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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 04 Dec 2011 05:34:13 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/04/t1322994877r5bsez4ae59etmm.htm/, Retrieved Mon, 29 Apr 2024 12:53:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150562, Retrieved Mon, 29 Apr 2024 12:53:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper - Central T...] [2011-11-29 18:53:10] [2ca9890f29577b21e1107ae30466e88a]
- R  D    [Central Tendency] [Central Tendency ...] [2011-12-04 10:34:13] [2489a3445a7d2af96337a363cd642931] [Current]
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Dataseries X:
1,9
1,9
1,8
2
2,6
2,5
2,5
1,6
1,4
0,8
1,1
1,3
1,2
1,3
1,1
1,3
1,2
1,6
1,7
1,5
0,9
1,5
1,4
1,6
1,7
1,4
1,8
1,7
1,4
1,2
1
1,7
2,4
2
2,1
2
1,8
2,7
2,3
1,9
2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8
2,8
2,8
2,2
2,6
2,8
2,5
2,4
2,3
1,9
1,7
2
2,1
1,7
1,8
1,8
1,8
1,3
1,3
1,3
1,2
1,4
2,2
2,9
3,1
3,5
3,6
4,4
4,1
5,1
5,8
5,9
5,4
5,5
4,8
3,2
2,7
2,1
1,9
0,6
0,7
-0,2
-1
-1,7
-0,7
-1
-0,9
0
0,3
0,8
0,8
1,9
2,1
2,5
2,7
2,4
2,4
2,9
3,1
3
3,4
3,7
3,5
3,5
3,3
3,1
3,4
4
3,4
3,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150562&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150562&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150562&T=0

As an alternative you can also use a 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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.152892561983470.11803647461302218.2392143533737
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.5113461537853
Winsorized Mean ( 1 / 40 )2.157851239669420.116377556376918.5418160240537
Winsorized Mean ( 2 / 40 )2.152892561983470.11513002817969518.6996615567854
Winsorized Mean ( 3 / 40 )2.152892561983470.11397570170321418.8890485411485
Winsorized Mean ( 4 / 40 )2.14958677685950.11024093303010119.4989893297851
Winsorized Mean ( 5 / 40 )2.157851239669420.10333790134386320.8815082521277
Winsorized Mean ( 6 / 40 )2.147933884297520.097454511346342722.0403740639979
Winsorized Mean ( 7 / 40 )2.147933884297520.091167051989911923.560418346479
Winsorized Mean ( 8 / 40 )2.161157024793390.086827874287031124.8901293799863
Winsorized Mean ( 9 / 40 )2.146280991735540.081986706258925926.1784024468219
Winsorized Mean ( 10 / 40 )2.146280991735540.07951333829851926.992716412908
Winsorized Mean ( 11 / 40 )2.137190082644630.078160076534754527.343756267873
Winsorized Mean ( 12 / 40 )2.137190082644630.078160076534754527.343756267873
Winsorized Mean ( 13 / 40 )2.147933884297520.076665162042551228.0170787756942
Winsorized Mean ( 14 / 40 )2.147933884297520.073453750122773129.2419907861395
Winsorized Mean ( 15 / 40 )2.16033057851240.071884121424740630.0529593419899
Winsorized Mean ( 16 / 40 )2.16033057851240.071884121424740630.0529593419899
Winsorized Mean ( 17 / 40 )2.174380165289260.070207572264913930.9707357076054
Winsorized Mean ( 18 / 40 )2.159504132231410.068086585131922831.7170280760476
Winsorized Mean ( 19 / 40 )2.143801652892560.065941920371158332.5104522407906
Winsorized Mean ( 20 / 40 )2.127272727272730.063787698840889233.3492627250742
Winsorized Mean ( 21 / 40 )2.144628099173550.061746286325276334.7329082736371
Winsorized Mean ( 22 / 40 )2.144628099173550.061746286325276334.7329082736371
Winsorized Mean ( 23 / 40 )2.125619834710740.059352903173971535.813241156549
Winsorized Mean ( 24 / 40 )2.125619834710740.059352903173971535.813241156549
Winsorized Mean ( 25 / 40 )2.104958677685950.056879981417419937.0070211914888
Winsorized Mean ( 26 / 40 )2.104958677685950.056879981417419937.0070211914888
Winsorized Mean ( 27 / 40 )2.127272727272730.054317706350144239.1635227297678
Winsorized Mean ( 28 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 29 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 30 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 31 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 32 / 40 )2.130578512396690.048714083685525743.7363971813709
Winsorized Mean ( 33 / 40 )2.103305785123970.04566517689197246.059293498406
Winsorized Mean ( 34 / 40 )2.131404958677690.042656825513398249.9663285541075
Winsorized Mean ( 35 / 40 )2.131404958677690.042656825513398249.9663285541075
Winsorized Mean ( 36 / 40 )2.131404958677690.042656825513398249.9663285541075
Winsorized Mean ( 37 / 40 )2.161983471074380.039578638086278554.6250092375948
Winsorized Mean ( 38 / 40 )2.130578512396690.036094515032565659.0277639268576
Winsorized Mean ( 39 / 40 )2.130578512396690.036094515032565659.0277639268576
Winsorized Mean ( 40 / 40 )2.097520661157020.032597867266117164.3453341297954
Trimmed Mean ( 1 / 40 )2.153781512605040.11112962411987119.380804440424
Trimmed Mean ( 2 / 40 )2.149572649572650.10518970786800220.4351993473549
Trimmed Mean ( 3 / 40 )2.147826086956520.099206215096567221.6501162237248
Trimmed Mean ( 4 / 40 )2.146017699115040.092872030056749123.1072551962494
Trimmed Mean ( 5 / 40 )2.145045045045050.086961058044849424.6667312159284
Trimmed Mean ( 6 / 40 )2.142201834862390.082326162138447226.020912176859
Trimmed Mean ( 7 / 40 )2.14112149532710.078616063251814227.2351655216937
Trimmed Mean ( 8 / 40 )2.140.075878252203837428.2030745021796
Trimmed Mean ( 9 / 40 )2.13689320388350.073683512574026929.0009681845263
Trimmed Mean ( 10 / 40 )2.135643564356440.072119045676841129.6127540833812
Trimmed Mean ( 11 / 40 )2.134343434343430.070778595622929630.1552102801541
Trimmed Mean ( 12 / 40 )2.13402061855670.069483344285005930.7126929556442
Trimmed Mean ( 13 / 40 )2.133684210526320.068016375841161631.3701543803083
Trimmed Mean ( 14 / 40 )2.132258064516130.066575930953567832.0274614860923
Trimmed Mean ( 15 / 40 )2.130769230769230.065403645869488932.5787531022524
Trimmed Mean ( 16 / 40 )2.128089887640450.064278599991494533.1072843515889
Trimmed Mean ( 17 / 40 )2.125287356321840.062987598453614333.7413619267761
Trimmed Mean ( 18 / 40 )2.121176470588240.061723475634393134.3657975962437
Trimmed Mean ( 19 / 40 )2.118072289156630.060562176245859934.9735168128378
Trimmed Mean ( 20 / 40 )2.116049382716050.059510783080465135.5574111645434
Trimmed Mean ( 21 / 40 )2.115189873417720.058574669528749936.1109996938102
Trimmed Mean ( 22 / 40 )2.112987012987010.057735539429021736.5976837470213
Trimmed Mean ( 23 / 40 )2.110666666666670.056745784725247137.1951269488322
Trimmed Mean ( 24 / 40 )2.109589041095890.055898785447144737.7394432494534
Trimmed Mean ( 25 / 40 )2.108450704225350.05489138640352238.4113217459209
Trimmed Mean ( 26 / 40 )2.108695652173910.054025471970466339.0315081990706
Trimmed Mean ( 27 / 40 )2.10895522388060.052985552389536739.8024580054593
Trimmed Mean ( 28 / 40 )2.107692307692310.052086636976092940.4651256071631
Trimmed Mean ( 29 / 40 )2.107936507936510.051366457847661741.0372175980686
Trimmed Mean ( 30 / 40 )2.108196721311480.050478317693816741.7644013831649
Trimmed Mean ( 31 / 40 )2.108196721311480.049384767525512642.6892101946691
Trimmed Mean ( 32 / 40 )2.108771929824560.048036685917637943.8991968230322
Trimmed Mean ( 33 / 40 )2.107272727272730.046843427536823344.9854512805711
Trimmed Mean ( 34 / 40 )2.107547169811320.045862881441060145.9532219431045
Trimmed Mean ( 35 / 40 )2.105882352941180.04510656355924946.6868275206784
Trimmed Mean ( 36 / 40 )2.104081632653060.044124050516221647.6855956793796
Trimmed Mean ( 37 / 40 )2.102127659574470.042850487839320949.0572631858229
Trimmed Mean ( 38 / 40 )2.097777777777780.041741011115911850.2569947803228
Trimmed Mean ( 39 / 40 )2.09534883720930.041021492944697751.0792925073231
Trimmed Mean ( 40 / 40 )2.092682926829270.040028990089567852.2791837152707
Median2.1
Midrange2.1
Midmean - Weighted Average at Xnp2.0969696969697
Midmean - Weighted Average at X(n+1)p2.0969696969697
Midmean - Empirical Distribution Function2.0969696969697
Midmean - Empirical Distribution Function - Averaging2.0969696969697
Midmean - Empirical Distribution Function - Interpolation2.0969696969697
Midmean - Closest Observation2.0969696969697
Midmean - True Basic - Statistics Graphics Toolkit2.0969696969697
Midmean - MS Excel (old versions)2.0969696969697
Number of observations121

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.15289256198347 & 0.118036474613022 & 18.2392143533737 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.5113461537853 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 2.15785123966942 & 0.1163775563769 & 18.5418160240537 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 2.15289256198347 & 0.115130028179695 & 18.6996615567854 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 2.15289256198347 & 0.113975701703214 & 18.8890485411485 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 2.1495867768595 & 0.110240933030101 & 19.4989893297851 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 2.15785123966942 & 0.103337901343863 & 20.8815082521277 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 2.14793388429752 & 0.0974545113463427 & 22.0403740639979 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 2.14793388429752 & 0.0911670519899119 & 23.560418346479 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 2.16115702479339 & 0.0868278742870311 & 24.8901293799863 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 2.14628099173554 & 0.0819867062589259 & 26.1784024468219 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 2.14628099173554 & 0.079513338298519 & 26.992716412908 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 2.13719008264463 & 0.0781600765347545 & 27.343756267873 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 2.13719008264463 & 0.0781600765347545 & 27.343756267873 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 2.14793388429752 & 0.0766651620425512 & 28.0170787756942 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 2.14793388429752 & 0.0734537501227731 & 29.2419907861395 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 2.1603305785124 & 0.0718841214247406 & 30.0529593419899 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 2.1603305785124 & 0.0718841214247406 & 30.0529593419899 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 2.17438016528926 & 0.0702075722649139 & 30.9707357076054 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 2.15950413223141 & 0.0680865851319228 & 31.7170280760476 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 2.14380165289256 & 0.0659419203711583 & 32.5104522407906 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 2.12727272727273 & 0.0637876988408892 & 33.3492627250742 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 2.14462809917355 & 0.0617462863252763 & 34.7329082736371 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 2.14462809917355 & 0.0617462863252763 & 34.7329082736371 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 2.12561983471074 & 0.0593529031739715 & 35.813241156549 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 2.12561983471074 & 0.0593529031739715 & 35.813241156549 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 2.10495867768595 & 0.0568799814174199 & 37.0070211914888 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 2.10495867768595 & 0.0568799814174199 & 37.0070211914888 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 2.12727272727273 & 0.0543177063501442 & 39.1635227297678 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 2.10413223140496 & 0.0516450682779194 & 40.7421715483445 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 2.10413223140496 & 0.0516450682779194 & 40.7421715483445 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 2.10413223140496 & 0.0516450682779194 & 40.7421715483445 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 2.10413223140496 & 0.0516450682779194 & 40.7421715483445 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 2.13057851239669 & 0.0487140836855257 & 43.7363971813709 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 2.10330578512397 & 0.045665176891972 & 46.059293498406 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 2.13140495867769 & 0.0426568255133982 & 49.9663285541075 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 2.13140495867769 & 0.0426568255133982 & 49.9663285541075 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 2.13140495867769 & 0.0426568255133982 & 49.9663285541075 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 2.16198347107438 & 0.0395786380862785 & 54.6250092375948 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 2.13057851239669 & 0.0360945150325656 & 59.0277639268576 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 2.13057851239669 & 0.0360945150325656 & 59.0277639268576 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 2.09752066115702 & 0.0325978672661171 & 64.3453341297954 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 2.15378151260504 & 0.111129624119871 & 19.380804440424 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 2.14957264957265 & 0.105189707868002 & 20.4351993473549 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 2.14782608695652 & 0.0992062150965672 & 21.6501162237248 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 2.14601769911504 & 0.0928720300567491 & 23.1072551962494 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 2.14504504504505 & 0.0869610580448494 & 24.6667312159284 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 2.14220183486239 & 0.0823261621384472 & 26.020912176859 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 2.1411214953271 & 0.0786160632518142 & 27.2351655216937 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 2.14 & 0.0758782522038374 & 28.2030745021796 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 2.1368932038835 & 0.0736835125740269 & 29.0009681845263 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 2.13564356435644 & 0.0721190456768411 & 29.6127540833812 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 2.13434343434343 & 0.0707785956229296 & 30.1552102801541 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 2.1340206185567 & 0.0694833442850059 & 30.7126929556442 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 2.13368421052632 & 0.0680163758411616 & 31.3701543803083 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 2.13225806451613 & 0.0665759309535678 & 32.0274614860923 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 2.13076923076923 & 0.0654036458694889 & 32.5787531022524 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 2.12808988764045 & 0.0642785999914945 & 33.1072843515889 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 2.12528735632184 & 0.0629875984536143 & 33.7413619267761 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 2.12117647058824 & 0.0617234756343931 & 34.3657975962437 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 2.11807228915663 & 0.0605621762458599 & 34.9735168128378 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 2.11604938271605 & 0.0595107830804651 & 35.5574111645434 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 2.11518987341772 & 0.0585746695287499 & 36.1109996938102 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 2.11298701298701 & 0.0577355394290217 & 36.5976837470213 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 2.11066666666667 & 0.0567457847252471 & 37.1951269488322 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 2.10958904109589 & 0.0558987854471447 & 37.7394432494534 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 2.10845070422535 & 0.054891386403522 & 38.4113217459209 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 2.10869565217391 & 0.0540254719704663 & 39.0315081990706 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 2.1089552238806 & 0.0529855523895367 & 39.8024580054593 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 2.10769230769231 & 0.0520866369760929 & 40.4651256071631 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 2.10793650793651 & 0.0513664578476617 & 41.0372175980686 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 2.10819672131148 & 0.0504783176938167 & 41.7644013831649 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 2.10819672131148 & 0.0493847675255126 & 42.6892101946691 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 2.10877192982456 & 0.0480366859176379 & 43.8991968230322 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 2.10727272727273 & 0.0468434275368233 & 44.9854512805711 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 2.10754716981132 & 0.0458628814410601 & 45.9532219431045 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 2.10588235294118 & 0.045106563559249 & 46.6868275206784 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 2.10408163265306 & 0.0441240505162216 & 47.6855956793796 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 2.10212765957447 & 0.0428504878393209 & 49.0572631858229 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 2.09777777777778 & 0.0417410111159118 & 50.2569947803228 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 2.0953488372093 & 0.0410214929446977 & 51.0792925073231 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 2.09268292682927 & 0.0400289900895678 & 52.2791837152707 \tabularnewline
Median & 2.1 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.0969696969697 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.0969696969697 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.0969696969697 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.0969696969697 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.0969696969697 &  &  \tabularnewline
Midmean - Closest Observation & 2.0969696969697 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.0969696969697 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.0969696969697 &  &  \tabularnewline
Number of observations & 121 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150562&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]2.15289256198347[/C][C]0.118036474613022[/C][C]18.2392143533737[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.5113461537853[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]2.15785123966942[/C][C]0.1163775563769[/C][C]18.5418160240537[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]2.15289256198347[/C][C]0.115130028179695[/C][C]18.6996615567854[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]2.15289256198347[/C][C]0.113975701703214[/C][C]18.8890485411485[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]2.1495867768595[/C][C]0.110240933030101[/C][C]19.4989893297851[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]2.15785123966942[/C][C]0.103337901343863[/C][C]20.8815082521277[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]2.14793388429752[/C][C]0.0974545113463427[/C][C]22.0403740639979[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]2.14793388429752[/C][C]0.0911670519899119[/C][C]23.560418346479[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]2.16115702479339[/C][C]0.0868278742870311[/C][C]24.8901293799863[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]2.14628099173554[/C][C]0.0819867062589259[/C][C]26.1784024468219[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]2.14628099173554[/C][C]0.079513338298519[/C][C]26.992716412908[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]2.13719008264463[/C][C]0.0781600765347545[/C][C]27.343756267873[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]2.13719008264463[/C][C]0.0781600765347545[/C][C]27.343756267873[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]2.14793388429752[/C][C]0.0766651620425512[/C][C]28.0170787756942[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]2.14793388429752[/C][C]0.0734537501227731[/C][C]29.2419907861395[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]2.1603305785124[/C][C]0.0718841214247406[/C][C]30.0529593419899[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]2.1603305785124[/C][C]0.0718841214247406[/C][C]30.0529593419899[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]2.17438016528926[/C][C]0.0702075722649139[/C][C]30.9707357076054[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]2.15950413223141[/C][C]0.0680865851319228[/C][C]31.7170280760476[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]2.14380165289256[/C][C]0.0659419203711583[/C][C]32.5104522407906[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]2.12727272727273[/C][C]0.0637876988408892[/C][C]33.3492627250742[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]2.14462809917355[/C][C]0.0617462863252763[/C][C]34.7329082736371[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]2.14462809917355[/C][C]0.0617462863252763[/C][C]34.7329082736371[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]2.12561983471074[/C][C]0.0593529031739715[/C][C]35.813241156549[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]2.12561983471074[/C][C]0.0593529031739715[/C][C]35.813241156549[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]2.10495867768595[/C][C]0.0568799814174199[/C][C]37.0070211914888[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]2.10495867768595[/C][C]0.0568799814174199[/C][C]37.0070211914888[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]2.12727272727273[/C][C]0.0543177063501442[/C][C]39.1635227297678[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]2.10413223140496[/C][C]0.0516450682779194[/C][C]40.7421715483445[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]2.10413223140496[/C][C]0.0516450682779194[/C][C]40.7421715483445[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]2.10413223140496[/C][C]0.0516450682779194[/C][C]40.7421715483445[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]2.10413223140496[/C][C]0.0516450682779194[/C][C]40.7421715483445[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]2.13057851239669[/C][C]0.0487140836855257[/C][C]43.7363971813709[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]2.10330578512397[/C][C]0.045665176891972[/C][C]46.059293498406[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]2.13140495867769[/C][C]0.0426568255133982[/C][C]49.9663285541075[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]2.13140495867769[/C][C]0.0426568255133982[/C][C]49.9663285541075[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]2.13140495867769[/C][C]0.0426568255133982[/C][C]49.9663285541075[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]2.16198347107438[/C][C]0.0395786380862785[/C][C]54.6250092375948[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]2.13057851239669[/C][C]0.0360945150325656[/C][C]59.0277639268576[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]2.13057851239669[/C][C]0.0360945150325656[/C][C]59.0277639268576[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]2.09752066115702[/C][C]0.0325978672661171[/C][C]64.3453341297954[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]2.15378151260504[/C][C]0.111129624119871[/C][C]19.380804440424[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]2.14957264957265[/C][C]0.105189707868002[/C][C]20.4351993473549[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]2.14782608695652[/C][C]0.0992062150965672[/C][C]21.6501162237248[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]2.14601769911504[/C][C]0.0928720300567491[/C][C]23.1072551962494[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]2.14504504504505[/C][C]0.0869610580448494[/C][C]24.6667312159284[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]2.14220183486239[/C][C]0.0823261621384472[/C][C]26.020912176859[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]2.1411214953271[/C][C]0.0786160632518142[/C][C]27.2351655216937[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]2.14[/C][C]0.0758782522038374[/C][C]28.2030745021796[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]2.1368932038835[/C][C]0.0736835125740269[/C][C]29.0009681845263[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]2.13564356435644[/C][C]0.0721190456768411[/C][C]29.6127540833812[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]2.13434343434343[/C][C]0.0707785956229296[/C][C]30.1552102801541[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]2.1340206185567[/C][C]0.0694833442850059[/C][C]30.7126929556442[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]2.13368421052632[/C][C]0.0680163758411616[/C][C]31.3701543803083[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]2.13225806451613[/C][C]0.0665759309535678[/C][C]32.0274614860923[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]2.13076923076923[/C][C]0.0654036458694889[/C][C]32.5787531022524[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]2.12808988764045[/C][C]0.0642785999914945[/C][C]33.1072843515889[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]2.12528735632184[/C][C]0.0629875984536143[/C][C]33.7413619267761[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]2.12117647058824[/C][C]0.0617234756343931[/C][C]34.3657975962437[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]2.11807228915663[/C][C]0.0605621762458599[/C][C]34.9735168128378[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]2.11604938271605[/C][C]0.0595107830804651[/C][C]35.5574111645434[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]2.11518987341772[/C][C]0.0585746695287499[/C][C]36.1109996938102[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]2.11298701298701[/C][C]0.0577355394290217[/C][C]36.5976837470213[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]2.11066666666667[/C][C]0.0567457847252471[/C][C]37.1951269488322[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]2.10958904109589[/C][C]0.0558987854471447[/C][C]37.7394432494534[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]2.10845070422535[/C][C]0.054891386403522[/C][C]38.4113217459209[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]2.10869565217391[/C][C]0.0540254719704663[/C][C]39.0315081990706[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]2.1089552238806[/C][C]0.0529855523895367[/C][C]39.8024580054593[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]2.10769230769231[/C][C]0.0520866369760929[/C][C]40.4651256071631[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]2.10793650793651[/C][C]0.0513664578476617[/C][C]41.0372175980686[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]2.10819672131148[/C][C]0.0504783176938167[/C][C]41.7644013831649[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]2.10819672131148[/C][C]0.0493847675255126[/C][C]42.6892101946691[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]2.10877192982456[/C][C]0.0480366859176379[/C][C]43.8991968230322[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]2.10727272727273[/C][C]0.0468434275368233[/C][C]44.9854512805711[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]2.10754716981132[/C][C]0.0458628814410601[/C][C]45.9532219431045[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]2.10588235294118[/C][C]0.045106563559249[/C][C]46.6868275206784[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]2.10408163265306[/C][C]0.0441240505162216[/C][C]47.6855956793796[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]2.10212765957447[/C][C]0.0428504878393209[/C][C]49.0572631858229[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]2.09777777777778[/C][C]0.0417410111159118[/C][C]50.2569947803228[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]2.0953488372093[/C][C]0.0410214929446977[/C][C]51.0792925073231[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]2.09268292682927[/C][C]0.0400289900895678[/C][C]52.2791837152707[/C][/ROW]
[ROW][C]Median[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.0969696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]121[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150562&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150562&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.152892561983470.11803647461302218.2392143533737
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.5113461537853
Winsorized Mean ( 1 / 40 )2.157851239669420.116377556376918.5418160240537
Winsorized Mean ( 2 / 40 )2.152892561983470.11513002817969518.6996615567854
Winsorized Mean ( 3 / 40 )2.152892561983470.11397570170321418.8890485411485
Winsorized Mean ( 4 / 40 )2.14958677685950.11024093303010119.4989893297851
Winsorized Mean ( 5 / 40 )2.157851239669420.10333790134386320.8815082521277
Winsorized Mean ( 6 / 40 )2.147933884297520.097454511346342722.0403740639979
Winsorized Mean ( 7 / 40 )2.147933884297520.091167051989911923.560418346479
Winsorized Mean ( 8 / 40 )2.161157024793390.086827874287031124.8901293799863
Winsorized Mean ( 9 / 40 )2.146280991735540.081986706258925926.1784024468219
Winsorized Mean ( 10 / 40 )2.146280991735540.07951333829851926.992716412908
Winsorized Mean ( 11 / 40 )2.137190082644630.078160076534754527.343756267873
Winsorized Mean ( 12 / 40 )2.137190082644630.078160076534754527.343756267873
Winsorized Mean ( 13 / 40 )2.147933884297520.076665162042551228.0170787756942
Winsorized Mean ( 14 / 40 )2.147933884297520.073453750122773129.2419907861395
Winsorized Mean ( 15 / 40 )2.16033057851240.071884121424740630.0529593419899
Winsorized Mean ( 16 / 40 )2.16033057851240.071884121424740630.0529593419899
Winsorized Mean ( 17 / 40 )2.174380165289260.070207572264913930.9707357076054
Winsorized Mean ( 18 / 40 )2.159504132231410.068086585131922831.7170280760476
Winsorized Mean ( 19 / 40 )2.143801652892560.065941920371158332.5104522407906
Winsorized Mean ( 20 / 40 )2.127272727272730.063787698840889233.3492627250742
Winsorized Mean ( 21 / 40 )2.144628099173550.061746286325276334.7329082736371
Winsorized Mean ( 22 / 40 )2.144628099173550.061746286325276334.7329082736371
Winsorized Mean ( 23 / 40 )2.125619834710740.059352903173971535.813241156549
Winsorized Mean ( 24 / 40 )2.125619834710740.059352903173971535.813241156549
Winsorized Mean ( 25 / 40 )2.104958677685950.056879981417419937.0070211914888
Winsorized Mean ( 26 / 40 )2.104958677685950.056879981417419937.0070211914888
Winsorized Mean ( 27 / 40 )2.127272727272730.054317706350144239.1635227297678
Winsorized Mean ( 28 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 29 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 30 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 31 / 40 )2.104132231404960.051645068277919440.7421715483445
Winsorized Mean ( 32 / 40 )2.130578512396690.048714083685525743.7363971813709
Winsorized Mean ( 33 / 40 )2.103305785123970.04566517689197246.059293498406
Winsorized Mean ( 34 / 40 )2.131404958677690.042656825513398249.9663285541075
Winsorized Mean ( 35 / 40 )2.131404958677690.042656825513398249.9663285541075
Winsorized Mean ( 36 / 40 )2.131404958677690.042656825513398249.9663285541075
Winsorized Mean ( 37 / 40 )2.161983471074380.039578638086278554.6250092375948
Winsorized Mean ( 38 / 40 )2.130578512396690.036094515032565659.0277639268576
Winsorized Mean ( 39 / 40 )2.130578512396690.036094515032565659.0277639268576
Winsorized Mean ( 40 / 40 )2.097520661157020.032597867266117164.3453341297954
Trimmed Mean ( 1 / 40 )2.153781512605040.11112962411987119.380804440424
Trimmed Mean ( 2 / 40 )2.149572649572650.10518970786800220.4351993473549
Trimmed Mean ( 3 / 40 )2.147826086956520.099206215096567221.6501162237248
Trimmed Mean ( 4 / 40 )2.146017699115040.092872030056749123.1072551962494
Trimmed Mean ( 5 / 40 )2.145045045045050.086961058044849424.6667312159284
Trimmed Mean ( 6 / 40 )2.142201834862390.082326162138447226.020912176859
Trimmed Mean ( 7 / 40 )2.14112149532710.078616063251814227.2351655216937
Trimmed Mean ( 8 / 40 )2.140.075878252203837428.2030745021796
Trimmed Mean ( 9 / 40 )2.13689320388350.073683512574026929.0009681845263
Trimmed Mean ( 10 / 40 )2.135643564356440.072119045676841129.6127540833812
Trimmed Mean ( 11 / 40 )2.134343434343430.070778595622929630.1552102801541
Trimmed Mean ( 12 / 40 )2.13402061855670.069483344285005930.7126929556442
Trimmed Mean ( 13 / 40 )2.133684210526320.068016375841161631.3701543803083
Trimmed Mean ( 14 / 40 )2.132258064516130.066575930953567832.0274614860923
Trimmed Mean ( 15 / 40 )2.130769230769230.065403645869488932.5787531022524
Trimmed Mean ( 16 / 40 )2.128089887640450.064278599991494533.1072843515889
Trimmed Mean ( 17 / 40 )2.125287356321840.062987598453614333.7413619267761
Trimmed Mean ( 18 / 40 )2.121176470588240.061723475634393134.3657975962437
Trimmed Mean ( 19 / 40 )2.118072289156630.060562176245859934.9735168128378
Trimmed Mean ( 20 / 40 )2.116049382716050.059510783080465135.5574111645434
Trimmed Mean ( 21 / 40 )2.115189873417720.058574669528749936.1109996938102
Trimmed Mean ( 22 / 40 )2.112987012987010.057735539429021736.5976837470213
Trimmed Mean ( 23 / 40 )2.110666666666670.056745784725247137.1951269488322
Trimmed Mean ( 24 / 40 )2.109589041095890.055898785447144737.7394432494534
Trimmed Mean ( 25 / 40 )2.108450704225350.05489138640352238.4113217459209
Trimmed Mean ( 26 / 40 )2.108695652173910.054025471970466339.0315081990706
Trimmed Mean ( 27 / 40 )2.10895522388060.052985552389536739.8024580054593
Trimmed Mean ( 28 / 40 )2.107692307692310.052086636976092940.4651256071631
Trimmed Mean ( 29 / 40 )2.107936507936510.051366457847661741.0372175980686
Trimmed Mean ( 30 / 40 )2.108196721311480.050478317693816741.7644013831649
Trimmed Mean ( 31 / 40 )2.108196721311480.049384767525512642.6892101946691
Trimmed Mean ( 32 / 40 )2.108771929824560.048036685917637943.8991968230322
Trimmed Mean ( 33 / 40 )2.107272727272730.046843427536823344.9854512805711
Trimmed Mean ( 34 / 40 )2.107547169811320.045862881441060145.9532219431045
Trimmed Mean ( 35 / 40 )2.105882352941180.04510656355924946.6868275206784
Trimmed Mean ( 36 / 40 )2.104081632653060.044124050516221647.6855956793796
Trimmed Mean ( 37 / 40 )2.102127659574470.042850487839320949.0572631858229
Trimmed Mean ( 38 / 40 )2.097777777777780.041741011115911850.2569947803228
Trimmed Mean ( 39 / 40 )2.09534883720930.041021492944697751.0792925073231
Trimmed Mean ( 40 / 40 )2.092682926829270.040028990089567852.2791837152707
Median2.1
Midrange2.1
Midmean - Weighted Average at Xnp2.0969696969697
Midmean - Weighted Average at X(n+1)p2.0969696969697
Midmean - Empirical Distribution Function2.0969696969697
Midmean - Empirical Distribution Function - Averaging2.0969696969697
Midmean - Empirical Distribution Function - Interpolation2.0969696969697
Midmean - Closest Observation2.0969696969697
Midmean - True Basic - Statistics Graphics Toolkit2.0969696969697
Midmean - MS Excel (old versions)2.0969696969697
Number of observations121



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('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')