966744 5.473128053
179 6.529581221 3.163521942
180 six.604001786 3.338420733 v.522778394
181 6.727290032 3.164081889 5.604317953
182 seven.727182523 iii.271305037 6.775289327
183 6.585840552
184 vi.236682989 5.144884782
185 6.750598465 3.293780293 6.022768974
186 6.267825001 2.726435819 5.13251046
187 5.084060905 2.459250609 4.643122219
188 seven.255458803 3.514863884 six.723481947
189 6.257109069 3.069849909 5.499189305
190 5.29045878 2.763953807 4.758097645
191 5.248249298 2.765725421 4.322178467
192 6.197662722 iii.124649836 4.902952645
193 vi.010748546 3.151295502 v.247275268
194 6.345150647 2.461619527 5.291160011
195 6.382340529 2.515344238 5.124481293
196 4.742123649 1.58560423 3.727960242
197 8.050102687 3.388625637 6.34535555
198 5.367090269 ii.683282031 iv.477070129
199 5.789875651 3.060283635 4.721495016
200 vii.060934829 2.888908381 5.777440892
201 5.579312157 ii.638520322
202 5.407984306 2.804468106 three.970304972
203 7.148962252 2.996374199 6.323515097
204 6.21996113 2.783326812 5.365056987
205 6.940566544 two.671973316 5.953801851
206 2.851085241 6.24884169
207 half dozen.104653012 2.832020146 5.904489021
208 6.519754562 ii.673512687 five.212443068
209 vi.24329454 2.948045361 5.158280301
210 vi.726815926 ii.680989145 5.805426901
211 v.864914459 2.231366834 iv.897888097
212 seven.684424618 2.628395105 6.331617828
213 6.301504366 2.806705235 v.035330369
214 5.934760174 2.731122755 5.167197478
215 two.374489734 5.155584496
216 half dozen.262896227 2.893371788 4.889274143
217 half dozen.13108405 5.255268995
218 vii.20345026 2.720879613 5.688009374
219 7.105877838 2.385246479 6.080502904
220 7.647816162 iii.639451525
221 5.864234272 3.114445292 five.485023223
222 6.919252083 iii.05592096 five.964954805
223 7.763399308 3.2864443 6.69982554
224 5.788338016 2.685650525 iv.46595344
225 5.524163548 two.426012627 4.857926829
226 5.48352112 3.265825448 4.957074521
227 6.623673254 two.995940275 5.426464583
228 6.007779669 3.034766575 5.021032533
229 six.136415972 2.905689718
230 7.520810679 two.978274163 5.980608183
231 7.007319537 2.887988637 5.845245019
232 six.853985014 iii.266344686 v.778224245
233 six.696603305 two.960287983 5.487629921
234 2.543641755 5.869672408
235 5.460273853 3.006902483 5.080712726
236 6.965434924 2.758561011 6.060851212
237 7.29459662 3.646288437 5.593804793
238 5.494701858 3.048535373 four.340565358
239 7.388649717 3.339175555 6.533795452
240 vii.061732471 3.481626588 5.369566725
241 6.827873459 iii.336083303 5.720575492
242 v.882931848 two.972155881 five.14349811
243 5.944861653 2.395395069 v.576154307
244 6.897629245 3.077573654 v.362000638
245 7.31903224 two.858639672 6.02236564
246 6.214176594 two.285488554 iv.951820611
247 6.502005371 3.036749653 5.438227763
248 5.732930279 2.609417703 4.857265443
249 6.374070178 3.034794344 five.357797353
250 7.062750527 3.708045937 5.949497907
251 half-dozen.968881831 3.17161348 6.051975841
252 6.383283577 ii.904838668 v.084764712
253 7.489233312 3.0227553
254 5.785144535 two.833847428 v.179988734
255 6.239538136 3.045525977 v.676288516
256 5.910886334 2.7305909 4.722666065
257 half dozen.831709152 2.857182027 six.160585597
258 6.661868375
259 vii.209293632 3.174941953 v.959259482
260 7.478288425 2.884518033 half-dozen.248677989
261 6.764856901 iii.059109185 six.106891685
262 vi.292423183 2.860118661 5.387718189
263 6.152288318 2.757391083 5.228163787
264 5.490373884 2.513561973 4.549994791
265 6.796748537 3.663243423 v.321266648
266 7.224875183 three.260390795 half-dozen.022155241
267 6.489760406 2.546732962 5.204169778
268 6.384950486 3.09994258 five.330099251
269 v.972655349 two.285614567 v.176702807
270 six.024848086 ii.636999519 5.22957755
271 7.497851908 3.178935022 5.635675904
272 6.71320192 three.208327813 5.738962687
273 5.795397655 ii.92554303 5.286875123
274 3.212513829 v.821696699
275 6.39816874 iii.101349167 5.0804893
276 seven.363001272 3.010460414 6.187855708
277 half-dozen.952919819 three.18807165 6.187265414
278 seven.136279958 2.776992939 5.68236817
279 6.330816734 two.428827377
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281 5.955293575 ii.805577637 5.040326988
282 five.339612485 2.428563209 4.628874963
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289 6.025796325 3.009191377 5.165651777
290 5.120077508 5.104576188
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292 6.460492607 3.159339623 5.554643192
293 7.683578464 3.165271742 5.898293465
294 6.061308104 3.103631111 five.02136703
295 vi.004742872 5.202700462
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297 half dozen.659672702 2.959363806 5.275847194
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308 7.00849646 2.683094782 5.756467239
309 vi.220640295 2.989893114 5.471363682
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319 5.473146305 2.91551627 4.315702705
320 half dozen.86522901 ii.945594873
321 half-dozen.339933519 2.834253485 5.352389791
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323 5.320680926 2.920050707 4.719784327
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329 7.13835392 iii.30242644 5.718863668
330 6.972067822 3.181677147 v.858378881
331 vi.50051194 5.767313174
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333 vi.324087522 2.975603081 v.575105182
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343 half dozen.03902117 ii.882757414 4.724060786
344 6.137179657 three.022856088 v.400781073
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347 seven.00370949 3.093788462 5.98940052
348 half-dozen.109695505 ii.983803035 5.005939023
349 7.147962261 iii.55545629 5.937072096
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351 half dozen.652649771 three.782313738 5.300462151
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353 6.701307119 ii.892037355 5.686978746
354 5.566148788 ii.755429314 4.509787748
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358 6.734198697 2.614315679 5.856583654
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360 vii.273577194 2.838807098 half-dozen.087718045
361 half-dozen.170174745 iii.109093932 v.378340266
362 6.042199513 2.927436281 4.961260032
363 6.936944229 three.002064809 v.560672109
364 ii.852576247 four.98835288
365 five.698551223 two.305921046 4.659019247
366 v.953564115 iii.039118675 four.412113706
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368 5.563337715 ii.372429655 4.723291406
369 half-dozen.468792446 2.744375567 5.210265724
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374 vi.741765062 iii.023471611 6.271044586
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378 half dozen.871294438 3.10589503 v.839366809
379 5.986644797 ii.740399535 5.34543683
380 6.030242507 2.580794808 four.618036568
381 6.386011075 2.939338767 5.375599279
382 5.143018717 3.302336166 4.38795219
383 half-dozen.62909903 3.338105823 5.674564334
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385 7.622568287 ii.916900388 6.398215079
386 6.222078631 3.086602044 5.044268346
387 half-dozen.759981734 6.060149757
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390 half dozen.483035948 2.881140435 5.284878107
391 v.945778669 2.892906406 five.142164843
392 6.959289924 3.11143364 v.88386006
393 7.127754138 2.764691762 half-dozen.044266855
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400 7.365178843 iii.327960695 6.26919767
401 5.728904742 2.307988729 v.004023773
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403 2.845011735 5.564082285
404 seven.003407176 3.054598898 five.662631828
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406 6.621754814 three.063932664 6.13365386
407 6.309612473 ii.501714395 5.607165443
408 half-dozen.266379337 2.971470195 5.526587699
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411 two.98372163 4.604274312
412 7.425910551 5.339248602
413 4.850483342 2.900805555 4.353456125
414 5.504382606 ii.314422701 5.133039945
415 6.760345707 5.766931077
416 6.716507923 3.401140211 5.886231972
417 5.308248557 2.692211728
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419 vi.759364258 3.089654475 5.668248024
420 6.441260428 2.822133229
421 6.395537919 3.062120374 5.29496318
422 5.902972628 2.576823442 four.523334927
423 vi.225657414 5.413470086
424 6.390023933 iii.338083745 five.826029664
425 half-dozen.381368633 2.8555836 5.466478726
426 6.974188115 3.16662334 v.769922609
427 6.335109578 ii.937419815 five.877506293
428 6.411706251 2.955063191 five.55657654
429 6.958841412 2.933161998 5.548058159
430 6.623833779 2.99872353 5.509827908
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432 seven.731876187 three.035412087 6.133501945
433 half-dozen.405943411 ii.406486042 5.861604572
434 6.840806017 three.215957931 5.847597204
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436 5.978727994 two.549256843 iv.791989334
437 half-dozen.132427623 2.922561853 four.97620071
438 7.253417304 3.05881894 6.095752104
439 6.372809206 ii.536527665 5.218491892
440 v.675799374 2.819998221 4.839337785
441 vi.907831172 3.148744887 5.628004197
442 6.583120564 ii.961808609 5.830905886
443 vii.006894698 two.903233637 5.714685252
444 5.765548452 2.706543133 4.763255651
445 7.386151503 3.106435708 6.583855534
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448 half-dozen.172592759 5.016938791
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451 6.512562974 3.135317391 5.089418542
452 vi.192296319 2.749249517 4.932514574
453 8.041155489 3.151087449 half dozen.463604473
454 seven.040782378 3.117186995 half dozen.194117367
455 vii.32666537 3.271351115 6.527213659
456 5.922743269 2.2718139 4.632549372
457 half dozen.866247981 3.32797765 6.250111611
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459 5.873029486 2.696964406 4.77295481
460 6.058473111 3.163592652 4.994953187
461 7.164980687 ii.807864081 five.684118892
462 half-dozen.119817385 3.163545327 v.172910785
463 6.53124599 3.116660407 five.934885285
464 half-dozen.300343643 2.626726673
465 6.864205399 iii.249353017 5.391733972
466 7.449468691 3.270424864 half-dozen.080417672
467 6.440608845 two.744038098 5.366470544
468 6.264293591 ii.673864739 5.094163613
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471 5.865724599 2.815408747 5.486911643
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473 6.551614678 2.376372066 5.787755594
474 vi.002482892 3.01363739 four.960008613
475 5.600454382 two.818711472 5.092103536
476 six.341944315 2.469020154 5.143368804
477 6.393885662 2.901057651 v.287032987
478 vii.341999758 3.384312239 6.077767612
479 7.575629549 iii.345308322 6.482343761
480 vi.790873711 3.038136987 5.849474897
481 half-dozen.311102102 2.984490689 iv.88513241
482 7.169401692 2.796441273 6.030268625
483 6.647638661 ii.855456477 five.84043515
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485 vii.747612673 3.849919732 6.594393325
486 v.84110975 2.556178743 4.810474238
487 5.68781391 two.139571066 v.116437319
488 5.723434744 two.471347237 iv.511726961
489 6.27832123 2.690440906
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491 5.428533722 ii.15776006 four.542888297
492 5.113873103 2.561480629 4.447640605
493 7.110082155 3.048379669 5.878810291
494 6.437024804 ii.638822095 5.415538022
495 6.569417072 2.573252527 4.860339292
496 v.689666731 2.489442982 v.004380909
497 6.600317017 three.078796446 v.609764778
498 6.446840097 2.904672773 5.330324537
499 6.097910425 2.633823973 5.007740254
500 half-dozen.555347601 three.062058542 5.720339011
501 5.879827142 2.643232629 iv.748931389
502 7.498975459 3.482701226 6.488584203
503 vi.638702235 five.816099179
504 6.428089356 2.963756952 5.644926515
505 7.551766492 3.327628471 half dozen.285783884
506 5.030273109 2.382428526 4.585296686
507 6.290762652 3.011655915 4.926721535
508 6.997922699 iii.488253598 5.830416248
509 6.104735661 three.334586469 5.153471002
510 6.345459436 ii.905901391 5.510293619
511 7.502452912 3.08974006 half dozen.767357884
512 6.622311723 3.096708115 5.992856145
513 6.288881507 2.9278343 5.204932577
514 5.411875767 ii.101234753 four.279110583
515 half-dozen.447014863 2.743455703
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517 half-dozen.979376294 3.151818421 5.891645587
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522 5.898797019 5.070133626
523 vi.61227679 3.055198533 5.580692107
524 3.384324655 5.709446392
525 half-dozen.812133494 3.106481422 half dozen.037291638
526 half dozen.01997507 iii.352796271
527 2.433014294 4.455099157
528 6.954648358 3.478515034 5.507365279
529 half-dozen.740772565 3.041421735 5.057507439
530 5.540114711 2.856574003
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535 6.277021353 two.514911166 five.527457606
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537 6.717228076 three.185488135 5.675099294
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539 vi.292823427 two.46054634 5.212601926
540 vi.565907012 3.197238521 6.019424693
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542 6.469449379 3.015055115 5.665790961
543 v.742346319 two.928296169 4.528179093
544 6.33592627 2.699044058 v.253192671
545 7.310946726 3.176237751 5.971968439
546 v.557114663 2.698836551 4.507434243
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549 six.420097165 2.661000648 five.268195154
550 6.805279462 3.002253563 5.734747263
551 5.765415869 ii.690056168 5.188694532
552 6.076908001 2.633463048 five.156397239
553 vi.019198897 2.730698369 5.494108505
554 six.202333452 2.873420611 5.739714467
555 6.719197256 3.081232176 5.847800818
556 half dozen.530690672 3.181613518 5.156705615
557 half-dozen.392246004 iii.19976668 5.261171966
558 6.289360259 2.910074237 v.326321906
559 7.485779349 3.240348437 6.120148532
560 half dozen.394580366 ii.553628015 five.606545027
561 6.707282416 2.262913408 5.542585923
562 6.745113199 2.724854868 5.566792537
563 5.487935301 2.863254489
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572 5.505803479 iii.014627564 4.662185713
573 vi.032925199 two.541278609 5.14967384
574 6.347619299 3.375776004 5.624434767
575 6.329965075 2.576034515 4.753881646
576 half dozen.351091646 2.0979197 v.704961066
577 5.392434435 2.233114993 4.570001554
578 vii.257374217 3.19342536 6.286034101
579 5.818378461 four.97727386
580 6.452948592 ii.613291975 5.062072369
581 6.295829768 2.697568991 5.376369856
582 7.862482092 iii.168308823 6.059153625
583 6.917023133 iii.234141075 6.013508121
584 6.188164373 two.628099499 5.521778155
585 6.572626017 3.104684069 5.251029151
586 5.641511337 2.583460776 iv.492538349
587 5.669708247 2.277983315 4.347505906
588 7.47103209 three.129383146 half-dozen.778526376
589 7.618153087 2.777143043 6.831610834
590 7.798703574 ii.944300182 6.740452757
591 7.029550605 2.815865345 5.763017682
592 7.339727259 iii.361741724 half dozen.176653226
593 vi.648438748 3.141217178 v.794335743
594 6.755581944 three.377012988 5.767101535
595 5.891962505 2.484806493 five.333059468
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597 6.446487673 iii.238856466 5.174232168
598 7.677656674 3.006032794 vi.39740796
599 5.390066272 2.725182129 5.291274744
600 6.538368723 3.23427878 v.645348596
601 3.113914563 5.470025549
602 7.900246972 6.920776309
603 vi.351450532 3.077454203 v.48453153
604 2.717870378 5.467056677
605 6.164923856 2.770899566 4.814069256
606 vii.067220539 2.723526264 5.91363292
607 vii.469224603 2.915791045 5.582955086
608 v.191750364 3.158086226 4.393772663
609 6.612652296 three.093602656 5.031797818
610 5.587634012 2.327826804 five.098527987
611 6.367463667 3.116328936 five.287218531
612 seven.387181428 iii.356592471 6.054308803
613 6.433775941 three.330287791 5.373859079
614 vi.405787701 ii.654215953 four.811085829
615 6.998228962 3.207979506 v.561095569
616 vi.285147499 three.204061489 5.510463282
617 5.73680434 iii.423292793 4.831911564
618 7.28601584 2.92603058 5.966309029
619 6.660387174 3.090362667 five.175151669
620 6.163642151 ii.429416338 5.06119182
621 vi.601545138 2.48788365 5.309025798
622 2.580880846 5.318516816
623 6.87054357 3.669405364 5.835363999
624 6.974657332 2.737491693 5.529412658
625 6.326144004 ii.578081053 5.454722442
626 7.02338706 3.309176071 5.584563246
627 6.34799272 3.058263589 5.81239401
628 seven.369863206 2.819013411 6.433765504
629 6.035591179 two.987740822 four.966720893
630 6.312125875 2.69473574 5.841148977
631 7.135353966 two.93778659 5.519890931
632 6.71122267 three.463321088 6.138937134
633 6.077418831 iii.268125481 5.169873694
634 6.891785557 3.582929763 v.785892205
635 6.751007478 three.004939705 v.97191479
636 v.910620112 2.9194914 5.184837187
637 six.956319649 2.639620324 v.818449433
638 6.044982054 3.223045852 iv.446406061
639 six.951763742 iii.354380821 6.017220469
640 6.028621431 2.536970392 four.823223814
641 half dozen.71995644 3.311795353 5.750033507
642 vi.859848514 2.927281933 5.606372092
643 5.308243727 2.742595199 5.309811021
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645 half-dozen.969030749 iii.339707659 6.250906762
646 half dozen.076483379 2.631741124 5.076068688
647 vi.574964848 ii.820190986 five.301861938
648 6.327643702 ii.856119321 5.414097446
649 five.840868674 3.091201421 iv.799055627
650 half-dozen.665013315 3.08835721 5.157151902
651 7.190809439 ii.983084201 six.05807209
652 5.30054416 ii.532071013 4.47836125
653 6.28622788 3.139148296 v.408487987
654 half dozen.065272521 two.497782318 v.583022829
655 seven.021146439 2.932862195 5.557556132
656 5.202064313 2.757104779
657 half dozen.839026869 ii.946569804 five.682390961
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660 v.859939355 2.908982699 4.848409318
661 6.58126522 two.836765608 6.193956317
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664 six.983181737 2.243119745 vi.066119538
665 half-dozen.640720276 two.943695355 5.466583014
666 6.561439537 3.053364878 five.349776457
667 7.803901092 iii.052054971
668 6.173901376 2.458687481 5.0857672
669 6.411885873 two.348779119 5.494069641
670 6.907124635 iii.203770823 5.822535493
671 half-dozen.773052091 iii.308786935 5.597897547
672 6.875996866 3.071182603 five.807833902
673 6.374848942 2.836221322 5.637856593
674 7.723698907 3.827801927 six.361280006
675 seven.790623623 3.197924573 half-dozen.553369902
676 six.633335605 three.279713598 5.318485791
677 5.842704711 2.293177675 5.36913402
678 7.19587509 3.095657644
679 2.162919479 five.32011476
680 6.095636972 3.056823087
681 vii.35677444 2.777208625 6.427840404
682 6.798846231 3.046898154 5.330408432
683 5.756830236 2.777807737 v.013815434
684 5.81377742 3.40737999 v.064669953
685 5.815406568 ii.969360976 5.329481915
686 v.788755982 2.313228351
687 2.701142064 5.13779489
688 6.862296848 2.79866518 five.925347261
689 six.344813071 2.607958519 5.657832706
690 half-dozen.117897001 iii.479434575 5.354741253
691 six.236267786 3.541420809 5.203276245
692 2.083277105 5.36645851
693 6.320562189 ii.98832012 v.135367344
694 6.53042271 2.890928531 5.388230695
695 6.318663383 2.577523386 5.523441852
696 vi.236598274 three.644981839 v.239226364
697 half-dozen.873232375 3.526012282 five.683983078
698 7.21910726 3.080199203 five.722077525
699 5.965145555 2.917907184 4.781154619
700 half-dozen.529135833 3.586178397
701 6.647882182 iii.063206338 6.056903059
702 five.491980665 2.681467513 four.682919201
703 half dozen.959292137 2.681792903 5.488107432
704 6.441914976 three.104948626 v.276847485
705 6.554693633 3.312885109 v.235580431
706 v.822954213 two.13724747 5.011883898
707 6.969717382 3.074993703 6.184726408
708 six.4949769 2.62751541 5.349595475
709 6.548366404 three.037629932 5.666084685
710 five.44121063 two.678299801 iv.768387262
711 half dozen.882534683 ii.774060617 half-dozen.25167915
712 6.149605037 iii.041513947 5.344477923
713 6.504210998 3.054186763 five.378619813
714 6.541726037 2.98113174 v.482986985
715 v.935450567 2.671557078
716 half-dozen.865264955 iii.074573652 6.248294868
717 7.093553427 2.503175962 5.802002725
718 3.096375539 5.50895027
719 6.760098312 3.210036232 vi.032279009
720 six.630965624 two.673107339 v.127649617
721 five.8383125 2.53801504 4.710535332
722 5.990428682 2.728738505 five.179668477
723 vi.906221388 two.855281852 5.54383149
724 6.184404157 iii.105228867 four.631220717
725 3.027782602 5.745608768
726 6.610255662 3.346680899 5.745695617
727 v.646048779 2.967915772 four.674766814
728 6.577690913 5.952842175
729 6.097459983 2.947614672 five.267755372
730 6.893944366 three.252066137 5.885174278
731 6.365304059 3.045120675 5.560593074
732 half-dozen.19204742 2.907025913 5.207118002
733 5.863596942 2.293239269 four.751303504
734 6.388881714 ii.693869695 five.356712127
735 6.373823385 two.398830419 5.182120392
736 6.346669703 2.927987914 v.411925151
737 7.290266728 3.38089829 6.13100335
738 seven.333680842 three.44118482 half dozen.55366392
739 5.862725791 two.805573385 four.923487697
740 6.816755963 2.911537388 5.68859797
741 6.104382464 three.062830097 v.344196013
742 6.088150338 2.609843922 4.70970449
743 6.724201195 ii.594256692 5.451185434
744 half dozen.04155974 3.030197934 v.457959941
745 half dozen.478882423 3.039459294 five.453958612
746 5.909400729 2.671665708 five.209582128
747 half-dozen.074869779 2.734110348
748 half-dozen.507591506 3.155259074
749 seven.048207764 3.561434196 six.173114664
750 vi.859591454 3.097637066 vi.077470429
751 vi.502828644 3.012544556 5.717094943
752 6.543688635 2.939206807 5.768513537
753 half-dozen.947365982 2.969083702 5.372936738
754 six.000902856 iii.040175793 4.907538681
755 half-dozen.385587802 three.180423433 5.514308339
756 7.616001392 6.167908098
757 6.194870953 iii.145440649 5.437958082
758 vii.484211558 ii.830996459 6.13372246
759 6.742442905 2.470008049 five.651739458
760 7.230229643 6.059799802
761 5.909346245 2.842542123 4.963689858
762 half dozen.886313716 iii.202925072 six.125879069
763 6.515937784 2.935279474 5.987526043
764 five.655381835 ii.856291665 4.526487173
765 3.683022288 6.191038619
766 six.47153464 2.870569859 5.537712449
767 half-dozen.793824238 2.975410333 5.542408798
768 4.731211564 two.030710062 four.734570511
769 six.201060414 3.17712095 4.930366476
770 six.928172109 two.843839525 five.835101158
771 6.18716629 3.057143967 5.366968415
772 6.43250576 2.723287975 v.571762394
773 half dozen.340395178 2.747118911 five.49767446
774 six.587795787 2.472987961 v.693176882
775 five.337454477 two.712772875 iv.192798717
776 half-dozen.005019979 two.999164885 5.123419032
777 6.382910703 2.88796337 five.136238929
778 vi.963540996 3.141993596 6.398804617
779 7.465998751 2.829080791 six.286658931
780 6.416408064 three.111623512 five.74152701
781 half-dozen.885784569 three.068747126
782 7.633157481 3.237200206 6.358721799
783 vii.242336185 3.340892136 5.904823771
784 five.448297305 two.762608645 4.273965391
785 half dozen.121447656 two.29909954
786 five.895130006 3.149235721 4.679209119
787 7.001117625 three.442429324 5.887806882
788 half dozen.44544705 6.240777935
789 vii.326822571 2.996530771 5.770012254
790 7.374211028 2.67010524 v.413709901
791 7.141049395 3.429032142 6.409921668
792 5.028619119 two.668689485 4.189503449
793 6.856599717 3.03932629 5.921794087
794 v.618907712 3.155653649 4.955563338
795 seven.370619549 two.773272278 six.152745663
796 6.390390721 5.189941699
797 v.848626072 2.813704365 5.028411705
798 five.654422583
799 half-dozen.414603995 3.166971957
800 v.976247094 3.187293627 5.309866398
801 5.801104254 iii.131410352 4.670557887
802 6.165851951 2.427969621 5.528737953
803 half dozen.761232539 2.959653609 5.624054851
804 2.926069319 5.456662471
805 vi.41446119 two.764500546 five.695601289
806 7.42328788 iii.11486796 vi.608234041
807 6.854933071 3.176664077 6.040458517
808 vii.185397014 2.959258567 5.702759296
809 v.953867368 4.656038955
810 6.864837403 3.289436966 5.583431265
811 5.975805122 ii.721746392 4.713245298
812 vii.053252891 iii.373140409 six.132593126
813 6.38353855 three.000919803 5.44152728
814 half-dozen.23576097 2.335090215 5.217804228
815 7.384244705 3.42323634 6.157317493
816 5.459339528 2.226694828 4.52981392
817 vi.433274339 3.431879647 five.604216662
818 v.91359456 2.852480831 5.520062754
819 v.831833057 2.926688687 4.931949498
820 6.016496629 2.342396427 four.988016639
821 six.592396415 3.148132239 5.283223494
822 7.110408296 2.857297872 5.095279256
823 5.895826338 2.751826931 five.201843687
824 vi.54228262 iii.309066932 five.402027328
825 6.081257005 3.021715472 5.36240234
826 6.674854567 3.319071752 vi.172638196
827 5.868795579 3.079178846
828 6.071459953 four.773271459
829 five.587883428 2.753072156 v.337453465
830 5.790877714 ii.712641662 5.308958325
831 4.872260779 2.67820185 4.392126164
832 half dozen.577404217 ii.738606092 5.639161327
833 6.57706149 2.891796508 5.241028987
834 five.646285293 2.38765375 4.583706529
835 five.854938269 2.238023484 4.895915242
836 6.24727529 2.775831413 5.573656648
837 5.007618331 ii.435818491 iv.632652221
838 vi.012049232 2.800169844 4.94654405
839 six.377780057 2.840692756 5.219683398
840 5.668558297 3.044608814 4.740876286
841 six.090831937 2.647675604 4.82150624
842 half-dozen.12346006 two.851475671 5.079451122
843 5.478560943 2.091431872 four.451142288
844 7.148930808 2.802860889 6.088743835
845 5.753584003 2.697651009 5.105016611
846 7.105606631 5.757815427
847 7.102723186 two.631286578 half dozen.254712377
848 7.626859731 2.974175109
849 5.931890939 ii.942109357
850 half dozen.869105517 three.37332911 5.647986087
851 6.443960535 2.630250388 five.397036229
852 7.100598544 3.785616322 6.01540748
853 6.682333655 ii.95234948 5.665606767
854 5.571719858 2.910688735 4.892076373
855 5.998584952 two.695259213 5.148601158
856 7.023660168 ii.92282203
857 six.616920258 2.869741238 5.410172661
858 2.714604072 5.770686798
859 6.195561216 3.191554174 five.431832405
860 six.457802178 2.23634164 5.501710938
861 half dozen.517772502 three.363905893 v.691272279
862 6.182661023 3.05337056 four.990015886
863 six.559883378 2.528630586 5.426205067
864 3.424832616 5.481893639
865 five.554973543 2.91263083 4.498922551
866 v.568143918 3.326514414 5.005013191
867 6.379341411 2.847326789 five.484690695
868 vii.199666346 2.406002178 5.790075623
869 7.164809316 3.283090619 6.18970345
870 v.744972618 2.537607748 5.026952945
871 7.523461135 three.247928271 6.461976569
872 6.347197704 2.996801274 5.078589226
873 three.296874914 5.16866565
874 six.583622509 2.706346071 6.02633288
875 6.516219506 5.450645461
876 vii.948161657 3.171346429 6.610814151
877 half dozen.214544783 v.274990073
878 7.101192664 3.254502449 v.520329751
879 8.224488512 3.220905495 six.755875487
880 half dozen.15025521 2.831042752 5.279647889
881 vii.255797825 3.10914736 6.316836621
882 6.126983222 two.761388593 five.565776554
883 7.06500477 3.285055429 6.002420824
884 6.889494908 3.046381288 5.731919586
885 half dozen.626984613 iii.417857339 6.047293674
886 seven.914676364 3.183004548 half-dozen.996488204
887 7.006554674 3.223244676 5.410157098
888 half dozen.088301774 2.713214818 five.201547565
889 6.348645017 two.979805177 v.211267281
890 5.521177409 2.716547177 4.623514324
891 2.935019872 iv.720309178
892 half-dozen.807214047 3.18175499 5.723933131
893 6.55028443 ii.861631184 v.27244163
894 6.78683453 3.156770113 5.888711697
895 half dozen.998304763 three.199458453 6.122541676
896 6.635739427 two.915487967 5.196476244
897 6.509810671 2.80277108 5.618761709
898 6.608027047 3.208097205 5.824851675
899 6.313161515 2.673293329
900 5.333504968 2.716981663 4.798877379
901 half dozen.704684173 2.750668852 5.660910808
902 6.952466001 2.639588188 5.587814883
903 7.105135303 2.981888546
904 6.129104899 2.610570784 v.68944185
905 6.303037744 ii.727467707 5.353794094
906 7.257309233 3.171028723 6.340405708
907 5.930714887 2.468681288 5.131516943
908 ii.83709289 v.28957019
909 seven.353579205 3.526518234 5.995529428
910 6.663205204 3.381587056 v.830106031
911 6.679811331 2.922999385 5.835536654
912 6.350602965 ii.527071862 5.059347192
913 6.352274786 2.816683128 5.159136146
914 5.983009204 2.68471771 five.224723627
915 6.529666447 ii.985662435 5.631478844
916 5.403304065 ii.565288344 iv.586527881
917 v.699791021 2.844288245 five.112924441
918 6.042107413 ii.574231537 4.992238098
919 7.596342714 3.127933704 six.02933704
920 6.622056951 3.216959006 5.592505729
921 5.980087269 2.516425661 4.781188786
922 half-dozen.48866896 3.26898359 5.096510092
923 7.508290067 3.265892954 half-dozen.126495936
924 3.03149215 v.461709597
925 v.124719534 2.573639988 4.081315679
926 6.173027636 2.439631461 5.42374891
927 6.346574484 ii.996543292 v.187475889
928 vi.964105185 iii.786238195 six.250289592
929 two.763767486 6.039445189
930 5.818982877 2.252896807 4.943672454
931 5.727388131 two.635368253 four.86443497
932 6.149169556 2.992043024 4.842139363
933 seven.297369441 2.752120128 6.085832098
934 7.091600427 3.336707587 6.044060525
935 five.824179096 2.793090697 5.147765179
936 5.667848685 three.074529731 v.362884075
937 6.524859292 5.431102226
938 vii.335477576 two.859445742 5.920663355
939 half-dozen.110587725 ii.667814196 5.229102796
940 6.536349456 5.787604321
941 v.723132068 3.013331066 4.5534081
942 2.906800113 4.872171615
943 half-dozen.621117993 3.226247301 5.204712195
944 7.34651448 3.049692728 vi.043312172
945 half dozen.134269523 three.153901241 5.981122228
946 half dozen.892555055 2.982528997
947 6.793105643 3.133454112
948 half dozen.190593978 ii.797565343 half dozen.064474062
949 5.946576321 three.225546531 5.212781795
950 6.920798909 3.304917306 5.963432457
951 6.820366716 3.175006316 5.864261754
952 6.114129009 two.769316459 5.184444695
953 7.089110832 2.522235518 half-dozen.332972597
954 6.575039524 2.477052652 five.620073905
955 6.815064637 3.065656017 5.866520539
956 half-dozen.055855733 ii.65699961
957 7.333391803 two.995660773 6.195690609
958 half dozen.36508711 3.153302066 5.587709589
959 6.727598272 3.021181639 v.749229167
960 6.80299592 iii.134445312 five.965444845
961 6.694415496 2.414763157 v.676912262
962 v.939014707 2.535329108 five.007509501
963 7.059810347 2.936987146 5.884478866
964 five.913797464 2.570626654 5.849111697
965 vi.446742802 ii.888090405 five.161475053
966 7.391870566 3.719151768 6.406988863
967 half-dozen.145695825 ii.532725619 five.4755056
968 7.026912174 3.544278859 v.658088358
969 6.544136366 2.670677935 five.305552886
970 vi.056404683 2.861245068 5.111073845
971 5.223327575 2.604560008 v.107479142
972 v.746141934 2.82393141 4.815151967
973 six.531449035 2.570165363 five.39013449
974 vii.400601534 2.783360466 6.17621021
975 6.500163146 2.844680062 4.818014476
976 6.465219917 3.102333151 5.271523119
977 v.134797901 2.580909163
978 8.162359078 6.968209607
979 5.644791814 2.93365626 5.455700419
980 half dozen.544821214 2.308736531 v.246605628
981 6.355384793 three.220849847 5.46918944
982 5.278224788 2.619898827 iv.710000995
983 seven.193750271 three.0197951
984 7.510068507 three.187937574 6.137844448
985 6.989657197 5.929510536
986 6.435838538 3.06777211 v.625525688
987 half-dozen.229067306 3.398439489 5.338445493
988 7.101462115 two.91433499 5.855362628
989 seven.011163248 2.714943701 5.85555988
990 6.175844835 ii.679135934 5.388903997
991 6.232457453 ii.923147266 v.171955231
992 vii.091996326 2.786810567 five.703815524
993 7.001000889 3.058238433 6.46804607
994 iv.816042295 ii.377223913 iv.541477951
995 5.542285388 two.609662416 4.862442696
996 half dozen.177736037 2.2213595 five.543332602
997 five.566539823
998 2.541728489
999 2.862564458 4.923337878

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Source: https://www.bayesserver.com/docs/walkthroughs/walkthrough-7-missing-data

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