FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Dec 2014 20:13:06 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/15/t1418674415um5v0su8gu2r8m6.htm/, Retrieved Sat, 18 May 2024 14:11:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268981, Retrieved Sat, 18 May 2024 14:11:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Chi-squared test] [2014-11-02 11:21:00] [5c51c91cab622bcf955f01721b682696]
- R  D  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 17:26:49] [e493208d2907342b139e6792bbaea494]
-    D    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 17:30:24] [e493208d2907342b139e6792bbaea494]
-    D      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 17:36:06] [e493208d2907342b139e6792bbaea494]
-    D        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 17:38:19] [e493208d2907342b139e6792bbaea494]
-    D          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 17:39:21] [e493208d2907342b139e6792bbaea494]
-    D            [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 17:40:38] [e493208d2907342b139e6792bbaea494]
-    D              [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 18:43:34] [e493208d2907342b139e6792bbaea494]
-    D                [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 18:53:25] [e493208d2907342b139e6792bbaea494]
-    D                  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 18:54:41] [e493208d2907342b139e6792bbaea494]
-    D                    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 18:55:52] [e493208d2907342b139e6792bbaea494]
-    D                      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 18:56:38] [e493208d2907342b139e6792bbaea494]
-    D                        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 18:59:28] [e493208d2907342b139e6792bbaea494]
-    D                          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:00:52] [e493208d2907342b139e6792bbaea494]
-    D                            [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:02:37] [e493208d2907342b139e6792bbaea494]
-    D                              [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:03:31] [e493208d2907342b139e6792bbaea494]
-    D                                [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:04:30] [e493208d2907342b139e6792bbaea494]
-    D                                  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:05:26] [e493208d2907342b139e6792bbaea494]
-    D                                    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:06:29] [e493208d2907342b139e6792bbaea494]
-    D                                      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:07:30] [e493208d2907342b139e6792bbaea494]
-    D                                        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 19:08:04] [e493208d2907342b139e6792bbaea494]
- RM D                                            [Central Tendency] [] [2014-12-15 20:13:06] [04df4205f362f56e0d1a9032a00a5d3d] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.95766
-2.51211
0.659189
2.32054
-2.28693
-1.96869
-0.346925
-2.37439
-1.40541
-1.70769
1.74412
-0.0973069
-3.1821
-0.899764
-0.725277
-2.19126
-2.32044
3.13639
-5.42505
-0.577127
0.4231
-3.43409
-1.69789
-3.52257
0.69679
-2.2929
0.228055
-1.77436
0.18985
-0.348927
-0.206086
-2.02222
-1.11574
2.73562
-1.29778
-1.80746
-1.01492
-2.26678
2.54526
-2.53014
-0.912864
-0.969082
-2.53071
2.01878
-4.78508
-3.51359
-1.23922
0.593188
0.0521611
1.47342
3.74901
0.134239
-2.62487
0.0928561
1.51999
0.514791
1.75526
-0.470489
0.370694
-3.10568
-5.20983
0.0744949
1.77329
-1.39932
-0.334077
4.23927
1.18635
2.63123
1.49113
-0.42408
-1.92094
3.39338
1.8434
-3.04887
-1.2835
0.460558
0.356353
1.11861
4.18649
-0.454636
1.18634
3.05363
2.29477
-3.01147
0.177974
3.29871
1.73554
-0.194108
0.68177
3.38396
1.42143
-2.85323
-0.682904
-0.703621
0.935406
-0.0386637
0.105748
-2.31415
2.53609
2.84698
2.04449
2.26953
2.4808
1.40907
1.76643
-1.15364
-2.75842
2.63123
1.0796
-0.173169
-2.07101
2.14941
1.54759
-5.67408
0.150621
1.90087
1.72753
2.09413
1.19468
4.02888
1.08075
1.12785
1.43244
1.76783

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268981&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268981&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-3.10483870959223e-070.19359788024715-1.60375656263826e-06
Geometric MeanNaN
Harmonic Mean4.05284646276342
Quadratic Mean2.14710435844452
Winsorized Mean ( 1 / 41 )0.001582350806451620.1930537181204690.00819642751176752
Winsorized Mean ( 2 / 41 )0.00251154435483870.1918326879034090.0130923690966751
Winsorized Mean ( 3 / 41 )0.006016705645161310.1885108266053910.0319170296661849
Winsorized Mean ( 4 / 41 )0.03527089919354840.1791916244190310.196833413994111
Winsorized Mean ( 5 / 41 )0.03525315725806450.1790754187879410.196862067930221
Winsorized Mean ( 6 / 41 )0.03497493145161290.1778391540544110.196666092107658
Winsorized Mean ( 7 / 41 )0.04003694758064510.174296009561840.229706621977712
Winsorized Mean ( 8 / 41 )0.03962791532258070.1727964698547210.229332898732815
Winsorized Mean ( 9 / 41 )0.02875243145161290.1701141372167880.1690184714923
Winsorized Mean ( 10 / 41 )0.02278791532258070.1684788017569030.135256869617705
Winsorized Mean ( 11 / 41 )0.02756493145161290.1652567141224470.166800674925611
Winsorized Mean ( 12 / 41 )0.03674009274193550.1639706827198840.224065010479341
Winsorized Mean ( 13 / 41 )0.04172831854838710.1609071266313480.259331699111067
Winsorized Mean ( 14 / 41 )0.05132396370967740.1593595714494760.322063891380063
Winsorized Mean ( 15 / 41 )0.04470460887096780.158508684489770.282032552442595
Winsorized Mean ( 16 / 41 )0.02635235080645160.1556696357364920.16928382135524
Winsorized Mean ( 17 / 41 )0.04170033467741940.1527804958482450.272942789234299
Winsorized Mean ( 18 / 41 )0.04586791532258060.1513407811592710.303077035622733
Winsorized Mean ( 19 / 41 )0.02842622177419350.1490537158273120.19071125879966
Winsorized Mean ( 20 / 41 )0.02293751209677420.1475917224232830.155411914165423
Winsorized Mean ( 21 / 41 )0.01554178629032270.1465097916126410.106080188356378
Winsorized Mean ( 22 / 41 )0.01455533467741940.1455414731027520.100008158273507
Winsorized Mean ( 23 / 41 )0.01722630241935480.142504127578770.120882831339975
Winsorized Mean ( 24 / 41 )0.02950888306451610.1383887258265050.213231843044142
Winsorized Mean ( 25 / 41 )0.02775888306451620.1359124452451340.204240921531871
Winsorized Mean ( 26 / 41 )0.02428243145161290.1329557489359720.182635438075767
Winsorized Mean ( 27 / 41 )0.03349073790322580.1315670509301250.25455262291326
Winsorized Mean ( 28 / 41 )0.0587991250.1284720999676130.457680111205647
Winsorized Mean ( 29 / 41 )0.06392791532258060.1272782074942680.502269136100614
Winsorized Mean ( 30 / 41 )0.07736259274193550.125103982372450.618386331712585
Winsorized Mean ( 31 / 41 )0.07766759274193550.1245877416996380.623396745798477
Winsorized Mean ( 32 / 41 )0.1510792056451610.1158578716471091.30400466966399
Winsorized Mean ( 33 / 41 )0.1048126733870970.1104864235831490.948647535035994
Winsorized Mean ( 34 / 41 )0.1250865443548390.1066307552564941.17308129398456
Winsorized Mean ( 35 / 41 )0.1209712217741940.1053296955803951.14850063040256
Winsorized Mean ( 36 / 41 )0.1286850927419360.1033977730665721.2445634845451
Winsorized Mean ( 37 / 41 )0.1419931572580640.09937882113889741.4288070197533
Winsorized Mean ( 38 / 41 )0.1502336411290320.09779568759157951.53619903728728
Winsorized Mean ( 39 / 41 )0.1780557379032260.09407972462087491.89260479471809
Winsorized Mean ( 40 / 41 )0.1236841250.08533395691255181.44941274816013
Winsorized Mean ( 41 / 41 )0.1395180604838710.08312808288226061.6783505122027
Trimmed Mean ( 1 / 41 )0.01176042213114750.1879487343393840.062572499742996
Trimmed Mean ( 2 / 41 )0.02227776250.1822791952662390.122217801474605
Trimmed Mean ( 3 / 41 )0.03266340254237290.1766916595682730.184861032049743
Trimmed Mean ( 4 / 41 )0.04215820258620690.1718560347976140.245311156142142
Trimmed Mean ( 5 / 41 )0.04403106578947370.1694882594614660.259788294064606
Trimmed Mean ( 6 / 41 )0.04597474553571430.1668852159373130.275487228017752
Trimmed Mean ( 7 / 41 )0.04804137727272730.1642705685833030.292452736281637
Trimmed Mean ( 8 / 41 )0.04935427314814820.1620802194516680.304505221643444
Trimmed Mean ( 9 / 41 )0.05077652358490570.1599067459650930.317538345730517
Trimmed Mean ( 10 / 41 )0.05369424519230770.1579273531136580.339993320559642
Trimmed Mean ( 11 / 41 )0.05745148529411770.1559594393335340.368374530837163
Trimmed Mean ( 12 / 41 )0.0608205150.154227164311070.394356696316658
Trimmed Mean ( 13 / 41 )0.06335960714285720.1524489155008850.415612055583887
Trimmed Mean ( 14 / 41 )0.06550886979166670.1508524662127910.434257864231802
Trimmed Mean ( 15 / 41 )0.06684544148936170.1492353282765460.447919686721171
Trimmed Mean ( 16 / 41 )0.06883490760869570.1474916930040640.466703623822388
Trimmed Mean ( 17 / 41 )0.07249312777777780.1458498503590820.497039438842753
Trimmed Mean ( 18 / 41 )0.07504547159090910.1443211995644920.519989244943699
Trimmed Mean ( 19 / 41 )0.07738269186046510.1427256870763820.542177749819152
Trimmed Mean ( 20 / 41 )0.08118632738095240.1411448680331140.575198577973837
Trimmed Mean ( 21 / 41 )0.0855905060975610.1394732882871030.613669521588783
Trimmed Mean ( 22 / 41 )0.090760768750.1376435993392330.65938967874789
Trimmed Mean ( 23 / 41 )0.09626745512820510.1356154089494750.709856319970771
Trimmed Mean ( 24 / 41 )0.1018744934210530.1336134977707450.762456601471879
Trimmed Mean ( 25 / 41 )0.1069270472972970.1317722515343960.811453443742569
Trimmed Mean ( 26 / 41 )0.1123808541666670.1298919006299260.865187541499221
Trimmed Mean ( 27 / 41 )0.1183831642857140.1280181677629350.924737217805966
Trimmed Mean ( 28 / 41 )0.1241166397058820.1259515463602690.985431646475081
Trimmed Mean ( 29 / 41 )0.1284994166666670.1238899308707371.03720629887782
Trimmed Mean ( 30 / 41 )0.13281346093750.1215573262849991.09259939319585
Trimmed Mean ( 31 / 41 )0.1365101854838710.1190400560260971.14675841091627
Trimmed Mean ( 32 / 41 )0.1404330250.1160436789839531.21017384341477
Trimmed Mean ( 33 / 41 )0.139721750.1137301103395031.228537891882
Trimmed Mean ( 34 / 41 )0.1420641339285710.111673417706521.2721392149197
Trimmed Mean ( 35 / 41 )0.1432107685185190.1096953264668971.30553208720095
Trimmed Mean ( 36 / 41 )0.1447259903846150.1073928694962961.34763128188513
Trimmed Mean ( 37 / 41 )0.145831030.1047939210636441.39159818164865
Trimmed Mean ( 38 / 41 )0.1460989895833330.1021951776707421.42960747183241
Trimmed Mean ( 39 / 41 )0.1458056847826090.09913301611523751.47080852067606
Trimmed Mean ( 40 / 41 )0.1434752613636360.0958969694826071.49613968134477
Trimmed Mean ( 41 / 41 )0.1449360357142860.09350684920822021.55000448567723
Median0.1199935
Midrange-0.717405
Midmean - Weighted Average at Xnp0.107237166666667
Midmean - Weighted Average at X(n+1)p0.136510185483871
Midmean - Empirical Distribution Function0.107237166666667
Midmean - Empirical Distribution Function - Averaging0.136510185483871
Midmean - Empirical Distribution Function - Interpolation0.136510185483871
Midmean - Closest Observation0.107237166666667
Midmean - True Basic - Statistics Graphics Toolkit0.136510185483871
Midmean - MS Excel (old versions)0.1328134609375
Number of observations124

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -3.10483870959223e-07 & 0.19359788024715 & -1.60375656263826e-06 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 4.05284646276342 &  &  \tabularnewline
Quadratic Mean & 2.14710435844452 &  &  \tabularnewline
Winsorized Mean ( 1 / 41 ) & 0.00158235080645162 & 0.193053718120469 & 0.00819642751176752 \tabularnewline
Winsorized Mean ( 2 / 41 ) & 0.0025115443548387 & 0.191832687903409 & 0.0130923690966751 \tabularnewline
Winsorized Mean ( 3 / 41 ) & 0.00601670564516131 & 0.188510826605391 & 0.0319170296661849 \tabularnewline
Winsorized Mean ( 4 / 41 ) & 0.0352708991935484 & 0.179191624419031 & 0.196833413994111 \tabularnewline
Winsorized Mean ( 5 / 41 ) & 0.0352531572580645 & 0.179075418787941 & 0.196862067930221 \tabularnewline
Winsorized Mean ( 6 / 41 ) & 0.0349749314516129 & 0.177839154054411 & 0.196666092107658 \tabularnewline
Winsorized Mean ( 7 / 41 ) & 0.0400369475806451 & 0.17429600956184 & 0.229706621977712 \tabularnewline
Winsorized Mean ( 8 / 41 ) & 0.0396279153225807 & 0.172796469854721 & 0.229332898732815 \tabularnewline
Winsorized Mean ( 9 / 41 ) & 0.0287524314516129 & 0.170114137216788 & 0.1690184714923 \tabularnewline
Winsorized Mean ( 10 / 41 ) & 0.0227879153225807 & 0.168478801756903 & 0.135256869617705 \tabularnewline
Winsorized Mean ( 11 / 41 ) & 0.0275649314516129 & 0.165256714122447 & 0.166800674925611 \tabularnewline
Winsorized Mean ( 12 / 41 ) & 0.0367400927419355 & 0.163970682719884 & 0.224065010479341 \tabularnewline
Winsorized Mean ( 13 / 41 ) & 0.0417283185483871 & 0.160907126631348 & 0.259331699111067 \tabularnewline
Winsorized Mean ( 14 / 41 ) & 0.0513239637096774 & 0.159359571449476 & 0.322063891380063 \tabularnewline
Winsorized Mean ( 15 / 41 ) & 0.0447046088709678 & 0.15850868448977 & 0.282032552442595 \tabularnewline
Winsorized Mean ( 16 / 41 ) & 0.0263523508064516 & 0.155669635736492 & 0.16928382135524 \tabularnewline
Winsorized Mean ( 17 / 41 ) & 0.0417003346774194 & 0.152780495848245 & 0.272942789234299 \tabularnewline
Winsorized Mean ( 18 / 41 ) & 0.0458679153225806 & 0.151340781159271 & 0.303077035622733 \tabularnewline
Winsorized Mean ( 19 / 41 ) & 0.0284262217741935 & 0.149053715827312 & 0.19071125879966 \tabularnewline
Winsorized Mean ( 20 / 41 ) & 0.0229375120967742 & 0.147591722423283 & 0.155411914165423 \tabularnewline
Winsorized Mean ( 21 / 41 ) & 0.0155417862903227 & 0.146509791612641 & 0.106080188356378 \tabularnewline
Winsorized Mean ( 22 / 41 ) & 0.0145553346774194 & 0.145541473102752 & 0.100008158273507 \tabularnewline
Winsorized Mean ( 23 / 41 ) & 0.0172263024193548 & 0.14250412757877 & 0.120882831339975 \tabularnewline
Winsorized Mean ( 24 / 41 ) & 0.0295088830645161 & 0.138388725826505 & 0.213231843044142 \tabularnewline
Winsorized Mean ( 25 / 41 ) & 0.0277588830645162 & 0.135912445245134 & 0.204240921531871 \tabularnewline
Winsorized Mean ( 26 / 41 ) & 0.0242824314516129 & 0.132955748935972 & 0.182635438075767 \tabularnewline
Winsorized Mean ( 27 / 41 ) & 0.0334907379032258 & 0.131567050930125 & 0.25455262291326 \tabularnewline
Winsorized Mean ( 28 / 41 ) & 0.058799125 & 0.128472099967613 & 0.457680111205647 \tabularnewline
Winsorized Mean ( 29 / 41 ) & 0.0639279153225806 & 0.127278207494268 & 0.502269136100614 \tabularnewline
Winsorized Mean ( 30 / 41 ) & 0.0773625927419355 & 0.12510398237245 & 0.618386331712585 \tabularnewline
Winsorized Mean ( 31 / 41 ) & 0.0776675927419355 & 0.124587741699638 & 0.623396745798477 \tabularnewline
Winsorized Mean ( 32 / 41 ) & 0.151079205645161 & 0.115857871647109 & 1.30400466966399 \tabularnewline
Winsorized Mean ( 33 / 41 ) & 0.104812673387097 & 0.110486423583149 & 0.948647535035994 \tabularnewline
Winsorized Mean ( 34 / 41 ) & 0.125086544354839 & 0.106630755256494 & 1.17308129398456 \tabularnewline
Winsorized Mean ( 35 / 41 ) & 0.120971221774194 & 0.105329695580395 & 1.14850063040256 \tabularnewline
Winsorized Mean ( 36 / 41 ) & 0.128685092741936 & 0.103397773066572 & 1.2445634845451 \tabularnewline
Winsorized Mean ( 37 / 41 ) & 0.141993157258064 & 0.0993788211388974 & 1.4288070197533 \tabularnewline
Winsorized Mean ( 38 / 41 ) & 0.150233641129032 & 0.0977956875915795 & 1.53619903728728 \tabularnewline
Winsorized Mean ( 39 / 41 ) & 0.178055737903226 & 0.0940797246208749 & 1.89260479471809 \tabularnewline
Winsorized Mean ( 40 / 41 ) & 0.123684125 & 0.0853339569125518 & 1.44941274816013 \tabularnewline
Winsorized Mean ( 41 / 41 ) & 0.139518060483871 & 0.0831280828822606 & 1.6783505122027 \tabularnewline
Trimmed Mean ( 1 / 41 ) & 0.0117604221311475 & 0.187948734339384 & 0.062572499742996 \tabularnewline
Trimmed Mean ( 2 / 41 ) & 0.0222777625 & 0.182279195266239 & 0.122217801474605 \tabularnewline
Trimmed Mean ( 3 / 41 ) & 0.0326634025423729 & 0.176691659568273 & 0.184861032049743 \tabularnewline
Trimmed Mean ( 4 / 41 ) & 0.0421582025862069 & 0.171856034797614 & 0.245311156142142 \tabularnewline
Trimmed Mean ( 5 / 41 ) & 0.0440310657894737 & 0.169488259461466 & 0.259788294064606 \tabularnewline
Trimmed Mean ( 6 / 41 ) & 0.0459747455357143 & 0.166885215937313 & 0.275487228017752 \tabularnewline
Trimmed Mean ( 7 / 41 ) & 0.0480413772727273 & 0.164270568583303 & 0.292452736281637 \tabularnewline
Trimmed Mean ( 8 / 41 ) & 0.0493542731481482 & 0.162080219451668 & 0.304505221643444 \tabularnewline
Trimmed Mean ( 9 / 41 ) & 0.0507765235849057 & 0.159906745965093 & 0.317538345730517 \tabularnewline
Trimmed Mean ( 10 / 41 ) & 0.0536942451923077 & 0.157927353113658 & 0.339993320559642 \tabularnewline
Trimmed Mean ( 11 / 41 ) & 0.0574514852941177 & 0.155959439333534 & 0.368374530837163 \tabularnewline
Trimmed Mean ( 12 / 41 ) & 0.060820515 & 0.15422716431107 & 0.394356696316658 \tabularnewline
Trimmed Mean ( 13 / 41 ) & 0.0633596071428572 & 0.152448915500885 & 0.415612055583887 \tabularnewline
Trimmed Mean ( 14 / 41 ) & 0.0655088697916667 & 0.150852466212791 & 0.434257864231802 \tabularnewline
Trimmed Mean ( 15 / 41 ) & 0.0668454414893617 & 0.149235328276546 & 0.447919686721171 \tabularnewline
Trimmed Mean ( 16 / 41 ) & 0.0688349076086957 & 0.147491693004064 & 0.466703623822388 \tabularnewline
Trimmed Mean ( 17 / 41 ) & 0.0724931277777778 & 0.145849850359082 & 0.497039438842753 \tabularnewline
Trimmed Mean ( 18 / 41 ) & 0.0750454715909091 & 0.144321199564492 & 0.519989244943699 \tabularnewline
Trimmed Mean ( 19 / 41 ) & 0.0773826918604651 & 0.142725687076382 & 0.542177749819152 \tabularnewline
Trimmed Mean ( 20 / 41 ) & 0.0811863273809524 & 0.141144868033114 & 0.575198577973837 \tabularnewline
Trimmed Mean ( 21 / 41 ) & 0.085590506097561 & 0.139473288287103 & 0.613669521588783 \tabularnewline
Trimmed Mean ( 22 / 41 ) & 0.09076076875 & 0.137643599339233 & 0.65938967874789 \tabularnewline
Trimmed Mean ( 23 / 41 ) & 0.0962674551282051 & 0.135615408949475 & 0.709856319970771 \tabularnewline
Trimmed Mean ( 24 / 41 ) & 0.101874493421053 & 0.133613497770745 & 0.762456601471879 \tabularnewline
Trimmed Mean ( 25 / 41 ) & 0.106927047297297 & 0.131772251534396 & 0.811453443742569 \tabularnewline
Trimmed Mean ( 26 / 41 ) & 0.112380854166667 & 0.129891900629926 & 0.865187541499221 \tabularnewline
Trimmed Mean ( 27 / 41 ) & 0.118383164285714 & 0.128018167762935 & 0.924737217805966 \tabularnewline
Trimmed Mean ( 28 / 41 ) & 0.124116639705882 & 0.125951546360269 & 0.985431646475081 \tabularnewline
Trimmed Mean ( 29 / 41 ) & 0.128499416666667 & 0.123889930870737 & 1.03720629887782 \tabularnewline
Trimmed Mean ( 30 / 41 ) & 0.1328134609375 & 0.121557326284999 & 1.09259939319585 \tabularnewline
Trimmed Mean ( 31 / 41 ) & 0.136510185483871 & 0.119040056026097 & 1.14675841091627 \tabularnewline
Trimmed Mean ( 32 / 41 ) & 0.140433025 & 0.116043678983953 & 1.21017384341477 \tabularnewline
Trimmed Mean ( 33 / 41 ) & 0.13972175 & 0.113730110339503 & 1.228537891882 \tabularnewline
Trimmed Mean ( 34 / 41 ) & 0.142064133928571 & 0.11167341770652 & 1.2721392149197 \tabularnewline
Trimmed Mean ( 35 / 41 ) & 0.143210768518519 & 0.109695326466897 & 1.30553208720095 \tabularnewline
Trimmed Mean ( 36 / 41 ) & 0.144725990384615 & 0.107392869496296 & 1.34763128188513 \tabularnewline
Trimmed Mean ( 37 / 41 ) & 0.14583103 & 0.104793921063644 & 1.39159818164865 \tabularnewline
Trimmed Mean ( 38 / 41 ) & 0.146098989583333 & 0.102195177670742 & 1.42960747183241 \tabularnewline
Trimmed Mean ( 39 / 41 ) & 0.145805684782609 & 0.0991330161152375 & 1.47080852067606 \tabularnewline
Trimmed Mean ( 40 / 41 ) & 0.143475261363636 & 0.095896969482607 & 1.49613968134477 \tabularnewline
Trimmed Mean ( 41 / 41 ) & 0.144936035714286 & 0.0935068492082202 & 1.55000448567723 \tabularnewline
Median & 0.1199935 &  &  \tabularnewline
Midrange & -0.717405 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.107237166666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.136510185483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.107237166666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.136510185483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.136510185483871 &  &  \tabularnewline
Midmean - Closest Observation & 0.107237166666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.136510185483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.1328134609375 &  &  \tabularnewline
Number of observations & 124 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268981&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]-3.10483870959223e-07[/C][C]0.19359788024715[/C][C]-1.60375656263826e-06[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.05284646276342[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.14710435844452[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 41 )[/C][C]0.00158235080645162[/C][C]0.193053718120469[/C][C]0.00819642751176752[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 41 )[/C][C]0.0025115443548387[/C][C]0.191832687903409[/C][C]0.0130923690966751[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 41 )[/C][C]0.00601670564516131[/C][C]0.188510826605391[/C][C]0.0319170296661849[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 41 )[/C][C]0.0352708991935484[/C][C]0.179191624419031[/C][C]0.196833413994111[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 41 )[/C][C]0.0352531572580645[/C][C]0.179075418787941[/C][C]0.196862067930221[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 41 )[/C][C]0.0349749314516129[/C][C]0.177839154054411[/C][C]0.196666092107658[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 41 )[/C][C]0.0400369475806451[/C][C]0.17429600956184[/C][C]0.229706621977712[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 41 )[/C][C]0.0396279153225807[/C][C]0.172796469854721[/C][C]0.229332898732815[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 41 )[/C][C]0.0287524314516129[/C][C]0.170114137216788[/C][C]0.1690184714923[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 41 )[/C][C]0.0227879153225807[/C][C]0.168478801756903[/C][C]0.135256869617705[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 41 )[/C][C]0.0275649314516129[/C][C]0.165256714122447[/C][C]0.166800674925611[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 41 )[/C][C]0.0367400927419355[/C][C]0.163970682719884[/C][C]0.224065010479341[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 41 )[/C][C]0.0417283185483871[/C][C]0.160907126631348[/C][C]0.259331699111067[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 41 )[/C][C]0.0513239637096774[/C][C]0.159359571449476[/C][C]0.322063891380063[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 41 )[/C][C]0.0447046088709678[/C][C]0.15850868448977[/C][C]0.282032552442595[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 41 )[/C][C]0.0263523508064516[/C][C]0.155669635736492[/C][C]0.16928382135524[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 41 )[/C][C]0.0417003346774194[/C][C]0.152780495848245[/C][C]0.272942789234299[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 41 )[/C][C]0.0458679153225806[/C][C]0.151340781159271[/C][C]0.303077035622733[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 41 )[/C][C]0.0284262217741935[/C][C]0.149053715827312[/C][C]0.19071125879966[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 41 )[/C][C]0.0229375120967742[/C][C]0.147591722423283[/C][C]0.155411914165423[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 41 )[/C][C]0.0155417862903227[/C][C]0.146509791612641[/C][C]0.106080188356378[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 41 )[/C][C]0.0145553346774194[/C][C]0.145541473102752[/C][C]0.100008158273507[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 41 )[/C][C]0.0172263024193548[/C][C]0.14250412757877[/C][C]0.120882831339975[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 41 )[/C][C]0.0295088830645161[/C][C]0.138388725826505[/C][C]0.213231843044142[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 41 )[/C][C]0.0277588830645162[/C][C]0.135912445245134[/C][C]0.204240921531871[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 41 )[/C][C]0.0242824314516129[/C][C]0.132955748935972[/C][C]0.182635438075767[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 41 )[/C][C]0.0334907379032258[/C][C]0.131567050930125[/C][C]0.25455262291326[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 41 )[/C][C]0.058799125[/C][C]0.128472099967613[/C][C]0.457680111205647[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 41 )[/C][C]0.0639279153225806[/C][C]0.127278207494268[/C][C]0.502269136100614[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 41 )[/C][C]0.0773625927419355[/C][C]0.12510398237245[/C][C]0.618386331712585[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 41 )[/C][C]0.0776675927419355[/C][C]0.124587741699638[/C][C]0.623396745798477[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 41 )[/C][C]0.151079205645161[/C][C]0.115857871647109[/C][C]1.30400466966399[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 41 )[/C][C]0.104812673387097[/C][C]0.110486423583149[/C][C]0.948647535035994[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 41 )[/C][C]0.125086544354839[/C][C]0.106630755256494[/C][C]1.17308129398456[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 41 )[/C][C]0.120971221774194[/C][C]0.105329695580395[/C][C]1.14850063040256[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 41 )[/C][C]0.128685092741936[/C][C]0.103397773066572[/C][C]1.2445634845451[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 41 )[/C][C]0.141993157258064[/C][C]0.0993788211388974[/C][C]1.4288070197533[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 41 )[/C][C]0.150233641129032[/C][C]0.0977956875915795[/C][C]1.53619903728728[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 41 )[/C][C]0.178055737903226[/C][C]0.0940797246208749[/C][C]1.89260479471809[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 41 )[/C][C]0.123684125[/C][C]0.0853339569125518[/C][C]1.44941274816013[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 41 )[/C][C]0.139518060483871[/C][C]0.0831280828822606[/C][C]1.6783505122027[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 41 )[/C][C]0.0117604221311475[/C][C]0.187948734339384[/C][C]0.062572499742996[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 41 )[/C][C]0.0222777625[/C][C]0.182279195266239[/C][C]0.122217801474605[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 41 )[/C][C]0.0326634025423729[/C][C]0.176691659568273[/C][C]0.184861032049743[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 41 )[/C][C]0.0421582025862069[/C][C]0.171856034797614[/C][C]0.245311156142142[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 41 )[/C][C]0.0440310657894737[/C][C]0.169488259461466[/C][C]0.259788294064606[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 41 )[/C][C]0.0459747455357143[/C][C]0.166885215937313[/C][C]0.275487228017752[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 41 )[/C][C]0.0480413772727273[/C][C]0.164270568583303[/C][C]0.292452736281637[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 41 )[/C][C]0.0493542731481482[/C][C]0.162080219451668[/C][C]0.304505221643444[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 41 )[/C][C]0.0507765235849057[/C][C]0.159906745965093[/C][C]0.317538345730517[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 41 )[/C][C]0.0536942451923077[/C][C]0.157927353113658[/C][C]0.339993320559642[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 41 )[/C][C]0.0574514852941177[/C][C]0.155959439333534[/C][C]0.368374530837163[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 41 )[/C][C]0.060820515[/C][C]0.15422716431107[/C][C]0.394356696316658[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 41 )[/C][C]0.0633596071428572[/C][C]0.152448915500885[/C][C]0.415612055583887[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 41 )[/C][C]0.0655088697916667[/C][C]0.150852466212791[/C][C]0.434257864231802[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 41 )[/C][C]0.0668454414893617[/C][C]0.149235328276546[/C][C]0.447919686721171[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 41 )[/C][C]0.0688349076086957[/C][C]0.147491693004064[/C][C]0.466703623822388[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 41 )[/C][C]0.0724931277777778[/C][C]0.145849850359082[/C][C]0.497039438842753[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 41 )[/C][C]0.0750454715909091[/C][C]0.144321199564492[/C][C]0.519989244943699[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 41 )[/C][C]0.0773826918604651[/C][C]0.142725687076382[/C][C]0.542177749819152[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 41 )[/C][C]0.0811863273809524[/C][C]0.141144868033114[/C][C]0.575198577973837[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 41 )[/C][C]0.085590506097561[/C][C]0.139473288287103[/C][C]0.613669521588783[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 41 )[/C][C]0.09076076875[/C][C]0.137643599339233[/C][C]0.65938967874789[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 41 )[/C][C]0.0962674551282051[/C][C]0.135615408949475[/C][C]0.709856319970771[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 41 )[/C][C]0.101874493421053[/C][C]0.133613497770745[/C][C]0.762456601471879[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 41 )[/C][C]0.106927047297297[/C][C]0.131772251534396[/C][C]0.811453443742569[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 41 )[/C][C]0.112380854166667[/C][C]0.129891900629926[/C][C]0.865187541499221[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 41 )[/C][C]0.118383164285714[/C][C]0.128018167762935[/C][C]0.924737217805966[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 41 )[/C][C]0.124116639705882[/C][C]0.125951546360269[/C][C]0.985431646475081[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 41 )[/C][C]0.128499416666667[/C][C]0.123889930870737[/C][C]1.03720629887782[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 41 )[/C][C]0.1328134609375[/C][C]0.121557326284999[/C][C]1.09259939319585[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 41 )[/C][C]0.136510185483871[/C][C]0.119040056026097[/C][C]1.14675841091627[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 41 )[/C][C]0.140433025[/C][C]0.116043678983953[/C][C]1.21017384341477[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 41 )[/C][C]0.13972175[/C][C]0.113730110339503[/C][C]1.228537891882[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 41 )[/C][C]0.142064133928571[/C][C]0.11167341770652[/C][C]1.2721392149197[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 41 )[/C][C]0.143210768518519[/C][C]0.109695326466897[/C][C]1.30553208720095[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 41 )[/C][C]0.144725990384615[/C][C]0.107392869496296[/C][C]1.34763128188513[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 41 )[/C][C]0.14583103[/C][C]0.104793921063644[/C][C]1.39159818164865[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 41 )[/C][C]0.146098989583333[/C][C]0.102195177670742[/C][C]1.42960747183241[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 41 )[/C][C]0.145805684782609[/C][C]0.0991330161152375[/C][C]1.47080852067606[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 41 )[/C][C]0.143475261363636[/C][C]0.095896969482607[/C][C]1.49613968134477[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 41 )[/C][C]0.144936035714286[/C][C]0.0935068492082202[/C][C]1.55000448567723[/C][/ROW]
[ROW][C]Median[/C][C]0.1199935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.717405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.107237166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.136510185483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.107237166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.136510185483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.136510185483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.107237166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.136510185483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.1328134609375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]124[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268981&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-3.10483870959223e-070.19359788024715-1.60375656263826e-06
Geometric MeanNaN
Harmonic Mean4.05284646276342
Quadratic Mean2.14710435844452
Winsorized Mean ( 1 / 41 )0.001582350806451620.1930537181204690.00819642751176752
Winsorized Mean ( 2 / 41 )0.00251154435483870.1918326879034090.0130923690966751
Winsorized Mean ( 3 / 41 )0.006016705645161310.1885108266053910.0319170296661849
Winsorized Mean ( 4 / 41 )0.03527089919354840.1791916244190310.196833413994111
Winsorized Mean ( 5 / 41 )0.03525315725806450.1790754187879410.196862067930221
Winsorized Mean ( 6 / 41 )0.03497493145161290.1778391540544110.196666092107658
Winsorized Mean ( 7 / 41 )0.04003694758064510.174296009561840.229706621977712
Winsorized Mean ( 8 / 41 )0.03962791532258070.1727964698547210.229332898732815
Winsorized Mean ( 9 / 41 )0.02875243145161290.1701141372167880.1690184714923
Winsorized Mean ( 10 / 41 )0.02278791532258070.1684788017569030.135256869617705
Winsorized Mean ( 11 / 41 )0.02756493145161290.1652567141224470.166800674925611
Winsorized Mean ( 12 / 41 )0.03674009274193550.1639706827198840.224065010479341
Winsorized Mean ( 13 / 41 )0.04172831854838710.1609071266313480.259331699111067
Winsorized Mean ( 14 / 41 )0.05132396370967740.1593595714494760.322063891380063
Winsorized Mean ( 15 / 41 )0.04470460887096780.158508684489770.282032552442595
Winsorized Mean ( 16 / 41 )0.02635235080645160.1556696357364920.16928382135524
Winsorized Mean ( 17 / 41 )0.04170033467741940.1527804958482450.272942789234299
Winsorized Mean ( 18 / 41 )0.04586791532258060.1513407811592710.303077035622733
Winsorized Mean ( 19 / 41 )0.02842622177419350.1490537158273120.19071125879966
Winsorized Mean ( 20 / 41 )0.02293751209677420.1475917224232830.155411914165423
Winsorized Mean ( 21 / 41 )0.01554178629032270.1465097916126410.106080188356378
Winsorized Mean ( 22 / 41 )0.01455533467741940.1455414731027520.100008158273507
Winsorized Mean ( 23 / 41 )0.01722630241935480.142504127578770.120882831339975
Winsorized Mean ( 24 / 41 )0.02950888306451610.1383887258265050.213231843044142
Winsorized Mean ( 25 / 41 )0.02775888306451620.1359124452451340.204240921531871
Winsorized Mean ( 26 / 41 )0.02428243145161290.1329557489359720.182635438075767
Winsorized Mean ( 27 / 41 )0.03349073790322580.1315670509301250.25455262291326
Winsorized Mean ( 28 / 41 )0.0587991250.1284720999676130.457680111205647
Winsorized Mean ( 29 / 41 )0.06392791532258060.1272782074942680.502269136100614
Winsorized Mean ( 30 / 41 )0.07736259274193550.125103982372450.618386331712585
Winsorized Mean ( 31 / 41 )0.07766759274193550.1245877416996380.623396745798477
Winsorized Mean ( 32 / 41 )0.1510792056451610.1158578716471091.30400466966399
Winsorized Mean ( 33 / 41 )0.1048126733870970.1104864235831490.948647535035994
Winsorized Mean ( 34 / 41 )0.1250865443548390.1066307552564941.17308129398456
Winsorized Mean ( 35 / 41 )0.1209712217741940.1053296955803951.14850063040256
Winsorized Mean ( 36 / 41 )0.1286850927419360.1033977730665721.2445634845451
Winsorized Mean ( 37 / 41 )0.1419931572580640.09937882113889741.4288070197533
Winsorized Mean ( 38 / 41 )0.1502336411290320.09779568759157951.53619903728728
Winsorized Mean ( 39 / 41 )0.1780557379032260.09407972462087491.89260479471809
Winsorized Mean ( 40 / 41 )0.1236841250.08533395691255181.44941274816013
Winsorized Mean ( 41 / 41 )0.1395180604838710.08312808288226061.6783505122027
Trimmed Mean ( 1 / 41 )0.01176042213114750.1879487343393840.062572499742996
Trimmed Mean ( 2 / 41 )0.02227776250.1822791952662390.122217801474605
Trimmed Mean ( 3 / 41 )0.03266340254237290.1766916595682730.184861032049743
Trimmed Mean ( 4 / 41 )0.04215820258620690.1718560347976140.245311156142142
Trimmed Mean ( 5 / 41 )0.04403106578947370.1694882594614660.259788294064606
Trimmed Mean ( 6 / 41 )0.04597474553571430.1668852159373130.275487228017752
Trimmed Mean ( 7 / 41 )0.04804137727272730.1642705685833030.292452736281637
Trimmed Mean ( 8 / 41 )0.04935427314814820.1620802194516680.304505221643444
Trimmed Mean ( 9 / 41 )0.05077652358490570.1599067459650930.317538345730517
Trimmed Mean ( 10 / 41 )0.05369424519230770.1579273531136580.339993320559642
Trimmed Mean ( 11 / 41 )0.05745148529411770.1559594393335340.368374530837163
Trimmed Mean ( 12 / 41 )0.0608205150.154227164311070.394356696316658
Trimmed Mean ( 13 / 41 )0.06335960714285720.1524489155008850.415612055583887
Trimmed Mean ( 14 / 41 )0.06550886979166670.1508524662127910.434257864231802
Trimmed Mean ( 15 / 41 )0.06684544148936170.1492353282765460.447919686721171
Trimmed Mean ( 16 / 41 )0.06883490760869570.1474916930040640.466703623822388
Trimmed Mean ( 17 / 41 )0.07249312777777780.1458498503590820.497039438842753
Trimmed Mean ( 18 / 41 )0.07504547159090910.1443211995644920.519989244943699
Trimmed Mean ( 19 / 41 )0.07738269186046510.1427256870763820.542177749819152
Trimmed Mean ( 20 / 41 )0.08118632738095240.1411448680331140.575198577973837
Trimmed Mean ( 21 / 41 )0.0855905060975610.1394732882871030.613669521588783
Trimmed Mean ( 22 / 41 )0.090760768750.1376435993392330.65938967874789
Trimmed Mean ( 23 / 41 )0.09626745512820510.1356154089494750.709856319970771
Trimmed Mean ( 24 / 41 )0.1018744934210530.1336134977707450.762456601471879
Trimmed Mean ( 25 / 41 )0.1069270472972970.1317722515343960.811453443742569
Trimmed Mean ( 26 / 41 )0.1123808541666670.1298919006299260.865187541499221
Trimmed Mean ( 27 / 41 )0.1183831642857140.1280181677629350.924737217805966
Trimmed Mean ( 28 / 41 )0.1241166397058820.1259515463602690.985431646475081
Trimmed Mean ( 29 / 41 )0.1284994166666670.1238899308707371.03720629887782
Trimmed Mean ( 30 / 41 )0.13281346093750.1215573262849991.09259939319585
Trimmed Mean ( 31 / 41 )0.1365101854838710.1190400560260971.14675841091627
Trimmed Mean ( 32 / 41 )0.1404330250.1160436789839531.21017384341477
Trimmed Mean ( 33 / 41 )0.139721750.1137301103395031.228537891882
Trimmed Mean ( 34 / 41 )0.1420641339285710.111673417706521.2721392149197
Trimmed Mean ( 35 / 41 )0.1432107685185190.1096953264668971.30553208720095
Trimmed Mean ( 36 / 41 )0.1447259903846150.1073928694962961.34763128188513
Trimmed Mean ( 37 / 41 )0.145831030.1047939210636441.39159818164865
Trimmed Mean ( 38 / 41 )0.1460989895833330.1021951776707421.42960747183241
Trimmed Mean ( 39 / 41 )0.1458056847826090.09913301611523751.47080852067606
Trimmed Mean ( 40 / 41 )0.1434752613636360.0958969694826071.49613968134477
Trimmed Mean ( 41 / 41 )0.1449360357142860.09350684920822021.55000448567723
Median0.1199935
Midrange-0.717405
Midmean - Weighted Average at Xnp0.107237166666667
Midmean - Weighted Average at X(n+1)p0.136510185483871
Midmean - Empirical Distribution Function0.107237166666667
Midmean - Empirical Distribution Function - Averaging0.136510185483871
Midmean - Empirical Distribution Function - Interpolation0.136510185483871
Midmean - Closest Observation0.107237166666667
Midmean - True Basic - Statistics Graphics Toolkit0.136510185483871
Midmean - MS Excel (old versions)0.1328134609375
Number of observations124


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = Pearson Chi-Squared ;
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('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('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('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('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('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('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('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('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('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('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')