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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 computationTue, 15 Dec 2015 19:22:20 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/15/t1450207346n51yuznmild4x2o.htm/, Retrieved Sat, 18 May 2024 13:45:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286572, Retrieved Sat, 18 May 2024 13:45:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-12-15 19:22:20] [9d441e5437781f0cd4d5053adc3d2c6c] [Current]
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Dataseries X:
62065
61943
62361
62919
62881
62892
62591
62417
62172
63113
63077
62438
62384
62506
62935
64433
64533
64184
63911
63673
63290
64652
64516
63995
64536
64776
65144
65238
65421
65821
66298
66523
67143
68835
68984
69170
69844
70528
71979
73608
73508
73973
73899
73566
73859
75287
75308
74871
75337
75449
76211
79371
80224
81014
80253
79169
79214
79783
79523
77265
76986




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286572&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286572&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean69078.6721311475810.95675658440585.1816962745261
Geometric Mean68800.3489892557
Harmonic Mean68530.2234586307
Quadratic Mean69363.6936377063
Winsorized Mean ( 1 / 20 )69068.1967213115807.69570191749685.5126461083566
Winsorized Mean ( 2 / 20 )69070.7540983607806.97305385492585.5923921727106
Winsorized Mean ( 3 / 20 )69058.3606557377800.74397204167986.2427480779626
Winsorized Mean ( 4 / 20 )69042.8196721312796.76205130385286.6542521184924
Winsorized Mean ( 5 / 20 )69033.0655737705793.66770202636586.9798095569691
Winsorized Mean ( 6 / 20 )69019.6885245902790.04401362520287.3618271061708
Winsorized Mean ( 7 / 20 )69022.3278688525787.85495312913887.6079125919248
Winsorized Mean ( 8 / 20 )68783.7704918033735.41112972485993.5310436728603
Winsorized Mean ( 9 / 20 )68785.393442623721.63566306477295.3187279443657
Winsorized Mean ( 10 / 20 )68660.1475409836697.89233901104698.3821482240069
Winsorized Mean ( 11 / 20 )68527.606557377673.042870563807101.817595214955
Winsorized Mean ( 12 / 20 )68508.7213114754668.843054659054102.428695094095
Winsorized Mean ( 13 / 20 )68532.8032786885663.616471063285103.271703260893
Winsorized Mean ( 14 / 20 )68536.2459016393661.666238588073103.581295076939
Winsorized Mean ( 15 / 20 )68477.4754098361638.510118883132107.245716840972
Winsorized Mean ( 16 / 20 )68342.393442623586.505516993459116.524723915573
Winsorized Mean ( 17 / 20 )68388.0983606557574.498117250178119.039725818413
Winsorized Mean ( 18 / 20 )68401.0819672131569.403647051897120.127579655244
Winsorized Mean ( 19 / 20 )68381.7704918033549.415472992552124.462767892833
Winsorized Mean ( 20 / 20 )68449.6393442623536.941960429966127.480518172672
Trimmed Mean ( 1 / 20 )68997.3220338983804.21919087943485.7941750413193
Trimmed Mean ( 2 / 20 )68921.4736842105799.07656137766186.2514019500025
Trimmed Mean ( 3 / 20 )68838.6909090909792.32155278771686.8822647407329
Trimmed Mean ( 4 / 20 )68754.4150943396785.93687838310887.4808359111315
Trimmed Mean ( 5 / 20 )68668.1764705882778.49740020263488.2060446864879
Trimmed Mean ( 6 / 20 )68577.3265306122769.14795843347189.1601229369238
Trimmed Mean ( 7 / 20 )68481.6382978723757.37381868282890.4198648125583
Trimmed Mean ( 8 / 20 )68376.9333333333741.86992611422692.1683585308259
Trimmed Mean ( 9 / 20 )68304.7906976744735.52325981873292.8655753381721
Trimmed Mean ( 10 / 20 )68225.3414634146729.18109147058993.5643316337509
Trimmed Mean ( 11 / 20 )68157.3333333333725.29051030361893.972459814484
Trimmed Mean ( 12 / 20 )68101.8378378378724.35026442726394.0178269855196
Trimmed Mean ( 13 / 20 )68042.7428571429721.64154064277194.2888387446996
Trimmed Mean ( 14 / 20 )67973.0606060606716.49223908783294.8692210436184
Trimmed Mean ( 15 / 20 )67893.9032258065706.95561959356596.0370090343708
Trimmed Mean ( 16 / 20 )67812.0689655172697.22461578372697.2600040652495
Trimmed Mean ( 17 / 20 )67737.1851851852695.41726398306397.4050957510237
Trimmed Mean ( 18 / 20 )67643.76691.21266452518197.8624430246326
Trimmed Mean ( 19 / 20 )67532.1739130435680.67033819399799.2142159334057
Trimmed Mean ( 20 / 20 )67402.2857142857665.395883390221101.296517451939
Median66298
Midrange71478.5
Midmean - Weighted Average at Xnp67661.3333333333
Midmean - Weighted Average at X(n+1)p67893.9032258065
Midmean - Empirical Distribution Function67893.9032258065
Midmean - Empirical Distribution Function - Averaging67893.9032258065
Midmean - Empirical Distribution Function - Interpolation67893.9032258065
Midmean - Closest Observation67744.5
Midmean - True Basic - Statistics Graphics Toolkit67893.9032258065
Midmean - MS Excel (old versions)67893.9032258065
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 69078.6721311475 & 810.956756584405 & 85.1816962745261 \tabularnewline
Geometric Mean & 68800.3489892557 &  &  \tabularnewline
Harmonic Mean & 68530.2234586307 &  &  \tabularnewline
Quadratic Mean & 69363.6936377063 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 69068.1967213115 & 807.695701917496 & 85.5126461083566 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 69070.7540983607 & 806.973053854925 & 85.5923921727106 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 69058.3606557377 & 800.743972041679 & 86.2427480779626 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 69042.8196721312 & 796.762051303852 & 86.6542521184924 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 69033.0655737705 & 793.667702026365 & 86.9798095569691 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 69019.6885245902 & 790.044013625202 & 87.3618271061708 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 69022.3278688525 & 787.854953129138 & 87.6079125919248 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 68783.7704918033 & 735.411129724859 & 93.5310436728603 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 68785.393442623 & 721.635663064772 & 95.3187279443657 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 68660.1475409836 & 697.892339011046 & 98.3821482240069 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 68527.606557377 & 673.042870563807 & 101.817595214955 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 68508.7213114754 & 668.843054659054 & 102.428695094095 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 68532.8032786885 & 663.616471063285 & 103.271703260893 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 68536.2459016393 & 661.666238588073 & 103.581295076939 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 68477.4754098361 & 638.510118883132 & 107.245716840972 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 68342.393442623 & 586.505516993459 & 116.524723915573 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 68388.0983606557 & 574.498117250178 & 119.039725818413 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 68401.0819672131 & 569.403647051897 & 120.127579655244 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 68381.7704918033 & 549.415472992552 & 124.462767892833 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 68449.6393442623 & 536.941960429966 & 127.480518172672 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 68997.3220338983 & 804.219190879434 & 85.7941750413193 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 68921.4736842105 & 799.076561377661 & 86.2514019500025 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 68838.6909090909 & 792.321552787716 & 86.8822647407329 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 68754.4150943396 & 785.936878383108 & 87.4808359111315 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 68668.1764705882 & 778.497400202634 & 88.2060446864879 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 68577.3265306122 & 769.147958433471 & 89.1601229369238 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 68481.6382978723 & 757.373818682828 & 90.4198648125583 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 68376.9333333333 & 741.869926114226 & 92.1683585308259 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 68304.7906976744 & 735.523259818732 & 92.8655753381721 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 68225.3414634146 & 729.181091470589 & 93.5643316337509 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 68157.3333333333 & 725.290510303618 & 93.972459814484 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 68101.8378378378 & 724.350264427263 & 94.0178269855196 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 68042.7428571429 & 721.641540642771 & 94.2888387446996 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 67973.0606060606 & 716.492239087832 & 94.8692210436184 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 67893.9032258065 & 706.955619593565 & 96.0370090343708 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 67812.0689655172 & 697.224615783726 & 97.2600040652495 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 67737.1851851852 & 695.417263983063 & 97.4050957510237 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 67643.76 & 691.212664525181 & 97.8624430246326 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 67532.1739130435 & 680.670338193997 & 99.2142159334057 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 67402.2857142857 & 665.395883390221 & 101.296517451939 \tabularnewline
Median & 66298 &  &  \tabularnewline
Midrange & 71478.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 67661.3333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 67893.9032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 67893.9032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 67893.9032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 67893.9032258065 &  &  \tabularnewline
Midmean - Closest Observation & 67744.5 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 67893.9032258065 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 67893.9032258065 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286572&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]69078.6721311475[/C][C]810.956756584405[/C][C]85.1816962745261[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]68800.3489892557[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]68530.2234586307[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]69363.6936377063[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]69068.1967213115[/C][C]807.695701917496[/C][C]85.5126461083566[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]69070.7540983607[/C][C]806.973053854925[/C][C]85.5923921727106[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]69058.3606557377[/C][C]800.743972041679[/C][C]86.2427480779626[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]69042.8196721312[/C][C]796.762051303852[/C][C]86.6542521184924[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]69033.0655737705[/C][C]793.667702026365[/C][C]86.9798095569691[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]69019.6885245902[/C][C]790.044013625202[/C][C]87.3618271061708[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]69022.3278688525[/C][C]787.854953129138[/C][C]87.6079125919248[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]68783.7704918033[/C][C]735.411129724859[/C][C]93.5310436728603[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]68785.393442623[/C][C]721.635663064772[/C][C]95.3187279443657[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]68660.1475409836[/C][C]697.892339011046[/C][C]98.3821482240069[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]68527.606557377[/C][C]673.042870563807[/C][C]101.817595214955[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]68508.7213114754[/C][C]668.843054659054[/C][C]102.428695094095[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]68532.8032786885[/C][C]663.616471063285[/C][C]103.271703260893[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]68536.2459016393[/C][C]661.666238588073[/C][C]103.581295076939[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]68477.4754098361[/C][C]638.510118883132[/C][C]107.245716840972[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]68342.393442623[/C][C]586.505516993459[/C][C]116.524723915573[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]68388.0983606557[/C][C]574.498117250178[/C][C]119.039725818413[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]68401.0819672131[/C][C]569.403647051897[/C][C]120.127579655244[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]68381.7704918033[/C][C]549.415472992552[/C][C]124.462767892833[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]68449.6393442623[/C][C]536.941960429966[/C][C]127.480518172672[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]68997.3220338983[/C][C]804.219190879434[/C][C]85.7941750413193[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]68921.4736842105[/C][C]799.076561377661[/C][C]86.2514019500025[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]68838.6909090909[/C][C]792.321552787716[/C][C]86.8822647407329[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]68754.4150943396[/C][C]785.936878383108[/C][C]87.4808359111315[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]68668.1764705882[/C][C]778.497400202634[/C][C]88.2060446864879[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]68577.3265306122[/C][C]769.147958433471[/C][C]89.1601229369238[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]68481.6382978723[/C][C]757.373818682828[/C][C]90.4198648125583[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]68376.9333333333[/C][C]741.869926114226[/C][C]92.1683585308259[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]68304.7906976744[/C][C]735.523259818732[/C][C]92.8655753381721[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]68225.3414634146[/C][C]729.181091470589[/C][C]93.5643316337509[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]68157.3333333333[/C][C]725.290510303618[/C][C]93.972459814484[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]68101.8378378378[/C][C]724.350264427263[/C][C]94.0178269855196[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]68042.7428571429[/C][C]721.641540642771[/C][C]94.2888387446996[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]67973.0606060606[/C][C]716.492239087832[/C][C]94.8692210436184[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]67893.9032258065[/C][C]706.955619593565[/C][C]96.0370090343708[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]67812.0689655172[/C][C]697.224615783726[/C][C]97.2600040652495[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]67737.1851851852[/C][C]695.417263983063[/C][C]97.4050957510237[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]67643.76[/C][C]691.212664525181[/C][C]97.8624430246326[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]67532.1739130435[/C][C]680.670338193997[/C][C]99.2142159334057[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]67402.2857142857[/C][C]665.395883390221[/C][C]101.296517451939[/C][/ROW]
[ROW][C]Median[/C][C]66298[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]71478.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]67661.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]67893.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]67893.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]67893.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]67893.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]67744.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]67893.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]67893.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286572&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 Mean69078.6721311475810.95675658440585.1816962745261
Geometric Mean68800.3489892557
Harmonic Mean68530.2234586307
Quadratic Mean69363.6936377063
Winsorized Mean ( 1 / 20 )69068.1967213115807.69570191749685.5126461083566
Winsorized Mean ( 2 / 20 )69070.7540983607806.97305385492585.5923921727106
Winsorized Mean ( 3 / 20 )69058.3606557377800.74397204167986.2427480779626
Winsorized Mean ( 4 / 20 )69042.8196721312796.76205130385286.6542521184924
Winsorized Mean ( 5 / 20 )69033.0655737705793.66770202636586.9798095569691
Winsorized Mean ( 6 / 20 )69019.6885245902790.04401362520287.3618271061708
Winsorized Mean ( 7 / 20 )69022.3278688525787.85495312913887.6079125919248
Winsorized Mean ( 8 / 20 )68783.7704918033735.41112972485993.5310436728603
Winsorized Mean ( 9 / 20 )68785.393442623721.63566306477295.3187279443657
Winsorized Mean ( 10 / 20 )68660.1475409836697.89233901104698.3821482240069
Winsorized Mean ( 11 / 20 )68527.606557377673.042870563807101.817595214955
Winsorized Mean ( 12 / 20 )68508.7213114754668.843054659054102.428695094095
Winsorized Mean ( 13 / 20 )68532.8032786885663.616471063285103.271703260893
Winsorized Mean ( 14 / 20 )68536.2459016393661.666238588073103.581295076939
Winsorized Mean ( 15 / 20 )68477.4754098361638.510118883132107.245716840972
Winsorized Mean ( 16 / 20 )68342.393442623586.505516993459116.524723915573
Winsorized Mean ( 17 / 20 )68388.0983606557574.498117250178119.039725818413
Winsorized Mean ( 18 / 20 )68401.0819672131569.403647051897120.127579655244
Winsorized Mean ( 19 / 20 )68381.7704918033549.415472992552124.462767892833
Winsorized Mean ( 20 / 20 )68449.6393442623536.941960429966127.480518172672
Trimmed Mean ( 1 / 20 )68997.3220338983804.21919087943485.7941750413193
Trimmed Mean ( 2 / 20 )68921.4736842105799.07656137766186.2514019500025
Trimmed Mean ( 3 / 20 )68838.6909090909792.32155278771686.8822647407329
Trimmed Mean ( 4 / 20 )68754.4150943396785.93687838310887.4808359111315
Trimmed Mean ( 5 / 20 )68668.1764705882778.49740020263488.2060446864879
Trimmed Mean ( 6 / 20 )68577.3265306122769.14795843347189.1601229369238
Trimmed Mean ( 7 / 20 )68481.6382978723757.37381868282890.4198648125583
Trimmed Mean ( 8 / 20 )68376.9333333333741.86992611422692.1683585308259
Trimmed Mean ( 9 / 20 )68304.7906976744735.52325981873292.8655753381721
Trimmed Mean ( 10 / 20 )68225.3414634146729.18109147058993.5643316337509
Trimmed Mean ( 11 / 20 )68157.3333333333725.29051030361893.972459814484
Trimmed Mean ( 12 / 20 )68101.8378378378724.35026442726394.0178269855196
Trimmed Mean ( 13 / 20 )68042.7428571429721.64154064277194.2888387446996
Trimmed Mean ( 14 / 20 )67973.0606060606716.49223908783294.8692210436184
Trimmed Mean ( 15 / 20 )67893.9032258065706.95561959356596.0370090343708
Trimmed Mean ( 16 / 20 )67812.0689655172697.22461578372697.2600040652495
Trimmed Mean ( 17 / 20 )67737.1851851852695.41726398306397.4050957510237
Trimmed Mean ( 18 / 20 )67643.76691.21266452518197.8624430246326
Trimmed Mean ( 19 / 20 )67532.1739130435680.67033819399799.2142159334057
Trimmed Mean ( 20 / 20 )67402.2857142857665.395883390221101.296517451939
Median66298
Midrange71478.5
Midmean - Weighted Average at Xnp67661.3333333333
Midmean - Weighted Average at X(n+1)p67893.9032258065
Midmean - Empirical Distribution Function67893.9032258065
Midmean - Empirical Distribution Function - Averaging67893.9032258065
Midmean - Empirical Distribution Function - Interpolation67893.9032258065
Midmean - Closest Observation67744.5
Midmean - True Basic - Statistics Graphics Toolkit67893.9032258065
Midmean - MS Excel (old versions)67893.9032258065
Number of observations61



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')