Example of generating error bars

	B	C	D	E	F	G	H	I	J	K	L	M
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 input	Error				OUTPUTS
6	a=	15.2	0.1				F =	628.2
7	k=	0.1250	0.00950				Error of F:	93.3
8	v=	36.0	4.0
9
10	RANDOM COLUMNS---->							---->\|	Add normal "noise" to each parameter:			Calculate the result:
11	Seed 1	Seed 2	Seed 3	Seed 4	Gaussian 1	Gaussian 2	Gaussian 3	Gaussian 4	Randomized a	Randomized k	Randomized v	Calculated F
12	[First row left with 0 deviations, rest filled with Box-Muller] ---				0	0	0	0	15.20000000	0.12500000	36.00000000	628.2
13	0.6721948549	0.5261182137	0.9840502564	0.6574525313	-0.8793243547	-0.14561152	-0.09849693438	-0.1498498355	15.11206756	0.11664642	32.48270258	552.4191287
14	0.01617231171	0.6935530898	0.5752190027	0.3414442736	-0.9974128656	-2.693339355	-0.571547281	0.8828038164	15.10025871	0.11552458	32.01034854	542.5513908
15	0.3343105838	0.7597734145	0.2820880277	0.4667281171	0.09084709021	-1.477537295	-1.556296245	0.3301729887	15.20908471	0.12586305	36.36338836	636.2679567
16	0.6162125529	0.8169269797	0.2654450619	0.2945165015	0.4017132579	-0.8983056839	-0.4496419744	1.565412681	15.24017133	0.12881628	37.60685303	664.225728
17	0.5379923641	0.3226563323	0.6640829613	0.8461325741	-0.4908422871	0.9994476841	0.5138959203	-0.7447196616	15.15091577	0.12033700	34.03663085	585.3908665
18	0.7216214418	0.09808668765	0.8080965451	0.4748309207	0.659168639	0.4669110176	-0.644653826	0.1028052861	15.26591686	0.13126210	38.63667456	687.7978103
19	0.3255668083	0.6077079223	0.8013108682	0.9661204829	-1.167956731	-0.9382175941	0.6505684105	-0.1406177702	15.08320433	0.11390441	31.32817307	528.42523
20	0.1113807173	0.2005396737	0.5617449571	0.702014472	0.6406728275	1.994778296	-0.3189209299	-1.02552627	15.26406728	0.13108639	38.56269131	686.0915667
21	0.7324676314	0.929105252	0.1037339278	0.4631970409	0.7120951579	-0.3399893271	-2.072152048	0.4878913603	15.27120952	0.13176490	38.84838063	692.6913377
22	0.1363374467	0.4970475289	0.2418903444	0.6894648331	-1.995964221	0.03703122616	-0.6254790816	-1.564390448	15.00040358	0.10603834	28.01614312	461.8684266
23	0.3376198097	0.03771670673	0.4410031739	0.807333311	1.432471552	0.3459695545	0.4510566718	-1.197478305	15.34324716	0.13860848	41.72988621	760.9572109
24	0.5844923299	0.1310350474	0.5467459145	0.6417477497	0.704502957	0.7600650136	-0.6911138386	-0.8543441027	15.27045030	0.13169278	38.81801183	691.9883642
25	0.8953501289	0.94583357	0.05931920448	0.0983376691	0.4432230688	-0.1569527787	1.937438158	1.376945071	15.24432231	0.12921062	37.77289228	668.0004438
26	0.783406635	0.7677646434	0.7141808828	0.4887677276	0.07782804095	-0.6943699106	-0.8184682977	0.05785904159	15.20778280	0.12573937	36.31131216	635.1089422
27	0.6073202771	0.1961008174	0.7544399273	0.08183017779	0.3317896295	0.9419732571	0.6536463329	0.3691960427	15.23317896	0.12815200	37.32715852	657.8894518
28	0.8309280828	0.1056571671	0.1791214716	0.3304112303	0.4793635048	0.3750129224	-0.8976358773	1.622846885	15.24793635	0.12955395	37.91745402	671.2949431
29	0.5832923126	0.6385448032	0.9836405589	0.79328349	-0.6691451153	-0.7939637673	0.04878912676	-0.1749545363	15.13308549	0.11864312	33.32341954	570.1598009
30	0.03353505144	0.9342530691	0.5075333738	0.1474668848	2.386625486	-1.046110387	0.6994669966	0.9311989792	15.43866255	0.14767294	45.54650194	856.3496397
31	0.3231255878	0.2235227298	0.7867061934	0.04909904844	0.248912811	1.482386873	0.6599757146	0.2103162052	15.22489128	0.12736467	36.99565124	650.4153936
32	0.3947091279	0.5928022743	0.870806095	0.8302212695	-1.138224038	-0.7507718561	0.2540411362	-0.4605811565	15.08617760	0.11418687	31.44710385	530.8774535
33	0.7435236524	0.1884335689	0.09607804324	0.2617628921	0.2904416572	0.7129888122	-0.1598313912	2.158620592	15.22904417	0.12775920	37.16176663	654.1557118
34	0.8309402804	0.2712885104	0.5837466246	0.347906866	-0.08116367675	0.6031642897	-0.5987833084	0.847369491	15.19188363	0.12422895	35.67534529	621.0306631
35	0.0640846134	0.5513876659	0.2852149417	0.844779678	-2.223031304	-0.7437968743	0.8885200269	-1.311318636	14.97769687	0.10388120	27.10787478	444.1814005
36	0.9004398514	0.3259075166	0.9544159439	0.645961225	-0.2102410602	0.4068691671	-0.1857630395	-0.2424943266	15.17897589	0.12300271	35.15903576	609.7035356
37	0.2786657233	0.8431188321	0.9963275513	0.9534493575	0.8828499468	-1.332689255	0.08213808498	-0.02473362733	15.28828499	0.13338707	39.53139979	708.5914023
38	0.3627065108	0.9788219965	0.6317737917	0.03278892245	1.411601851	-0.1889517889	0.938090488	0.1960458703	15.34116019	0.13841022	41.64640740	758.9351568
39	0.5685848965	0.1547421897	0.3462800834	0.9688861101	0.5987166442	0.8779223572	1.428629093	-0.2829020995	15.25987166	0.13068781	38.39486658	682.2284838
40	0.2022032341	0.7157297546	0.237733313	0.275469532	-0.38203637	-1.746714678	-0.2701029757	1.673396521	15.16179636	0.12137065	34.47185452	594.7681441
41	0.7905069542	0.5771491951	0.3031369124	0.04236559159	-0.6066891136	-0.3195152104	1.490621329	0.4064351015	15.13933109	0.11923645	33.57324355	575.4758901
42	0.656130395	0.8658524508	0.7370851864	0.9398229772	0.6107882424	-0.6853679281	0.7259200533	-0.28834648	15.26107882	0.13080249	38.44315297	683.3389175
43	0.5988841637	0.009645455563	0.2041959759	0.07063433256	1.010748589	0.06133069905	1.609827643	0.7653790695	15.30107486	0.13460211	40.04299436	720.6141531
44	0.7973154793	0.1819482104	0.3382787444	0.2127465313	0.279098919	0.6124650876	0.3414917115	1.432184863	15.22790989	0.12765144	37.11639568	653.1331529
45	0.1735441342	0.7507578747	0.2261522965	0.6438538477	0.008911972259	-1.871514694	-1.066598884	-1.354791525	15.20089120	0.12508466	36.03564789	628.9894285
46	0.8044060174	0.3705691905	0.7898127966	0.2652218718	-0.4533638287	0.4793365415	-0.06560231887	0.6838238015	15.15466362	0.12069304	34.18654469	588.6137621
47	0.3285804229	0.7109759335	0.874157799	0.09814276588	-0.3621674266	-1.447336195	0.4231183303	0.2999326953	15.16378326	0.12155941	34.55133029	596.4873565
48	0.8717916422	0.04584541544	0.5036893366	0.33742616	0.5022580298	0.1488170813	-0.61146059	0.9988529122	15.25022580	0.12977145	38.00903212	673.3858557
49	0.7183554085	0.04167901988	0.8119942992	0.6941030231	0.7856452264	0.2105783633	-0.2220357205	-0.6059901468	15.27856452	0.13246363	39.14258091	699.5189693
50	0.893066572	0.2875231524	0.7148373071	0.04066315867	-0.1110921554	0.4624357656	0.7927917705	0.2070792556	15.18889078	0.12394462	35.55563138	618.3961801
51	0.2475582352	0.3208949078	0.2714899447	0.8392814551	-0.7199646406	1.507935601	0.8591022007	-1.367334546	15.12800354	0.11816034	33.12014144	565.8492389
52	0.4195693211	0.1228903832	0.7925680719	0.7151790986	0.9442185436	0.9195131218	-0.1479975273	-0.665620384	15.29442185	0.13397008	39.77687417	714.3480021
53	0.7803771889	0.6172178662	0.8449406425	0.9623555515	-0.5217181352	-0.4730390984	0.5643354612	-0.1360267858	15.14782819	0.12004368	33.91312746	582.7413577
54	0.7279218038	0.7727797218	0.2290480147	0.1022892045	0.1136772264	-0.7887970499	1.374319799	1.029024948	15.21136772	0.12607993	36.45470891	638.3026816
55	0.05258118904	0.03869523084	0.2470319049	0.2442031781	2.355713332	0.5843016265	0.06089467435	1.671157503	15.43557133	0.14737928	45.42285333	853.1667782
56	0.1089830437	0.307369355	0.8156633571	0.5806847097	-0.7426239123	1.970186709	-0.5580733953	-0.3099374274	15.12573761	0.11794507	33.02950435	563.9315961
57	0.8714152715	0.1124020916	0.02810098309	0.6083003049	0.3991678781	0.3404971153	-2.077510794	-1.681621342	15.23991679	0.12879209	37.59667151	663.9945836
58	0.1497997611	0.5544519862	0.1093270332	0.980511139	-1.835630666	-0.6537366934	2.088247154	-0.2569960989	15.01643693	0.10756151	28.65747734	474.5006998
59	0.3715835698	0.2095222046	0.7021647219	0.6905977994	0.3540243795	1.361847904	-0.3066304457	-0.7830404086	15.23540244	0.12836323	37.41609752	659.9012776
60	0.9576768157	0.2507787906	0.7186840594	0.6781286525	-0.001439068047	0.2940879989	-0.3547028296	-0.7313362918	15.19985609	0.12498633	35.99424373	628.0725676
61	0.2392284037	0.4849230652	0.1227261947	0.5457907374	-1.683769008	0.1599842691	-1.964121549	-0.581227556	15.03162310	0.10900419	29.26492397	486.576853
62	0.06222202878	0.7887084464	0.8893785892	0.6458281772	0.5675473524	-2.287352698	-0.2947841013	-0.3841443513	15.25675474	0.13039170	38.27018941	679.3652176
63	0.4558472144	0.5224606574	0.5768431788	0.5294691112	-1.241011783	-0.1763091546	-1.031054585	-0.193122021	15.07589882	0.11321039	31.03595287	522.4187273
64	0.421088087	0.7015161412	0.7257499015	0.1937538851	-0.3944938441	-1.2546717	0.2771130802	0.7512043426	15.16055062	0.12125231	34.42202462	593.6913083
65	0.6147802741	0.2287092897	0.1813028483	0.628909302	0.1315606623	0.9775850336	-1.274258115	-1.338446547	15.21315607	0.12624983	36.52624265	639.8985682
66	0.2952121501	0.6702945693	0.4943456703	0.8085685067	-0.7500072804	-1.370259514	0.4270305908	-1.107558311	15.12499927	0.11787493	32.99997088	563.3073221
67	0.1666316638	0.9877406207	0.04013227135	0.8322407711	1.887515943	-0.1456797219	1.252879234	-2.204867937	15.38875159	0.14293140	43.55006377	805.7235369
68	0.1998314268	0.1954743319	0.3564231831	0.2308131228	0.6028615862	1.6903018	0.1727468137	1.425984437	15.26028616	0.13072719	38.41144634	682.6096703
69	0.8272633023	0.7453565399	0.8743417333	0.3375334361	-0.0179651591	-0.6155824538	-0.2708700924	0.4418114464	15.19820348	0.12482933	35.92813936	626.6099703
70	0.08175664035	0.7318025566	0.5692255168	0.3894037046	-0.2553150655	-2.223247784	-0.8154222885	0.6797379351	15.17446849	0.12257451	34.97873974	605.7694884
71	0.681459747	0.4283214861	0.6551288632	0.2492562102	-0.7884762261	0.3812367123	0.004298078551	0.9196891738	15.12115238	0.11750948	32.84609510	560.0592959
72	0.9277556354	0.5654655811	0.3794622896	0.149340652	-0.3549623659	-0.1548403318	0.8229268278	1.122849744	15.16450376	0.12162786	34.58015054	597.1113169
73	0.4137565688	0.8962729358	0.1812760765	0.2069399764	1.056212489	-0.8058350515	0.4939328504	1.780870178	15.30562125	0.13503402	40.22484996	724.9114424
74	0.2330089254	0.7473694243	0.1604164767	0.8526839526	-0.02821030371	-1.706622752	1.150433315	-1.528550595	15.19717897	0.12473200	35.88715879	625.7040095
75	0.3501421123	0.7728727147	0.6387825001	0.2852450259	0.2074867982	-1.433799697	-0.2079547744	0.9236543334	15.22074868	0.12697112	36.82994719	646.6940443
76	0.9151432362	0.1719710654	0.6728836438	0.1214822913	0.1982944733	0.3715220977	0.643187647	0.6153660399	15.21982945	0.12688380	36.79317789	645.8695977
77	0.183386356	0.888278891	0.3926439178	0.7196183232	1.406372064	-1.189301413	-0.2594401659	-1.342533083	15.34063721	0.13836053	41.62548826	758.4288675
78	0.06414657778	0.2941787666	0.9692987048	0.3260859612	-0.6422635788	2.2540334	-0.1148905027	0.2217319999	15.13577364	0.11889850	33.43094568	572.4453784
79	0.0417582275	0.3951762713	0.5920121606	0.09908603917	-1.993106772	1.542479484	0.83182862	0.5970907404	15.00068932	0.10606549	28.02757291	462.0925114
80	0.2904667105	0.8485333743	0.4226130083	0.9376923177	0.9124887295	-1.280584603	1.213176991	-0.5007977382	15.29124887	0.13366864	39.64995492	711.3688301
81	0.9351172174	0.6815354743	0.4537365469	0.7573454187	-0.1527530696	-0.3329163293	0.05800111388	-1.255831579	15.18472469	0.12354885	35.38898772	614.7371154
82	0.7448625094	0.3190863135	0.6125716793	0.8177620548	-0.3228085457	0.6963518511	0.4089007182	-0.9016533894	15.16771915	0.12193332	34.70876582	599.8992503
83	0.1411935293	0.1092347805	0.2366485637	0.1432053506	1.53065992	1.253924946	1.055623794	1.329667849	15.35306599	0.13954127	42.12263968	770.5068741
84	0.2093109379	0.3021780874	0.5109535154	0.4399262198	-0.5694877814	1.674381214	-1.077281625	0.4271037607	15.14305122	0.11958987	33.72204887	578.6521109
85	0.1738082609	0.05105725118	0.1691524341	0.9977080624	1.775284041	0.5898912145	1.884986215	-0.02714693845	15.37752840	0.14186520	43.10113617	794.5609983
86	0.02679118125	0.5078858768	0.1961417095	0.3861229166	-2.687304703	-0.1332607881	-1.362299058	1.184051106	14.93126953	0.09947061	25.25078119	408.7375457
87	0.07746527257	0.1998762106	0.763114032	0.572205178	0.7006151926	2.150578859	-0.6609358225	-0.3222723258	15.27006152	0.13165584	38.80246077	691.6285208
88	0.2805171581	0.1125725264	0.5212922014	0.9550291672	1.211950128	1.036058714	1.096177574	-0.318251192	15.32119501	0.13651353	40.84780051	739.7264486
89	0.7209273811	0.2816986077	0.6832043491	0.8316415842	-0.1600581614	0.7929786365	0.4283810724	-0.7605341533	15.18399418	0.12347945	35.35976735	614.0964902
90	0.2347411479	0.8611759918	0.03767292419	0.817582559	1.094884559	-1.303752869	1.05501093	-2.33336221	15.30948846	0.13540140	40.37953823	728.5765497
91	0.8959528868	0.04540443025	0.3663855362	0.3708272906	0.4498124252	0.1319230092	-0.9754199427	1.027956312	15.24498124	0.12927322	37.79924970	668.6005588
92	0.9972980772	0.5331984069	0.5169125147	0.754839648	-0.07196604697	-0.01523309999	0.03492808165	-1.148278408	15.19280340	0.12431632	35.71213581	621.8412822
93	0.574324492	0.2313850668	0.9528850744	0.4771858675	0.1228967131	1.045953081	-0.3074933741	0.04438217178	15.21228967	0.12616752	36.49158685	639.1251892
94	0.9994255643	0.6434845061	0.5574856985	0.2240393079	-0.02103158842	-0.02658709962	0.1755530383	1.066685515	15.19789684	0.12480020	35.91587365	626.3387503
95	0.9227807745	0.4718523786	0.4276686184	0.5781126804	-0.3946544026	0.07053421858	-1.14953078	-0.6143226053	15.16053456	0.12125078	34.42138239	593.6774349
96	0.7550204189	0.01363715153	0.6394756856	0.8790984637	0.7469302311	0.06415761954	0.68565571	-0.6512216263	15.27469302	0.13209584	38.98772092	695.9211044
97	0.2357216749	0.1584943476	0.6381045721	0.969543255	0.9244766003	1.426727038	0.9305922702	-0.1802893019	15.29244766	0.13378253	39.69790640	712.4936887
98	0.4564527537	0.7912524988	0.1983064214	0.9845616158	0.3209993374	-1.210578204	1.790399752	-0.1742195453	15.23209993	0.12804949	37.28399735	656.9141474
99	0.01198481845	0.9676527629	0.5853429774	0.8176266791	2.913371174	-0.6004144559	0.4266460663	-0.9429145078	15.49133712	0.15267703	47.65348470	911.5698601
100	0.9875450083	0.7341353559	0.6166788365	0.6230736033	-0.01575566836	-0.1575378347	-0.70363911	-0.6868084395	15.19842443	0.12485032	35.93697733	626.8054279