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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 computationMon, 19 Oct 2009 15:16:21 -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/19/t1255987271wyw5e29x9afevtl.htm/, Retrieved Mon, 29 Apr 2024 19:47:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48255, Retrieved Mon, 29 Apr 2024 19:47:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS3P2ST1MLDG
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Workshop 3: part ...] [2009-10-19 21:01:57] [7c2a5b25a196bd646844b8f5223c9b3e]
- RMP     [Central Tendency] [Workshop 3: part ...] [2009-10-19 21:16:21] [3d2053c5f7c50d3c075d87ce0bd87294] [Current]
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Dataseries X:
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
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570
596594
580523




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48255&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48255&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48255&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean557943.6393442625386.15673969929103.588452083445
Geometric Mean556368.951508754
Harmonic Mean554781.535026324
Quadratic Mean559501.336683119
Winsorized Mean ( 1 / 20 )558067.7540983615348.42824706657104.342384027390
Winsorized Mean ( 2 / 20 )558403.4918032795234.01750294221106.687356603103
Winsorized Mean ( 3 / 20 )558270.9508196725156.92555597329108.256546417085
Winsorized Mean ( 4 / 20 )558613.311475415064.9778692109110.289388404068
Winsorized Mean ( 5 / 20 )558847.3278688525008.3933127013111.582156787011
Winsorized Mean ( 6 / 20 )558587.065573774796.17849679851116.465028552760
Winsorized Mean ( 7 / 20 )558689.311475414756.75587735994117.451751967034
Winsorized Mean ( 8 / 20 )558884.9836065574684.32866856417119.309515439673
Winsorized Mean ( 9 / 20 )556968.2786885254293.55539572244129.721926784366
Winsorized Mean ( 10 / 20 )557406.4754098364187.16048192858133.122787582552
Winsorized Mean ( 11 / 20 )557540.4590163934097.51945791156136.067800224813
Winsorized Mean ( 12 / 20 )557684.2622950824070.24310413054137.014976262508
Winsorized Mean ( 13 / 20 )557638.6557377053993.53337297063139.635406457841
Winsorized Mean ( 14 / 20 )558761.6393442623758.09220231633148.682259312282
Winsorized Mean ( 15 / 20 )558707.2950819673574.9614555868156.283445856134
Winsorized Mean ( 16 / 20 )558801.1967213113497.97392425456159.749960640543
Winsorized Mean ( 17 / 20 )558929.1147540983420.97290831103163.383087131797
Winsorized Mean ( 18 / 20 )558457.8688524593337.94110525002167.306088167373
Winsorized Mean ( 19 / 20 )559155.2622950823138.09962566551178.182763135348
Winsorized Mean ( 20 / 20 )558769.3606557382990.60747790531186.841424287186
Trimmed Mean ( 1 / 20 )558242.7288135595221.39026950504106.91457638666
Trimmed Mean ( 2 / 20 )558429.982456145064.95178548426110.253760767586
Trimmed Mean ( 3 / 20 )558444.6727272734947.44496661457112.875368295285
Trimmed Mean ( 4 / 20 )558511.3207547174837.12864941106115.463400135681
Trimmed Mean ( 5 / 20 )558480.8235294124733.35477512729117.988371897265
Trimmed Mean ( 6 / 20 )558389.5714285714619.66201056276120.872386367623
Trimmed Mean ( 7 / 20 )558346.851063834538.25102922212123.031283961287
Trimmed Mean ( 8 / 20 )558280.5333333334441.38721283603125.699585868093
Trimmed Mean ( 9 / 20 )558173.3488372094332.35240791429128.838399161053
Trimmed Mean ( 10 / 20 )558372.560975614288.06262098898130.215579931720
Trimmed Mean ( 11 / 20 )558523.6666666674248.33106333084131.468960008207
Trimmed Mean ( 12 / 20 )558671.0270270274208.05231609883132.762376762691
Trimmed Mean ( 13 / 20 )558814.3428571434149.88616629195134.657752156238
Trimmed Mean ( 14 / 20 )558981.5151515154079.30555334827137.028596618046
Trimmed Mean ( 15 / 20 )559012.4193548394034.17371208769138.569248438623
Trimmed Mean ( 16 / 20 )559055.2068965524005.15740801822139.583829034369
Trimmed Mean ( 17 / 20 )559091.0740740743965.73544909524140.980426266615
Trimmed Mean ( 18 / 20 )559114.323909.41657442642143.017329915022
Trimmed Mean ( 19 / 20 )559211.0434782613827.39987153079146.107295356783
Trimmed Mean ( 20 / 20 )559219.5714285713749.77172611336149.134297305133
Median564591
Midrange549120.5
Midmean - Weighted Average at Xnp557950.666666667
Midmean - Weighted Average at X(n+1)p559012.419354839
Midmean - Empirical Distribution Function559012.419354839
Midmean - Empirical Distribution Function - Averaging559012.419354839
Midmean - Empirical Distribution Function - Interpolation559012.419354839
Midmean - Closest Observation557905.6875
Midmean - True Basic - Statistics Graphics Toolkit559012.419354839
Midmean - MS Excel (old versions)559012.419354839
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 557943.639344262 & 5386.15673969929 & 103.588452083445 \tabularnewline
Geometric Mean & 556368.951508754 &  &  \tabularnewline
Harmonic Mean & 554781.535026324 &  &  \tabularnewline
Quadratic Mean & 559501.336683119 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 558067.754098361 & 5348.42824706657 & 104.342384027390 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 558403.491803279 & 5234.01750294221 & 106.687356603103 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 558270.950819672 & 5156.92555597329 & 108.256546417085 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 558613.31147541 & 5064.9778692109 & 110.289388404068 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 558847.327868852 & 5008.3933127013 & 111.582156787011 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 558587.06557377 & 4796.17849679851 & 116.465028552760 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 558689.31147541 & 4756.75587735994 & 117.451751967034 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 558884.983606557 & 4684.32866856417 & 119.309515439673 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 556968.278688525 & 4293.55539572244 & 129.721926784366 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 557406.475409836 & 4187.16048192858 & 133.122787582552 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 557540.459016393 & 4097.51945791156 & 136.067800224813 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 557684.262295082 & 4070.24310413054 & 137.014976262508 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 557638.655737705 & 3993.53337297063 & 139.635406457841 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 558761.639344262 & 3758.09220231633 & 148.682259312282 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 558707.295081967 & 3574.9614555868 & 156.283445856134 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 558801.196721311 & 3497.97392425456 & 159.749960640543 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 558929.114754098 & 3420.97290831103 & 163.383087131797 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 558457.868852459 & 3337.94110525002 & 167.306088167373 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 559155.262295082 & 3138.09962566551 & 178.182763135348 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 558769.360655738 & 2990.60747790531 & 186.841424287186 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 558242.728813559 & 5221.39026950504 & 106.91457638666 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 558429.98245614 & 5064.95178548426 & 110.253760767586 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 558444.672727273 & 4947.44496661457 & 112.875368295285 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 558511.320754717 & 4837.12864941106 & 115.463400135681 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 558480.823529412 & 4733.35477512729 & 117.988371897265 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 558389.571428571 & 4619.66201056276 & 120.872386367623 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 558346.85106383 & 4538.25102922212 & 123.031283961287 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 558280.533333333 & 4441.38721283603 & 125.699585868093 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 558173.348837209 & 4332.35240791429 & 128.838399161053 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 558372.56097561 & 4288.06262098898 & 130.215579931720 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 558523.666666667 & 4248.33106333084 & 131.468960008207 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 558671.027027027 & 4208.05231609883 & 132.762376762691 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 558814.342857143 & 4149.88616629195 & 134.657752156238 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 558981.515151515 & 4079.30555334827 & 137.028596618046 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 559012.419354839 & 4034.17371208769 & 138.569248438623 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 559055.206896552 & 4005.15740801822 & 139.583829034369 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 559091.074074074 & 3965.73544909524 & 140.980426266615 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 559114.32 & 3909.41657442642 & 143.017329915022 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 559211.043478261 & 3827.39987153079 & 146.107295356783 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 559219.571428571 & 3749.77172611336 & 149.134297305133 \tabularnewline
Median & 564591 &  &  \tabularnewline
Midrange & 549120.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 557950.666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 559012.419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 559012.419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 559012.419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 559012.419354839 &  &  \tabularnewline
Midmean - Closest Observation & 557905.6875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 559012.419354839 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 559012.419354839 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48255&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]557943.639344262[/C][C]5386.15673969929[/C][C]103.588452083445[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]556368.951508754[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]554781.535026324[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]559501.336683119[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]558067.754098361[/C][C]5348.42824706657[/C][C]104.342384027390[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]558403.491803279[/C][C]5234.01750294221[/C][C]106.687356603103[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]558270.950819672[/C][C]5156.92555597329[/C][C]108.256546417085[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]558613.31147541[/C][C]5064.9778692109[/C][C]110.289388404068[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]558847.327868852[/C][C]5008.3933127013[/C][C]111.582156787011[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]558587.06557377[/C][C]4796.17849679851[/C][C]116.465028552760[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]558689.31147541[/C][C]4756.75587735994[/C][C]117.451751967034[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]558884.983606557[/C][C]4684.32866856417[/C][C]119.309515439673[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]556968.278688525[/C][C]4293.55539572244[/C][C]129.721926784366[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]557406.475409836[/C][C]4187.16048192858[/C][C]133.122787582552[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]557540.459016393[/C][C]4097.51945791156[/C][C]136.067800224813[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]557684.262295082[/C][C]4070.24310413054[/C][C]137.014976262508[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]557638.655737705[/C][C]3993.53337297063[/C][C]139.635406457841[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]558761.639344262[/C][C]3758.09220231633[/C][C]148.682259312282[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]558707.295081967[/C][C]3574.9614555868[/C][C]156.283445856134[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]558801.196721311[/C][C]3497.97392425456[/C][C]159.749960640543[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]558929.114754098[/C][C]3420.97290831103[/C][C]163.383087131797[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]558457.868852459[/C][C]3337.94110525002[/C][C]167.306088167373[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]559155.262295082[/C][C]3138.09962566551[/C][C]178.182763135348[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]558769.360655738[/C][C]2990.60747790531[/C][C]186.841424287186[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]558242.728813559[/C][C]5221.39026950504[/C][C]106.91457638666[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]558429.98245614[/C][C]5064.95178548426[/C][C]110.253760767586[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]558444.672727273[/C][C]4947.44496661457[/C][C]112.875368295285[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]558511.320754717[/C][C]4837.12864941106[/C][C]115.463400135681[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]558480.823529412[/C][C]4733.35477512729[/C][C]117.988371897265[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]558389.571428571[/C][C]4619.66201056276[/C][C]120.872386367623[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]558346.85106383[/C][C]4538.25102922212[/C][C]123.031283961287[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]558280.533333333[/C][C]4441.38721283603[/C][C]125.699585868093[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]558173.348837209[/C][C]4332.35240791429[/C][C]128.838399161053[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]558372.56097561[/C][C]4288.06262098898[/C][C]130.215579931720[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]558523.666666667[/C][C]4248.33106333084[/C][C]131.468960008207[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]558671.027027027[/C][C]4208.05231609883[/C][C]132.762376762691[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]558814.342857143[/C][C]4149.88616629195[/C][C]134.657752156238[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]558981.515151515[/C][C]4079.30555334827[/C][C]137.028596618046[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]559012.419354839[/C][C]4034.17371208769[/C][C]138.569248438623[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]559055.206896552[/C][C]4005.15740801822[/C][C]139.583829034369[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]559091.074074074[/C][C]3965.73544909524[/C][C]140.980426266615[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]559114.32[/C][C]3909.41657442642[/C][C]143.017329915022[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]559211.043478261[/C][C]3827.39987153079[/C][C]146.107295356783[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]559219.571428571[/C][C]3749.77172611336[/C][C]149.134297305133[/C][/ROW]
[ROW][C]Median[/C][C]564591[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]549120.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]557950.666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]559012.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]559012.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]559012.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]559012.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]557905.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]559012.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]559012.419354839[/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=48255&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48255&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 Mean557943.6393442625386.15673969929103.588452083445
Geometric Mean556368.951508754
Harmonic Mean554781.535026324
Quadratic Mean559501.336683119
Winsorized Mean ( 1 / 20 )558067.7540983615348.42824706657104.342384027390
Winsorized Mean ( 2 / 20 )558403.4918032795234.01750294221106.687356603103
Winsorized Mean ( 3 / 20 )558270.9508196725156.92555597329108.256546417085
Winsorized Mean ( 4 / 20 )558613.311475415064.9778692109110.289388404068
Winsorized Mean ( 5 / 20 )558847.3278688525008.3933127013111.582156787011
Winsorized Mean ( 6 / 20 )558587.065573774796.17849679851116.465028552760
Winsorized Mean ( 7 / 20 )558689.311475414756.75587735994117.451751967034
Winsorized Mean ( 8 / 20 )558884.9836065574684.32866856417119.309515439673
Winsorized Mean ( 9 / 20 )556968.2786885254293.55539572244129.721926784366
Winsorized Mean ( 10 / 20 )557406.4754098364187.16048192858133.122787582552
Winsorized Mean ( 11 / 20 )557540.4590163934097.51945791156136.067800224813
Winsorized Mean ( 12 / 20 )557684.2622950824070.24310413054137.014976262508
Winsorized Mean ( 13 / 20 )557638.6557377053993.53337297063139.635406457841
Winsorized Mean ( 14 / 20 )558761.6393442623758.09220231633148.682259312282
Winsorized Mean ( 15 / 20 )558707.2950819673574.9614555868156.283445856134
Winsorized Mean ( 16 / 20 )558801.1967213113497.97392425456159.749960640543
Winsorized Mean ( 17 / 20 )558929.1147540983420.97290831103163.383087131797
Winsorized Mean ( 18 / 20 )558457.8688524593337.94110525002167.306088167373
Winsorized Mean ( 19 / 20 )559155.2622950823138.09962566551178.182763135348
Winsorized Mean ( 20 / 20 )558769.3606557382990.60747790531186.841424287186
Trimmed Mean ( 1 / 20 )558242.7288135595221.39026950504106.91457638666
Trimmed Mean ( 2 / 20 )558429.982456145064.95178548426110.253760767586
Trimmed Mean ( 3 / 20 )558444.6727272734947.44496661457112.875368295285
Trimmed Mean ( 4 / 20 )558511.3207547174837.12864941106115.463400135681
Trimmed Mean ( 5 / 20 )558480.8235294124733.35477512729117.988371897265
Trimmed Mean ( 6 / 20 )558389.5714285714619.66201056276120.872386367623
Trimmed Mean ( 7 / 20 )558346.851063834538.25102922212123.031283961287
Trimmed Mean ( 8 / 20 )558280.5333333334441.38721283603125.699585868093
Trimmed Mean ( 9 / 20 )558173.3488372094332.35240791429128.838399161053
Trimmed Mean ( 10 / 20 )558372.560975614288.06262098898130.215579931720
Trimmed Mean ( 11 / 20 )558523.6666666674248.33106333084131.468960008207
Trimmed Mean ( 12 / 20 )558671.0270270274208.05231609883132.762376762691
Trimmed Mean ( 13 / 20 )558814.3428571434149.88616629195134.657752156238
Trimmed Mean ( 14 / 20 )558981.5151515154079.30555334827137.028596618046
Trimmed Mean ( 15 / 20 )559012.4193548394034.17371208769138.569248438623
Trimmed Mean ( 16 / 20 )559055.2068965524005.15740801822139.583829034369
Trimmed Mean ( 17 / 20 )559091.0740740743965.73544909524140.980426266615
Trimmed Mean ( 18 / 20 )559114.323909.41657442642143.017329915022
Trimmed Mean ( 19 / 20 )559211.0434782613827.39987153079146.107295356783
Trimmed Mean ( 20 / 20 )559219.5714285713749.77172611336149.134297305133
Median564591
Midrange549120.5
Midmean - Weighted Average at Xnp557950.666666667
Midmean - Weighted Average at X(n+1)p559012.419354839
Midmean - Empirical Distribution Function559012.419354839
Midmean - Empirical Distribution Function - Averaging559012.419354839
Midmean - Empirical Distribution Function - Interpolation559012.419354839
Midmean - Closest Observation557905.6875
Midmean - True Basic - Statistics Graphics Toolkit559012.419354839
Midmean - MS Excel (old versions)559012.419354839
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')