Home » date » 2010 » Nov » 07 »

Workshop 6 - Tutorial 1

*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: Sun, 07 Nov 2010 15:03:02 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/07/t1289142325yqyz6203feez3s0.htm/, Retrieved Thu, 23 May 2013 01:01:11 +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	4 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	308.350833333333	2.58343930017487	119.356716959621
Geometric Mean	304.740684063582
Harmonic Mean	301.385051546288
Quadratic Mean	312.211882158753
Winsorized Mean ( 1 / 120 )	308.342777777778	2.58125582324881	119.454559676186
Winsorized Mean ( 2 / 120 )	308.351666666667	2.57909722322486	119.557984821181
Winsorized Mean ( 3 / 120 )	308.253333333333	2.56016364983931	120.403761436376
Winsorized Mean ( 4 / 120 )	308.258888888889	2.55925749257575	120.448563610004
Winsorized Mean ( 5 / 120 )	308.253333333333	2.5528466399674	120.748864623247
Winsorized Mean ( 6 / 120 )	308.245	2.55049668820525	120.856851696956
Winsorized Mean ( 7 / 120 )	308.21	2.54360152695897	121.170708828943
Winsorized Mean ( 8 / 120 )	308.154444444444	2.533083316245	121.651918224801
Winsorized Mean ( 9 / 120 )	308.156944444444	2.52969630102449	121.815786471936
Winsorized Mean ( 10 / 120 )	308.154166666667	2.52397622857242	122.090756314675
Winsorized Mean ( 11 / 120 )	307.915833333333	2.48991376025427	123.665260318851
Winsorized Mean ( 12 / 120 )	307.735833333333	2.45564724718033	125.317605648241
Winsorized Mean ( 13 / 120 )	307.483055555556	2.42113790362435	126.999397719256
Winsorized Mean ( 14 / 120 )	307.280833333333	2.39632168370765	128.230210252031
Winsorized Mean ( 15 / 120 )	307.293333333333	2.39467479598391	128.323617824304
Winsorized Mean ( 16 / 120 )	307.222222222222	2.37951083661946	129.111503715061
Winsorized Mean ( 17 / 120 )	307.146666666667	2.36973863947835	129.612043096144
Winsorized Mean ( 18 / 120 )	307.116666666667	2.36439129114747	129.892487684481
Winsorized Mean ( 19 / 120 )	307.090277777778	2.35841755507132	130.210308652698
Winsorized Mean ( 20 / 120 )	307.001388888889	2.3461609351434	130.852655625742
Winsorized Mean ( 21 / 120 )	306.966388888889	2.3421676560823	131.060809456461
Winsorized Mean ( 22 / 120 )	306.996944444444	2.33789272448535	131.313529157769
Winsorized Mean ( 23 / 120 )	306.830833333333	2.31572662796359	132.498728316285
Winsorized Mean ( 24 / 120 )	306.6775	2.29875204619832	133.410430458206
Winsorized Mean ( 25 / 120 )	306.594166666667	2.28718970603506	134.048420145332
Winsorized Mean ( 26 / 120 )	306.435277777778	2.26751800395686	135.141276604218
Winsorized Mean ( 27 / 120 )	306.135277777778	2.23460326075896	136.997597360438
Winsorized Mean ( 28 / 120 )	306.1275	2.23246036402142	137.125614829981
Winsorized Mean ( 29 / 120 )	306.046944444444	2.21863812443503	137.943606518696
Winsorized Mean ( 30 / 120 )	305.955277777778	2.20643937804125	138.664710584248
Winsorized Mean ( 31 / 120 )	305.593611111111	2.16163843245596	141.37128879778
Winsorized Mean ( 32 / 120 )	305.575833333333	2.15842160180225	141.573746796354
Winsorized Mean ( 33 / 120 )	305.5025	2.1497531541733	142.110502039237
Winsorized Mean ( 34 / 120 )	305.341944444444	2.13115646798793	143.275235315183
Winsorized Mean ( 35 / 120 )	305.205833333333	2.11661197509015	144.195458083589
Winsorized Mean ( 36 / 120 )	305.015833333333	2.09877383059714	145.330491969471
Winsorized Mean ( 37 / 120 )	305.015833333333	2.09877383059714	145.330491969471
Winsorized Mean ( 38 / 120 )	304.920833333333	2.08825530697204	146.017027858278
Winsorized Mean ( 39 / 120 )	304.8775	2.08251483968061	146.398716681778
Winsorized Mean ( 40 / 120 )	304.533055555556	2.04767560140954	148.721338158215
Winsorized Mean ( 41 / 120 )	304.476111111111	2.04078018682423	149.19593647414
Winsorized Mean ( 42 / 120 )	304.429444444444	2.02926017115177	150.019917984029
Winsorized Mean ( 43 / 120 )	304.345833333333	2.01063366596284	151.368117666323
Winsorized Mean ( 44 / 120 )	304.235833333333	1.99720817939404	152.330556459888
Winsorized Mean ( 45 / 120 )	303.885833333333	1.95752873245674	155.239526396096
Winsorized Mean ( 46 / 120 )	303.7325	1.94268666795853	156.346622957565
Winsorized Mean ( 47 / 120 )	303.523611111111	1.91943526434894	158.131725903277
Winsorized Mean ( 48 / 120 )	303.496944444444	1.90519185629071	159.299937926112
Winsorized Mean ( 49 / 120 )	303.469722222222	1.90092974363112	159.642787030383
Winsorized Mean ( 50 / 120 )	303.455833333333	1.88940637534018	160.609087221217
Winsorized Mean ( 51 / 120 )	303.385	1.87946270523063	161.421133367353
Winsorized Mean ( 52 / 120 )	303.428333333333	1.87007827374221	162.254349239695
Winsorized Mean ( 53 / 120 )	303.089722222222	1.84099591379172	164.633565969181
Winsorized Mean ( 54 / 120 )	303.059722222222	1.82110572875478	166.415226440172
Winsorized Mean ( 55 / 120 )	302.9375	1.80940466651727	167.423852500111
Winsorized Mean ( 56 / 120 )	302.953055555556	1.79934772871471	168.368265189052
Winsorized Mean ( 57 / 120 )	302.873888888889	1.79098514289662	169.110218524226
Winsorized Mean ( 58 / 120 )	302.777222222222	1.77667152089131	170.418233568761
Winsorized Mean ( 59 / 120 )	302.646111111111	1.76441885555274	171.527361634492
Winsorized Mean ( 60 / 120 )	302.512777777778	1.75442982072208	172.427973011352
Winsorized Mean ( 61 / 120 )	302.394166666667	1.73122947849091	174.670181176824
Winsorized Mean ( 62 / 120 )	302.445833333333	1.72775362049101	175.051482888736
Winsorized Mean ( 63 / 120 )	302.498333333333	1.72423554980106	175.439100167164
Winsorized Mean ( 64 / 120 )	302.409444444444	1.71519428227333	176.312064219121
Winsorized Mean ( 65 / 120 )	302.228888888889	1.70201270778776	177.571464364517
Winsorized Mean ( 66 / 120 )	302.228888888889	1.69945140973613	177.839088047722
Winsorized Mean ( 67 / 120 )	302.098611111111	1.69003274758524	178.753110874778
Winsorized Mean ( 68 / 120 )	302.1175	1.65996955237428	182.001832243174
Winsorized Mean ( 69 / 120 )	302.1175	1.65996955237428	182.001832243174
Winsorized Mean ( 70 / 120 )	302.136944444444	1.65599788338568	182.450078877352
Winsorized Mean ( 71 / 120 )	302.215833333333	1.65077779082645	183.074811772232
Winsorized Mean ( 72 / 120 )	302.235833333333	1.64396434081423	183.845735476014
Winsorized Mean ( 73 / 120 )	302.296666666667	1.63996879476015	184.330743141291
Winsorized Mean ( 74 / 120 )	302.173333333333	1.63117517965685	185.248854385401
Winsorized Mean ( 75 / 120 )	302.319166666667	1.61312071695273	187.412611771402
Winsorized Mean ( 76 / 120 )	302.255833333333	1.60575515293848	188.232827887997
Winsorized Mean ( 77 / 120 )	302.234444444444	1.6013372934126	188.738778324681
Winsorized Mean ( 78 / 120 )	302.277777777778	1.59559025126748	189.445741184279
Winsorized Mean ( 79 / 120 )	302.453333333333	1.58428236231056	190.908729736931
Winsorized Mean ( 80 / 120 )	302.386666666667	1.56758545925986	192.899637388471
Winsorized Mean ( 81 / 120 )	302.454166666667	1.56025529259535	193.849152829061
Winsorized Mean ( 82 / 120 )	302.431388888889	1.54948633002041	195.181708305168
Winsorized Mean ( 83 / 120 )	302.177777777778	1.52556919227937	198.075432636583
Winsorized Mean ( 84 / 120 )	301.991111111111	1.50642534785379	200.468686710137
Winsorized Mean ( 85 / 120 )	302.014722222222	1.50178803977303	201.103427530204
Winsorized Mean ( 86 / 120 )	302.158055555556	1.48638168779465	203.284296380069
Winsorized Mean ( 87 / 120 )	301.916388888889	1.469775323823	205.416694643901
Winsorized Mean ( 88 / 120 )	301.183055555556	1.41718398615913	212.522197891768
Winsorized Mean ( 89 / 120 )	301.183055555556	1.41074546782319	213.49213052606
Winsorized Mean ( 90 / 120 )	301.208055555556	1.39940349254036	215.240320008612
Winsorized Mean ( 91 / 120 )	301.1575	1.39278977346334	216.226099399865
Winsorized Mean ( 92 / 120 )	301.234166666667	1.38130207880663	218.079861956711
Winsorized Mean ( 93 / 120 )	301.26	1.3729941166373	219.41827452097
Winsorized Mean ( 94 / 120 )	301.181666666667	1.36784665808604	220.186718215985
Winsorized Mean ( 95 / 120 )	301.234444444444	1.36111184254555	221.314983110481
Winsorized Mean ( 96 / 120 )	301.261111111111	1.35943006619932	221.608392076669
Winsorized Mean ( 97 / 120 )	301.180277777778	1.35066827222171	222.986120257618
Winsorized Mean ( 98 / 120 )	300.935277777778	1.32425788439573	227.24824320385
Winsorized Mean ( 99 / 120 )	301.320277777778	1.29662694194896	232.38779638873
Winsorized Mean ( 100 / 120 )	301.375833333333	1.28259942281394	234.972687475668
Winsorized Mean ( 101 / 120 )	301.628333333333	1.2458330142567	242.109761004602
Winsorized Mean ( 102 / 120 )	301.486666666667	1.23308761887707	244.49735935328
Winsorized Mean ( 103 / 120 )	301.601111111111	1.22254143013749	246.700114757822
Winsorized Mean ( 104 / 120 )	301.687777777778	1.19204856267822	253.083462556227
Winsorized Mean ( 105 / 120 )	301.716944444444	1.18666904869356	254.255341686559
Winsorized Mean ( 106 / 120 )	301.628611111111	1.15906568668894	260.23426849324
Winsorized Mean ( 107 / 120 )	301.866388888889	1.14495239895146	263.649728290307
Winsorized Mean ( 108 / 120 )	301.836388888889	1.13932605530768	264.925380651788
Winsorized Mean ( 109 / 120 )	301.654722222222	1.12769451712649	267.496842133166
Winsorized Mean ( 110 / 120 )	301.5325	1.11615375680785	270.15319185268
Winsorized Mean ( 111 / 120 )	301.563333333333	1.11432873787628	270.623311670182
Winsorized Mean ( 112 / 120 )	301.594444444444	1.08203539449089	278.728816062758
Winsorized Mean ( 113 / 120 )	301.500277777778	1.02277345329771	294.786960695603
Winsorized Mean ( 114 / 120 )	301.500277777778	1.0189543419034	295.891842626213
Winsorized Mean ( 115 / 120 )	301.532222222222	1.01325640125359	297.587285754295
Winsorized Mean ( 116 / 120 )	301.661111111111	0.994219814207515	303.414905637908
Winsorized Mean ( 117 / 120 )	301.498611111111	0.98407447836326	306.377837999185
Winsorized Mean ( 118 / 120 )	301.531388888889	0.970437269246936	310.717032872077
Winsorized Mean ( 119 / 120 )	301.729722222222	0.947345049561988	318.50034194165
Winsorized Mean ( 120 / 120 )	301.663055555556	0.935290669763099	322.534015689437
Trimmed Mean ( 1 / 120 )	308.112290502793	2.55153447947348	120.755683680345
Trimmed Mean ( 2 / 120 )	307.879213483146	2.52063603068887	122.14346289377
Trimmed Mean ( 3 / 120 )	307.638983050847	2.48964643100863	123.567338405644
Trimmed Mean ( 4 / 120 )	307.429545454545	2.46432160954437	124.752201280817
Trimmed Mean ( 5 / 120 )	307.216285714286	2.43825749428643	125.998294451749
Trimmed Mean ( 6 / 120 )	307.001724137931	2.41261734222551	127.248411409801
Trimmed Mean ( 7 / 120 )	306.78612716763	2.38641223093029	128.55537831703
Trimmed Mean ( 8 / 120 )	306.573255813953	2.36032690047429	129.885930526127
Trimmed Mean ( 9 / 120 )	306.365204678363	2.33478639726257	131.217658727823
Trimmed Mean ( 10 / 120 )	306.154411764706	2.30867154096763	132.610640505573
Trimmed Mean ( 11 / 120 )	305.941420118343	2.28220302631716	134.055303840363
Trimmed Mean ( 12 / 120 )	305.749107142857	2.25865479816305	135.36778944331
Trimmed Mean ( 13 / 120 )	305.749107142857	2.2378669977221	136.625236197717
Trimmed Mean ( 14 / 120 )	305.411144578313	2.21974153293115	137.588606622601
Trimmed Mean ( 15 / 120 )	305.265454545455	2.20325457430232	138.55205753612
Trimmed Mean ( 16 / 120 )	305.117073170732	2.18626261103946	139.561035179422
Trimmed Mean ( 17 / 120 )	304.971779141104	2.16988544282839	140.547410071373
Trimmed Mean ( 18 / 120 )	304.82962962963	2.15365660691892	141.540498448231
Trimmed Mean ( 19 / 120 )	304.687577639752	2.13719758937363	142.564065744174
Trimmed Mean ( 20 / 120 )	304.5453125	2.12052565312006	143.617839308807
Trimmed Mean ( 21 / 120 )	304.406289308176	2.10407650583293	144.674534630418
Trimmed Mean ( 22 / 120 )	304.267405063291	2.08724292420284	145.774792926653
Trimmed Mean ( 23 / 120 )	304.125159235669	2.07000066220272	146.920319780016
Trimmed Mean ( 24 / 120 )	303.989423076923	2.05353703070286	148.032111684335
Trimmed Mean ( 25 / 120 )	303.85935483871	2.03750549048841	149.133023816231
Trimmed Mean ( 26 / 120 )	303.85935483871	2.02154263735387	150.310633683418
Trimmed Mean ( 27 / 120 )	303.609150326797	2.00613618409792	151.340249347688
Trimmed Mean ( 28 / 120 )	303.498355263158	1.99207847266043	152.352610315514
Trimmed Mean ( 29 / 120 )	303.38642384106	1.97755639479642	153.414802550949
Trimmed Mean ( 30 / 120 )	303.276333333333	1.96321597571393	154.479352799198
Trimmed Mean ( 31 / 120 )	303.168456375839	1.94895896546866	155.554047954487
Trimmed Mean ( 32 / 120 )	303.073310810811	1.93657434452827	156.499703544631
Trimmed Mean ( 33 / 120 )	302.977551020408	1.92383238894886	157.486459195101
Trimmed Mean ( 34 / 120 )	302.883219178082	1.91100528557651	158.494181813165
Trimmed Mean ( 35 / 120 )	302.793448275862	1.89860176746472	159.482337720666
Trimmed Mean ( 36 / 120 )	302.707291666667	1.88641272653399	160.467159391385
Trimmed Mean ( 37 / 120 )	302.626573426573	1.87460417624426	161.434919041353
Trimmed Mean ( 38 / 120 )	302.544718309859	1.86227542313785	162.459706309223
Trimmed Mean ( 39 / 120 )	302.464893617021	1.84992659168524	163.501024838765
Trimmed Mean ( 40 / 120 )	302.385357142857	1.83731048137498	164.580434394823
Trimmed Mean ( 41 / 120 )	302.31582733813	1.8258349746896	165.576753391705
Trimmed Mean ( 42 / 120 )	302.247101449275	1.81417216783874	166.603317373867
Trimmed Mean ( 43 / 120 )	302.178832116788	1.80252125511483	167.642312821181
Trimmed Mean ( 44 / 120 )	302.112132352941	1.79120574804887	168.664115042075
Trimmed Mean ( 45 / 120 )	302.047777777778	1.77999482394498	169.690256238135
Trimmed Mean ( 46 / 120 )	301.992910447761	1.77008852285704	170.608930880092
Trimmed Mean ( 47 / 120 )	301.941729323308	1.76038904670284	171.519886407403
Trimmed Mean ( 48 / 120 )	301.895833333333	1.75126731972899	172.387065031313
Trimmed Mean ( 49 / 120 )	301.895833333333	1.74232509816111	173.271815720247
Trimmed Mean ( 50 / 120 )	301.804230769231	1.73313411660617	174.1378395806
Trimmed Mean ( 51 / 120 )	301.758139534884	1.72398944132705	175.034795632277
Trimmed Mean ( 52 / 120 )	301.758139534884	1.71482575557802	175.970146560558
Trimmed Mean ( 53 / 120 )	301.666535433071	1.70560110311662	176.8681638877
Trimmed Mean ( 54 / 120 )	301.628174603175	1.6971756550078	177.723604338285
Trimmed Mean ( 55 / 120 )	301.59	1.68915256431803	178.54515120235
Trimmed Mean ( 56 / 120 )	301.554435483871	1.68120936224408	179.367568523028
Trimmed Mean ( 57 / 120 )	301.517886178862	1.67326423365624	180.197413005128
Trimmed Mean ( 58 / 120 )	301.482786885246	1.66525131010502	181.043416723829
Trimmed Mean ( 59 / 120 )	301.44958677686	1.65740932623171	181.879987041123
Trimmed Mean ( 60 / 120 )	301.419166666667	1.64965821992363	182.716130545284
Trimmed Mean ( 61 / 120 )	301.391596638655	1.64190442580637	183.562204901565
Trimmed Mean ( 62 / 120 )	301.366525423729	1.63467886782598	184.358243906662
Trimmed Mean ( 63 / 120 )	301.366525423729	1.62718527887329	185.207259023634
Trimmed Mean ( 64 / 120 )	301.311206896552	1.61940950380989	186.062392611427
Trimmed Mean ( 65 / 120 )	301.284347826087	1.61157176073767	186.950624952736
Trimmed Mean ( 66 / 120 )	301.261403508772	1.60384071950344	187.837482765773
Trimmed Mean ( 67 / 120 )	301.238053097345	1.59577029878274	188.772816067031
Trimmed Mean ( 68 / 120 )	301.217410714286	1.587631756288	189.727504203213
Trimmed Mean ( 69 / 120 )	301.195945945946	1.58025469174371	190.599621389888
Trimmed Mean ( 70 / 120 )	301.174090909091	1.57243655217964	191.533382057049
Trimmed Mean ( 71 / 120 )	301.151376146789	1.56431480385053	192.513281473467
Trimmed Mean ( 72 / 120 )	301.126388888889	1.55591851328031	193.536092230197
Trimmed Mean ( 73 / 120 )	301.10046728972	1.54730130443037	194.597177955956
Trimmed Mean ( 74 / 120 )	301.072641509434	1.5383262861605	195.714423018071
Trimmed Mean ( 75 / 120 )	301.047142857143	1.52919088833651	196.86694784366
Trimmed Mean ( 76 / 120 )	301.017788461538	1.52025470951349	198.004838648301
Trimmed Mean ( 77 / 120 )	300.98932038835	1.51108553867943	199.187479916848
Trimmed Mean ( 78 / 120 )	300.960784313725	1.50153665996464	200.435189055466
Trimmed Mean ( 79 / 120 )	300.930693069307	1.49163529588915	201.745489596989
Trimmed Mean ( 80 / 120 )	300.896	1.4815874686078	203.090270655935
Trimmed Mean ( 81 / 120 )	300.862121212121	1.47164717967668	204.439029522159
Trimmed Mean ( 82 / 120 )	300.826020408163	1.46138377052344	205.850117180659
Trimmed Mean ( 83 / 120 )	300.789690721649	1.45094123702646	207.306597294102
Trimmed Mean ( 84 / 120 )	300.758333333333	1.44092918118047	208.725270652746
Trimmed Mean ( 85 / 120 )	300.730526315789	1.43114015872759	210.13352499532
Trimmed Mean ( 86 / 120 )	300.701595744681	1.42089983893828	211.627580990769
Trimmed Mean ( 87 / 120 )	300.668817204301	1.41065937432828	213.140622517375
Trimmed Mean ( 88 / 120 )	300.640760869565	1.40051754821965	214.664044196906
Trimmed Mean ( 89 / 120 )	300.628571428571	1.39216424561319	215.943321613002
Trimmed Mean ( 90 / 120 )	300.616111111111	1.3835026402167	217.286257627976
Trimmed Mean ( 91 / 120 )	300.602808988764	1.37473748347238	218.661971905711
Trimmed Mean ( 92 / 120 )	300.590340909091	1.36564210647309	220.109162923657
Trimmed Mean ( 93 / 120 )	300.575862068966	1.35641748789155	221.595389879695
Trimmed Mean ( 94 / 120 )	300.560465116279	1.34690273826991	223.149345959714
Trimmed Mean ( 95 / 120 )	300.546470588235	1.33692873799697	224.803657851295
Trimmed Mean ( 96 / 120 )	300.530952380952	1.32653141493023	226.553965476015
Trimmed Mean ( 97 / 120 )	300.514457831325	1.31542406231483	228.45443263558
Trimmed Mean ( 98 / 120 )	300.514457831325	1.30392497211221	230.469133008878
Trimmed Mean ( 99 / 120 )	300.48950617284	1.29293337727125	232.409118254049
Trimmed Mean ( 100 / 120 )	300.470625	1.28249786888975	234.285477027821
Trimmed Mean ( 101 / 120 )	300.45	1.2719582269847	236.210587443776
Trimmed Mean ( 102 / 120 )	300.423076923077	1.26247778683219	237.963059672439
Trimmed Mean ( 103 / 120 )	300.398701298701	1.25289715596831	239.763255800941
Trimmed Mean ( 104 / 120 )	300.398701298701	1.24305376776426	241.661872630814
Trimmed Mean ( 105 / 120 )	300.340666666667	1.23400843606653	243.386234557697
Trimmed Mean ( 106 / 120 )	300.308783783784	1.22444982563041	245.260179304749
Trimmed Mean ( 107 / 120 )	300.278082191781	1.21558859747432	247.022786175917
Trimmed Mean ( 108 / 120 )	300.240972222222	1.20665421199675	248.821053485894
Trimmed Mean ( 109 / 120 )	300.240972222222	1.19721124524017	250.783621867827
Trimmed Mean ( 110 / 120 )	300.169285714286	1.18759773608877	252.753332709156
Trimmed Mean ( 111 / 120 )	300.136956521739	1.17777969148682	254.832850906818
Trimmed Mean ( 112 / 120 )	300.102941176471	1.16712126585537	257.130899724056
Trimmed Mean ( 113 / 120 )	300.067164179104	1.15741294764015	259.256788850437
Trimmed Mean ( 114 / 120 )	300.032575757576	1.15035044606125	260.818411280557
Trimmed Mean ( 115 / 120 )	300.032575757576	1.14274300887426	262.554724402247
Trimmed Mean ( 116 / 120 )	299.959375	1.13464665355355	264.363688960409
Trimmed Mean ( 117 / 120 )	299.91746031746	1.12682336434414	266.16191126994
Trimmed Mean ( 118 / 120 )	299.878225806452	1.11881341484197	268.032383084009
Trimmed Mean ( 119 / 120 )	299.836885245902	1.11076636831022	269.936949659392
Trimmed Mean ( 120 / 120 )	299.789166666667	1.10323676820225	271.736018330117
Median	296.45
Midrange	351.05
Midmean - Weighted Average at Xnp	300.440331491713
Midmean - Weighted Average at X(n+1)p	300.616111111111
Midmean - Empirical Distribution Function	300.440331491713
Midmean - Empirical Distribution Function - Averaging	300.616111111111
Midmean - Empirical Distribution Function - Interpolation	300.616111111111
Midmean - Closest Observation	300.440331491713
Midmean - True Basic - Statistics Graphics Toolkit	300.616111111111
Midmean - MS Excel (old versions)	300.628571428571
Number of observations	360

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/07/t1289142325yqyz6203feez3s0/1k1zd1289142176.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Nov/07/t1289142325yqyz6203feez3s0/1k1zd1289142176.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2010/Nov/07/t1289142325yqyz6203feez3s0/2dsgg1289142176.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Nov/07/t1289142325yqyz6203feez3s0/2dsgg1289142176.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

Parameters (R input):

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')