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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 computationFri, 17 Dec 2010 14:34:21 +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/2010/Dec/17/t1292596318y0ha2y1ldddng11.htm/, Retrieved Mon, 06 May 2024 18:25:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111491, Retrieved Mon, 06 May 2024 18:25:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [s 0650692 paper] [2008-01-06 17:05:54] [d530bc48164a192180949b2df4f47d02]
-  M D    [Central Tendency] [] [2010-12-17 14:34:21] [44163a3390d803b6e1dc8c2f0815c192] [Current]
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Dataseries X:
2.26
2.57
3.07
2.76
2.51
2.87
3.14
3.11
3.16
2.47
2.57
2.89
2.63
2.38
1.69
1.96
2.19
1.87
1.60
1.63
1.22
1.21
1.49
1.64
1.66
1.77
1.82
1.78
1.28
1.29
1.37
1.12
1.51
2.24
2.94
3.09
3.46
3.64
4.39
4.15
5.21
5.80
5.91
5.39
5.46
4.72
3.14
2.63
2.32
1.93
0.62
0.60
-0.37
-1.10
-1.68
-0.78
-1.19
-0.79
-0.12
0.26
0.62
0.70
1.66
1.80
2.27
2.46
2.57




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111491&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111491&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111491&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.125970149253730.1976599947583810.7556926319487
Geometric MeanNaN
Harmonic Mean3.5115989873212
Quadratic Mean2.66426994284705
Winsorized Mean ( 1 / 22 )2.131641791044780.19517756785756710.9215511518227
Winsorized Mean ( 2 / 22 )2.124179104477610.19170485914333211.0804656385336
Winsorized Mean ( 3 / 22 )2.134925373134330.18746872172512511.3881684021116
Winsorized Mean ( 4 / 22 )2.124776119402990.18455201522426111.5131558808558
Winsorized Mean ( 5 / 22 )2.118805970149250.16854815732668412.5709233714287
Winsorized Mean ( 6 / 22 )2.111641791044780.15691516763311913.4572191005905
Winsorized Mean ( 7 / 22 )2.126268656716420.14325808230805214.842224762888
Winsorized Mean ( 8 / 22 )2.105970149253730.12315027787552217.1008152444642
Winsorized Mean ( 9 / 22 )2.08447761194030.11823350849898917.6301764060239
Winsorized Mean ( 10 / 22 )2.039701492537310.11084192625730318.4018950356605
Winsorized Mean ( 11 / 22 )2.049552238805970.10781859751434519.0092645059058
Winsorized Mean ( 12 / 22 )2.124776119402990.094559455620108122.4702659873515
Winsorized Mean ( 13 / 22 )2.136417910447760.090857690498791523.5138918755169
Winsorized Mean ( 14 / 22 )2.134328358208960.089859235584535423.7519086861258
Winsorized Mean ( 15 / 22 )2.143283582089550.087092953991659324.6091501534649
Winsorized Mean ( 16 / 22 )2.114626865671640.081853342159707325.8343374855203
Winsorized Mean ( 17 / 22 )2.122238805970150.076868499462766127.6086930381427
Winsorized Mean ( 18 / 22 )2.149104477611940.071401531586851530.098856843117
Winsorized Mean ( 19 / 22 )2.123582089552240.065934023151780532.2076825899694
Winsorized Mean ( 20 / 22 )2.111641791044780.056659455076908237.2690098797894
Winsorized Mean ( 21 / 22 )2.12104477611940.055384489028809138.2967291621325
Winsorized Mean ( 22 / 22 )2.104626865671640.052240324330198540.2874004450815
Trimmed Mean ( 1 / 22 )2.126307692307690.18602684995807811.4301117972317
Trimmed Mean ( 2 / 22 )2.120634920634920.17488565103470512.1258371289368
Trimmed Mean ( 3 / 22 )2.118688524590160.16358425168531512.9516655959392
Trimmed Mean ( 4 / 22 )2.112542372881360.15172562697445413.9234380836471
Trimmed Mean ( 5 / 22 )2.108947368421050.13803006378840615.2788987452326
Trimmed Mean ( 6 / 22 )2.106545454545450.12693199700664716.5958584456458
Trimmed Mean ( 7 / 22 )2.105471698113210.11692745385805818.0066496673151
Trimmed Mean ( 8 / 22 )2.101568627450980.10863407638887719.3453904825224
Trimmed Mean ( 9 / 22 )2.100816326530610.10406689238026120.1871726778793
Trimmed Mean ( 10 / 22 )2.103404255319150.099563002889990321.1263641539946
Trimmed Mean ( 11 / 22 )2.112888888888890.09563853573427522.0924428910058
Trimmed Mean ( 12 / 22 )2.121860465116280.091304836563239223.2392997456016
Trimmed Mean ( 13 / 22 )2.121463414634150.08908584581096423.8136978475323
Trimmed Mean ( 14 / 22 )2.119487179487180.086961722944540124.3726447420882
Trimmed Mean ( 15 / 22 )2.117567567567570.084257403953194225.132124516249
Trimmed Mean ( 16 / 22 )2.114285714285710.081205503098579426.0362368757087
Trimmed Mean ( 17 / 22 )2.114242424242420.078371239582870826.9772742589684
Trimmed Mean ( 18 / 22 )2.113225806451610.075706545926230727.9133829261048
Trimmed Mean ( 19 / 22 )2.108620689655170.073348355910417928.7480293659272
Trimmed Mean ( 20 / 22 )2.106666666666670.071470114089577429.4761900621324
Trimmed Mean ( 21 / 22 )2.1060.071358251099645129.5130551484392
Trimmed Mean ( 22 / 22 )2.103913043478260.071044547430041729.6139974084571
Median2.19
Midrange2.115
Midmean - Weighted Average at Xnp2.09
Midmean - Weighted Average at X(n+1)p2.11428571428571
Midmean - Empirical Distribution Function2.11428571428571
Midmean - Empirical Distribution Function - Averaging2.11428571428571
Midmean - Empirical Distribution Function - Interpolation2.11424242424243
Midmean - Closest Observation2.09
Midmean - True Basic - Statistics Graphics Toolkit2.11428571428571
Midmean - MS Excel (old versions)2.11428571428571
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.12597014925373 & 0.19765999475838 & 10.7556926319487 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 3.5115989873212 &  &  \tabularnewline
Quadratic Mean & 2.66426994284705 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 2.13164179104478 & 0.195177567857567 & 10.9215511518227 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 2.12417910447761 & 0.191704859143332 & 11.0804656385336 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 2.13492537313433 & 0.187468721725125 & 11.3881684021116 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 2.12477611940299 & 0.184552015224261 & 11.5131558808558 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 2.11880597014925 & 0.168548157326684 & 12.5709233714287 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 2.11164179104478 & 0.156915167633119 & 13.4572191005905 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 2.12626865671642 & 0.143258082308052 & 14.842224762888 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 2.10597014925373 & 0.123150277875522 & 17.1008152444642 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 2.0844776119403 & 0.118233508498989 & 17.6301764060239 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 2.03970149253731 & 0.110841926257303 & 18.4018950356605 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 2.04955223880597 & 0.107818597514345 & 19.0092645059058 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 2.12477611940299 & 0.0945594556201081 & 22.4702659873515 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 2.13641791044776 & 0.0908576904987915 & 23.5138918755169 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 2.13432835820896 & 0.0898592355845354 & 23.7519086861258 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 2.14328358208955 & 0.0870929539916593 & 24.6091501534649 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 2.11462686567164 & 0.0818533421597073 & 25.8343374855203 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 2.12223880597015 & 0.0768684994627661 & 27.6086930381427 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 2.14910447761194 & 0.0714015315868515 & 30.098856843117 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 2.12358208955224 & 0.0659340231517805 & 32.2076825899694 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 2.11164179104478 & 0.0566594550769082 & 37.2690098797894 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 2.1210447761194 & 0.0553844890288091 & 38.2967291621325 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 2.10462686567164 & 0.0522403243301985 & 40.2874004450815 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 2.12630769230769 & 0.186026849958078 & 11.4301117972317 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 2.12063492063492 & 0.174885651034705 & 12.1258371289368 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 2.11868852459016 & 0.163584251685315 & 12.9516655959392 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 2.11254237288136 & 0.151725626974454 & 13.9234380836471 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 2.10894736842105 & 0.138030063788406 & 15.2788987452326 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 2.10654545454545 & 0.126931997006647 & 16.5958584456458 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 2.10547169811321 & 0.116927453858058 & 18.0066496673151 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 2.10156862745098 & 0.108634076388877 & 19.3453904825224 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 2.10081632653061 & 0.104066892380261 & 20.1871726778793 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 2.10340425531915 & 0.0995630028899903 & 21.1263641539946 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 2.11288888888889 & 0.095638535734275 & 22.0924428910058 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 2.12186046511628 & 0.0913048365632392 & 23.2392997456016 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 2.12146341463415 & 0.089085845810964 & 23.8136978475323 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 2.11948717948718 & 0.0869617229445401 & 24.3726447420882 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 2.11756756756757 & 0.0842574039531942 & 25.132124516249 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 2.11428571428571 & 0.0812055030985794 & 26.0362368757087 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 2.11424242424242 & 0.0783712395828708 & 26.9772742589684 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 2.11322580645161 & 0.0757065459262307 & 27.9133829261048 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 2.10862068965517 & 0.0733483559104179 & 28.7480293659272 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 2.10666666666667 & 0.0714701140895774 & 29.4761900621324 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 2.106 & 0.0713582510996451 & 29.5130551484392 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 2.10391304347826 & 0.0710445474300417 & 29.6139974084571 \tabularnewline
Median & 2.19 &  &  \tabularnewline
Midrange & 2.115 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.09 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.11428571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.11428571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.11428571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.11424242424243 &  &  \tabularnewline
Midmean - Closest Observation & 2.09 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.11428571428571 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.11428571428571 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111491&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]2.12597014925373[/C][C]0.19765999475838[/C][C]10.7556926319487[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.5115989873212[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.66426994284705[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]2.13164179104478[/C][C]0.195177567857567[/C][C]10.9215511518227[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]2.12417910447761[/C][C]0.191704859143332[/C][C]11.0804656385336[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]2.13492537313433[/C][C]0.187468721725125[/C][C]11.3881684021116[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]2.12477611940299[/C][C]0.184552015224261[/C][C]11.5131558808558[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]2.11880597014925[/C][C]0.168548157326684[/C][C]12.5709233714287[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]2.11164179104478[/C][C]0.156915167633119[/C][C]13.4572191005905[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]2.12626865671642[/C][C]0.143258082308052[/C][C]14.842224762888[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]2.10597014925373[/C][C]0.123150277875522[/C][C]17.1008152444642[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]2.0844776119403[/C][C]0.118233508498989[/C][C]17.6301764060239[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]2.03970149253731[/C][C]0.110841926257303[/C][C]18.4018950356605[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]2.04955223880597[/C][C]0.107818597514345[/C][C]19.0092645059058[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]2.12477611940299[/C][C]0.0945594556201081[/C][C]22.4702659873515[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]2.13641791044776[/C][C]0.0908576904987915[/C][C]23.5138918755169[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]2.13432835820896[/C][C]0.0898592355845354[/C][C]23.7519086861258[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]2.14328358208955[/C][C]0.0870929539916593[/C][C]24.6091501534649[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]2.11462686567164[/C][C]0.0818533421597073[/C][C]25.8343374855203[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]2.12223880597015[/C][C]0.0768684994627661[/C][C]27.6086930381427[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]2.14910447761194[/C][C]0.0714015315868515[/C][C]30.098856843117[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]2.12358208955224[/C][C]0.0659340231517805[/C][C]32.2076825899694[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]2.11164179104478[/C][C]0.0566594550769082[/C][C]37.2690098797894[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]2.1210447761194[/C][C]0.0553844890288091[/C][C]38.2967291621325[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]2.10462686567164[/C][C]0.0522403243301985[/C][C]40.2874004450815[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]2.12630769230769[/C][C]0.186026849958078[/C][C]11.4301117972317[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]2.12063492063492[/C][C]0.174885651034705[/C][C]12.1258371289368[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]2.11868852459016[/C][C]0.163584251685315[/C][C]12.9516655959392[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]2.11254237288136[/C][C]0.151725626974454[/C][C]13.9234380836471[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]2.10894736842105[/C][C]0.138030063788406[/C][C]15.2788987452326[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]2.10654545454545[/C][C]0.126931997006647[/C][C]16.5958584456458[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]2.10547169811321[/C][C]0.116927453858058[/C][C]18.0066496673151[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]2.10156862745098[/C][C]0.108634076388877[/C][C]19.3453904825224[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]2.10081632653061[/C][C]0.104066892380261[/C][C]20.1871726778793[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]2.10340425531915[/C][C]0.0995630028899903[/C][C]21.1263641539946[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]2.11288888888889[/C][C]0.095638535734275[/C][C]22.0924428910058[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]2.12186046511628[/C][C]0.0913048365632392[/C][C]23.2392997456016[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]2.12146341463415[/C][C]0.089085845810964[/C][C]23.8136978475323[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]2.11948717948718[/C][C]0.0869617229445401[/C][C]24.3726447420882[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]2.11756756756757[/C][C]0.0842574039531942[/C][C]25.132124516249[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]2.11428571428571[/C][C]0.0812055030985794[/C][C]26.0362368757087[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]2.11424242424242[/C][C]0.0783712395828708[/C][C]26.9772742589684[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]2.11322580645161[/C][C]0.0757065459262307[/C][C]27.9133829261048[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]2.10862068965517[/C][C]0.0733483559104179[/C][C]28.7480293659272[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]2.10666666666667[/C][C]0.0714701140895774[/C][C]29.4761900621324[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]2.106[/C][C]0.0713582510996451[/C][C]29.5130551484392[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]2.10391304347826[/C][C]0.0710445474300417[/C][C]29.6139974084571[/C][/ROW]
[ROW][C]Median[/C][C]2.19[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.11428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.11428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.11428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.11424242424243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.11428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.11428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]67[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111491&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111491&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 Mean2.125970149253730.1976599947583810.7556926319487
Geometric MeanNaN
Harmonic Mean3.5115989873212
Quadratic Mean2.66426994284705
Winsorized Mean ( 1 / 22 )2.131641791044780.19517756785756710.9215511518227
Winsorized Mean ( 2 / 22 )2.124179104477610.19170485914333211.0804656385336
Winsorized Mean ( 3 / 22 )2.134925373134330.18746872172512511.3881684021116
Winsorized Mean ( 4 / 22 )2.124776119402990.18455201522426111.5131558808558
Winsorized Mean ( 5 / 22 )2.118805970149250.16854815732668412.5709233714287
Winsorized Mean ( 6 / 22 )2.111641791044780.15691516763311913.4572191005905
Winsorized Mean ( 7 / 22 )2.126268656716420.14325808230805214.842224762888
Winsorized Mean ( 8 / 22 )2.105970149253730.12315027787552217.1008152444642
Winsorized Mean ( 9 / 22 )2.08447761194030.11823350849898917.6301764060239
Winsorized Mean ( 10 / 22 )2.039701492537310.11084192625730318.4018950356605
Winsorized Mean ( 11 / 22 )2.049552238805970.10781859751434519.0092645059058
Winsorized Mean ( 12 / 22 )2.124776119402990.094559455620108122.4702659873515
Winsorized Mean ( 13 / 22 )2.136417910447760.090857690498791523.5138918755169
Winsorized Mean ( 14 / 22 )2.134328358208960.089859235584535423.7519086861258
Winsorized Mean ( 15 / 22 )2.143283582089550.087092953991659324.6091501534649
Winsorized Mean ( 16 / 22 )2.114626865671640.081853342159707325.8343374855203
Winsorized Mean ( 17 / 22 )2.122238805970150.076868499462766127.6086930381427
Winsorized Mean ( 18 / 22 )2.149104477611940.071401531586851530.098856843117
Winsorized Mean ( 19 / 22 )2.123582089552240.065934023151780532.2076825899694
Winsorized Mean ( 20 / 22 )2.111641791044780.056659455076908237.2690098797894
Winsorized Mean ( 21 / 22 )2.12104477611940.055384489028809138.2967291621325
Winsorized Mean ( 22 / 22 )2.104626865671640.052240324330198540.2874004450815
Trimmed Mean ( 1 / 22 )2.126307692307690.18602684995807811.4301117972317
Trimmed Mean ( 2 / 22 )2.120634920634920.17488565103470512.1258371289368
Trimmed Mean ( 3 / 22 )2.118688524590160.16358425168531512.9516655959392
Trimmed Mean ( 4 / 22 )2.112542372881360.15172562697445413.9234380836471
Trimmed Mean ( 5 / 22 )2.108947368421050.13803006378840615.2788987452326
Trimmed Mean ( 6 / 22 )2.106545454545450.12693199700664716.5958584456458
Trimmed Mean ( 7 / 22 )2.105471698113210.11692745385805818.0066496673151
Trimmed Mean ( 8 / 22 )2.101568627450980.10863407638887719.3453904825224
Trimmed Mean ( 9 / 22 )2.100816326530610.10406689238026120.1871726778793
Trimmed Mean ( 10 / 22 )2.103404255319150.099563002889990321.1263641539946
Trimmed Mean ( 11 / 22 )2.112888888888890.09563853573427522.0924428910058
Trimmed Mean ( 12 / 22 )2.121860465116280.091304836563239223.2392997456016
Trimmed Mean ( 13 / 22 )2.121463414634150.08908584581096423.8136978475323
Trimmed Mean ( 14 / 22 )2.119487179487180.086961722944540124.3726447420882
Trimmed Mean ( 15 / 22 )2.117567567567570.084257403953194225.132124516249
Trimmed Mean ( 16 / 22 )2.114285714285710.081205503098579426.0362368757087
Trimmed Mean ( 17 / 22 )2.114242424242420.078371239582870826.9772742589684
Trimmed Mean ( 18 / 22 )2.113225806451610.075706545926230727.9133829261048
Trimmed Mean ( 19 / 22 )2.108620689655170.073348355910417928.7480293659272
Trimmed Mean ( 20 / 22 )2.106666666666670.071470114089577429.4761900621324
Trimmed Mean ( 21 / 22 )2.1060.071358251099645129.5130551484392
Trimmed Mean ( 22 / 22 )2.103913043478260.071044547430041729.6139974084571
Median2.19
Midrange2.115
Midmean - Weighted Average at Xnp2.09
Midmean - Weighted Average at X(n+1)p2.11428571428571
Midmean - Empirical Distribution Function2.11428571428571
Midmean - Empirical Distribution Function - Averaging2.11428571428571
Midmean - Empirical Distribution Function - Interpolation2.11424242424243
Midmean - Closest Observation2.09
Midmean - True Basic - Statistics Graphics Toolkit2.11428571428571
Midmean - MS Excel (old versions)2.11428571428571
Number of observations67



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')