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winsorised coffee mean

*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Tue, 15 Nov 2011 05:02:05 -0500

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Nov/15/t1321351347kl4m0ng1pr5dd6e.htm/, Retrieved Fri, 24 May 2013 05:21:13 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1199655142l1mf45ba5ydsjhm (pk = 7910)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	77.5381666666667	0.993560981023033	78.0406720348745
Geometric Mean	75.4064875707584
Harmonic Mean	73.3492143886423
Quadratic Mean	79.7907197541725
Winsorized Mean ( 1 / 120 )	77.5415555555555	0.993194541446671	78.072877286065
Winsorized Mean ( 2 / 120 )	77.4627777777778	0.973042432546294	79.6088384091023
Winsorized Mean ( 3 / 120 )	77.3803611111111	0.955044856652947	81.0227504729972
Winsorized Mean ( 4 / 120 )	77.2186944444444	0.924609648060975	83.5149131380815
Winsorized Mean ( 5 / 120 )	77.1274444444444	0.909725896869446	84.7809705207424
Winsorized Mean ( 6 / 120 )	77.1084444444445	0.905989502540267	85.1096444586204
Winsorized Mean ( 7 / 120 )	77.0425277777778	0.896283439210147	85.9577722931841
Winsorized Mean ( 8 / 120 )	76.9774166666667	0.885616688030129	86.9195643070897
Winsorized Mean ( 9 / 120 )	76.9804166666667	0.884119772360002	87.0701222541161
Winsorized Mean ( 10 / 120 )	76.9223611111111	0.876301225032592	87.7807298606141
Winsorized Mean ( 11 / 120 )	76.8630833333333	0.868738956463745	88.4766163200615
Winsorized Mean ( 12 / 120 )	76.8340833333333	0.863359864768634	88.994272804103
Winsorized Mean ( 13 / 120 )	76.8250555555556	0.86218105581302	89.1054785274898
Winsorized Mean ( 14 / 120 )	76.806	0.858033680555072	89.513968671152
Winsorized Mean ( 15 / 120 )	76.7793333333333	0.853804611040914	89.926116983285
Winsorized Mean ( 16 / 120 )	76.7468888888889	0.849553612808801	90.3378994942387
Winsorized Mean ( 17 / 120 )	76.75775	0.847797381369426	90.5378474701292
Winsorized Mean ( 18 / 120 )	76.67775	0.838736421206311	91.4205560427654
Winsorized Mean ( 19 / 120 )	76.6708888888889	0.836272071381071	91.6817522822087
Winsorized Mean ( 20 / 120 )	76.642	0.832342300033991	92.0799051025883
Winsorized Mean ( 21 / 120 )	76.64375	0.831729941405852	92.1498026997213
Winsorized Mean ( 22 / 120 )	76.5918055555556	0.824516820731613	92.8929569776319
Winsorized Mean ( 23 / 120 )	76.5809444444444	0.816656487529123	93.77375385353
Winsorized Mean ( 24 / 120 )	76.5696111111111	0.81555133105194	93.8869304674516
Winsorized Mean ( 25 / 120 )	76.5494722222222	0.813077536566036	94.1478134367387
Winsorized Mean ( 26 / 120 )	76.52925	0.811131884598025	94.348713758091
Winsorized Mean ( 27 / 120 )	76.45275	0.79766859864512	95.8452546958208
Winsorized Mean ( 28 / 120 )	76.4216388888889	0.793949437803454	96.2550450319828
Winsorized Mean ( 29 / 120 )	76.4264722222222	0.78882457943024	96.8865248562923
Winsorized Mean ( 30 / 120 )	76.4923055555556	0.782650864255735	97.7349020476663
Winsorized Mean ( 31 / 120 )	76.5043611111111	0.776507878318169	98.5236122482249
Winsorized Mean ( 32 / 120 )	76.42525	0.757250506810145	100.92466008631
Winsorized Mean ( 33 / 120 )	76.3995833333333	0.754857678510186	101.210579832901
Winsorized Mean ( 34 / 120 )	76.4156388888889	0.75167843477487	101.660012252148
Winsorized Mean ( 35 / 120 )	76.3718888888889	0.746746624268885	102.272827766261
Winsorized Mean ( 36 / 120 )	76.3668888888889	0.746148739300877	102.348077355787
Winsorized Mean ( 37 / 120 )	76.26925	0.737239165366731	103.452520678362
Winsorized Mean ( 38 / 120 )	76.2703055555556	0.732865862790889	104.071303396646
Winsorized Mean ( 39 / 120 )	76.2172222222222	0.725254082107508	105.090373294754
Winsorized Mean ( 40 / 120 )	76.1638888888889	0.719305581529136	105.885302220199
Winsorized Mean ( 41 / 120 )	76.1593333333333	0.710294828738455	107.222142484972
Winsorized Mean ( 42 / 120 )	76.1196666666666	0.69920593507719	108.865876057335
Winsorized Mean ( 43 / 120 )	76.1399722222222	0.694585948750852	109.619223307285
Winsorized Mean ( 44 / 120 )	76.0898611111111	0.687817299633067	110.625105172119
Winsorized Mean ( 45 / 120 )	76.0898611111111	0.681634744260152	111.628495688991
Winsorized Mean ( 46 / 120 )	76.09625	0.680489556952096	111.825742544579
Winsorized Mean ( 47 / 120 )	76.1093055555556	0.678982503620495	112.093176406937
Winsorized Mean ( 48 / 120 )	76.0866388888889	0.675599264192376	112.620961746967
Winsorized Mean ( 49 / 120 )	76.02675	0.67052950118423	113.383154455886
Winsorized Mean ( 50 / 120 )	75.9878611111111	0.666386411920811	114.029727725212
Winsorized Mean ( 51 / 120 )	76.0076944444444	0.661630003652437	114.879455322241
Winsorized Mean ( 52 / 120 )	76.0813611111111	0.654403588220279	116.260611158968
Winsorized Mean ( 53 / 120 )	76.1284722222222	0.64963361730725	117.186780662271
Winsorized Mean ( 54 / 120 )	76.0219722222222	0.62691939195975	121.26275434642
Winsorized Mean ( 55 / 120 )	76.0051666666667	0.625748110543662	121.462878410663
Winsorized Mean ( 56 / 120 )	76.0611666666667	0.619123056382654	122.853067548588
Winsorized Mean ( 57 / 120 )	76.0880833333333	0.616256688088322	123.46816643786
Winsorized Mean ( 58 / 120 )	76.1090277777778	0.614586949281793	123.837689470495
Winsorized Mean ( 59 / 120 )	76.1073888888889	0.613493788213614	124.055679700523
Winsorized Mean ( 60 / 120 )	75.9923888888889	0.604343645807638	125.743671528694
Winsorized Mean ( 61 / 120 )	76.0110277777778	0.602104334417477	126.242286316236
Winsorized Mean ( 62 / 120 )	76.0006944444444	0.596838805138381	127.338728296702
Winsorized Mean ( 63 / 120 )	76.0199444444444	0.595053027755498	127.753226853054
Winsorized Mean ( 64 / 120 )	76.0110555555556	0.592108264976506	128.373576340083
Winsorized Mean ( 65 / 120 )	76.2168888888889	0.575772991889226	132.373157411927
Winsorized Mean ( 66 / 120 )	76.1857222222222	0.569949114645801	133.671094953044
Winsorized Mean ( 67 / 120 )	76.2192222222222	0.566844583887636	134.462292467332
Winsorized Mean ( 68 / 120 )	76.1946666666667	0.55760913523203	136.645298386227
Winsorized Mean ( 69 / 120 )	76.2809166666667	0.551076628342768	138.421614605692
Winsorized Mean ( 70 / 120 )	76.3450833333333	0.542686868673236	140.67980587034
Winsorized Mean ( 71 / 120 )	76.3312777777778	0.541761563091016	140.894598247743
Winsorized Mean ( 72 / 120 )	76.3192777777778	0.540394145651254	141.22891299239
Winsorized Mean ( 73 / 120 )	76.3476666666667	0.528876227256766	144.358287878953
Winsorized Mean ( 74 / 120 )	76.2448888888889	0.521265827083413	146.268726871075
Winsorized Mean ( 75 / 120 )	76.2803055555556	0.518646047195635	147.075844823285
Winsorized Mean ( 76 / 120 )	76.4048611111111	0.507780550872865	150.468270160747
Winsorized Mean ( 77 / 120 )	76.4198333333333	0.501102533954626	152.503386343389
Winsorized Mean ( 78 / 120 )	76.6625	0.480084930956597	159.685287032954
Winsorized Mean ( 79 / 120 )	76.6361666666667	0.478352125567853	160.208688475444
Winsorized Mean ( 80 / 120 )	76.6428333333333	0.475489264953848	161.187305334375
Winsorized Mean ( 81 / 120 )	76.7305833333333	0.46914369613728	163.554544087662
Winsorized Mean ( 82 / 120 )	76.6986944444444	0.464305286086242	165.190224498539
Winsorized Mean ( 83 / 120 )	76.80475	0.453740460255789	169.270225442762
Winsorized Mean ( 84 / 120 )	76.80475	0.45064876011655	170.43151295953
Winsorized Mean ( 85 / 120 )	76.8071111111111	0.449553717933252	170.851909454156
Winsorized Mean ( 86 / 120 )	76.8548888888889	0.444164428541761	173.03251667679
Winsorized Mean ( 87 / 120 )	76.8621388888889	0.443683873439305	173.23626908744
Winsorized Mean ( 88 / 120 )	76.8816944444444	0.436294722290048	176.215045739961
Winsorized Mean ( 89 / 120 )	76.8915833333333	0.434997783655332	176.763161152697
Winsorized Mean ( 90 / 120 )	76.9465833333333	0.428468424855271	179.585189642211
Winsorized Mean ( 91 / 120 )	76.9971388888889	0.424866592503677	181.226625598299
Winsorized Mean ( 92 / 120 )	77.0073611111111	0.422549979215991	182.24438504054
Winsorized Mean ( 93 / 120 )	77.0125277777778	0.418872585956862	183.856691413338
Winsorized Mean ( 94 / 120 )	77.0073055555555	0.416170368180146	185.037935046403
Winsorized Mean ( 95 / 120 )	76.9413333333333	0.41053730485223	187.41617978183
Winsorized Mean ( 96 / 120 )	76.968	0.407458435504251	188.8977949487
Winsorized Mean ( 97 / 120 )	76.9248888888889	0.404686420202919	190.085174714578
Winsorized Mean ( 98 / 120 )	76.9058333333333	0.398245173381078	193.111777552525
Winsorized Mean ( 99 / 120 )	76.8645833333333	0.388280228948572	197.961620506601
Winsorized Mean ( 100 / 120 )	76.95625	0.380017586594581	202.507075237284
Winsorized Mean ( 101 / 120 )	76.8833055555556	0.375070736817405	204.983481803819
Winsorized Mean ( 102 / 120 )	76.8918055555556	0.373822804363409	205.690516089558
Winsorized Mean ( 103 / 120 )	76.8832222222222	0.372566849611933	206.360878060687
Winsorized Mean ( 104 / 120 )	76.9034444444444	0.370570331020731	207.527257329573
Winsorized Mean ( 105 / 120 )	76.9034444444444	0.369108178566174	208.349337430509
Winsorized Mean ( 106 / 120 )	76.927	0.364318527496121	211.153137142659
Winsorized Mean ( 107 / 120 )	76.90025	0.362278640057109	212.268241892146
Winsorized Mean ( 108 / 120 )	76.82825	0.354455834187868	216.749853126355
Winsorized Mean ( 109 / 120 )	76.9433055555555	0.346549433859355	222.026926140593
Winsorized Mean ( 110 / 120 )	76.9280277777778	0.341830081849195	225.047565625649
Winsorized Mean ( 111 / 120 )	76.9434444444444	0.338600419308836	227.239660841249
Winsorized Mean ( 112 / 120 )	76.9527777777778	0.334200698607936	230.259176890752
Winsorized Mean ( 113 / 120 )	76.97475	0.329775595665591	233.415543817427
Winsorized Mean ( 114 / 120 )	76.9335833333333	0.326085655181052	235.930597102217
Winsorized Mean ( 115 / 120 )	76.9176111111111	0.324327754448249	237.160126002674
Winsorized Mean ( 116 / 120 )	76.9305	0.320000617914716	240.40734827738
Winsorized Mean ( 117 / 120 )	76.84275	0.313486202775661	245.123228134511
Winsorized Mean ( 118 / 120 )	76.8558611111111	0.312286658009559	246.10677126257
Winsorized Mean ( 119 / 120 )	76.8228055555555	0.308287796411395	249.191847519774
Winsorized Mean ( 120 / 120 )	76.7861388888889	0.305682842846176	251.195448766252
Trimmed Mean ( 1 / 120 )	77.3665363128492	0.959119157088214	80.6641549603971
Trimmed Mean ( 2 / 120 )	77.1895505617978	0.922845871913721	83.642949392761
Trimmed Mean ( 3 / 120 )	77.0506214689266	0.89564947342803	86.027652284572
Trimmed Mean ( 4 / 120 )	76.9382102272727	0.873850527828105	88.0450463519172
Trimmed Mean ( 5 / 120 )	76.8660857142857	0.859808183053018	89.3991092773141
Trimmed Mean ( 6 / 120 )	76.8120114942529	0.848626317557062	90.513350699954
Trimmed Mean ( 7 / 120 )	76.7606069364162	0.837725363493644	91.6297993130998
Trimmed Mean ( 8 / 120 )	76.7184593023256	0.828048959721277	92.6496657011068
Trimmed Mean ( 9 / 120 )	76.6843859649123	0.819608716915409	93.5621893499539
Trimmed Mean ( 10 / 120 )	76.6495588235294	0.811047446016324	94.5068740429603
Trimmed Mean ( 11 / 120 )	76.6205029585799	0.803134488558204	95.4018337528125
Trimmed Mean ( 12 / 120 )	76.596875	0.795790452999308	96.2525683882094
Trimmed Mean ( 13 / 120 )	76.596875	0.788742066811061	97.1127041691671
Trimmed Mean ( 14 / 120 )	76.5547590361446	0.781544424043551	97.9531766602158
Trimmed Mean ( 15 / 120 )	76.5351818181818	0.774464146005729	98.8234022361258
Trimmed Mean ( 16 / 120 )	76.5173170731707	0.767492480974379	99.6978067798492
Trimmed Mean ( 17 / 120 )	76.501472392638	0.760616892112443	100.578192761631
Trimmed Mean ( 18 / 120 )	76.4847222222222	0.753617633463439	101.490091030272
Trimmed Mean ( 19 / 120 )	76.4727329192547	0.747060309484031	102.364871949993
Trimmed Mean ( 20 / 120 )	76.461	0.740433440532594	103.26519010946
Trimmed Mean ( 21 / 120 )	76.4507547169811	0.733834035941838	104.179897596138
Trimmed Mean ( 22 / 120 )	76.4402848101266	0.727017028713808	105.14235814443
Trimmed Mean ( 23 / 120 )	76.4323885350318	0.72042553649169	106.093391563048
Trimmed Mean ( 24 / 120 )	76.4249358974359	0.714093804227907	107.023664741172
Trimmed Mean ( 25 / 120 )	76.417935483871	0.707580161186524	107.998979727933
Trimmed Mean ( 26 / 120 )	76.417935483871	0.700960352376692	109.018912731322
Trimmed Mean ( 27 / 120 )	76.4064705882353	0.694191700535534	110.065376075933
Trimmed Mean ( 28 / 120 )	76.4044407894737	0.687963469128034	111.058863178176
Trimmed Mean ( 29 / 120 )	76.4037086092715	0.681699797601429	112.078232791177
Trimmed Mean ( 30 / 120 )	76.4027666666667	0.675474890577047	113.109706567178
Trimmed Mean ( 31 / 120 )	76.3991610738255	0.669342414247238	114.140624361518
Trimmed Mean ( 32 / 120 )	76.3950337837838	0.663297254494715	115.174657012533
Trimmed Mean ( 33 / 120 )	76.3938775510204	0.658051260744696	116.091073915074
Trimmed Mean ( 34 / 120 )	76.3936643835616	0.652712987442241	117.040208871777
Trimmed Mean ( 35 / 120 )	76.3928620689655	0.647316643495638	118.014673091717
Trimmed Mean ( 36 / 120 )	76.3936111111111	0.641947387615581	119.00291610324
Trimmed Mean ( 37 / 120 )	76.3945454545455	0.636378472056591	120.045772773646
Trimmed Mean ( 38 / 120 )	76.398838028169	0.63102184164364	121.071622226532
Trimmed Mean ( 39 / 120 )	76.4031560283688	0.625652380462062	122.11758224582
Trimmed Mean ( 40 / 120 )	76.4092857142857	0.620425052681766	123.156351253079
Trimmed Mean ( 41 / 120 )	76.4172302158273	0.615257601163317	124.203634496086
Trimmed Mean ( 42 / 120 )	76.4254347826087	0.610298424246716	125.226334767191
Trimmed Mean ( 43 / 120 )	76.435	0.605646172752605	126.204050217324
Trimmed Mean ( 44 / 120 )	76.4440808823529	0.60100416308521	127.193929056885
Trimmed Mean ( 45 / 120 )	76.4548148148148	0.596465745591069	128.179724284169
Trimmed Mean ( 46 / 120 )	76.4657089552239	0.592006914092867	129.163540382619
Trimmed Mean ( 47 / 120 )	76.4765789473684	0.587396063275608	130.195933763835
Trimmed Mean ( 48 / 120 )	76.4872348484848	0.582641658817966	131.276632370672
Trimmed Mean ( 49 / 120 )	76.4872348484848	0.577819035516275	132.372300230892
Trimmed Mean ( 50 / 120 )	76.5120384615385	0.572996658861515	133.529641540249
Trimmed Mean ( 51 / 120 )	76.5266666666667	0.568130496392898	134.699100211202
Trimmed Mean ( 52 / 120 )	76.5266666666667	0.563249841386019	135.86629066482
Trimmed Mean ( 53 / 120 )	76.5535039370079	0.558469004047475	137.077444553217
Trimmed Mean ( 54 / 120 )	76.5649603174603	0.553675597237758	138.284874210524
Trimmed Mean ( 55 / 120 )	76.57944	0.549651039667196	139.323742653826
Trimmed Mean ( 56 / 120 )	76.5945967741935	0.545476102016566	140.417878053744
Trimmed Mean ( 57 / 120 )	76.6085365853659	0.541390026073028	141.503413243583
Trimmed Mean ( 58 / 120 )	76.6220081967213	0.537226586254322	142.625123471549
Trimmed Mean ( 59 / 120 )	76.6351652892562	0.532927234481041	143.800429647553
Trimmed Mean ( 60 / 120 )	76.6485833333333	0.528455753336589	145.042575181339
Trimmed Mean ( 61 / 120 )	76.6651260504202	0.524144706552887	146.26709969966
Trimmed Mean ( 62 / 120 )	76.6814830508475	0.519709813565343	147.546729057881
Trimmed Mean ( 63 / 120 )	76.6814830508475	0.515273513072799	148.817047850107
Trimmed Mean ( 64 / 120 )	76.7150862068966	0.510683321454534	150.220465372544
Trimmed Mean ( 65 / 120 )	76.7323043478261	0.505977354181655	151.651657359111
Trimmed Mean ( 66 / 120 )	76.7448245614035	0.501774394090386	152.946873067379
Trimmed Mean ( 67 / 120 )	76.7583185840708	0.497596819829531	154.258056975458
Trimmed Mean ( 68 / 120 )	76.77125	0.493331456415312	155.617990707185
Trimmed Mean ( 69 / 120 )	76.785	0.489237379276313	156.948351153343
Trimmed Mean ( 70 / 120 )	76.7969545454545	0.485214443772572	158.274254880695
Trimmed Mean ( 71 / 120 )	76.8076146788991	0.481343192278728	159.569338282908
Trimmed Mean ( 72 / 120 )	76.8187962962963	0.477290445087174	160.947693562702
Trimmed Mean ( 73 / 120 )	76.8304672897196	0.473064351801941	162.410181610739
Trimmed Mean ( 74 / 120 )	76.8416981132075	0.469115664878895	163.801177121307
Trimmed Mean ( 75 / 120 )	76.8555238095238	0.465263001259857	165.187267419527
Trimmed Mean ( 76 / 120 )	76.8687980769231	0.461304009171525	166.633709112945
Trimmed Mean ( 77 / 120 )	76.8794660194175	0.457614443560102	168.000523369233
Trimmed Mean ( 78 / 120 )	76.89	0.454003356396236	169.359981411445
Trimmed Mean ( 79 / 120 )	76.895198019802	0.451125953511553	170.451727330808
Trimmed Mean ( 80 / 120 )	76.9011	0.448140915730486	171.600265230521
Trimmed Mean ( 81 / 120 )	76.9069696969697	0.445093310110218	172.788419753883
Trimmed Mean ( 82 / 120 )	76.9109693877551	0.442138324694538	173.952279393312
Trimmed Mean ( 83 / 120 )	76.9157731958763	0.43920576294788	175.124690258228
Trimmed Mean ( 84 / 120 )	76.91828125	0.436556647278521	176.193128038494
Trimmed Mean ( 85 / 120 )	76.9208421052632	0.433866347377724	177.291561261136
Trimmed Mean ( 86 / 120 )	76.9234042553192	0.431041902843514	178.459225768696
Trimmed Mean ( 87 / 120 )	76.9249462365591	0.428270857099177	179.617512986052
Trimmed Mean ( 88 / 120 )	76.9263586956522	0.425329434335582	180.863002852885
Trimmed Mean ( 89 / 120 )	76.9273626373626	0.422526498911457	182.065178954571
Trimmed Mean ( 90 / 120 )	76.9281666666667	0.419585215914513	183.343368042644
Trimmed Mean ( 91 / 120 )	76.9277528089888	0.416742555183588	184.592986370446
Trimmed Mean ( 92 / 120 )	76.9261931818182	0.413863964939035	185.873136341189
Trimmed Mean ( 93 / 120 )	76.924367816092	0.410885318649921	187.216150893024
Trimmed Mean ( 94 / 120 )	76.9223837209302	0.407865535362539	188.597410302286
Trimmed Mean ( 95 / 120 )	76.9204705882353	0.404753643702255	190.042688398426
Trimmed Mean ( 96 / 120 )	76.92	0.401689607680064	191.491137757452
Trimmed Mean ( 97 / 120 )	76.9189156626506	0.398546208277207	192.998739080087
Trimmed Mean ( 98 / 120 )	76.9189156626506	0.395302449383711	194.582441324534
Trimmed Mean ( 99 / 120 )	76.9190740740741	0.392139503391394	196.152321836602
Trimmed Mean ( 100 / 120 )	76.9203125	0.389242455098642	197.615423221259
Trimmed Mean ( 101 / 120 )	76.9194936708861	0.386538061466049	198.995910982603
Trimmed Mean ( 102 / 120 )	76.9203205128205	0.383865298738306	200.383626146055
Trimmed Mean ( 103 / 120 )	76.920974025974	0.381031560695428	201.875597616072
Trimmed Mean ( 104 / 120 )	76.920974025974	0.378023957465234	203.481743701517
Trimmed Mean ( 105 / 120 )	76.9222666666667	0.374869166100343	205.197635929535
Trimmed Mean ( 106 / 120 )	76.9227027027027	0.371524707816399	207.045994746375
Trimmed Mean ( 107 / 120 )	76.922602739726	0.368164901835762	208.93518734722
Trimmed Mean ( 108 / 120 )	76.923125	0.364628440016867	210.963042258694
Trimmed Mean ( 109 / 120 )	76.923125	0.361240021082387	212.941868316568
Trimmed Mean ( 110 / 120 )	76.9249285714286	0.358018563546746	214.862960762046
Trimmed Mean ( 111 / 120 )	76.9248550724638	0.354783264945283	216.822107109048
Trimmed Mean ( 112 / 120 )	76.9244117647059	0.35144178239492	218.882374316737
Trimmed Mean ( 113 / 120 )	76.9237313432836	0.348057592773596	221.008628860227
Trimmed Mean ( 114 / 120 )	76.9225	0.344628192356518	223.204316147251
Trimmed Mean ( 115 / 120 )	76.9225	0.341103356602257	225.510826883171
Trimmed Mean ( 116 / 120 )	76.92234375	0.337345774115623	228.022253877813
Trimmed Mean ( 117 / 120 )	76.9221428571429	0.333507356614663	230.646015242235
Trimmed Mean ( 118 / 120 )	76.9241129032258	0.32973001958112	233.294235693032
Trimmed Mean ( 119 / 120 )	76.9258196721311	0.32564714347501	236.224457095643
Trimmed Mean ( 120 / 120 )	76.9284166666667	0.321428272551474	239.333074393284
Median	76.775
Midrange	108.26
Midmean - Weighted Average at Xnp	76.8713259668508
Midmean - Weighted Average at X(n+1)p	76.9281666666666
Midmean - Empirical Distribution Function	76.8713259668508
Midmean - Empirical Distribution Function - Averaging	76.9281666666666
Midmean - Empirical Distribution Function - Interpolation	76.9281666666666
Midmean - Closest Observation	76.8713259668508
Midmean - True Basic - Statistics Graphics Toolkit	76.9281666666666
Midmean - MS Excel (old versions)	76.9273626373626
Number of observations	360

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Nov/15/t1321351347kl4m0ng1pr5dd6e/1p8uf1321351322.png (opens in new window)

http://www.freestatistics.org/blog/date/2011/Nov/15/t1321351347kl4m0ng1pr5dd6e/1p8uf1321351322.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2011/Nov/15/t1321351347kl4m0ng1pr5dd6e/233vw1321351322.png (opens in new window)

http://www.freestatistics.org/blog/date/2011/Nov/15/t1321351347kl4m0ng1pr5dd6e/233vw1321351322.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

par1 = 3 ; par2 = 4 ; par3 = Pearson Chi-Squared ;

Parameters (R input):

par1 = 3 ; par2 = 4 ; par3 = Pearson Chi-Squared ;

R code (references can be found in the software module):

geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')