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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 29 Dec 2012 15:29:42 -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/2012/Dec/29/t13568131149qroxue629f8i90.htm/, Retrieved Thu, 02 May 2024 09:36:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204911, Retrieved Thu, 02 May 2024 09:36:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-12-29 20:29:42] [3f9aa5867cfe47c4a12580af2904c765] [Current]
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Dataseries X:
103,24
103,43
103,43
103,43
103,31
103,31
103,31
103,31
104,06
104,8
105,36
105,38
105,38
105,38
108,37
112,21
112,05
112,05
112,06
112,05
111,36
111,36
111,36
111,36
111,78
111,89
111,89
111,89
112,02
112,02
112,02
112,02
112,02
112,02
112,02
111,28
111,28
111,28
111,28
110,56
110,56
110,56
110,56
110,56
111,37
109,43
109,43
109,57
109,57
109,57
109,57
109,57
109,39
111,68
111,68
111,68
111,93
111,93
111,93
111,93
111,56
111,89
111,89
111,89
110,82
110,82
110,82
110,82
110,98
110,98
111,78
111,78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204911&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204911&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204911&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.821250.352014487532413311.979347128115
Geometric Mean109.780179581893
Harmonic Mean109.738082735054
Quadratic Mean109.861298279796
Winsorized Mean ( 1 / 24 )109.8201388888890.351566664299416312.373583848551
Winsorized Mean ( 2 / 24 )109.8198611111110.351541791518032312.39489517558
Winsorized Mean ( 3 / 24 )109.8198611111110.351541791518032312.39489517558
Winsorized Mean ( 4 / 24 )109.8198611111110.351541791518032312.39489517558
Winsorized Mean ( 5 / 24 )109.8261111111110.349194834855796314.512415845054
Winsorized Mean ( 6 / 24 )109.8261111111110.349194834855796314.512415845054
Winsorized Mean ( 7 / 24 )109.8261111111110.349194834855796314.512415845054
Winsorized Mean ( 8 / 24 )109.8961111111110.331477141425734331.534508347789
Winsorized Mean ( 9 / 24 )109.9886111111110.309053233025205355.888886954763
Winsorized Mean ( 10 / 24 )110.0663888888890.29098850102554378.24996005333
Winsorized Mean ( 11 / 24 )110.0694444444440.290292867126585379.166892848413
Winsorized Mean ( 12 / 24 )110.0544444444440.288897240158573380.946679809183
Winsorized Mean ( 13 / 24 )110.0544444444440.288897240158573380.946679809183
Winsorized Mean ( 14 / 24 )110.6358333333330.163188921259714677.961668471703
Winsorized Mean ( 15 / 24 )110.8483333333330.124436130395199890.805049797742
Winsorized Mean ( 16 / 24 )110.8483333333330.121894923835917909.376123673096
Winsorized Mean ( 17 / 24 )110.8483333333330.121894923835917909.376123673096
Winsorized Mean ( 18 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 19 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 20 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 21 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 22 / 24 )110.8497222222220.112226710697515987.730296408631
Winsorized Mean ( 23 / 24 )111.1659722222220.06477288470649721716.24241726988
Winsorized Mean ( 24 / 24 )111.1659722222220.06477288470649721716.24241726988
Trimmed Mean ( 1 / 24 )109.8811428571430.347775929317597315.953847273878
Trimmed Mean ( 2 / 24 )109.9457352941180.342987015637976320.553636963813
Trimmed Mean ( 3 / 24 )110.0143939393940.336994886889467326.457160685284
Trimmed Mean ( 4 / 24 )110.087343750.329502935696052334.101253202641
Trimmed Mean ( 5 / 24 )110.1650.320135460983572344.119953664405
Trimmed Mean ( 6 / 24 )110.2463333333330.309184544992992356.571294130605
Trimmed Mean ( 7 / 24 )110.3332758620690.29533573008062373.58593838934
Trimmed Mean ( 8 / 24 )110.4264285714290.277613721704573397.770066599736
Trimmed Mean ( 9 / 24 )110.5148148148150.260275178350646424.607584615417
Trimmed Mean ( 10 / 24 )110.5957692307690.244560329186694452.222850691136
Trimmed Mean ( 11 / 24 )110.6720.22935864438713482.528139698971
Trimmed Mean ( 12 / 24 )110.7541666666670.20920396095993529.407598969314
Trimmed Mean ( 13 / 24 )110.8454347826090.181365381471502611.171955106691
Trimmed Mean ( 14 / 24 )110.9450.139096108043063797.613977564726
Trimmed Mean ( 15 / 24 )110.9828571428570.129648988154238856.025632925308
Trimmed Mean ( 16 / 24 )110.9990.127852479093119868.180271413867
Trimmed Mean ( 17 / 24 )111.0168421052630.12574789363787882.852498706423
Trimmed Mean ( 18 / 24 )111.0366666666670.122596900450216905.70533397585
Trimmed Mean ( 19 / 24 )111.0547058823530.119593216720609928.603719572126
Trimmed Mean ( 20 / 24 )111.0750.11505696345163965.391373697219
Trimmed Mean ( 21 / 24 )111.0980.1082094605675581026.69396388533
Trimmed Mean ( 22 / 24 )111.1242857142860.0976285322531371138.23575085771
Trimmed Mean ( 23 / 24 )111.1588461538460.08160755418102131362.11466290577
Trimmed Mean ( 24 / 24 )111.1579166666670.08058207438730061379.43726953975
Median111.28
Midrange107.725
Midmean - Weighted Average at Xnp110.999
Midmean - Weighted Average at X(n+1)p111.081578947368
Midmean - Empirical Distribution Function110.999
Midmean - Empirical Distribution Function - Averaging111.081578947368
Midmean - Empirical Distribution Function - Interpolation111.081578947368
Midmean - Closest Observation110.999
Midmean - True Basic - Statistics Graphics Toolkit111.081578947368
Midmean - MS Excel (old versions)110.999
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.82125 & 0.352014487532413 & 311.979347128115 \tabularnewline
Geometric Mean & 109.780179581893 &  &  \tabularnewline
Harmonic Mean & 109.738082735054 &  &  \tabularnewline
Quadratic Mean & 109.861298279796 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 109.820138888889 & 0.351566664299416 & 312.373583848551 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 109.819861111111 & 0.351541791518032 & 312.39489517558 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 109.819861111111 & 0.351541791518032 & 312.39489517558 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 109.819861111111 & 0.351541791518032 & 312.39489517558 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 109.826111111111 & 0.349194834855796 & 314.512415845054 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 109.826111111111 & 0.349194834855796 & 314.512415845054 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 109.826111111111 & 0.349194834855796 & 314.512415845054 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 109.896111111111 & 0.331477141425734 & 331.534508347789 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 109.988611111111 & 0.309053233025205 & 355.888886954763 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 110.066388888889 & 0.29098850102554 & 378.24996005333 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 110.069444444444 & 0.290292867126585 & 379.166892848413 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 110.054444444444 & 0.288897240158573 & 380.946679809183 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 110.054444444444 & 0.288897240158573 & 380.946679809183 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 110.635833333333 & 0.163188921259714 & 677.961668471703 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 110.848333333333 & 0.124436130395199 & 890.805049797742 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 110.848333333333 & 0.121894923835917 & 909.376123673096 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 110.848333333333 & 0.121894923835917 & 909.376123673096 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 110.883333333333 & 0.116240166090868 & 953.91581982645 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 110.883333333333 & 0.116240166090868 & 953.91581982645 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 110.883333333333 & 0.116240166090868 & 953.91581982645 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 110.883333333333 & 0.116240166090868 & 953.91581982645 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 110.849722222222 & 0.112226710697515 & 987.730296408631 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 111.165972222222 & 0.0647728847064972 & 1716.24241726988 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 111.165972222222 & 0.0647728847064972 & 1716.24241726988 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 109.881142857143 & 0.347775929317597 & 315.953847273878 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 109.945735294118 & 0.342987015637976 & 320.553636963813 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 110.014393939394 & 0.336994886889467 & 326.457160685284 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 110.08734375 & 0.329502935696052 & 334.101253202641 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 110.165 & 0.320135460983572 & 344.119953664405 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 110.246333333333 & 0.309184544992992 & 356.571294130605 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 110.333275862069 & 0.29533573008062 & 373.58593838934 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 110.426428571429 & 0.277613721704573 & 397.770066599736 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 110.514814814815 & 0.260275178350646 & 424.607584615417 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 110.595769230769 & 0.244560329186694 & 452.222850691136 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 110.672 & 0.22935864438713 & 482.528139698971 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 110.754166666667 & 0.20920396095993 & 529.407598969314 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 110.845434782609 & 0.181365381471502 & 611.171955106691 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 110.945 & 0.139096108043063 & 797.613977564726 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 110.982857142857 & 0.129648988154238 & 856.025632925308 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 110.999 & 0.127852479093119 & 868.180271413867 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 111.016842105263 & 0.12574789363787 & 882.852498706423 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 111.036666666667 & 0.122596900450216 & 905.70533397585 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 111.054705882353 & 0.119593216720609 & 928.603719572126 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 111.075 & 0.11505696345163 & 965.391373697219 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 111.098 & 0.108209460567558 & 1026.69396388533 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 111.124285714286 & 0.097628532253137 & 1138.23575085771 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 111.158846153846 & 0.0816075541810213 & 1362.11466290577 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 111.157916666667 & 0.0805820743873006 & 1379.43726953975 \tabularnewline
Median & 111.28 &  &  \tabularnewline
Midrange & 107.725 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.999 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.081578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.999 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.081578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.081578947368 &  &  \tabularnewline
Midmean - Closest Observation & 110.999 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.081578947368 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.999 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204911&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]109.82125[/C][C]0.352014487532413[/C][C]311.979347128115[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]109.780179581893[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.738082735054[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.861298279796[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]109.820138888889[/C][C]0.351566664299416[/C][C]312.373583848551[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]109.819861111111[/C][C]0.351541791518032[/C][C]312.39489517558[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]109.819861111111[/C][C]0.351541791518032[/C][C]312.39489517558[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]109.819861111111[/C][C]0.351541791518032[/C][C]312.39489517558[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]109.826111111111[/C][C]0.349194834855796[/C][C]314.512415845054[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]109.826111111111[/C][C]0.349194834855796[/C][C]314.512415845054[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]109.826111111111[/C][C]0.349194834855796[/C][C]314.512415845054[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]109.896111111111[/C][C]0.331477141425734[/C][C]331.534508347789[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]109.988611111111[/C][C]0.309053233025205[/C][C]355.888886954763[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]110.066388888889[/C][C]0.29098850102554[/C][C]378.24996005333[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]110.069444444444[/C][C]0.290292867126585[/C][C]379.166892848413[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]110.054444444444[/C][C]0.288897240158573[/C][C]380.946679809183[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]110.054444444444[/C][C]0.288897240158573[/C][C]380.946679809183[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]110.635833333333[/C][C]0.163188921259714[/C][C]677.961668471703[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]110.848333333333[/C][C]0.124436130395199[/C][C]890.805049797742[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]110.848333333333[/C][C]0.121894923835917[/C][C]909.376123673096[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]110.848333333333[/C][C]0.121894923835917[/C][C]909.376123673096[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]110.883333333333[/C][C]0.116240166090868[/C][C]953.91581982645[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]110.883333333333[/C][C]0.116240166090868[/C][C]953.91581982645[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]110.883333333333[/C][C]0.116240166090868[/C][C]953.91581982645[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]110.883333333333[/C][C]0.116240166090868[/C][C]953.91581982645[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]110.849722222222[/C][C]0.112226710697515[/C][C]987.730296408631[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]111.165972222222[/C][C]0.0647728847064972[/C][C]1716.24241726988[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]111.165972222222[/C][C]0.0647728847064972[/C][C]1716.24241726988[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]109.881142857143[/C][C]0.347775929317597[/C][C]315.953847273878[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]109.945735294118[/C][C]0.342987015637976[/C][C]320.553636963813[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]110.014393939394[/C][C]0.336994886889467[/C][C]326.457160685284[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]110.08734375[/C][C]0.329502935696052[/C][C]334.101253202641[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]110.165[/C][C]0.320135460983572[/C][C]344.119953664405[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]110.246333333333[/C][C]0.309184544992992[/C][C]356.571294130605[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]110.333275862069[/C][C]0.29533573008062[/C][C]373.58593838934[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]110.426428571429[/C][C]0.277613721704573[/C][C]397.770066599736[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]110.514814814815[/C][C]0.260275178350646[/C][C]424.607584615417[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]110.595769230769[/C][C]0.244560329186694[/C][C]452.222850691136[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]110.672[/C][C]0.22935864438713[/C][C]482.528139698971[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]110.754166666667[/C][C]0.20920396095993[/C][C]529.407598969314[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]110.845434782609[/C][C]0.181365381471502[/C][C]611.171955106691[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]110.945[/C][C]0.139096108043063[/C][C]797.613977564726[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]110.982857142857[/C][C]0.129648988154238[/C][C]856.025632925308[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]110.999[/C][C]0.127852479093119[/C][C]868.180271413867[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]111.016842105263[/C][C]0.12574789363787[/C][C]882.852498706423[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]111.036666666667[/C][C]0.122596900450216[/C][C]905.70533397585[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]111.054705882353[/C][C]0.119593216720609[/C][C]928.603719572126[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]111.075[/C][C]0.11505696345163[/C][C]965.391373697219[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]111.098[/C][C]0.108209460567558[/C][C]1026.69396388533[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]111.124285714286[/C][C]0.097628532253137[/C][C]1138.23575085771[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]111.158846153846[/C][C]0.0816075541810213[/C][C]1362.11466290577[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]111.157916666667[/C][C]0.0805820743873006[/C][C]1379.43726953975[/C][/ROW]
[ROW][C]Median[/C][C]111.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.999[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.081578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.999[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.081578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.081578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.999[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.081578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.999[/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=204911&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204911&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 Mean109.821250.352014487532413311.979347128115
Geometric Mean109.780179581893
Harmonic Mean109.738082735054
Quadratic Mean109.861298279796
Winsorized Mean ( 1 / 24 )109.8201388888890.351566664299416312.373583848551
Winsorized Mean ( 2 / 24 )109.8198611111110.351541791518032312.39489517558
Winsorized Mean ( 3 / 24 )109.8198611111110.351541791518032312.39489517558
Winsorized Mean ( 4 / 24 )109.8198611111110.351541791518032312.39489517558
Winsorized Mean ( 5 / 24 )109.8261111111110.349194834855796314.512415845054
Winsorized Mean ( 6 / 24 )109.8261111111110.349194834855796314.512415845054
Winsorized Mean ( 7 / 24 )109.8261111111110.349194834855796314.512415845054
Winsorized Mean ( 8 / 24 )109.8961111111110.331477141425734331.534508347789
Winsorized Mean ( 9 / 24 )109.9886111111110.309053233025205355.888886954763
Winsorized Mean ( 10 / 24 )110.0663888888890.29098850102554378.24996005333
Winsorized Mean ( 11 / 24 )110.0694444444440.290292867126585379.166892848413
Winsorized Mean ( 12 / 24 )110.0544444444440.288897240158573380.946679809183
Winsorized Mean ( 13 / 24 )110.0544444444440.288897240158573380.946679809183
Winsorized Mean ( 14 / 24 )110.6358333333330.163188921259714677.961668471703
Winsorized Mean ( 15 / 24 )110.8483333333330.124436130395199890.805049797742
Winsorized Mean ( 16 / 24 )110.8483333333330.121894923835917909.376123673096
Winsorized Mean ( 17 / 24 )110.8483333333330.121894923835917909.376123673096
Winsorized Mean ( 18 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 19 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 20 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 21 / 24 )110.8833333333330.116240166090868953.91581982645
Winsorized Mean ( 22 / 24 )110.8497222222220.112226710697515987.730296408631
Winsorized Mean ( 23 / 24 )111.1659722222220.06477288470649721716.24241726988
Winsorized Mean ( 24 / 24 )111.1659722222220.06477288470649721716.24241726988
Trimmed Mean ( 1 / 24 )109.8811428571430.347775929317597315.953847273878
Trimmed Mean ( 2 / 24 )109.9457352941180.342987015637976320.553636963813
Trimmed Mean ( 3 / 24 )110.0143939393940.336994886889467326.457160685284
Trimmed Mean ( 4 / 24 )110.087343750.329502935696052334.101253202641
Trimmed Mean ( 5 / 24 )110.1650.320135460983572344.119953664405
Trimmed Mean ( 6 / 24 )110.2463333333330.309184544992992356.571294130605
Trimmed Mean ( 7 / 24 )110.3332758620690.29533573008062373.58593838934
Trimmed Mean ( 8 / 24 )110.4264285714290.277613721704573397.770066599736
Trimmed Mean ( 9 / 24 )110.5148148148150.260275178350646424.607584615417
Trimmed Mean ( 10 / 24 )110.5957692307690.244560329186694452.222850691136
Trimmed Mean ( 11 / 24 )110.6720.22935864438713482.528139698971
Trimmed Mean ( 12 / 24 )110.7541666666670.20920396095993529.407598969314
Trimmed Mean ( 13 / 24 )110.8454347826090.181365381471502611.171955106691
Trimmed Mean ( 14 / 24 )110.9450.139096108043063797.613977564726
Trimmed Mean ( 15 / 24 )110.9828571428570.129648988154238856.025632925308
Trimmed Mean ( 16 / 24 )110.9990.127852479093119868.180271413867
Trimmed Mean ( 17 / 24 )111.0168421052630.12574789363787882.852498706423
Trimmed Mean ( 18 / 24 )111.0366666666670.122596900450216905.70533397585
Trimmed Mean ( 19 / 24 )111.0547058823530.119593216720609928.603719572126
Trimmed Mean ( 20 / 24 )111.0750.11505696345163965.391373697219
Trimmed Mean ( 21 / 24 )111.0980.1082094605675581026.69396388533
Trimmed Mean ( 22 / 24 )111.1242857142860.0976285322531371138.23575085771
Trimmed Mean ( 23 / 24 )111.1588461538460.08160755418102131362.11466290577
Trimmed Mean ( 24 / 24 )111.1579166666670.08058207438730061379.43726953975
Median111.28
Midrange107.725
Midmean - Weighted Average at Xnp110.999
Midmean - Weighted Average at X(n+1)p111.081578947368
Midmean - Empirical Distribution Function110.999
Midmean - Empirical Distribution Function - Averaging111.081578947368
Midmean - Empirical Distribution Function - Interpolation111.081578947368
Midmean - Closest Observation110.999
Midmean - True Basic - Statistics Graphics Toolkit111.081578947368
Midmean - MS Excel (old versions)110.999
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')