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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 computationTue, 25 Feb 2014 16:43:51 -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/2014/Feb/25/t1393364637mr2297rbw2zm568.htm/, Retrieved Thu, 16 May 2024 13:48:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234054, Retrieved Thu, 16 May 2024 13:48:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-02-25 21:43:51] [0a29af7e4d8d6424b8240e38ffd48a3a] [Current]
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Dataseries X:
3200944
3153170
3741498
3918719
4403449
4400407
4847473
4716136
4297440
4272253
3271834
3168388
2911748
2720999
3199918
3672623
3892013
3850845
4532467
4484739
4014972
3983758
3158459
3100569
2935404
2855719
3465611
3006985
4095110
4104793
4730788
4642726
4246919
4308032
3508154
3236641
3257275
3045631
3657692
4125747
4472507
4513455
5150896
5057815
4681742
4603682
3580181
3534002
3422762
3295209
3868093
4189245
4544332
4612845
5221595
5137505
4760439
4643697
3692267
3587603




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234054&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234054&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234054&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean394513287063.883276715145.3130718677134
Geometric Mean3887496.62026432
Harmonic Mean3829437.37470715
Quadratic Mean4001411.44646812
Winsorized Mean ( 1 / 20 )3946199.0166666786269.816842173745.7425222530151
Winsorized Mean ( 2 / 20 )3947620.2833333385773.28104137646.0238927018432
Winsorized Mean ( 3 / 20 )3944818.5833333384619.917268577246.6180860330173
Winsorized Mean ( 4 / 20 )3935567.8580762.074804104348.7303955420422
Winsorized Mean ( 5 / 20 )3931535.5166666778800.208576039949.8924506382854
Winsorized Mean ( 6 / 20 )3934064.2166666777250.715948921550.9259256479628
Winsorized Mean ( 7 / 20 )3938491.675853.020311228951.9226733996901
Winsorized Mean ( 8 / 20 )3934610.9333333374943.322381759352.5011543161982
Winsorized Mean ( 9 / 20 )3930393.5333333373732.039239130753.3064536650902
Winsorized Mean ( 10 / 20 )3935486.772795.133852551654.0624969241959
Winsorized Mean ( 11 / 20 )3930196.6166666771870.784098886554.684203963312
Winsorized Mean ( 12 / 20 )3935503.4166666770360.784152200855.9331943793234
Winsorized Mean ( 13 / 20 )3927114.9567577.900119856358.1124146064743
Winsorized Mean ( 14 / 20 )3927743.5566581.533627505458.9914851161886
Winsorized Mean ( 15 / 20 )3928834.364881.151394019960.5543245701728
Winsorized Mean ( 16 / 20 )3955190.8333333358247.002438059467.9037661644362
Winsorized Mean ( 17 / 20 )3963865.6555853.763648785370.9686400888798
Winsorized Mean ( 18 / 20 )3955911.1550786.280502598477.8933032868514
Winsorized Mean ( 19 / 20 )3963133.0549428.202758544580.1795903719138
Winsorized Mean ( 20 / 20 )3947734.3833333342650.285659332392.5605613726886
Trimmed Mean ( 1 / 20 )3944229.7586206984678.884175567546.5786694879326
Trimmed Mean ( 2 / 20 )3942119.8392857182699.128035101447.6682152877415
Trimmed Mean ( 3 / 20 )3939064.0370370480558.525798906348.8969230503286
Trimmed Mean ( 4 / 20 )3936850.7578432.659873228250.1940232087397
Trimmed Mean ( 5 / 20 )3937235.6277249.583368529250.9677262751943
Trimmed Mean ( 6 / 20 )3938660.6458333376340.416521574651.5933869016844
Trimmed Mean ( 7 / 20 )3939659.8695652275558.279846851252.140677071401
Trimmed Mean ( 8 / 20 )3939887.4545454574836.881415829952.646334000124
Trimmed Mean ( 9 / 20 )3940829.6904761974021.84991238253.2387355239144
Trimmed Mean ( 10 / 20 )3942569.0573136.821939588153.9067592143477
Trimmed Mean ( 11 / 20 )3943687.3157894772068.769079472354.7211693242694
Trimmed Mean ( 12 / 20 )3945731.3611111170727.758073712355.7875927157041
Trimmed Mean ( 13 / 20 )3947235.4705882469163.957963706957.0706996360664
Trimmed Mean ( 14 / 20 )3950137.4687567609.078157525958.4261400450745
Trimmed Mean ( 15 / 20 )3953336.665520.982318022560.3369555848764
Trimmed Mean ( 16 / 20 )3956836.9285714362864.825309954862.9419855867293
Trimmed Mean ( 17 / 20 )3957074.3461538561064.70114198464.8013381241823
Trimmed Mean ( 18 / 20 )3956075.62558923.810756656667.1388285007192
Trimmed Mean ( 19 / 20 )3956100.5454545557279.141229434569.0670366304583
Trimmed Mean ( 20 / 20 )3954990.1554776.477424754272.2023455311255
Median3951238.5
Midrange3971297
Midmean - Weighted Average at Xnp3931352.64516129
Midmean - Weighted Average at X(n+1)p3953336.6
Midmean - Empirical Distribution Function3931352.64516129
Midmean - Empirical Distribution Function - Averaging3953336.6
Midmean - Empirical Distribution Function - Interpolation3953336.6
Midmean - Closest Observation3931352.64516129
Midmean - True Basic - Statistics Graphics Toolkit3953336.6
Midmean - MS Excel (old versions)3950137.46875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3945132 & 87063.8832767151 & 45.3130718677134 \tabularnewline
Geometric Mean & 3887496.62026432 &  &  \tabularnewline
Harmonic Mean & 3829437.37470715 &  &  \tabularnewline
Quadratic Mean & 4001411.44646812 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3946199.01666667 & 86269.8168421737 & 45.7425222530151 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3947620.28333333 & 85773.281041376 & 46.0238927018432 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3944818.58333333 & 84619.9172685772 & 46.6180860330173 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3935567.85 & 80762.0748041043 & 48.7303955420422 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3931535.51666667 & 78800.2085760399 & 49.8924506382854 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3934064.21666667 & 77250.7159489215 & 50.9259256479628 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3938491.6 & 75853.0203112289 & 51.9226733996901 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3934610.93333333 & 74943.3223817593 & 52.5011543161982 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3930393.53333333 & 73732.0392391307 & 53.3064536650902 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3935486.7 & 72795.1338525516 & 54.0624969241959 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3930196.61666667 & 71870.7840988865 & 54.684203963312 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3935503.41666667 & 70360.7841522008 & 55.9331943793234 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3927114.95 & 67577.9001198563 & 58.1124146064743 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3927743.55 & 66581.5336275054 & 58.9914851161886 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3928834.3 & 64881.1513940199 & 60.5543245701728 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3955190.83333333 & 58247.0024380594 & 67.9037661644362 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3963865.65 & 55853.7636487853 & 70.9686400888798 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3955911.15 & 50786.2805025984 & 77.8933032868514 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3963133.05 & 49428.2027585445 & 80.1795903719138 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3947734.38333333 & 42650.2856593323 & 92.5605613726886 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3944229.75862069 & 84678.8841755675 & 46.5786694879326 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3942119.83928571 & 82699.1280351014 & 47.6682152877415 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3939064.03703704 & 80558.5257989063 & 48.8969230503286 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3936850.75 & 78432.6598732282 & 50.1940232087397 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3937235.62 & 77249.5833685292 & 50.9677262751943 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3938660.64583333 & 76340.4165215746 & 51.5933869016844 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3939659.86956522 & 75558.2798468512 & 52.140677071401 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3939887.45454545 & 74836.8814158299 & 52.646334000124 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3940829.69047619 & 74021.849912382 & 53.2387355239144 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3942569.05 & 73136.8219395881 & 53.9067592143477 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3943687.31578947 & 72068.7690794723 & 54.7211693242694 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3945731.36111111 & 70727.7580737123 & 55.7875927157041 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3947235.47058824 & 69163.9579637069 & 57.0706996360664 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3950137.46875 & 67609.0781575259 & 58.4261400450745 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3953336.6 & 65520.9823180225 & 60.3369555848764 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3956836.92857143 & 62864.8253099548 & 62.9419855867293 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3957074.34615385 & 61064.701141984 & 64.8013381241823 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3956075.625 & 58923.8107566566 & 67.1388285007192 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3956100.54545455 & 57279.1412294345 & 69.0670366304583 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3954990.15 & 54776.4774247542 & 72.2023455311255 \tabularnewline
Median & 3951238.5 &  &  \tabularnewline
Midrange & 3971297 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3931352.64516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3953336.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3931352.64516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3953336.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3953336.6 &  &  \tabularnewline
Midmean - Closest Observation & 3931352.64516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3953336.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3950137.46875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234054&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]3945132[/C][C]87063.8832767151[/C][C]45.3130718677134[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3887496.62026432[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3829437.37470715[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4001411.44646812[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3946199.01666667[/C][C]86269.8168421737[/C][C]45.7425222530151[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3947620.28333333[/C][C]85773.281041376[/C][C]46.0238927018432[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3944818.58333333[/C][C]84619.9172685772[/C][C]46.6180860330173[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3935567.85[/C][C]80762.0748041043[/C][C]48.7303955420422[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3931535.51666667[/C][C]78800.2085760399[/C][C]49.8924506382854[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3934064.21666667[/C][C]77250.7159489215[/C][C]50.9259256479628[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3938491.6[/C][C]75853.0203112289[/C][C]51.9226733996901[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3934610.93333333[/C][C]74943.3223817593[/C][C]52.5011543161982[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3930393.53333333[/C][C]73732.0392391307[/C][C]53.3064536650902[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3935486.7[/C][C]72795.1338525516[/C][C]54.0624969241959[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3930196.61666667[/C][C]71870.7840988865[/C][C]54.684203963312[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3935503.41666667[/C][C]70360.7841522008[/C][C]55.9331943793234[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3927114.95[/C][C]67577.9001198563[/C][C]58.1124146064743[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3927743.55[/C][C]66581.5336275054[/C][C]58.9914851161886[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3928834.3[/C][C]64881.1513940199[/C][C]60.5543245701728[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3955190.83333333[/C][C]58247.0024380594[/C][C]67.9037661644362[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3963865.65[/C][C]55853.7636487853[/C][C]70.9686400888798[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3955911.15[/C][C]50786.2805025984[/C][C]77.8933032868514[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3963133.05[/C][C]49428.2027585445[/C][C]80.1795903719138[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3947734.38333333[/C][C]42650.2856593323[/C][C]92.5605613726886[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3944229.75862069[/C][C]84678.8841755675[/C][C]46.5786694879326[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3942119.83928571[/C][C]82699.1280351014[/C][C]47.6682152877415[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3939064.03703704[/C][C]80558.5257989063[/C][C]48.8969230503286[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3936850.75[/C][C]78432.6598732282[/C][C]50.1940232087397[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3937235.62[/C][C]77249.5833685292[/C][C]50.9677262751943[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3938660.64583333[/C][C]76340.4165215746[/C][C]51.5933869016844[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3939659.86956522[/C][C]75558.2798468512[/C][C]52.140677071401[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3939887.45454545[/C][C]74836.8814158299[/C][C]52.646334000124[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3940829.69047619[/C][C]74021.849912382[/C][C]53.2387355239144[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3942569.05[/C][C]73136.8219395881[/C][C]53.9067592143477[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3943687.31578947[/C][C]72068.7690794723[/C][C]54.7211693242694[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3945731.36111111[/C][C]70727.7580737123[/C][C]55.7875927157041[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3947235.47058824[/C][C]69163.9579637069[/C][C]57.0706996360664[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3950137.46875[/C][C]67609.0781575259[/C][C]58.4261400450745[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3953336.6[/C][C]65520.9823180225[/C][C]60.3369555848764[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3956836.92857143[/C][C]62864.8253099548[/C][C]62.9419855867293[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3957074.34615385[/C][C]61064.701141984[/C][C]64.8013381241823[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3956075.625[/C][C]58923.8107566566[/C][C]67.1388285007192[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3956100.54545455[/C][C]57279.1412294345[/C][C]69.0670366304583[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3954990.15[/C][C]54776.4774247542[/C][C]72.2023455311255[/C][/ROW]
[ROW][C]Median[/C][C]3951238.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3971297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3931352.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3953336.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3931352.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3953336.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3953336.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3931352.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3953336.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3950137.46875[/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=234054&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234054&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 Mean394513287063.883276715145.3130718677134
Geometric Mean3887496.62026432
Harmonic Mean3829437.37470715
Quadratic Mean4001411.44646812
Winsorized Mean ( 1 / 20 )3946199.0166666786269.816842173745.7425222530151
Winsorized Mean ( 2 / 20 )3947620.2833333385773.28104137646.0238927018432
Winsorized Mean ( 3 / 20 )3944818.5833333384619.917268577246.6180860330173
Winsorized Mean ( 4 / 20 )3935567.8580762.074804104348.7303955420422
Winsorized Mean ( 5 / 20 )3931535.5166666778800.208576039949.8924506382854
Winsorized Mean ( 6 / 20 )3934064.2166666777250.715948921550.9259256479628
Winsorized Mean ( 7 / 20 )3938491.675853.020311228951.9226733996901
Winsorized Mean ( 8 / 20 )3934610.9333333374943.322381759352.5011543161982
Winsorized Mean ( 9 / 20 )3930393.5333333373732.039239130753.3064536650902
Winsorized Mean ( 10 / 20 )3935486.772795.133852551654.0624969241959
Winsorized Mean ( 11 / 20 )3930196.6166666771870.784098886554.684203963312
Winsorized Mean ( 12 / 20 )3935503.4166666770360.784152200855.9331943793234
Winsorized Mean ( 13 / 20 )3927114.9567577.900119856358.1124146064743
Winsorized Mean ( 14 / 20 )3927743.5566581.533627505458.9914851161886
Winsorized Mean ( 15 / 20 )3928834.364881.151394019960.5543245701728
Winsorized Mean ( 16 / 20 )3955190.8333333358247.002438059467.9037661644362
Winsorized Mean ( 17 / 20 )3963865.6555853.763648785370.9686400888798
Winsorized Mean ( 18 / 20 )3955911.1550786.280502598477.8933032868514
Winsorized Mean ( 19 / 20 )3963133.0549428.202758544580.1795903719138
Winsorized Mean ( 20 / 20 )3947734.3833333342650.285659332392.5605613726886
Trimmed Mean ( 1 / 20 )3944229.7586206984678.884175567546.5786694879326
Trimmed Mean ( 2 / 20 )3942119.8392857182699.128035101447.6682152877415
Trimmed Mean ( 3 / 20 )3939064.0370370480558.525798906348.8969230503286
Trimmed Mean ( 4 / 20 )3936850.7578432.659873228250.1940232087397
Trimmed Mean ( 5 / 20 )3937235.6277249.583368529250.9677262751943
Trimmed Mean ( 6 / 20 )3938660.6458333376340.416521574651.5933869016844
Trimmed Mean ( 7 / 20 )3939659.8695652275558.279846851252.140677071401
Trimmed Mean ( 8 / 20 )3939887.4545454574836.881415829952.646334000124
Trimmed Mean ( 9 / 20 )3940829.6904761974021.84991238253.2387355239144
Trimmed Mean ( 10 / 20 )3942569.0573136.821939588153.9067592143477
Trimmed Mean ( 11 / 20 )3943687.3157894772068.769079472354.7211693242694
Trimmed Mean ( 12 / 20 )3945731.3611111170727.758073712355.7875927157041
Trimmed Mean ( 13 / 20 )3947235.4705882469163.957963706957.0706996360664
Trimmed Mean ( 14 / 20 )3950137.4687567609.078157525958.4261400450745
Trimmed Mean ( 15 / 20 )3953336.665520.982318022560.3369555848764
Trimmed Mean ( 16 / 20 )3956836.9285714362864.825309954862.9419855867293
Trimmed Mean ( 17 / 20 )3957074.3461538561064.70114198464.8013381241823
Trimmed Mean ( 18 / 20 )3956075.62558923.810756656667.1388285007192
Trimmed Mean ( 19 / 20 )3956100.5454545557279.141229434569.0670366304583
Trimmed Mean ( 20 / 20 )3954990.1554776.477424754272.2023455311255
Median3951238.5
Midrange3971297
Midmean - Weighted Average at Xnp3931352.64516129
Midmean - Weighted Average at X(n+1)p3953336.6
Midmean - Empirical Distribution Function3931352.64516129
Midmean - Empirical Distribution Function - Averaging3953336.6
Midmean - Empirical Distribution Function - Interpolation3953336.6
Midmean - Closest Observation3931352.64516129
Midmean - True Basic - Statistics Graphics Toolkit3953336.6
Midmean - MS Excel (old versions)3950137.46875
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')