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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, 20 Oct 2009 12:49:22 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256064647zx4sz4fxssb3th1.htm/, Retrieved Thu, 02 May 2024 15:42:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48990, Retrieved Thu, 02 May 2024 15:42:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [shw-ws3p2] [2009-10-20 18:49:22] [5b5bced41faf164488f2c271c918b21f] [Current]
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Dataseries X:
476049
474605
470439
461251
454724
455626
516847
525192
522975
518585
509239
512238
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48990&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48990&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean558178.46057.4037406259492.1481254842558
Geometric Mean556167.482187121
Harmonic Mean554084.343733239
Quadratic Mean560114.2405716
Winsorized Mean ( 1 / 20 )558182.5666666676050.9275027643592.2474391589823
Winsorized Mean ( 2 / 20 )558289.35982.5659949377393.3193717332007
Winsorized Mean ( 3 / 20 )5584955813.0803699076596.0755682806554
Winsorized Mean ( 4 / 20 )558718.1333333335732.9932505134897.4566180211866
Winsorized Mean ( 5 / 20 )558809.3833333335697.9600371854698.0718326710765
Winsorized Mean ( 6 / 20 )560594.7833333335014.56252239537111.793358010730
Winsorized Mean ( 7 / 20 )561250.2166666674864.82090194093115.369142663144
Winsorized Mean ( 8 / 20 )561431.954792.34824370482117.151743039019
Winsorized Mean ( 9 / 20 )561364.64774.43718404659117.577125504082
Winsorized Mean ( 10 / 20 )559209.9333333334385.88622910056127.502152158656
Winsorized Mean ( 11 / 20 )559323.2333333334261.17025896800131.260475254700
Winsorized Mean ( 12 / 20 )560235.0333333334090.4715488647136.960990106098
Winsorized Mean ( 13 / 20 )560002.1166666674045.44289817872138.427888061103
Winsorized Mean ( 14 / 20 )560221.2166666673958.3017747722141.530698906580
Winsorized Mean ( 15 / 20 )560335.4666666673928.19012352907142.644691078054
Winsorized Mean ( 16 / 20 )560673.63653.08223565416153.479599919163
Winsorized Mean ( 17 / 20 )561077.0666666673512.29273839050159.7466693291
Winsorized Mean ( 18 / 20 )564310.1666666672905.2206180671194.240039175446
Winsorized Mean ( 19 / 20 )565673.7333333332520.29176600654224.447717110807
Winsorized Mean ( 20 / 20 )564900.42320.21716183617243.468762015772
Trimmed Mean ( 1 / 20 )558743.0344827595876.5684091459295.0798145416237
Trimmed Mean ( 2 / 20 )559343.5357142865660.5136404175898.8149788599437
Trimmed Mean ( 3 / 20 )559929.2222222225437.82692019734102.969298294971
Trimmed Mean ( 4 / 20 )560480.8461538465243.23756918629106.895947162056
Trimmed Mean ( 5 / 20 )561009.665029.9666878931111.533474237578
Trimmed Mean ( 6 / 20 )561559.7291666674769.72316629618117.734239407176
Trimmed Mean ( 7 / 20 )561769.54664.14541237489120.444250839503
Trimmed Mean ( 8 / 20 )561870.6590909094568.77824189559122.980505803186
Trimmed Mean ( 9 / 20 )5619494460.78028673802125.975493944565
Trimmed Mean ( 10 / 20 )562046.44319.29121334057130.124683018377
Trimmed Mean ( 11 / 20 )562494.2631578954229.26974748482133.000327891692
Trimmed Mean ( 12 / 20 )562974.7222222224133.523945223136.197280984143
Trimmed Mean ( 13 / 20 )563377.6176470594043.37463450567139.333519293331
Trimmed Mean ( 14 / 20 )563864.468753919.27387787677143.869626446077
Trimmed Mean ( 15 / 20 )564384.9333333333759.95560194298150.104148315391
Trimmed Mean ( 16 / 20 )564963.4285714293526.6896083617160.196527426716
Trimmed Mean ( 17 / 20 )565582.1538461543272.00410273032172.854964752093
Trimmed Mean ( 18 / 20 )566244.6666666672923.31203659223193.699700743117
Trimmed Mean ( 19 / 20 )566537.7727272732674.65020161582211.817520057394
Trimmed Mean ( 20 / 20 )566674.22456.35576092115230.697120105881
Median568242
Midrange541804
Midmean - Weighted Average at Xnp562907.516129032
Midmean - Weighted Average at X(n+1)p564384.933333333
Midmean - Empirical Distribution Function562907.516129032
Midmean - Empirical Distribution Function - Averaging564384.933333333
Midmean - Empirical Distribution Function - Interpolation564384.933333333
Midmean - Closest Observation562907.516129032
Midmean - True Basic - Statistics Graphics Toolkit564384.933333333
Midmean - MS Excel (old versions)563864.46875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 558178.4 & 6057.40374062594 & 92.1481254842558 \tabularnewline
Geometric Mean & 556167.482187121 &  &  \tabularnewline
Harmonic Mean & 554084.343733239 &  &  \tabularnewline
Quadratic Mean & 560114.2405716 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 558182.566666667 & 6050.92750276435 & 92.2474391589823 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 558289.3 & 5982.56599493773 & 93.3193717332007 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 558495 & 5813.08036990765 & 96.0755682806554 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 558718.133333333 & 5732.99325051348 & 97.4566180211866 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 558809.383333333 & 5697.96003718546 & 98.0718326710765 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 560594.783333333 & 5014.56252239537 & 111.793358010730 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 561250.216666667 & 4864.82090194093 & 115.369142663144 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 561431.95 & 4792.34824370482 & 117.151743039019 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 561364.6 & 4774.43718404659 & 117.577125504082 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 559209.933333333 & 4385.88622910056 & 127.502152158656 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 559323.233333333 & 4261.17025896800 & 131.260475254700 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 560235.033333333 & 4090.4715488647 & 136.960990106098 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 560002.116666667 & 4045.44289817872 & 138.427888061103 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 560221.216666667 & 3958.3017747722 & 141.530698906580 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 560335.466666667 & 3928.19012352907 & 142.644691078054 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 560673.6 & 3653.08223565416 & 153.479599919163 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 561077.066666667 & 3512.29273839050 & 159.7466693291 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 564310.166666667 & 2905.2206180671 & 194.240039175446 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 565673.733333333 & 2520.29176600654 & 224.447717110807 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 564900.4 & 2320.21716183617 & 243.468762015772 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 558743.034482759 & 5876.56840914592 & 95.0798145416237 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 559343.535714286 & 5660.51364041758 & 98.8149788599437 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 559929.222222222 & 5437.82692019734 & 102.969298294971 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 560480.846153846 & 5243.23756918629 & 106.895947162056 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 561009.66 & 5029.9666878931 & 111.533474237578 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 561559.729166667 & 4769.72316629618 & 117.734239407176 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 561769.5 & 4664.14541237489 & 120.444250839503 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 561870.659090909 & 4568.77824189559 & 122.980505803186 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 561949 & 4460.78028673802 & 125.975493944565 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 562046.4 & 4319.29121334057 & 130.124683018377 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 562494.263157895 & 4229.26974748482 & 133.000327891692 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 562974.722222222 & 4133.523945223 & 136.197280984143 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 563377.617647059 & 4043.37463450567 & 139.333519293331 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 563864.46875 & 3919.27387787677 & 143.869626446077 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 564384.933333333 & 3759.95560194298 & 150.104148315391 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 564963.428571429 & 3526.6896083617 & 160.196527426716 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 565582.153846154 & 3272.00410273032 & 172.854964752093 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 566244.666666667 & 2923.31203659223 & 193.699700743117 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 566537.772727273 & 2674.65020161582 & 211.817520057394 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 566674.2 & 2456.35576092115 & 230.697120105881 \tabularnewline
Median & 568242 &  &  \tabularnewline
Midrange & 541804 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 562907.516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 564384.933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 562907.516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 564384.933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 564384.933333333 &  &  \tabularnewline
Midmean - Closest Observation & 562907.516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 564384.933333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 563864.46875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48990&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]558178.4[/C][C]6057.40374062594[/C][C]92.1481254842558[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]556167.482187121[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]554084.343733239[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]560114.2405716[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]558182.566666667[/C][C]6050.92750276435[/C][C]92.2474391589823[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]558289.3[/C][C]5982.56599493773[/C][C]93.3193717332007[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]558495[/C][C]5813.08036990765[/C][C]96.0755682806554[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]558718.133333333[/C][C]5732.99325051348[/C][C]97.4566180211866[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]558809.383333333[/C][C]5697.96003718546[/C][C]98.0718326710765[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]560594.783333333[/C][C]5014.56252239537[/C][C]111.793358010730[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]561250.216666667[/C][C]4864.82090194093[/C][C]115.369142663144[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]561431.95[/C][C]4792.34824370482[/C][C]117.151743039019[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]561364.6[/C][C]4774.43718404659[/C][C]117.577125504082[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]559209.933333333[/C][C]4385.88622910056[/C][C]127.502152158656[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]559323.233333333[/C][C]4261.17025896800[/C][C]131.260475254700[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]560235.033333333[/C][C]4090.4715488647[/C][C]136.960990106098[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]560002.116666667[/C][C]4045.44289817872[/C][C]138.427888061103[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]560221.216666667[/C][C]3958.3017747722[/C][C]141.530698906580[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]560335.466666667[/C][C]3928.19012352907[/C][C]142.644691078054[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]560673.6[/C][C]3653.08223565416[/C][C]153.479599919163[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]561077.066666667[/C][C]3512.29273839050[/C][C]159.7466693291[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]564310.166666667[/C][C]2905.2206180671[/C][C]194.240039175446[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]565673.733333333[/C][C]2520.29176600654[/C][C]224.447717110807[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]564900.4[/C][C]2320.21716183617[/C][C]243.468762015772[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]558743.034482759[/C][C]5876.56840914592[/C][C]95.0798145416237[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]559343.535714286[/C][C]5660.51364041758[/C][C]98.8149788599437[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]559929.222222222[/C][C]5437.82692019734[/C][C]102.969298294971[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]560480.846153846[/C][C]5243.23756918629[/C][C]106.895947162056[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]561009.66[/C][C]5029.9666878931[/C][C]111.533474237578[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]561559.729166667[/C][C]4769.72316629618[/C][C]117.734239407176[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]561769.5[/C][C]4664.14541237489[/C][C]120.444250839503[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]561870.659090909[/C][C]4568.77824189559[/C][C]122.980505803186[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]561949[/C][C]4460.78028673802[/C][C]125.975493944565[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]562046.4[/C][C]4319.29121334057[/C][C]130.124683018377[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]562494.263157895[/C][C]4229.26974748482[/C][C]133.000327891692[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]562974.722222222[/C][C]4133.523945223[/C][C]136.197280984143[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]563377.617647059[/C][C]4043.37463450567[/C][C]139.333519293331[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]563864.46875[/C][C]3919.27387787677[/C][C]143.869626446077[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]564384.933333333[/C][C]3759.95560194298[/C][C]150.104148315391[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]564963.428571429[/C][C]3526.6896083617[/C][C]160.196527426716[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]565582.153846154[/C][C]3272.00410273032[/C][C]172.854964752093[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]566244.666666667[/C][C]2923.31203659223[/C][C]193.699700743117[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]566537.772727273[/C][C]2674.65020161582[/C][C]211.817520057394[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]566674.2[/C][C]2456.35576092115[/C][C]230.697120105881[/C][/ROW]
[ROW][C]Median[/C][C]568242[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]541804[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]562907.516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]564384.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]562907.516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]564384.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]564384.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]562907.516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]564384.933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]563864.46875[/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=48990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48990&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 Mean558178.46057.4037406259492.1481254842558
Geometric Mean556167.482187121
Harmonic Mean554084.343733239
Quadratic Mean560114.2405716
Winsorized Mean ( 1 / 20 )558182.5666666676050.9275027643592.2474391589823
Winsorized Mean ( 2 / 20 )558289.35982.5659949377393.3193717332007
Winsorized Mean ( 3 / 20 )5584955813.0803699076596.0755682806554
Winsorized Mean ( 4 / 20 )558718.1333333335732.9932505134897.4566180211866
Winsorized Mean ( 5 / 20 )558809.3833333335697.9600371854698.0718326710765
Winsorized Mean ( 6 / 20 )560594.7833333335014.56252239537111.793358010730
Winsorized Mean ( 7 / 20 )561250.2166666674864.82090194093115.369142663144
Winsorized Mean ( 8 / 20 )561431.954792.34824370482117.151743039019
Winsorized Mean ( 9 / 20 )561364.64774.43718404659117.577125504082
Winsorized Mean ( 10 / 20 )559209.9333333334385.88622910056127.502152158656
Winsorized Mean ( 11 / 20 )559323.2333333334261.17025896800131.260475254700
Winsorized Mean ( 12 / 20 )560235.0333333334090.4715488647136.960990106098
Winsorized Mean ( 13 / 20 )560002.1166666674045.44289817872138.427888061103
Winsorized Mean ( 14 / 20 )560221.2166666673958.3017747722141.530698906580
Winsorized Mean ( 15 / 20 )560335.4666666673928.19012352907142.644691078054
Winsorized Mean ( 16 / 20 )560673.63653.08223565416153.479599919163
Winsorized Mean ( 17 / 20 )561077.0666666673512.29273839050159.7466693291
Winsorized Mean ( 18 / 20 )564310.1666666672905.2206180671194.240039175446
Winsorized Mean ( 19 / 20 )565673.7333333332520.29176600654224.447717110807
Winsorized Mean ( 20 / 20 )564900.42320.21716183617243.468762015772
Trimmed Mean ( 1 / 20 )558743.0344827595876.5684091459295.0798145416237
Trimmed Mean ( 2 / 20 )559343.5357142865660.5136404175898.8149788599437
Trimmed Mean ( 3 / 20 )559929.2222222225437.82692019734102.969298294971
Trimmed Mean ( 4 / 20 )560480.8461538465243.23756918629106.895947162056
Trimmed Mean ( 5 / 20 )561009.665029.9666878931111.533474237578
Trimmed Mean ( 6 / 20 )561559.7291666674769.72316629618117.734239407176
Trimmed Mean ( 7 / 20 )561769.54664.14541237489120.444250839503
Trimmed Mean ( 8 / 20 )561870.6590909094568.77824189559122.980505803186
Trimmed Mean ( 9 / 20 )5619494460.78028673802125.975493944565
Trimmed Mean ( 10 / 20 )562046.44319.29121334057130.124683018377
Trimmed Mean ( 11 / 20 )562494.2631578954229.26974748482133.000327891692
Trimmed Mean ( 12 / 20 )562974.7222222224133.523945223136.197280984143
Trimmed Mean ( 13 / 20 )563377.6176470594043.37463450567139.333519293331
Trimmed Mean ( 14 / 20 )563864.468753919.27387787677143.869626446077
Trimmed Mean ( 15 / 20 )564384.9333333333759.95560194298150.104148315391
Trimmed Mean ( 16 / 20 )564963.4285714293526.6896083617160.196527426716
Trimmed Mean ( 17 / 20 )565582.1538461543272.00410273032172.854964752093
Trimmed Mean ( 18 / 20 )566244.6666666672923.31203659223193.699700743117
Trimmed Mean ( 19 / 20 )566537.7727272732674.65020161582211.817520057394
Trimmed Mean ( 20 / 20 )566674.22456.35576092115230.697120105881
Median568242
Midrange541804
Midmean - Weighted Average at Xnp562907.516129032
Midmean - Weighted Average at X(n+1)p564384.933333333
Midmean - Empirical Distribution Function562907.516129032
Midmean - Empirical Distribution Function - Averaging564384.933333333
Midmean - Empirical Distribution Function - Interpolation564384.933333333
Midmean - Closest Observation562907.516129032
Midmean - True Basic - Statistics Graphics Toolkit564384.933333333
Midmean - MS Excel (old versions)563864.46875
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')