ABCDEFGHIJKLMNOPQRSTUVWXYZ
1
Example to generate standard deviation "errors" numerically with a spreadsheet.
2
Formula: suppose we have a formula F = - a v - (1/2) k v^2 or so, we know a, k, v and we want to know F.
3
Analytically this is hard to calculate because v correlates with v^2. Instead we just simulate a bunch of applications of this formula to "plausible" data
4
5
INPUTS:Raw inputErrorOUTPUTS
6
a=15.20.1F = 628.2
7
k=0.12500.00950Error of F:93.3
8
v=36.04.0
9
10
RANDOM COLUMNS---->
---->|
Add normal "noise" to each parameter:
Calculate the result:
11
Seed 1Seed 2Seed 3Seed 4Gaussian 1Gaussian 2Gaussian 3Gaussian 4Randomized aRandomized kRandomized vCalculated F
12
[First row left with 0 deviations, rest filled with Box-Muller] ---
000015.200000000.1250000036.00000000628.2
13
0.67219485490.52611821370.98405025640.6574525313-0.8793243547-0.14561152-0.09849693438-0.149849835515.112067560.1166464232.48270258552.4191287
14
0.016172311710.69355308980.57521900270.3414442736-0.9974128656-2.693339355-0.5715472810.882803816415.100258710.1155245832.01034854542.5513908
15
0.33431058380.75977341450.28208802770.46672811710.09084709021-1.477537295-1.5562962450.330172988715.209084710.1258630536.36338836636.2679567
16
0.61621255290.81692697970.26544506190.29451650150.4017132579-0.8983056839-0.44964197441.56541268115.240171330.1288162837.60685303664.225728
17
0.53799236410.32265633230.66408296130.8461325741-0.49084228710.99944768410.5138959203-0.744719661615.150915770.1203370034.03663085585.3908665
18
0.72162144180.098086687650.80809654510.47483092070.6591686390.4669110176-0.6446538260.102805286115.265916860.1312621038.63667456687.7978103
19
0.32556680830.60770792230.80131086820.9661204829-1.167956731-0.93821759410.6505684105-0.140617770215.083204330.1139044131.32817307528.42523
20
0.11138071730.20053967370.56174495710.7020144720.64067282751.994778296-0.3189209299-1.0255262715.264067280.1310863938.56269131686.0915667
21
0.73246763140.9291052520.10373392780.46319704090.7120951579-0.3399893271-2.0721520480.487891360315.271209520.1317649038.84838063692.6913377
22
0.13633744670.49704752890.24189034440.6894648331-1.9959642210.03703122616-0.6254790816-1.56439044815.000403580.1060383428.01614312461.8684266
23
0.33761980970.037716706730.44100317390.8073333111.4324715520.34596955450.4510566718-1.19747830515.343247160.1386084841.72988621760.9572109
24
0.58449232990.13103504740.54674591450.64174774970.7045029570.7600650136-0.6911138386-0.854344102715.270450300.1316927838.81801183691.9883642
25
0.89535012890.945833570.059319204480.09833766910.4432230688-0.15695277871.9374381581.37694507115.244322310.1292106237.77289228668.0004438
26
0.7834066350.76776464340.71418088280.48876772760.07782804095-0.6943699106-0.81846829770.0578590415915.207782800.1257393736.31131216635.1089422
27
0.60732027710.19610081740.75443992730.081830177790.33178962950.94197325710.65364633290.369196042715.233178960.1281520037.32715852657.8894518
28
0.83092808280.10565716710.17912147160.33041123030.47936350480.3750129224-0.89763587731.62284688515.247936350.1295539537.91745402671.2949431
29
0.58329231260.63854480320.98364055890.79328349-0.6691451153-0.79396376730.04878912676-0.174954536315.133085490.1186431233.32341954570.1598009
30
0.033535051440.93425306910.50753337380.14746688482.386625486-1.0461103870.69946699660.931198979215.438662550.1476729445.54650194856.3496397
31
0.32312558780.22352272980.78670619340.049099048440.2489128111.4823868730.65997571460.210316205215.224891280.1273646736.99565124650.4153936
32
0.39470912790.59280227430.8708060950.8302212695-1.138224038-0.75077185610.2540411362-0.460581156515.086177600.1141868731.44710385530.8774535
33
0.74352365240.18843356890.096078043240.26176289210.29044165720.7129888122-0.15983139122.15862059215.229044170.1277592037.16176663654.1557118
34
0.83094028040.27128851040.58374662460.347906866-0.081163676750.6031642897-0.59878330840.84736949115.191883630.1242289535.67534529621.0306631
35
0.06408461340.55138766590.28521494170.844779678-2.223031304-0.74379687430.8885200269-1.31131863614.977696870.1038812027.10787478444.1814005
36
0.90043985140.32590751660.95441594390.645961225-0.21024106020.4068691671-0.1857630395-0.242494326615.178975890.1230027135.15903576609.7035356
37
0.27866572330.84311883210.99632755130.95344935750.8828499468-1.3326892550.08213808498-0.0247336273315.288284990.1333870739.53139979708.5914023
38
0.36270651080.97882199650.63177379170.032788922451.411601851-0.18895178890.9380904880.196045870315.341160190.1384102241.64640740758.9351568
39
0.56858489650.15474218970.34628008340.96888611010.59871664420.87792235721.428629093-0.282902099515.259871660.1306878138.39486658682.2284838
40
0.20220323410.71572975460.2377333130.275469532-0.38203637-1.746714678-0.27010297571.67339652115.161796360.1213706534.47185452594.7681441
41
0.79050695420.57714919510.30313691240.04236559159-0.6066891136-0.31951521041.4906213290.406435101515.139331090.1192364533.57324355575.4758901
42
0.6561303950.86585245080.73708518640.93982297720.6107882424-0.68536792810.7259200533-0.2883464815.261078820.1308024938.44315297683.3389175
43
0.59888416370.0096454555630.20419597590.070634332561.0107485890.061330699051.6098276430.765379069515.301074860.1346021140.04299436720.6141531
44
0.79731547930.18194821040.33827874440.21274653130.2790989190.61246508760.34149171151.43218486315.227909890.1276514437.11639568653.1331529
45
0.17354413420.75075787470.22615229650.64385384770.008911972259-1.871514694-1.066598884-1.35479152515.200891200.1250846636.03564789628.9894285
46
0.80440601740.37056919050.78981279660.2652218718-0.45336382870.4793365415-0.065602318870.683823801515.154663620.1206930434.18654469588.6137621
47
0.32858042290.71097593350.8741577990.09814276588-0.3621674266-1.4473361950.42311833030.299932695315.163783260.1215594134.55133029596.4873565
48
0.87179164220.045845415440.50368933660.337426160.50225802980.1488170813-0.611460590.998852912215.250225800.1297714538.00903212673.3858557
49
0.71835540850.041679019880.81199429920.69410302310.78564522640.2105783633-0.2220357205-0.605990146815.278564520.1324636339.14258091699.5189693
50
0.8930665720.28752315240.71483730710.04066315867-0.11109215540.46243576560.79279177050.207079255615.188890780.1239446235.55563138618.3961801
51
0.24755823520.32089490780.27148994470.8392814551-0.71996464061.5079356010.8591022007-1.36733454615.128003540.1181603433.12014144565.8492389
52
0.41956932110.12289038320.79256807190.71517909860.94421854360.9195131218-0.1479975273-0.66562038415.294421850.1339700839.77687417714.3480021
53
0.78037718890.61721786620.84494064250.9623555515-0.5217181352-0.47303909840.5643354612-0.136026785815.147828190.1200436833.91312746582.7413577
54
0.72792180380.77277972180.22904801470.10228920450.1136772264-0.78879704991.3743197991.02902494815.211367720.1260799336.45470891638.3026816
55
0.052581189040.038695230840.24703190490.24420317812.3557133320.58430162650.060894674351.67115750315.435571330.1473792845.42285333853.1667782
56
0.10898304370.3073693550.81566335710.5806847097-0.74262391231.970186709-0.5580733953-0.309937427415.125737610.1179450733.02950435563.9315961
57
0.87141527150.11240209160.028100983090.60830030490.39916787810.3404971153-2.077510794-1.68162134215.239916790.1287920937.59667151663.9945836
58
0.14979976110.55445198620.10932703320.980511139-1.835630666-0.65373669342.088247154-0.256996098915.016436930.1075615128.65747734474.5006998
59
0.37158356980.20952220460.70216472190.69059779940.35402437951.361847904-0.3066304457-0.783040408615.235402440.1283632337.41609752659.9012776
60
0.95767681570.25077879060.71868405940.6781286525-0.0014390680470.2940879989-0.3547028296-0.731336291815.199856090.1249863335.99424373628.0725676
61
0.23922840370.48492306520.12272619470.5457907374-1.6837690080.1599842691-1.964121549-0.58122755615.031623100.1090041929.26492397486.576853
62
0.062222028780.78870844640.88937858920.64582817720.5675473524-2.287352698-0.2947841013-0.384144351315.256754740.1303917038.27018941679.3652176
63
0.45584721440.52246065740.57684317880.5294691112-1.241011783-0.1763091546-1.031054585-0.19312202115.075898820.1132103931.03595287522.4187273
64
0.4210880870.70151614120.72574990150.1937538851-0.3944938441-1.25467170.27711308020.751204342615.160550620.1212523134.42202462593.6913083
65
0.61478027410.22870928970.18130284830.6289093020.13156066230.9775850336-1.274258115-1.33844654715.213156070.1262498336.52624265639.8985682
66
0.29521215010.67029456930.49434567030.8085685067-0.7500072804-1.3702595140.4270305908-1.10755831115.124999270.1178749332.99997088563.3073221
67
0.16663166380.98774062070.040132271350.83224077111.887515943-0.14567972191.252879234-2.20486793715.388751590.1429314043.55006377805.7235369
68
0.19983142680.19547433190.35642318310.23081312280.60286158621.69030180.17274681371.42598443715.260286160.1307271938.41144634682.6096703
69
0.82726330230.74535653990.87434173330.3375334361-0.0179651591-0.6155824538-0.27087009240.441811446415.198203480.1248293335.92813936626.6099703
70
0.081756640350.73180255660.56922551680.3894037046-0.2553150655-2.223247784-0.81542228850.679737935115.174468490.1225745134.97873974605.7694884
71
0.6814597470.42832148610.65512886320.2492562102-0.78847622610.38123671230.0042980785510.919689173815.121152380.1175094832.84609510560.0592959
72
0.92775563540.56546558110.37946228960.149340652-0.3549623659-0.15484033180.82292682781.12284974415.164503760.1216278634.58015054597.1113169
73
0.41375656880.89627293580.18127607650.20693997641.056212489-0.80583505150.49393285041.78087017815.305621250.1350340240.22484996724.9114424
74
0.23300892540.74736942430.16041647670.8526839526-0.02821030371-1.7066227521.150433315-1.52855059515.197178970.1247320035.88715879625.7040095
75
0.35014211230.77287271470.63878250010.28524502590.2074867982-1.433799697-0.20795477440.923654333415.220748680.1269711236.82994719646.6940443
76
0.91514323620.17197106540.67288364380.12148229130.19829447330.37152209770.6431876470.615366039915.219829450.1268838036.79317789645.8695977
77
0.1833863560.8882788910.39264391780.71961832321.406372064-1.189301413-0.2594401659-1.34253308315.340637210.1383605341.62548826758.4288675
78
0.064146577780.29417876660.96929870480.3260859612-0.64226357882.2540334-0.11489050270.221731999915.135773640.1188985033.43094568572.4453784
79
0.04175822750.39517627130.59201216060.09908603917-1.9931067721.5424794840.831828620.597090740415.000689320.1060654928.02757291462.0925114
80
0.29046671050.84853337430.42261300830.93769231770.9124887295-1.2805846031.213176991-0.500797738215.291248870.1336686439.64995492711.3688301
81
0.93511721740.68153547430.45373654690.7573454187-0.1527530696-0.33291632930.05800111388-1.25583157915.184724690.1235488535.38898772614.7371154
82
0.74486250940.31908631350.61257167930.8177620548-0.32280854570.69635185110.4089007182-0.901653389415.167719150.1219333234.70876582599.8992503
83
0.14119352930.10923478050.23664856370.14320535061.530659921.2539249461.0556237941.32966784915.353065990.1395412742.12263968770.5068741
84
0.20931093790.30217808740.51095351540.4399262198-0.56948778141.674381214-1.0772816250.427103760715.143051220.1195898733.72204887578.6521109
85
0.17380826090.051057251180.16915243410.99770806241.7752840410.58989121451.884986215-0.0271469384515.377528400.1418652043.10113617794.5609983
86
0.026791181250.50788587680.19614170950.3861229166-2.687304703-0.1332607881-1.3622990581.18405110614.931269530.0994706125.25078119408.7375457
87
0.077465272570.19987621060.7631140320.5722051780.70061519262.150578859-0.6609358225-0.322272325815.270061520.1316558438.80246077691.6285208
88
0.28051715810.11257252640.52129220140.95502916721.2119501281.0360587141.096177574-0.31825119215.321195010.1365135340.84780051739.7264486
89
0.72092738110.28169860770.68320434910.8316415842-0.16005816140.79297863650.4283810724-0.760534153315.183994180.1234794535.35976735614.0964902
90
0.23474114790.86117599180.037672924190.8175825591.094884559-1.3037528691.05501093-2.3333622115.309488460.1354014040.37953823728.5765497
91
0.89595288680.045404430250.36638553620.37082729060.44981242520.1319230092-0.97541994271.02795631215.244981240.1292732237.79924970668.6005588
92
0.99729807720.53319840690.51691251470.754839648-0.07196604697-0.015233099990.03492808165-1.14827840815.192803400.1243163235.71213581621.8412822
93
0.5743244920.23138506680.95288507440.47718586750.12289671311.045953081-0.30749337410.0443821717815.212289670.1261675236.49158685639.1251892
94
0.99942556430.64348450610.55748569850.2240393079-0.02103158842-0.026587099620.17555303831.06668551515.197896840.1248002035.91587365626.3387503
95
0.92278077450.47185237860.42766861840.5781126804-0.39465440260.07053421858-1.14953078-0.614322605315.160534560.1212507834.42138239593.6774349
96
0.75502041890.013637151530.63947568560.87909846370.74693023110.064157619540.68565571-0.651221626315.274693020.1320958438.98772092695.9211044
97
0.23572167490.15849434760.63810457210.9695432550.92447660031.4267270380.9305922702-0.180289301915.292447660.1337825339.69790640712.4936887
98
0.45645275370.79125249880.19830642140.98456161580.3209993374-1.2105782041.790399752-0.174219545315.232099930.1280494937.28399735656.9141474
99
0.011984818450.96765276290.58534297740.81762667912.913371174-0.60041445590.4266460663-0.942914507815.491337120.1526770347.65348470911.5698601
100
0.98754500830.73413535590.61667883650.6230736033-0.01575566836-0.1575378347-0.70363911-0.686808439515.198424430.1248503235.93697733626.8054279