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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Oct 2012 15:41:28 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/15/t1350330131mh8flq90snowyji.htm/, Retrieved Tue, 07 May 2024 23:09:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=177807, Retrieved Tue, 07 May 2024 23:09:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten meer...] [2012-10-15 19:41:28] [085453999911cf7fe9b8fc00057e83b9] [Current]
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Dataseries X:
2,1
2,1
2,11
2,12
2,13
2,13
2,13
2,13
2,14
2,15
2,16
2,17
2,16
2,2
2,19
2,2
2,2
2,2
2,21
2,22
2,25
2,33
2,33
2,35
2,37
2,38
2,38
2,41
2,41
2,41
2,41
2,42
2,42
2,43
2,44
2,44
2,43
2,44
2,44
2,44
2,44
2,44
2,43
2,42
2,43
2,43
2,43
2,43
2,43
2,44
2,43
2,43
2,44
2,43
2,43
2,44
2,46
2,48
2,49
2,5
2,53
2,55
2,57
2,56
2,56
2,57
2,56
2,57
2,58
2,58
2,58
2,59




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=177807&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=177807&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=177807&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.371250.0175504387142041135.110582624973
Geometric Mean2.36653205373782
Harmonic Mean2.36171216315138
Quadratic Mean2.37585686297246
Winsorized Mean ( 1 / 24 )2.371111111111110.0175265900780363135.286504708209
Winsorized Mean ( 2 / 24 )2.371388888888890.0174670554596413135.763517461093
Winsorized Mean ( 3 / 24 )2.371805555555560.017380630654381136.462571624679
Winsorized Mean ( 4 / 24 )2.371805555555560.0171768468707992138.081545081924
Winsorized Mean ( 5 / 24 )2.371805555555560.0171768468707992138.081545081924
Winsorized Mean ( 6 / 24 )2.371805555555560.0171768468707992138.081545081924
Winsorized Mean ( 7 / 24 )2.370833333333330.0170217457346779139.282619437988
Winsorized Mean ( 8 / 24 )2.371944444444440.0168030090932775141.161885426427
Winsorized Mean ( 9 / 24 )2.373194444444440.0165628531956776143.284156202252
Winsorized Mean ( 10 / 24 )2.373194444444440.0160834900973762147.554693047102
Winsorized Mean ( 11 / 24 )2.370138888888890.0156265757334481151.673593071046
Winsorized Mean ( 12 / 24 )2.366805555555560.0146287206372914161.79169827894
Winsorized Mean ( 13 / 24 )2.368611111111110.0137270302601662172.550877081146
Winsorized Mean ( 14 / 24 )2.368611111111110.0131357209817471180.318317845091
Winsorized Mean ( 15 / 24 )2.364444444444440.0126650123840809186.691048752261
Winsorized Mean ( 16 / 24 )2.360.0122234670016287193.071245636409
Winsorized Mean ( 17 / 24 )2.360.0122234670016287193.071245636409
Winsorized Mean ( 18 / 24 )2.36250.0117647619786014200.811542494194
Winsorized Mean ( 19 / 24 )2.365138888888890.011284819278504209.585889726577
Winsorized Mean ( 20 / 24 )2.373472222222220.00978877011841781242.468889708266
Winsorized Mean ( 21 / 24 )2.396805555555560.00576952488560961415.425117852197
Winsorized Mean ( 22 / 24 )2.396805555555560.00576952488560961415.425117852197
Winsorized Mean ( 23 / 24 )2.403194444444440.00474228798576603506.758436361863
Winsorized Mean ( 24 / 24 )2.409861111111110.00370832637313033649.851406977661
Trimmed Mean ( 1 / 24 )2.3720.0173451146456399136.753203911296
Trimmed Mean ( 2 / 24 )2.372941176470590.0171230361799969138.581800069
Trimmed Mean ( 3 / 24 )2.373787878787880.0168895564364714140.547674399661
Trimmed Mean ( 4 / 24 )2.374531250.0166427353298943142.676741709326
Trimmed Mean ( 5 / 24 )2.375322580645160.0164123841459612144.727454556301
Trimmed Mean ( 6 / 24 )2.376166666666670.0161264278773342147.346125548757
Trimmed Mean ( 7 / 24 )2.377068965517240.0157721384767201150.713168605882
Trimmed Mean ( 8 / 24 )2.378214285714290.0153722366175871154.708410030158
Trimmed Mean ( 9 / 24 )2.379259259259260.0149301936180054159.358901842367
Trimmed Mean ( 10 / 24 )2.380192307692310.0144363438228834164.87500830504
Trimmed Mean ( 11 / 24 )2.38120.0139287985329471170.95516130609
Trimmed Mean ( 12 / 24 )2.382708333333330.0133844529242977178.02059948284
Trimmed Mean ( 13 / 24 )2.384782608695650.0129089682731718184.738435964077
Trimmed Mean ( 14 / 24 )2.386818181818180.0125027385045595190.903631308273
Trimmed Mean ( 15 / 24 )2.389047619047620.0120962531696566197.503109891957
Trimmed Mean ( 16 / 24 )2.3920.0116255686378708205.753376416182
Trimmed Mean ( 17 / 24 )2.395789473684210.0110322917906786217.161539881355
Trimmed Mean ( 18 / 24 )2.40.0101653004546513236.097300882223
Trimmed Mean ( 19 / 24 )2.404411764705880.00904722386262359265.762382053917
Trimmed Mean ( 20 / 24 )2.40906250.00750482875468167321.001661563187
Trimmed Mean ( 21 / 24 )2.413333333333330.00578013509235068417.521960088285
Trimmed Mean ( 22 / 24 )2.415357142857140.00530753041091017455.081168803505
Trimmed Mean ( 23 / 24 )2.417692307692310.0045168979248933535.255024110252
Trimmed Mean ( 24 / 24 )2.419583333333330.00382966901106343631.799595824981
Median2.43
Midrange2.345
Midmean - Weighted Average at Xnp2.38285714285714
Midmean - Weighted Average at X(n+1)p2.40210526315789
Midmean - Empirical Distribution Function2.38285714285714
Midmean - Empirical Distribution Function - Averaging2.40210526315789
Midmean - Empirical Distribution Function - Interpolation2.40210526315789
Midmean - Closest Observation2.38285714285714
Midmean - True Basic - Statistics Graphics Toolkit2.40210526315789
Midmean - MS Excel (old versions)2.38285714285714
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.37125 & 0.0175504387142041 & 135.110582624973 \tabularnewline
Geometric Mean & 2.36653205373782 &  &  \tabularnewline
Harmonic Mean & 2.36171216315138 &  &  \tabularnewline
Quadratic Mean & 2.37585686297246 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.37111111111111 & 0.0175265900780363 & 135.286504708209 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.37138888888889 & 0.0174670554596413 & 135.763517461093 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.37180555555556 & 0.017380630654381 & 136.462571624679 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.37180555555556 & 0.0171768468707992 & 138.081545081924 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.37180555555556 & 0.0171768468707992 & 138.081545081924 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.37180555555556 & 0.0171768468707992 & 138.081545081924 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.37083333333333 & 0.0170217457346779 & 139.282619437988 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.37194444444444 & 0.0168030090932775 & 141.161885426427 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.37319444444444 & 0.0165628531956776 & 143.284156202252 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.37319444444444 & 0.0160834900973762 & 147.554693047102 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.37013888888889 & 0.0156265757334481 & 151.673593071046 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.36680555555556 & 0.0146287206372914 & 161.79169827894 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.36861111111111 & 0.0137270302601662 & 172.550877081146 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.36861111111111 & 0.0131357209817471 & 180.318317845091 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.36444444444444 & 0.0126650123840809 & 186.691048752261 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.36 & 0.0122234670016287 & 193.071245636409 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.36 & 0.0122234670016287 & 193.071245636409 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.3625 & 0.0117647619786014 & 200.811542494194 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.36513888888889 & 0.011284819278504 & 209.585889726577 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.37347222222222 & 0.00978877011841781 & 242.468889708266 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.39680555555556 & 0.00576952488560961 & 415.425117852197 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.39680555555556 & 0.00576952488560961 & 415.425117852197 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.40319444444444 & 0.00474228798576603 & 506.758436361863 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.40986111111111 & 0.00370832637313033 & 649.851406977661 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.372 & 0.0173451146456399 & 136.753203911296 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.37294117647059 & 0.0171230361799969 & 138.581800069 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.37378787878788 & 0.0168895564364714 & 140.547674399661 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.37453125 & 0.0166427353298943 & 142.676741709326 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.37532258064516 & 0.0164123841459612 & 144.727454556301 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.37616666666667 & 0.0161264278773342 & 147.346125548757 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.37706896551724 & 0.0157721384767201 & 150.713168605882 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.37821428571429 & 0.0153722366175871 & 154.708410030158 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.37925925925926 & 0.0149301936180054 & 159.358901842367 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.38019230769231 & 0.0144363438228834 & 164.87500830504 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.3812 & 0.0139287985329471 & 170.95516130609 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.38270833333333 & 0.0133844529242977 & 178.02059948284 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.38478260869565 & 0.0129089682731718 & 184.738435964077 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.38681818181818 & 0.0125027385045595 & 190.903631308273 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.38904761904762 & 0.0120962531696566 & 197.503109891957 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.392 & 0.0116255686378708 & 205.753376416182 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.39578947368421 & 0.0110322917906786 & 217.161539881355 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.4 & 0.0101653004546513 & 236.097300882223 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.40441176470588 & 0.00904722386262359 & 265.762382053917 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.4090625 & 0.00750482875468167 & 321.001661563187 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.41333333333333 & 0.00578013509235068 & 417.521960088285 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.41535714285714 & 0.00530753041091017 & 455.081168803505 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.41769230769231 & 0.0045168979248933 & 535.255024110252 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.41958333333333 & 0.00382966901106343 & 631.799595824981 \tabularnewline
Median & 2.43 &  &  \tabularnewline
Midrange & 2.345 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.38285714285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.40210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.38285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.40210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.40210526315789 &  &  \tabularnewline
Midmean - Closest Observation & 2.38285714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.40210526315789 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.38285714285714 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=177807&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]2.37125[/C][C]0.0175504387142041[/C][C]135.110582624973[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.36653205373782[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.36171216315138[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.37585686297246[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.37111111111111[/C][C]0.0175265900780363[/C][C]135.286504708209[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.37138888888889[/C][C]0.0174670554596413[/C][C]135.763517461093[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.37180555555556[/C][C]0.017380630654381[/C][C]136.462571624679[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.37180555555556[/C][C]0.0171768468707992[/C][C]138.081545081924[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.37180555555556[/C][C]0.0171768468707992[/C][C]138.081545081924[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.37180555555556[/C][C]0.0171768468707992[/C][C]138.081545081924[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.37083333333333[/C][C]0.0170217457346779[/C][C]139.282619437988[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.37194444444444[/C][C]0.0168030090932775[/C][C]141.161885426427[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.37319444444444[/C][C]0.0165628531956776[/C][C]143.284156202252[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.37319444444444[/C][C]0.0160834900973762[/C][C]147.554693047102[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.37013888888889[/C][C]0.0156265757334481[/C][C]151.673593071046[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.36680555555556[/C][C]0.0146287206372914[/C][C]161.79169827894[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.36861111111111[/C][C]0.0137270302601662[/C][C]172.550877081146[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.36861111111111[/C][C]0.0131357209817471[/C][C]180.318317845091[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.36444444444444[/C][C]0.0126650123840809[/C][C]186.691048752261[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.36[/C][C]0.0122234670016287[/C][C]193.071245636409[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.36[/C][C]0.0122234670016287[/C][C]193.071245636409[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.3625[/C][C]0.0117647619786014[/C][C]200.811542494194[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.36513888888889[/C][C]0.011284819278504[/C][C]209.585889726577[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.37347222222222[/C][C]0.00978877011841781[/C][C]242.468889708266[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.39680555555556[/C][C]0.00576952488560961[/C][C]415.425117852197[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.39680555555556[/C][C]0.00576952488560961[/C][C]415.425117852197[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.40319444444444[/C][C]0.00474228798576603[/C][C]506.758436361863[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.40986111111111[/C][C]0.00370832637313033[/C][C]649.851406977661[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.372[/C][C]0.0173451146456399[/C][C]136.753203911296[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.37294117647059[/C][C]0.0171230361799969[/C][C]138.581800069[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.37378787878788[/C][C]0.0168895564364714[/C][C]140.547674399661[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.37453125[/C][C]0.0166427353298943[/C][C]142.676741709326[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.37532258064516[/C][C]0.0164123841459612[/C][C]144.727454556301[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.37616666666667[/C][C]0.0161264278773342[/C][C]147.346125548757[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.37706896551724[/C][C]0.0157721384767201[/C][C]150.713168605882[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.37821428571429[/C][C]0.0153722366175871[/C][C]154.708410030158[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.37925925925926[/C][C]0.0149301936180054[/C][C]159.358901842367[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.38019230769231[/C][C]0.0144363438228834[/C][C]164.87500830504[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.3812[/C][C]0.0139287985329471[/C][C]170.95516130609[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.38270833333333[/C][C]0.0133844529242977[/C][C]178.02059948284[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.38478260869565[/C][C]0.0129089682731718[/C][C]184.738435964077[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.38681818181818[/C][C]0.0125027385045595[/C][C]190.903631308273[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.38904761904762[/C][C]0.0120962531696566[/C][C]197.503109891957[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.392[/C][C]0.0116255686378708[/C][C]205.753376416182[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.39578947368421[/C][C]0.0110322917906786[/C][C]217.161539881355[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.4[/C][C]0.0101653004546513[/C][C]236.097300882223[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.40441176470588[/C][C]0.00904722386262359[/C][C]265.762382053917[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.4090625[/C][C]0.00750482875468167[/C][C]321.001661563187[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.41333333333333[/C][C]0.00578013509235068[/C][C]417.521960088285[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.41535714285714[/C][C]0.00530753041091017[/C][C]455.081168803505[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.41769230769231[/C][C]0.0045168979248933[/C][C]535.255024110252[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.41958333333333[/C][C]0.00382966901106343[/C][C]631.799595824981[/C][/ROW]
[ROW][C]Median[/C][C]2.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.38285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.40210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.38285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.40210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.40210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.38285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.40210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.38285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=177807&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=177807&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 Mean2.371250.0175504387142041135.110582624973
Geometric Mean2.36653205373782
Harmonic Mean2.36171216315138
Quadratic Mean2.37585686297246
Winsorized Mean ( 1 / 24 )2.371111111111110.0175265900780363135.286504708209
Winsorized Mean ( 2 / 24 )2.371388888888890.0174670554596413135.763517461093
Winsorized Mean ( 3 / 24 )2.371805555555560.017380630654381136.462571624679
Winsorized Mean ( 4 / 24 )2.371805555555560.0171768468707992138.081545081924
Winsorized Mean ( 5 / 24 )2.371805555555560.0171768468707992138.081545081924
Winsorized Mean ( 6 / 24 )2.371805555555560.0171768468707992138.081545081924
Winsorized Mean ( 7 / 24 )2.370833333333330.0170217457346779139.282619437988
Winsorized Mean ( 8 / 24 )2.371944444444440.0168030090932775141.161885426427
Winsorized Mean ( 9 / 24 )2.373194444444440.0165628531956776143.284156202252
Winsorized Mean ( 10 / 24 )2.373194444444440.0160834900973762147.554693047102
Winsorized Mean ( 11 / 24 )2.370138888888890.0156265757334481151.673593071046
Winsorized Mean ( 12 / 24 )2.366805555555560.0146287206372914161.79169827894
Winsorized Mean ( 13 / 24 )2.368611111111110.0137270302601662172.550877081146
Winsorized Mean ( 14 / 24 )2.368611111111110.0131357209817471180.318317845091
Winsorized Mean ( 15 / 24 )2.364444444444440.0126650123840809186.691048752261
Winsorized Mean ( 16 / 24 )2.360.0122234670016287193.071245636409
Winsorized Mean ( 17 / 24 )2.360.0122234670016287193.071245636409
Winsorized Mean ( 18 / 24 )2.36250.0117647619786014200.811542494194
Winsorized Mean ( 19 / 24 )2.365138888888890.011284819278504209.585889726577
Winsorized Mean ( 20 / 24 )2.373472222222220.00978877011841781242.468889708266
Winsorized Mean ( 21 / 24 )2.396805555555560.00576952488560961415.425117852197
Winsorized Mean ( 22 / 24 )2.396805555555560.00576952488560961415.425117852197
Winsorized Mean ( 23 / 24 )2.403194444444440.00474228798576603506.758436361863
Winsorized Mean ( 24 / 24 )2.409861111111110.00370832637313033649.851406977661
Trimmed Mean ( 1 / 24 )2.3720.0173451146456399136.753203911296
Trimmed Mean ( 2 / 24 )2.372941176470590.0171230361799969138.581800069
Trimmed Mean ( 3 / 24 )2.373787878787880.0168895564364714140.547674399661
Trimmed Mean ( 4 / 24 )2.374531250.0166427353298943142.676741709326
Trimmed Mean ( 5 / 24 )2.375322580645160.0164123841459612144.727454556301
Trimmed Mean ( 6 / 24 )2.376166666666670.0161264278773342147.346125548757
Trimmed Mean ( 7 / 24 )2.377068965517240.0157721384767201150.713168605882
Trimmed Mean ( 8 / 24 )2.378214285714290.0153722366175871154.708410030158
Trimmed Mean ( 9 / 24 )2.379259259259260.0149301936180054159.358901842367
Trimmed Mean ( 10 / 24 )2.380192307692310.0144363438228834164.87500830504
Trimmed Mean ( 11 / 24 )2.38120.0139287985329471170.95516130609
Trimmed Mean ( 12 / 24 )2.382708333333330.0133844529242977178.02059948284
Trimmed Mean ( 13 / 24 )2.384782608695650.0129089682731718184.738435964077
Trimmed Mean ( 14 / 24 )2.386818181818180.0125027385045595190.903631308273
Trimmed Mean ( 15 / 24 )2.389047619047620.0120962531696566197.503109891957
Trimmed Mean ( 16 / 24 )2.3920.0116255686378708205.753376416182
Trimmed Mean ( 17 / 24 )2.395789473684210.0110322917906786217.161539881355
Trimmed Mean ( 18 / 24 )2.40.0101653004546513236.097300882223
Trimmed Mean ( 19 / 24 )2.404411764705880.00904722386262359265.762382053917
Trimmed Mean ( 20 / 24 )2.40906250.00750482875468167321.001661563187
Trimmed Mean ( 21 / 24 )2.413333333333330.00578013509235068417.521960088285
Trimmed Mean ( 22 / 24 )2.415357142857140.00530753041091017455.081168803505
Trimmed Mean ( 23 / 24 )2.417692307692310.0045168979248933535.255024110252
Trimmed Mean ( 24 / 24 )2.419583333333330.00382966901106343631.799595824981
Median2.43
Midrange2.345
Midmean - Weighted Average at Xnp2.38285714285714
Midmean - Weighted Average at X(n+1)p2.40210526315789
Midmean - Empirical Distribution Function2.38285714285714
Midmean - Empirical Distribution Function - Averaging2.40210526315789
Midmean - Empirical Distribution Function - Interpolation2.40210526315789
Midmean - Closest Observation2.38285714285714
Midmean - True Basic - Statistics Graphics Toolkit2.40210526315789
Midmean - MS Excel (old versions)2.38285714285714
Number of observations72



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')