Spreadsheet: 101079d1299240026-how-to-draw-gaussian-shape-with-histogram-histogramwithnormalcurve
Sheet: Normal

MPG |  | Bins |  | Bins | Frequency
27 |  | 5 |  | 5 | 0
29 |  | 10 |  | 10 | 1
33 |  | 15 |  | 15 | 2
21 |  | 20 |  | 20 | 4
21 |  | 25 |  | 25 | 4
12 |  | 30 |  | 30 | 2
16 |  | 35 |  | 35 | 2
25 |  | 40 |  | 40 | 1
8 |  | 45 |  | 45 | 1
17 |  |  |  | More | 0
24
34
38
15
19
19
41
Mean | 23.47058823529412 |  |  | The histogram was created using the Better Histogram add-in. The chart
[NAME] | 9.213560977296071 |  |  | is a combination Column chart type for the vertical bars and XY
 |  |  |  | Scatter chart type for the horizontal axis. The XY Scatter chart type
From Mean - 3*StDev |  |  |  | originally uses two hidden data points. To show the normal curve, the
to Mean + 3*StDev |  |  |  | x and d*n*step data values replace the original two hidden data
in steps of StDev/100 |  |  |  | points. The secondary Y-axis remains hidden.
x | density | d*n*step |  | To align the normal curve with the histogram data, I chose to use
-4.170094696594099 | 0.0004810136301109748 | 0.04088615855943285 |  | identical Y-axis scales. (In the example, each Y-axis goes from 0 to
-4.077959086821138 | 0.0004956378935270599 | 0.04212922094980009 |  | 5.)
-3.98582347704818 | 0.0005106557104823928 | 0.04340573539100339
-3.89368786727522 | 0.000526075956725411 | 0.04471645632165994 |  | The total area of the histogram is n*step, where n = number of data
-3.80155225750226 | 0.0005419076539370391 | 0.04606215058464832 |  | values and step = width of each vertical bar. (In the example, n = 17
-3.70941664772929 | 0.0005581599704746478 | 0.04744359749034507 |  | and step = 5, so n*step = 85.) The total area of the original normal
-3.61728103795633 | 0.0005748422220639985 | 0.04886158887543987 |  | density is 1, so it is multiplied by n*step so that the charted
-3.52514542818337 | 0.0005919638724372098 | 0.05031692915716283 |  | density function has the same total area as the histogram.
-3.43300981841041 | 0.0006095345339147146 | 0.05181043538275074
-3.34087420863745 | 0.0006275639679291904 | 0.05334293727398118
-3.24873859886449 | 0.000646062085489421 | 0.05491527726660078
-3.15660298909153 | 0.0006650389475820129 | 0.0565283105444711
-3.06446737931857 | 0.0006845047655088916 | 0.05818290506825578
-2.97233176954561 | 0.0007044699011584762 | 0.05987994159847047
-2.88019615977265 | 0.0007249448672084231 | 0.06162031371271596
-2.78806054999969 | 0.0007459403272578034 | 0.06340492781691329
-2.69592494022673 | 0.0007674670958865907 | 0.06523470315036022
-2.60378933045377 | 0.0007895361386402907 | 0.06711057178442471
-2.5116537206808 | 0.000812158571937577 | 0.06903347861469405
-2.41951811090784 | 0.000835345662898738 | 0.07100438134639273
-2.32738250113488 | 0.0008591088290928023 | 0.07302425047288819
-2.23524689136192 | 0.0008834596382011286 | 0.07509406924709593
-2.14311128158896 | 0.0009084098075952934 | 0.07721483364559993
-2.050975671816 | 0.0009339712038271071 | 0.0793875523253041
-1.95884006204304 | 0.000960155842028563 | 0.08161324657242786
-1.86670445227008 | 0.0009869758852195448 | 0.08389295024366131
-1.77456884249712 | 0.001014443643521124 | 0.08622770969929557
-1.68243323272416 | 0.001042571573272272 | 0.08861858372814309
-1.5902976229512 | 0.001071372276047826 | 0.09106664346406523
-1.49816201317823 | 0.001100858497575574 | 0.09357297229392382
-1.40602640340527 | 0.001131043126550281 | 0.09613866575677385
-1.31389079363231 | 0.001161939193342594 | 0.09876483143412047
-1.22175518385935 | 0.001193559868600652 | 0.1014525888310554
-1.12961957408639 | 0.00122591846174235 | 0.1042030692480997
-1.03748396431343 | 0.001259028419336178 | 0.1070174156435751
-0.945348354540469 | 0.001292903323368584 | 0.1098967824863297
-0.853212744767509 | 0.001327556889395831 | 0.1128423355986456
-0.761077134994549 | 0.00136300296457838 | 0.1158552519891623
-0.668941525221589 | 0.001399255525595795 | 0.1189367196756426
-0.576805915448629 | 0.001436328676440269 | 0.1220879374974228
-0.484670305675669 | 0.001474236646086848 | 0.125310114917382
-0.392534695902699 | 0.001512993786038509 | 0.1286044718132733
-0.300399086129739 | 0.001552614567744238 | 0.1319722382582602
-0.208263476356779 | 0.001593113579888384 | 0.1354146542905126
-0.116127866583819 | 0.001634505525549478 | 0.1389329696717056
-0.0239922568108586 | 0.001676805219226882 | 0.142528443634285
0.0681433529621014 | 0.001720027583733611 | 0.1462023446173569
0.160278962735061 | 0.001764187646953713 | 0.1499559499910656
0.252414572508021 | 0.001809300538462739 | 0.1537905457693328
0.344550182280981 | 0.001855381486009741 | 0.157707426310828
0.436685792053941 | 0.001902445811859447 | 0.161707894008053
0.528821401826901 | 0.001950508928993236 | 0.165793258964425
0.620957011599871 | 0.001999586337167634 | 0.1699648386592489
0.713092621372831 | 0.002049693618829063 | 0.1742239576004703
0.805228231145791 | 0.002100846434883805 | 0.1785719469651234
0.897363840918751 | 0.002153060520321979 | 0.1830101442273682
0.989499450691711 | 0.002206351679694607 | 0.1875398927740416
1.08163506046467 | 0.002260735782442837 | 0.1921625415076411
1.17377067023763 | 0.002316228758078479 | 0.1968794444366707
1.26590628001059 | 0.002372846591215097 | 0.2016919602532833
1.35804188978355 | 0.002430605316449005 | 0.2066014518981654
1.45017749955651 | 0.002489521013089577 | 0.2116092861126141
1.54231310932947 | 0.0025496097997384 | 0.216716832977764
1.63444871910243 | 0.002610887828716867 | 0.2219254654409336
1.7265843288754 | 0.002673371280341944 | 0.2272365588290652
1.81871993864836 | 0.002737076357049879 | 0.2326514903492398
1.91085554842132 | 0.002802019277367849 | 0.2381716385762672
2.00299115819428 | 0.002868216269733447 | 0.243798382927343
2.09512676796724 | 0.002935683566162245 | 0.2495331031237908
2.1872623777402 | 0.00300443739576361 | 0.2553771786399068
2.27939798751316 | 0.003074493978105134 | 0.2613319881389364
2.37153359728612 | 0.003145869516426174 | 0.2673989088962248
2.46366920705908 | 0.003218580190701047 | 0.273579316209589
2.55580481683204 | 0.003292642150552604 | 0.2798745827969713
2.647940426605 | 0.003368071508017013 | 0.2862860781814461
2.74007603637797 | 0.00344488433016072 | 0.2928151680636612
2.83221164615093 | 0.003523096631550569 | 0.2994632136817983
2.92434725592389 | 0.003602724366578483 | 0.306231571159171
3.01648286569685 | 0.003683783421641822 | 0.3131215908395548
3.10861847546981 | 0.003766289607181032 | 0.3201346166103878
3.20075408524277 | 0.003850258649576155 | 0.3272719852139732
3.29288969501573 | 0.003935706182903905 | 0.334535025546832
3.38502530478869 | 0.004022647740557259 | 0.341925057947367
3.47716091456165 | 0.004111098746729483 | 0.349443393472006
3.56929652433461 | 0.004201074507764868 | 0.3570913331600138
3.66143213410757 | 0.004292590203378363 | 0.3648701672871608
3.75356774388053 | 0.004385660877746627 | 0.3727811746084633
3.8457033536535 | 0.004480301430473082 | 0.380825621590212
3.93783896342646 | 0.004576526607429593 | 0.3890047616315154
4.02997457319942 | 0.004674350991477883 | 0.3973198342756201
4.12211018297238 | 0.004773788993073479 | 0.4057720644112457
4.21424579274534 | 0.00487485484075544 | 0.4143626614642124
4.3063814025183 | 0.004977562571525299 | 0.4230928185796504
4.39851701229126 | 0.005081926021118537 | 0.4319637117950756
4.49065262206422 | 0.005187958814172301 | 0.4409764992046456
4.58278823183718 | 0.005295674354293142 | 0.4501323201149171
4.67492384161014 | 0.005405085814028644 | 0.4594322941924347
4.7670594513831 | 0.005516206124747078 | 0.4688775206035016
4.85919506115607 | 0.005629047966429298 | 0.4784690771464903
4.95133067092903 | 0.005743623757377123 | 0.4882080193770555
5.04346628070199 | 0.005859945643843031 | 0.4980953797266576
5.13560189047495 | 0.005978025489585473 | 0.5081321666147652
5.22773750024791 | 0.006097874865354879 | 0.5183193635551647
5.31987311002087 | 0.006219505038315207 | 0.5286579282567926
5.41200871979383 | 0.006342926961406237 | 0.5391487917195301
5.50414432956679 | 0.006468151262651725 | 0.5497928573253966
5.59627993933975 | 0.006595188234418986 | 0.5605909999256138
5.68841554911271 | 0.00672404782263531 | 0.5715440649240013
5.78055115888567 | 0.006854739615966977 | 0.582652867357193
5.8726867686586 | 0.006987272834966589 | 0.59391819097216
5.9648223784316 | 0.007121656321195074 | 0.6053407873015813
6.0569579882046 | 0.007257898526323404 | 0.6169213747374893
6.1490935979775 | 0.007396007501221619 | 0.6286606376038376
6.2412292077505 | 0.007535990885041223 | 0.640559225228504
6.3333648175234 | 0.007677855894295434 | 0.6526177510151119
6.4255004272964 | 0.007821609311947841 | 0.6648367915155665
6.5176360370694 | 0.007967257476511606 | 0.6772168855034866
6.6097716468423 | 0.008114806271169802 | 0.6897585330494332
6.7019072566153 | 0.008264261112922461 | 0.7024621945984092
6.7940428663882 | 0.008415626941765657 | 0.7153282900500809
6.8861784761612 | 0.008568908209913862 | 0.7283571978426783
6.9783140859342 | 0.008724108871068038 | 0.7415492540407833
7.0704496957071 | 0.00888123236974081 | 0.7549047514279689
7.1625853054801 | 0.009040281630644745 | 0.7684239386048034
7.254720915253 | 0.009201259048149401 | 0.7821070190926991
7.346856525026 | 0.009364166475819176 | 0.7959541504446299
7.438992134799 | 0.009529005216034527 | 0.8099654433629349
7.5311277445719 | 0.009695776009708622 | 0.8241409608252329
7.6232633543449 | 0.009864479026105728 | 0.8384807172189869
7.7153989641179 | 0.01003511385276749 | 0.8529846774852365
7.8075345738908 | 0.01020767948555845 | 0.8676527562724684
7.8996701836638 | 0.0103821743188373 | 0.8824848171011708
7.9918057934367 | 0.01055859613575998 | 0.897480671539598
8.0839414032097 | 0.01073694209872761 | 0.912640078391847
8.1760770129827 | 0.01091720873998177 | 0.9279627428984506
8.2682126227556 | 0.01109939195235999 | 0.9434483159505989
8.3603482325286 | 0.01128348698021801 | 0.9590963933185306
8.4524838423015 | 0.01146948841052506 | 0.9749065148946301
8.5446194520745 | 0.0116573901641453 | 0.9908781639523503
8.6367550618475 | 0.01184718548730791 | 1.007010766421172
8.7288906716204 | 0.01203886694327905 | 1.023303690178719
8.8210262813934 | 0.01223242640424212 | 1.03975624436058
8.9131618911663 | 0.01242785504339235 | 1.05636767868835
9.0052975009393 | 0.01262514332725943 | 1.073137182817052
9.0974331107123 | 0.01282428100825999 | 1.090063885702099
9.1895687204852 | 0.01302525711749344 | 1.107146854986942
9.2817043302582 | 0.01322805995778737 | 1.124385096411927
9.3738399400311 | 0.01343267709699834 | 1.141777553244859
9.4659755498041 | 0.01363909536158163 | 1.159323105734438
9.5581111595771 | 0.01384730083043148 | 1.177020570586676
9.65024676935 | 0.01405727882900509 | 1.194868700465433
9.742382379123 | 0.01426901392373637 | 1.212866183517591
9.834517988896 | 0.0144824899167448 | 1.231011642923308
9.9266535986689 | 0.01469768984085163 | 1.249303636472388
10.0187892084419 | 0.0149145959549085 | 1.267740656167222
10.1109248182148 | 0.01513318973944415 | 1.286321127852753
10.2030604279878 | 0.01535345189264205 | 1.305043410874575
10.2951960377608 | 0.01557536232664936 | 1.323905797765195
10.3873316475337 | 0.01579890016423018 | 1.342906513959565
10.4794672573067 | 0.0160240437357679 | 1.362043717540272
10.5716028670796 | 0.01625077057662079 | 1.381315499012767
10.6637384768526 | 0.01647905742484383 | 1.400719881111725
10.7558740866256 | 0.01670888021927595 | 1.420254818638456
10.8480096963985 | 0.01694021409800514 | 1.439918198330437
10.9401453061715 | 0.01717303339721518 | 1.45970783876329
11.0322809159444 | 0.01740731165041762 | 1.479621490285498
11.1244165257174 | 0.01764302158808093 | 1.499656834986879
11.2165521354904 | 0.01788013513765497 | 1.519811486700673
11.3086877452633 | 0.01811862342400269 | 1.540082991040229
11.4008233550363 | 0.01835845677024143 | 1.560468825470521
11.4929589648092 | 0.01859960469899649 | 1.580966399414702
11.5850945745822 | 0.01884203593407821 | 1.601573054396648
11.6772301843552 | 0.01908571840257903 | 1.622286064219218
11.7693657941281 | 0.01933061923740174 | 1.643102635179148
11.8615014039011 | 0.01957670478022007 | 1.664019906318706
11.9536370136741 | 0.01982394058487321 | 1.685034949714223
12.045772623447 | 0.02007229142120245 | 1.706144770802208
12.13790823322 | 0.02032172127933094 | 1.72734630874313
12.2300438429929 | 0.02057219337438691 | 1.748636436822887
12.3221794527659 | 0.02082367015167959 | 1.770011962892766
12.4143150625389 | 0.02107611329232262 | 1.791469629847422
12.5064506723118 | 0.02132948371931328 | 1.813006116141629
12.5985862820848 | 0.0215837416040674 | 1.834618036345729
12.6907218918577 | 0.02183884637340814 | 1.856301941739692
12.7828575016307 | 0.02209475671701722 | 1.878054320946463
12.8749931114037 | 0.02235143059534112 | 1.899871600603995
12.9671287211766 | 0.02260882524795978 | 1.921750146076582
13.0592643309496 | 0.02286689720241553 | 1.94368626220532
13.1513999407225 | 0.02312560228349923 | 1.965676194097435
13.2435355504955 | 0.02338489562300063 | 1.987716127955053
13.3356711602685 | 0.02364473166991356 | 2.009802191942653
13.4278067700414 | 0.02390506420110229 | 2.031930457093694
13.5199423798144 | 0.02416584633242476 | 2.054096938256105
13.6120779895873 | 0.02442703053030839 | 2.076297595076213
13.7042135993603 | 0.02468856862378334 | 2.098528333021584
13.7963492091333 | 0.02495041181696273 | 2.120785004441832
13.8884848189062 | 0.02521251070197388 | 2.14306340966778
13.9806204286792 | 0.02547481527233511 | 2.165359298148485
14.0727560384522 | 0.02573727493677188 | 2.18766836962561
14.1648916482251 | 0.02599983853347389 | 2.209986275345281
14.2570272579981 | 0.02626245434478652 | 2.232308619306854
14.349162867771 | 0.02652507011232928 | 2.254630959547989
14.441298477544 | 0.02678763305254376 | 2.276948809466219
14.533434087317 | 0.02705008987265739 | 2.299257639175878
14.6255696970899 | 0.02731238678706483 | 2.32155287690051
14.7177053068629 | 0.02757446953411815 | 2.343829910400042
14.8098409166358 | 0.02783628339331699 | 2.366084088431944
14.9019765264088 | 0.02809777320289945 | 2.388310722246453
14.9941121361818 | 0.02835888337781808 | 2.410505087114537
15.0862477459547 | 0.02861955792810128 | 2.432662423888609
15.1783833557277 | 0.02887974047758946 | 2.454777940595104
15.2705189655006 | 0.02913937428303566 | 2.476846814058031
15.3626545752736 | 0.02939840225356927 | 2.498864191553388
15.4547901850466 | 0.02965676697050609 | 2.520825192493017
15.5469257948195 | 0.02991441070750293 | 2.542724910137749
15.6390614045925 | 0.03017127545104483 | 2.564558413338811
15.7311970143654 | 0.03042730292125264 | 2.586320748306475
15.8233326241384 | 0.03068243459300835 | 2.60800694040571
15.9154682339114 | 0.03093661171737956 | 2.629611995977263
16.0076038436843 | 0.03118977534333997 | 2.651130904183898
16.0997394534573 | 0.03144186633977217 | 2.672558638880635
16.1918750632303 | 0.03169282541773968 | 2.693890160507873
16.2840106730032 | 0.03194259315302171 | 2.715120418006845
16.3761462827762 | 0.03219111000889686 | 2.736244350756234
16.4682818925491 | 0.03243831635916123 | 2.757256890528704
16.5604175023221 | 0.03268415251137578 | 2.778152963466941
16.6525531120951 | 0.03292855873032257 | 2.798927492077418
16.744688721868 | 0.03317147526166409 | 2.819575397241447
16.836824331641 | 0.03341284235579024 | 2.84009160024217
16.9289599414139 | 0.03365260029183745 | 2.860471024806184
17.0210955511869 | 0.03389068940187337 | 2.880708599159236
17.1132311609599 | 0.03412705009522562 | 2.900799258094178
17.2053667707328 | 0.03436162288294797 | 2.920737945050577
17.2975023805058 | 0.0345943484024071 | 2.940519614204603
17.3896379902787 | 0.03482516744197389 | 2.960139232567781
17.4817736000517 | 0.03505402096581103 | 2.979591782093938
17.5739092098247 | 0.03528085013873545 | 2.998872261792513
17.6660448195976 | 0.0355055963511471 | 3.017975689847503
17.7581804293706 | 0.03572820124400722 | 3.036897105740613
17.8503160391435 | 0.03594860673384886 | 3.055631572377154
17.9424516489165 | 0.03616675503781085 | 3.074174178213922
18.0345872586895 | 0.03638258869867309 | 3.092520039387213
18.1267228684624 | 0.03659605060988415 | 3.110664301840153
18.2188584782354 | 0.03680708404056353 | 3.1286021434479
18.3109940880084 | 0.03701563266046153 | 3.14632877613923
18.4031296977813 | 0.0372216405648654 | 3.163839448013559
18.4952653075543 | 0.03742505229943453 | 3.181129445451935
18.5874009173272 | 0.03762581288494703 | 3.198194095220497
18.6795365271002 | 0.03782386784194794 | 3.215028766565575
18.7716721368732 | 0.0380191632152771 | 3.231628873298554
18.8638077466461 | 0.03821164559846668 | 3.247989875869668
18.9559433564191 | 0.03840126215799084 | 3.264107283429222
19.048078966192 | 0.03858796065735012 | 3.27997665587476
19.140214575965 | 0.03877168948098039 | 3.295593605883333
19.232350185738 | 0.03895239765796508 | 3.310953800927032
19.3244857955109 | 0.03913003488554032 | 3.326052965270927
19.4166214052839 | 0.03930455155237599 | 3.340886881951959
19.5087570150568 | 0.03947589876161577 | 3.35545139473734
19.6008926248298 | 0.03964402835366582 | 3.369742410061595
19.6930282346028 | 0.03980889292871188 | 3.383755898940509
19.7851638443757 | 0.03997044586895443 | 3.397487898861126
19.8772994541487 | 0.04012864136054572 | 3.410934515646386
19.9694350639216 | 0.04028343441521232 | 3.424091925293047
20.0615706736946 | 0.04043478089155346 | 3.436956375782044
20.1537062834676 | 0.04058263751599567 | 3.449524188859632
20.2458418932405 | 0.04072696190339436 | 3.461791761788521
20.3379775030135 | 0.04086771257726651 | 3.473755569067654
20.4301131127865 | 0.04100484898964005 | 3.485412164119404
20.5222487225594 | 0.04113833154050901 | 3.496758180943266
20.6143843323324 | 0.04126812159688031 | 3.507790335734827
20.7065199421053 | 0.04139418151139768 | 3.518505428468802
20.7986555518783 | 0.04151647464053385 | 3.528900344445377
20.8907911616513 | 0.04163496536233458 | 3.538972055798439
20.9829267714242 | 0.04174961909370584 | 3.548717622964996
21.0750623811972 | 0.04186040230723086 | 3.558134196114624
21.1671979909701 | 0.04196728254750486 | 3.567219016537913
21.2593336007431 | 0.04207022844697875 | 3.575969417993194
21.3514692105161 | 0.042169209741298 | 3.58438282801033
21.443604820289 | 0.04226419728412868 | 3.592456769150937
21.535740430062 | 0.04235516306145945 | 3.600188860224053
21.6278760398349 | 0.04244208020536878 | 3.607576817456347
21.7200116496079 | 0.04252492300725032 | 3.614618455616277
21.8121472593809 | 0.04260366693048433 | 3.621311689091168
21.9042828691538 | 0.0426782886225491 | 3.627654532916673
21.9964184789268 | 0.04274876592656261 | 3.633645103757821
22.0885540886997 | 0.04281507789224593 | 3.639281620840904
22.1806896984727 | 0.04287720478630275 | 3.644562406835734
22.2728253082457 | 0.04293512810220542 | 3.649485888687461
22.3649609180186 | 0.04298883056938262 | 3.654050598397522
22.4570965277916 | 0.04303829616180155 | 3.658255173753131
22.5492321375646 | 0.0430835101059381 | 3.662098359004738
22.6413677473375 | 0.04312445888813056 | 3.665579005491097
22.7335033571105 | 0.04316113026131116 | 3.668696072211449
22.8256389668834 | 0.04319351325111034 | 3.671448626344379
22.9177745766564 | 0.04322159816133057 | 3.673835843713099
23.0099101864294 | 0.0432453765787847 | 3.6758570091967
23.1020457962023 | 0.04326484137749637 | 3.677511517087192
23.1941814059753 | 0.04327998672225924 | 3.678798871392035
23.2863170157482 | 0.04329080807155208 | 3.679718686081927
23.3784526255212 | 0.04329730217980877 | 3.680270685283745
23.4705882352942 | 0.04329946709904028 | 3.680454703418424
23.5627238450671 | 0.04329730217980876 | 3.680270685283745
23.6548594548401 | 0.04329080807155208 | 3.679718686081927
23.746995064613 | 0.04327998672225922 | 3.678798871392034
23.839130674386 | 0.04326484137749637 | 3.677511517087192
23.931266284159 | 0.04324537657878466 | 3.675857009196696
24.0234018939319 | 0.04322159816133055 | 3.673835843713097
24.1155375037049 | 0.04319351325111032 | 3.671448626344378
24.2076731134778 | 0.04316113026131114 | 3.668696072211447
24.2998087232508 | 0.04312445888813052 | 3.665579005491095
24.3919443330238 | 0.04308351010593801 | 3.662098359004731
24.4840799427967 | 0.04303829616180151 | 3.658255173753129
24.5762155525697 | 0.04298883056938257 | 3.654050598397519
24.6683511623427 | 0.04293512810220532 | 3.649485888687452
24.7604867721156 | 0.04287720478630272 | 3.644562406835731
24.8526223818886 | 0.04281507789224589 | 3.6392816208409
24.9447579916615 | 0.04274876592656256 | 3.633645103757817
25.0368936014345 | 0.04267828862254905 | 3.627654532916669
25.1290292112075 | 0.04260366693048419 | 3.621311689091156
25.2211648209804 | 0.04252492300725025 | 3.614618455616271
25.3133004307534 | 0.04244208020536872 | 3.607576817456341
25.4054360405263 | 0.04235516306145938 | 3.600188860224047
25.4975716502993 | 0.04226419728412861 | 3.592456769150932
25.5897072600723 | 0.04216920974129783 | 3.584382828010315
25.6818428698452 | 0.04207022844697868 | 3.575969417993188
25.7739784796182 | 0.04196728254750479 | 3.567219016537907
25.8661140893911 | 0.04186040230723079 | 3.558134196114617
25.9582496991641 | 0.04174961909370575 | 3.548717622964988
26.0503853089371 | 0.04163496536233437 | 3.538972055798422
26.14252091871 | 0.04151647464053375 | 3.528900344445369
26.234656528483 | 0.04139418151139759 | 3.518505428468795
26.3267921382559 | 0.04126812159688022 | 3.507790335734819
26.4189277480289 | 0.04113833154050892 | 3.496758180943258
26.5110633578019 | 0.0410048489896398 | 3.485412164119383
26.6031989675748 | 0.0408677125772664 | 3.473755569067644
26.6953345773478 | 0.04072696190339425 | 3.461791761788512
26.7874701871208 | 0.04058263751599541 | 3.44952418885961
26.8796057968937 | 0.04043478089155336 | 3.436956375782035
26.9717414066667 | 0.04028343441521221 | 3.424091925293038
27.0638770164396 | 0.0401286413605456 | 3.410934515646376
27.1560126262126 | 0.03997044586895431 | 3.397487898861117
27.2481482359856 | 0.03980889292871159 | 3.383755898940485
27.3402838457585 | 0.0396440283536657 | 3.369742410061584
27.4324194555315 | 0.03947589876161563 | 3.355451394737329
27.5245550653044 | 0.03930455155237586 | 3.340886881951948
27.6166906750774 | 0.03913003488554018 | 3.326052965270915
27.7088262848504 | 0.03895239765796476 | 3.310953800927004
27.8009618946233 | 0.03877168948098025 | 3.295593605883322
27.8930975043963 | 0.03858796065734997 | 3.279976655874747
27.9852331141692 | 0.0384012621579907 | 3.26410728342921
28.0773687239422 | 0.03821164559846654 | 3.247989875869656
28.1695043337152 | 0.03801916321527675 | 3.231628873298524
28.2616399434881 | 0.0378238678419478 | 3.215028766565563
28.3537755532611 | 0.03762581288494687 | 3.198194095220484
28.445911163034 | 0.03742505229943437 | 3.181129445451922
28.538046772807 | 0.03722164056486525 | 3.163839448013547
28.63018238258 | 0.03701563266046115 | 3.146328776139198
28.7223179923529 | 0.03680708404056337 | 3.128602143447886
28.8144536021259 | 0.03659605060988398 | 3.110664301840139
28.9065892118989 | 0.0363825886986727 | 3.09252003938718
28.9987248216718 | 0.03616675503781069 | 3.074174178213909
29.0908604314448 | 0.0359486067338487 | 3.055631572377139
29.1829960412177 | 0.03572820124400705 | 3.0368971057406
29.2751316509907 | 0.03550559635114692 | 3.017975689847489
29.3672672607637 | 0.03528085013873504 | 2.998872261792478
29.4594028705366 | 0.03505402096581087 | 2.979591782093924
29.5515384803096 | 0.03482516744197373 | 2.960139232567767
29.6436740900825 | 0.03459434840240693 | 2.940519614204589
29.7358096998555 | 0.03436162288294779 | 2.920737945050562
29.8279453096285 | 0.03412705009522519 | 2.900799258094142
29.9200809194014 | 0.0338906894018732 | 2.880708599159222
30.0122165291744 | 0.03365260029183729 | 2.86047102480617
30.1043521389473 | 0.03341284235579006 | 2.840091600242155
30.1964877487203 | 0.03317147526166391 | 2.819575397241433
30.2886233584933 | 0.03292855873032213 | 2.798927492077381
30.3807589682662 | 0.0326841525113756 | 2.778152963466926
30.4728945780392 | 0.03243831635916106 | 2.75725689052869
30.5650301878121 | 0.03219111000889669 | 2.736244350756219
30.6571657975851 | 0.03194259315302153 | 2.71512041800683
30.7493014073581 | 0.03169282541773923 | 2.693890160507834
30.841437017131 | 0.03144186633977199 | 2.672558638880619
30.933572626904 | 0.03118977534333978 | 2.651130904183882
31.025708236677 | 0.0309366117173791 | 2.629611995977224
31.1178438464499 | 0.03068243459300816 | 2.608006940405694
31.2099794562229 | 0.03042730292125245 | 2.586320748306458
31.3021150659958 | 0.03017127545104464 | 2.564558413338795
31.3942506757688 | 0.02991441070750275 | 2.542724910137734
31.4863862855418 | 0.02965676697050562 | 2.520825192492977
31.5785218953147 | 0.02939840225356907 | 2.498864191553371
31.6706575050877 | 0.02913937428303546 | 2.476846814058014
31.7627931148606 | 0.02887974047758927 | 2.454777940595088
31.8549287246336 | 0.02861955792810109 | 2.432662423888593
31.9470643344066 | 0.02835888337781761 | 2.410505087114497
32.0391999441795 | 0.02809777320289926 | 2.388310722246437
32.1313355539525 | 0.02783628339331679 | 2.366084088431927
32.2234711637254 | 0.02757446953411796 | 2.343829910400026
32.3156067734984 | 0.02731238678706464 | 2.321552876900494
32.4077423832714 | 0.02705008987265693 | 2.299257639175839
32.4998779930443 | 0.02678763305254356 | 2.276948809466202
32.5920136028173 | 0.02652507011232908 | 2.254630959547971
32.6841492125902 | 0.02626245434478634 | 2.232308619306838
32.7762848223632 | 0.02599983853347369 | 2.209986275345264
32.8684204321362 | 0.0257372749367714 | 2.187668369625569
32.9605560419091 | 0.02547481527233492 | 2.165359298148468
33.0526916516821 | 0.02521251070197367 | 2.143063409667762
33.1448272614551 | 0.02495041181696225 | 2.120785004441792
33.236962871228 | 0.02468856862378314 | 2.098528333021567
33.329098481001 | 0.02442703053030821 | 2.076297595076197
33.4212340907739 | 0.02416584633242457 | 2.054096938256089
33.5133697005469 | 0.02390506420110209 | 2.031930457093677
33.6055053103199 | 0.02364473166991309 | 2.009802191942613
33.6976409200928 | 0.02338489562300043 | 1.987716127955037
33.7897765298658 | 0.02312560228349905 | 1.965676194097419
33.8819121396387 | 0.02286689720241534 | 1.943686262205304
33.9740477494117 | 0.02260882524795959 | 1.921750146076565
34.0661833591847 | 0.02235143059534065 | 1.899871600603956
34.1583189689576 | 0.02209475671701703 | 1.878054320946447
34.2504545787306 | 0.02183884637340795 | 1.856301941739676
34.3425901885035 | 0.02158374160406721 | 1.834618036345713
34.4347257982765 | 0.02132948371931308 | 1.813006116141612
34.5268614080495 | 0.02107611329232216 | 1.791469629847384
34.6189970178224 | 0.02082367015167941 | 1.77001196289275
34.7111326275954 | 0.02057219337438673 | 1.748636436822872
34.8032682373683 | 0.02032172127933076 | 1.727346308743115
34.8954038471413 | 0.02007229142120226 | 1.706144770802192
34.9875394569143 | 0.01982394058487277 | 1.685034949714185
35.0796750666872 | 0.01957670478021989 | 1.66401990631869
35.1718106764602 | 0.01933061923740157 | 1.643102635179133
35.2639462862332 | 0.01908571840257859 | 1.62228606421918
35.3560818960061 | 0.01884203593407803 | 1.601573054396632
35.4482175057791 | 0.01859960469899632 | 1.580966399414688
35.540353115552 | 0.01835845677024124 | 1.560468825470506
35.632488725325 | 0.01811862342400253 | 1.540082991040215
35.724624335098 | 0.01788013513765454 | 1.519811486700636
35.8167599448709 | 0.01764302158808074 | 1.499656834986863
35.9088955546439 | 0.01740731165041746 | 1.479621490285484
36.0010311644168 | 0.017173033397215 | 1.459707838763275
36.0931667741898 | 0.01694021409800497 | 1.439918198330423
36.1853023839628 | 0.01670888021927553 | 1.42025481863842
36.2774379937357 | 0.01647905742484365 | 1.40071988111171
36.3695736035087 | 0.01625077057662062 | 1.381315499012753
36.4617092132816 | 0.01602404373576773 | 1.362043717540257
36.5538448230546 | 0.01579890016423002 | 1.342906513959552
36.6459804328276 | 0.01557536232664895 | 1.323905797765161
36.7381160426005 | 0.01535345189264189 | 1.30504341087456
36.8302516523735 | 0.015133189739444 | 1.28632112785274
36.9223872621464 | 0.01491459595490834 | 1.267740656167209
37.0145228719194 | 0.01469768984085147 | 1.249303636472375
37.1066584816924 | 0.01448248991674442 | 1.231011642923276
37.1987940914653 | 0.0142690139237362 | 1.212866183517577
37.2909297012383 | 0.01405727882900494 | 1.19486870046542
37.3830653110112 | 0.01384730083043132 | 1.177020570586662
37.4752009207842 | 0.01363909536158148 | 1.159323105734426
37.5673365305572 | 0.01343267709699819 | 1.141777553244846
37.6594721403301 | 0.01322805995778721 | 1.124385096411913
37.7516077501031 | 0.01302525711749329 | 1.10714685498693
37.8437433598761 | 0.01282428100825962 | 1.090063885702068
37.935878969649 | 0.01262514332725928 | 1.073137182817039
38.028014579422 | 0.0124278550433922 | 1.056367678688337
38.1201501891949 | 0.01223242640424197 | 1.039756244360567
38.2122857989679 | 0.01203886694327892 | 1.023303690178708
38.3044214087409 | 0.01184718548730756 | 1.007010766421143
38.3965570185138 | 0.01165739016414515 | 0.9908781639523379
38.4886926282868 | 0.01146948841052492 | 0.9749065148946184
38.5808282380597 | 0.01128348698021787 | 0.9590963933185189
38.6729638478327 | 0.01109939195235985 | 0.9434483159505876
38.7650994576057 | 0.01091720873998144 | 0.9279627428984224
38.8572350673786 | 0.01073694209872747 | 0.9126400783918353
38.9493706771516 | 0.01055859613575985 | 0.8974806715395869
39.0415062869246 | 0.01038217431883698 | 0.882484817101143
39.1336418966975 | 0.01020767948555833 | 0.867652756272458
39.2257775064705 | 0.01003511385276718 | 0.8529846774852101
39.3179131162434 | 0.009864479026105596 | 0.8384807172189757
39.4100487260164 | 0.0096957760097085 | 0.8241409608252225
39.5021843357894 | 0.009529005216034217 | 0.8099654433629084
39.5943199455623 | 0.009364166475819061 | 0.7959541504446203
39.6864555553353 | 0.009201259048149281 | 0.7821070190926889
39.7785911651082 | 0.009040281630644622 | 0.7684239386047929
39.8707267748812 | 0.008881232369740696 | 0.7549047514279591
39.9628623846542 | 0.008724108871067749 | 0.7415492540407587
40.0549979944271 | 0.008568908209913758 | 0.7283571978426695
40.1471336042001 | 0.008415626941765548 | 0.7153282900500716
40.239269213973 | 0.008264261112922347 | 0.7024621945983995
40.331404823746 | 0.008114806271169693 | 0.6897585330494239
40.423540433519 | 0.007967257476511334 | 0.6772168855034634
40.5156760432919 | 0.007821609311947739 | 0.6648367915155577
40.6078116530649 | 0.007677855894295329 | 0.6526177510151029
40.6999472628378 | 0.007535990885041114 | 0.6405592252284946
40.7920828726108 | 0.007396007501221519 | 0.6286606376038291
40.8842184823838 | 0.007257898526323147 | 0.6169213747374674
40.9763540921567 | 0.007121656321194978 | 0.6053407873015731
41.0684897019297 | 0.006987272834966492 | 0.5939181909721518
41.1606253117027 | 0.006854739615966775 | 0.5826528673571759
41.2527609214756 | 0.006724047822635199 | 0.5715440649239919
41.3448965312486 | 0.006595188234418817 | 0.5605909999255995
41.4370321410215 | 0.006468151262651646 | 0.54979285732539
41.5291677507945 | 0.006342926961406101 | 0.5391487917195186
41.6213033605675 | 0.006219505038315021 | 0.5286579282567767
41.7134389703404 | 0.006097874865354775 | 0.518319363555156
41.8055745801134 | 0.005978025489585318 | 0.508132166614752
41.8977101898863 | 0.005859945643842959 | 0.4980953797266515
41.9898457996593 | 0.005743623757376998 | 0.4882080193770448
42.0819814094323 | 0.005629047966429123 | 0.4784690771464755
42.1741170192052 | 0.005516206124746998 | 0.4688775206034949
42.2662526289782 | 0.005405085814028511 | 0.4594322941924234
42.3583882387511 | 0.005295674354293087 | 0.4501323201149124
42.4505238485241 | 0.005187958814172201 | 0.4409764992046371
42.5426594582971 | 0.005081926021118391 | 0.4319637117950632
42.63479506807 | 0.004977562571525229 | 0.4230928185796444
42.726930677843 | 0.004874854840755324 | 0.4143626614642025
42.8190662876159 | 0.004773788993073432 | 0.4057720644112417
42.9112018973889 | 0.004674350991477794 | 0.3973198342756125
43.0033375071619 | 0.004576526607429455 | 0.3890047616315037
43.0954731169348 | 0.004480301430473011 | 0.3808256215902059
43.1876087267078 | 0.004385660877746525 | 0.3727811746084547
43.2797443364807 | 0.004292590203378327 | 0.3648701672871578
43.3718799462537 | 0.004201074507764789 | 0.3570913331600071
43.4640155560267 | 0.004111098746729366 | 0.349443393471996
43.5561511657996 | 0.004022647740557203 | 0.3419250579473623
43.6482867755726 | 0.003935706182903813 | 0.3345350255468241
43.7404223853456 | 0.003850258649576025 | 0.3272719852139621
43.8325579951185 | 0.003766289607180963 | 0.3201346166103818
43.9246936048915 | 0.003683783421641715 | 0.3131215908395458
44.0168292146644 | 0.003602724366578434 | 0.3062315711591669
44.1089648244374 | 0.003523096631550484 | 0.2994632136817911
44.2011004342104 | 0.0034448843301606 | 0.292815168063651
44.2932360439833 | 0.003368071508016958 | 0.2862860781814414
44.3853716537563 | 0.003292642150552513 | 0.2798745827969636
44.4775072635292 | 0.00321858019070101 | 0.2735793162095858
44.5696428733022 | 0.003145869516426105 | 0.267398908896219
44.6617784830752 | 0.003074493978105033 | 0.2613319881389278
44.7539140928481 | 0.003004437395763558 | 0.2553771786399024
44.8460497026211 | 0.002935683566162165 | 0.249533103123784
44.938185312394 | 0.002868216269733414 | 0.2437983829273402
45.030320922167 | 0.002802019277367785 | 0.2381716385762618
45.12245653194 | 0.002737076357049788 | 0.232651490349232
45.2145921417129 | 0.002673371280341898 | 0.2272365588290613
45.3067277514859 | 0.002610887828716799 | 0.2219254654409279
45.3988633612588 | 0.002549609799738378 | 0.2167168329777621
45.4909989710318 | 0.002489521013089527 | 0.2116092861126098
45.5831345808048 | 0.002430605316448928 | 0.2066014518981589
45.6752701905777 | 0.002372846591215061 | 0.2016919602532802
45.7674058003507 | 0.002316228758078419 | 0.1968794444366656
45.8595414101237 | 0.002260735782442756 | 0.1921625415076343
45.9516770198966 | 0.002206351679694561 | 0.1875398927740377
46.0438126296696 | 0.002153060520321911 | 0.1830101442273624
46.1359482394425 | 0.002100846434883773 | 0.1785719469651207
46.2280838492155 | 0.002049693618829007 | 0.1742239576004656
46.3202194589885 | 0.001999586337167561 | 0.1699648386592427
46.4123550687614 | 0.001950508928993201 | 0.1657932589644221
46.5044906785344 | 0.00190244581185939 | 0.1617078940080481
46.5966262883073 | 0.001855381486009718 | 0.1577074263108261
46.6887618980803 | 0.001809300538462696 | 0.1537905457693292
46.7808975078533 | 0.001764187646953652 | 0.1499559499910604
46.8730331176262 | 0.001720027583733577 | 0.146202344617354
46.9651687273992 | 0.001676805219226832 | 0.1425284436342807
47.0573043371721 | 0.001634505525549457 | 0.1389329696717038
47.1494399469451 | 0.001593113579888344 | 0.1354146542905093
47.2415755567181 | 0.001552614567744184 | 0.1319722382582557
47.333711166491 | 0.00151299378603848 | 0.1286044718132708
47.425846776264 | 0.001474236646086805 | 0.1253101149173785
47.5179823860369 | 0.001436328676440253 | 0.1220879374974215
47.6101179958099 | 0.001399255525595762 | 0.1189367196756398
47.7022536055829 | 0.001363002964578334 | 0.1158552519891584
47.7943892153558 | 0.001327556889395808 | 0.1128423355986437
47.8865248251288 | 0.001292903323368546 | 0.1098967824863264
47.9786604349018 | 0.00125902841933613 | 0.107017415643571
48.0707960446747 | 0.001225918461742322 | 0.1042030692480974
48.1629316544477 | 0.001193559868600609 | 0.1014525888310518
48.2550672642206 | 0.001161939193342574 | 0.0987648314341188
48.3472028739936 | 0.001131043126550248 | 0.09613866575677109
48.4393384837666 | 0.001100858497575531 | 0.09357297229392011
48.5314740935395 | 0.001071372276047805 | 0.0910666434640634
48.6236097033125 | 0.001042571573272238 | 0.08861858372814022
48.7157453130854 | 0.00101444364352111 | 0.08622770969929439
48.8078809228584 | 0.0009869758852195185 | 0.08389295024365907
48.9000165326314 | 0.0009601558420285275 | 0.08161324657242483
48.9921521424043 | 0.0009339712038270883 | 0.07938755232530251
49.0842877521773 | 0.0009084098075952628 | 0.07721483364559734
49.1764233619502 | 0.0008834596382011162 | 0.07509406924709487
49.2685589717232 | 0.0008591088290927796 | 0.07302425047288627
49.3606945814962 | 0.0008353456628987061 | 0.07100438134639002
49.4528301912691 | 0.0008121585719375602 | 0.06903347861469263
49.5449658010421 | 0.0007895361386402662 | 0.06711057178442263
49.637101410815 | 0.0007674670958865827 | 0.06523470315035954
49.729237020588 | 0.0007459403272577855 | 0.06340492781691176
49.821372630361 | 0.0007249448672083972 | 0.06162031371271376
49.9135082401339 | 0.0007044699011584637 | 0.05987994159846941
50.0056438499069 | 0.0006845047655088698 | 0.05818290506825393
50.0977794596799 | 0.0006650389475819845 | 0.05652831054446868
50.1899150694528 | 0.0006460620854894055 | 0.05491527726659946
50.2820506792258 | 0.0006275639679291681 | 0.05334293727397928
50.3741862889987 | 0.0006095345339147038 | 0.05181043538274982
50.4663218987717 | 0.0005919638724371913 | 0.05031692915716126
50.5584575085447 | 0.0005748422220639735 | 0.04886158887543775
50.6505931183176 | 0.000558159970474634 | 0.04744359749034389
50.7427287280906 | 0.0005419076539370203 | 0.04606215058464673
50.8348643378635 | 0.0005260759567254027 | 0.04471645632165923
50.9269999476365 | 0.0005106557104823774 | 0.04340573539100208
51.0191355574095 | 0.0004956378935270393 | 0.04212922094979834