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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 15:35:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t12298990831pdzwkr4n9jjtea.htm/, Retrieved Sun, 19 May 2024 09:23:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35894, Retrieved Sun, 19 May 2024 09:23:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [] [2008-12-21 22:35:28] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
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Dataseries X:
5732
4491
4755
5208
4962
4163
5592
5754
4929
5219
4429
4142
4308
3996
4634
4138
3759
3922
5560
4004
3937
5250
3908
4814
4407
3243
3740
3949
3711
3796
4145
3499
4164
3902
3186
3353
3475
3032
3341
3811
3655
4058
3682
3348
3848
3289
3851
2766
2837
2734
3764
3215
3287
3507
3060
3734
3849
4404
3497
3389




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35894&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35894&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35894&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' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4002.2333333333395.833053892984941.7625565580176
Geometric Mean3937.64613878965
Harmonic Mean3875.97137142892
Quadratic Mean4069.36434020515
Winsorized Mean ( 1 / 20 )4002.495.601766997829841.8653349795392
Winsorized Mean ( 2 / 20 )4000.193.705545241674742.687975292
Winsorized Mean ( 3 / 20 )4008.2591.334227051382343.8855194750273
Winsorized Mean ( 4 / 20 )3989.4585.419835300191646.7040235558854
Winsorized Mean ( 5 / 20 )3997.3666666666782.934062593302148.199335009901
Winsorized Mean ( 6 / 20 )3999.1666666666782.184672738564948.6607360400192
Winsorized Mean ( 7 / 20 )3973.7333333333374.844410615467153.0932544014467
Winsorized Mean ( 8 / 20 )3975.272.90927261945754.5225573809819
Winsorized Mean ( 9 / 20 )3958.2569.136071614643357.2530360426442
Winsorized Mean ( 10 / 20 )3957.0833333333365.69154634219460.2373296667501
Winsorized Mean ( 11 / 20 )3936.1833333333361.047571020436964.4773128158631
Winsorized Mean ( 12 / 20 )3908.5833333333355.559268967232370.3497977203145
Winsorized Mean ( 13 / 20 )3902.9551.894669642345175.2090730492918
Winsorized Mean ( 14 / 20 )3917.8833333333347.742015581551282.0636348425832
Winsorized Mean ( 15 / 20 )3922.6333333333346.75467870884883.8981988895798
Winsorized Mean ( 16 / 20 )3897.5666666666742.32728525682792.0816594548318
Winsorized Mean ( 17 / 20 )3859.0333333333335.6096219989446108.370522255128
Winsorized Mean ( 18 / 20 )3903.1333333333328.5223122756867136.844912698768
Winsorized Mean ( 19 / 20 )3905.9833333333326.3990186821840147.959413959936
Winsorized Mean ( 20 / 20 )3914.6524.8784937074684157.350764319982
Trimmed Mean ( 1 / 20 )3993.8965517241491.750034211278843.5301914169005
Trimmed Mean ( 2 / 20 )3984.7857142857186.970575387945.8176308080411
Trimmed Mean ( 3 / 20 )3976.2777777777882.315152664971948.3055385192747
Trimmed Mean ( 4 / 20 )3963.9807692307777.636162147480651.0584328176944
Trimmed Mean ( 5 / 20 )3956.3474.260020886347853.276850084045
Trimmed Mean ( 6 / 20 )3946.0833333333370.829262502965255.7126135990494
Trimmed Mean ( 7 / 20 )3934.5434782608766.611656336743259.0668915117572
Trimmed Mean ( 8 / 20 )3926.9090909090963.58044810114161.7628407503882
Trimmed Mean ( 9 / 20 )3918.2857142857160.156428736813765.1349456170069
Trimmed Mean ( 10 / 20 )3911.62556.791834094980568.8765394239261
Trimmed Mean ( 11 / 20 )3904.4473684210553.288950351292973.26936152208
Trimmed Mean ( 12 / 20 )3899.6388888888949.999383373622877.9937396377202
Trimmed Mean ( 13 / 20 )3898.3235294117647.216094430194782.563447410398
Trimmed Mean ( 14 / 20 )3897.6562544.453437250873487.6795247126457
Trimmed Mean ( 15 / 20 )3894.7666666666741.825848119090593.1186536989548
Trimmed Mean ( 16 / 20 )3890.7857142857138.2140780294015101.815506612306
Trimmed Mean ( 17 / 20 )3889.8076923076934.5612063193477112.548377402271
Trimmed Mean ( 18 / 20 )3894.3333333333331.6855969352022122.905474727124
Trimmed Mean ( 19 / 20 )389330.3191537192429128.400681498217
Trimmed Mean ( 20 / 20 )3890.9528.8637885502524134.803856161355
Median3876.5
Midrange4244
Midmean - Weighted Average at Xnp3881.22580645161
Midmean - Weighted Average at X(n+1)p3894.76666666667
Midmean - Empirical Distribution Function3881.22580645161
Midmean - Empirical Distribution Function - Averaging3894.76666666667
Midmean - Empirical Distribution Function - Interpolation3894.76666666667
Midmean - Closest Observation3881.22580645161
Midmean - True Basic - Statistics Graphics Toolkit3894.76666666667
Midmean - MS Excel (old versions)3897.65625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4002.23333333333 & 95.8330538929849 & 41.7625565580176 \tabularnewline
Geometric Mean & 3937.64613878965 &  &  \tabularnewline
Harmonic Mean & 3875.97137142892 &  &  \tabularnewline
Quadratic Mean & 4069.36434020515 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4002.4 & 95.6017669978298 & 41.8653349795392 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4000.1 & 93.7055452416747 & 42.687975292 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4008.25 & 91.3342270513823 & 43.8855194750273 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3989.45 & 85.4198353001916 & 46.7040235558854 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3997.36666666667 & 82.9340625933021 & 48.199335009901 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3999.16666666667 & 82.1846727385649 & 48.6607360400192 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3973.73333333333 & 74.8444106154671 & 53.0932544014467 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3975.2 & 72.909272619457 & 54.5225573809819 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3958.25 & 69.1360716146433 & 57.2530360426442 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3957.08333333333 & 65.691546342194 & 60.2373296667501 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3936.18333333333 & 61.0475710204369 & 64.4773128158631 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3908.58333333333 & 55.5592689672323 & 70.3497977203145 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3902.95 & 51.8946696423451 & 75.2090730492918 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3917.88333333333 & 47.7420155815512 & 82.0636348425832 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3922.63333333333 & 46.754678708848 & 83.8981988895798 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3897.56666666667 & 42.327285256827 & 92.0816594548318 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3859.03333333333 & 35.6096219989446 & 108.370522255128 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3903.13333333333 & 28.5223122756867 & 136.844912698768 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3905.98333333333 & 26.3990186821840 & 147.959413959936 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3914.65 & 24.8784937074684 & 157.350764319982 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3993.89655172414 & 91.7500342112788 & 43.5301914169005 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3984.78571428571 & 86.9705753879 & 45.8176308080411 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3976.27777777778 & 82.3151526649719 & 48.3055385192747 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3963.98076923077 & 77.6361621474806 & 51.0584328176944 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3956.34 & 74.2600208863478 & 53.276850084045 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3946.08333333333 & 70.8292625029652 & 55.7126135990494 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3934.54347826087 & 66.6116563367432 & 59.0668915117572 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3926.90909090909 & 63.580448101141 & 61.7628407503882 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3918.28571428571 & 60.1564287368137 & 65.1349456170069 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3911.625 & 56.7918340949805 & 68.8765394239261 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3904.44736842105 & 53.2889503512929 & 73.26936152208 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3899.63888888889 & 49.9993833736228 & 77.9937396377202 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3898.32352941176 & 47.2160944301947 & 82.563447410398 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3897.65625 & 44.4534372508734 & 87.6795247126457 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3894.76666666667 & 41.8258481190905 & 93.1186536989548 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3890.78571428571 & 38.2140780294015 & 101.815506612306 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3889.80769230769 & 34.5612063193477 & 112.548377402271 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3894.33333333333 & 31.6855969352022 & 122.905474727124 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3893 & 30.3191537192429 & 128.400681498217 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3890.95 & 28.8637885502524 & 134.803856161355 \tabularnewline
Median & 3876.5 &  &  \tabularnewline
Midrange & 4244 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3881.22580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3894.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3881.22580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3894.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3894.76666666667 &  &  \tabularnewline
Midmean - Closest Observation & 3881.22580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3894.76666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3897.65625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35894&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]4002.23333333333[/C][C]95.8330538929849[/C][C]41.7625565580176[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3937.64613878965[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3875.97137142892[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4069.36434020515[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4002.4[/C][C]95.6017669978298[/C][C]41.8653349795392[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4000.1[/C][C]93.7055452416747[/C][C]42.687975292[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4008.25[/C][C]91.3342270513823[/C][C]43.8855194750273[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3989.45[/C][C]85.4198353001916[/C][C]46.7040235558854[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3997.36666666667[/C][C]82.9340625933021[/C][C]48.199335009901[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3999.16666666667[/C][C]82.1846727385649[/C][C]48.6607360400192[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3973.73333333333[/C][C]74.8444106154671[/C][C]53.0932544014467[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3975.2[/C][C]72.909272619457[/C][C]54.5225573809819[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3958.25[/C][C]69.1360716146433[/C][C]57.2530360426442[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3957.08333333333[/C][C]65.691546342194[/C][C]60.2373296667501[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3936.18333333333[/C][C]61.0475710204369[/C][C]64.4773128158631[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3908.58333333333[/C][C]55.5592689672323[/C][C]70.3497977203145[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3902.95[/C][C]51.8946696423451[/C][C]75.2090730492918[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3917.88333333333[/C][C]47.7420155815512[/C][C]82.0636348425832[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3922.63333333333[/C][C]46.754678708848[/C][C]83.8981988895798[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3897.56666666667[/C][C]42.327285256827[/C][C]92.0816594548318[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3859.03333333333[/C][C]35.6096219989446[/C][C]108.370522255128[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3903.13333333333[/C][C]28.5223122756867[/C][C]136.844912698768[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3905.98333333333[/C][C]26.3990186821840[/C][C]147.959413959936[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3914.65[/C][C]24.8784937074684[/C][C]157.350764319982[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3993.89655172414[/C][C]91.7500342112788[/C][C]43.5301914169005[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3984.78571428571[/C][C]86.9705753879[/C][C]45.8176308080411[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3976.27777777778[/C][C]82.3151526649719[/C][C]48.3055385192747[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3963.98076923077[/C][C]77.6361621474806[/C][C]51.0584328176944[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3956.34[/C][C]74.2600208863478[/C][C]53.276850084045[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3946.08333333333[/C][C]70.8292625029652[/C][C]55.7126135990494[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3934.54347826087[/C][C]66.6116563367432[/C][C]59.0668915117572[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3926.90909090909[/C][C]63.580448101141[/C][C]61.7628407503882[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3918.28571428571[/C][C]60.1564287368137[/C][C]65.1349456170069[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3911.625[/C][C]56.7918340949805[/C][C]68.8765394239261[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3904.44736842105[/C][C]53.2889503512929[/C][C]73.26936152208[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3899.63888888889[/C][C]49.9993833736228[/C][C]77.9937396377202[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3898.32352941176[/C][C]47.2160944301947[/C][C]82.563447410398[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3897.65625[/C][C]44.4534372508734[/C][C]87.6795247126457[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3894.76666666667[/C][C]41.8258481190905[/C][C]93.1186536989548[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3890.78571428571[/C][C]38.2140780294015[/C][C]101.815506612306[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3889.80769230769[/C][C]34.5612063193477[/C][C]112.548377402271[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3894.33333333333[/C][C]31.6855969352022[/C][C]122.905474727124[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3893[/C][C]30.3191537192429[/C][C]128.400681498217[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3890.95[/C][C]28.8637885502524[/C][C]134.803856161355[/C][/ROW]
[ROW][C]Median[/C][C]3876.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3881.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3894.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3881.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3894.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3894.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3881.22580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3894.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3897.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35894&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35894&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 Mean4002.2333333333395.833053892984941.7625565580176
Geometric Mean3937.64613878965
Harmonic Mean3875.97137142892
Quadratic Mean4069.36434020515
Winsorized Mean ( 1 / 20 )4002.495.601766997829841.8653349795392
Winsorized Mean ( 2 / 20 )4000.193.705545241674742.687975292
Winsorized Mean ( 3 / 20 )4008.2591.334227051382343.8855194750273
Winsorized Mean ( 4 / 20 )3989.4585.419835300191646.7040235558854
Winsorized Mean ( 5 / 20 )3997.3666666666782.934062593302148.199335009901
Winsorized Mean ( 6 / 20 )3999.1666666666782.184672738564948.6607360400192
Winsorized Mean ( 7 / 20 )3973.7333333333374.844410615467153.0932544014467
Winsorized Mean ( 8 / 20 )3975.272.90927261945754.5225573809819
Winsorized Mean ( 9 / 20 )3958.2569.136071614643357.2530360426442
Winsorized Mean ( 10 / 20 )3957.0833333333365.69154634219460.2373296667501
Winsorized Mean ( 11 / 20 )3936.1833333333361.047571020436964.4773128158631
Winsorized Mean ( 12 / 20 )3908.5833333333355.559268967232370.3497977203145
Winsorized Mean ( 13 / 20 )3902.9551.894669642345175.2090730492918
Winsorized Mean ( 14 / 20 )3917.8833333333347.742015581551282.0636348425832
Winsorized Mean ( 15 / 20 )3922.6333333333346.75467870884883.8981988895798
Winsorized Mean ( 16 / 20 )3897.5666666666742.32728525682792.0816594548318
Winsorized Mean ( 17 / 20 )3859.0333333333335.6096219989446108.370522255128
Winsorized Mean ( 18 / 20 )3903.1333333333328.5223122756867136.844912698768
Winsorized Mean ( 19 / 20 )3905.9833333333326.3990186821840147.959413959936
Winsorized Mean ( 20 / 20 )3914.6524.8784937074684157.350764319982
Trimmed Mean ( 1 / 20 )3993.8965517241491.750034211278843.5301914169005
Trimmed Mean ( 2 / 20 )3984.7857142857186.970575387945.8176308080411
Trimmed Mean ( 3 / 20 )3976.2777777777882.315152664971948.3055385192747
Trimmed Mean ( 4 / 20 )3963.9807692307777.636162147480651.0584328176944
Trimmed Mean ( 5 / 20 )3956.3474.260020886347853.276850084045
Trimmed Mean ( 6 / 20 )3946.0833333333370.829262502965255.7126135990494
Trimmed Mean ( 7 / 20 )3934.5434782608766.611656336743259.0668915117572
Trimmed Mean ( 8 / 20 )3926.9090909090963.58044810114161.7628407503882
Trimmed Mean ( 9 / 20 )3918.2857142857160.156428736813765.1349456170069
Trimmed Mean ( 10 / 20 )3911.62556.791834094980568.8765394239261
Trimmed Mean ( 11 / 20 )3904.4473684210553.288950351292973.26936152208
Trimmed Mean ( 12 / 20 )3899.6388888888949.999383373622877.9937396377202
Trimmed Mean ( 13 / 20 )3898.3235294117647.216094430194782.563447410398
Trimmed Mean ( 14 / 20 )3897.6562544.453437250873487.6795247126457
Trimmed Mean ( 15 / 20 )3894.7666666666741.825848119090593.1186536989548
Trimmed Mean ( 16 / 20 )3890.7857142857138.2140780294015101.815506612306
Trimmed Mean ( 17 / 20 )3889.8076923076934.5612063193477112.548377402271
Trimmed Mean ( 18 / 20 )3894.3333333333331.6855969352022122.905474727124
Trimmed Mean ( 19 / 20 )389330.3191537192429128.400681498217
Trimmed Mean ( 20 / 20 )3890.9528.8637885502524134.803856161355
Median3876.5
Midrange4244
Midmean - Weighted Average at Xnp3881.22580645161
Midmean - Weighted Average at X(n+1)p3894.76666666667
Midmean - Empirical Distribution Function3881.22580645161
Midmean - Empirical Distribution Function - Averaging3894.76666666667
Midmean - Empirical Distribution Function - Interpolation3894.76666666667
Midmean - Closest Observation3881.22580645161
Midmean - True Basic - Statistics Graphics Toolkit3894.76666666667
Midmean - MS Excel (old versions)3897.65625
Number of observations60



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')