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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, 20 Oct 2008 14:40:16 -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/2008/Oct/20/t1224535843k7jpgobkoeq9l00.htm/, Retrieved Sun, 19 May 2024 13:07:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18121, Retrieved Sun, 19 May 2024 13:07:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ9: Make a prediction
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Niet werkende wer...] [2008-10-13 17:04:19] [fe7291e888d31b8c4db0b24d6c0f75c6]
F RMPD    [Central Tendency] [Q9: Make a predic...] [2008-10-20 20:40:16] [783db4b4a0f63b73ca8b14666b7f4329] [Current]
-    D      [Central Tendency] [1] [2008-12-22 14:18:45] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D      [Central Tendency] [2] [2008-12-22 14:20:20] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D      [Central Tendency] [3] [2008-12-22 14:22:21] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D      [Central Tendency] [4] [2008-12-22 14:26:43] [fe7291e888d31b8c4db0b24d6c0f75c6]
Feedback Forum
2008-10-27 18:46:50 [Steffi Van Isveldt] [reply
Aan beide grafieken kan je zien dat de reeksen vrij robuust zijn, met weinig of geen outliers.

Post a new message
Dataseries X:
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
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18121&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18121&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean563109.9333333335154.20041527574109.252626588679
Geometric Mean561688.82708944
Harmonic Mean560238.16314564
Quadratic Mean564499.936361378
Winsorized Mean ( 1 / 20 )563236.1166666675111.25724951046110.195219917881
Winsorized Mean ( 2 / 20 )563577.454981.29796522144113.138674685755
Winsorized Mean ( 3 / 20 )563442.74899.87198006983114.991310444803
Winsorized Mean ( 4 / 20 )563790.7666666674793.32350633309117.620011651992
Winsorized Mean ( 5 / 20 )564503.2666666674624.58697076908122.065661265483
Winsorized Mean ( 6 / 20 )564036.3666666674442.39238620088126.966804737622
Winsorized Mean ( 7 / 20 )564117.5666666674403.09973546286128.118280429404
Winsorized Mean ( 8 / 20 )564441.1666666674297.18788161801131.351288846635
Winsorized Mean ( 9 / 20 )564756.6166666674203.50754244284134.353658454116
Winsorized Mean ( 10 / 20 )563985.7833333333527.05450502366159.902769444032
Winsorized Mean ( 11 / 20 )563887.5166666673439.91406306825163.924884845438
Winsorized Mean ( 12 / 20 )564139.3166666673391.21079442950166.353361930004
Winsorized Mean ( 13 / 20 )5645853223.84908075428175.127614803825
Winsorized Mean ( 14 / 20 )564883.6666666673124.05946485093180.817194109851
Winsorized Mean ( 15 / 20 )565621.1666666672991.03099188966189.105752565045
Winsorized Mean ( 16 / 20 )566275.0333333332671.08317043311212.002022101585
Winsorized Mean ( 17 / 20 )566352.12589.19900181831218.736412149962
Winsorized Mean ( 18 / 20 )566407.32516.41394734785225.085105968738
Winsorized Mean ( 19 / 20 )567037.7833333332251.21438729542251.880845526473
Winsorized Mean ( 20 / 20 )566475.452013.33462062082281.361798579376
Trimmed Mean ( 1 / 20 )563592.3275862074947.19639880419113.921559233516
Trimmed Mean ( 2 / 20 )563973.9821428574744.40771565817118.871314596667
Trimmed Mean ( 3 / 20 )564194.2777777784581.22281473829123.15364272672
Trimmed Mean ( 4 / 20 )564483.3461538464417.10685061809127.794813493103
Trimmed Mean ( 5 / 20 )564691.124253.94614922691132.745244107668
Trimmed Mean ( 6 / 20 )564738.0833333334107.38086647672137.493478616158
Trimmed Mean ( 7 / 20 )564890.6304347833977.82525724273142.009915947475
Trimmed Mean ( 8 / 20 )565041.2272727273820.93725964444147.880268341624
Trimmed Mean ( 9 / 20 )565148.3809523813646.77772694252154.971984384199
Trimmed Mean ( 10 / 20 )565213.6753443.14714703537164.156119638007
Trimmed Mean ( 11 / 20 )565407.5526315793365.94052739994167.979067968956
Trimmed Mean ( 12 / 20 )565637.8611111113279.91588746022172.454989859240
Trimmed Mean ( 13 / 20 )565858.2352941183170.57997389616178.471522545689
Trimmed Mean ( 14 / 20 )566041.8753063.1617431039184.790070675938
Trimmed Mean ( 15 / 20 )566207.3333333332935.7788300036192.864437724908
Trimmed Mean ( 16 / 20 )566291.0714285712790.13624429270202.961798939724
Trimmed Mean ( 17 / 20 )566293.3846153852681.7442022666211.166070252620
Trimmed Mean ( 18 / 20 )566284.752537.26011449101223.187503230665
Trimmed Mean ( 19 / 20 )566266.1818181822328.81862795045243.155982617909
Trimmed Mean ( 20 / 20 )566144.352109.54229667181268.373073577713
Median565603
Midrange549120.5
Midmean - Weighted Average at Xnp565155.161290323
Midmean - Weighted Average at X(n+1)p566207.333333333
Midmean - Empirical Distribution Function565155.161290323
Midmean - Empirical Distribution Function - Averaging566207.333333333
Midmean - Empirical Distribution Function - Interpolation566207.333333333
Midmean - Closest Observation565155.161290323
Midmean - True Basic - Statistics Graphics Toolkit566207.333333333
Midmean - MS Excel (old versions)566041.875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 563109.933333333 & 5154.20041527574 & 109.252626588679 \tabularnewline
Geometric Mean & 561688.82708944 &  &  \tabularnewline
Harmonic Mean & 560238.16314564 &  &  \tabularnewline
Quadratic Mean & 564499.936361378 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 563236.116666667 & 5111.25724951046 & 110.195219917881 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 563577.45 & 4981.29796522144 & 113.138674685755 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 563442.7 & 4899.87198006983 & 114.991310444803 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 563790.766666667 & 4793.32350633309 & 117.620011651992 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 564503.266666667 & 4624.58697076908 & 122.065661265483 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 564036.366666667 & 4442.39238620088 & 126.966804737622 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 564117.566666667 & 4403.09973546286 & 128.118280429404 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 564441.166666667 & 4297.18788161801 & 131.351288846635 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 564756.616666667 & 4203.50754244284 & 134.353658454116 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 563985.783333333 & 3527.05450502366 & 159.902769444032 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 563887.516666667 & 3439.91406306825 & 163.924884845438 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 564139.316666667 & 3391.21079442950 & 166.353361930004 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 564585 & 3223.84908075428 & 175.127614803825 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 564883.666666667 & 3124.05946485093 & 180.817194109851 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 565621.166666667 & 2991.03099188966 & 189.105752565045 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 566275.033333333 & 2671.08317043311 & 212.002022101585 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 566352.1 & 2589.19900181831 & 218.736412149962 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 566407.3 & 2516.41394734785 & 225.085105968738 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 567037.783333333 & 2251.21438729542 & 251.880845526473 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 566475.45 & 2013.33462062082 & 281.361798579376 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 563592.327586207 & 4947.19639880419 & 113.921559233516 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 563973.982142857 & 4744.40771565817 & 118.871314596667 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 564194.277777778 & 4581.22281473829 & 123.15364272672 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 564483.346153846 & 4417.10685061809 & 127.794813493103 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 564691.12 & 4253.94614922691 & 132.745244107668 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 564738.083333333 & 4107.38086647672 & 137.493478616158 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 564890.630434783 & 3977.82525724273 & 142.009915947475 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 565041.227272727 & 3820.93725964444 & 147.880268341624 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 565148.380952381 & 3646.77772694252 & 154.971984384199 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 565213.675 & 3443.14714703537 & 164.156119638007 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 565407.552631579 & 3365.94052739994 & 167.979067968956 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 565637.861111111 & 3279.91588746022 & 172.454989859240 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 565858.235294118 & 3170.57997389616 & 178.471522545689 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 566041.875 & 3063.1617431039 & 184.790070675938 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 566207.333333333 & 2935.7788300036 & 192.864437724908 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 566291.071428571 & 2790.13624429270 & 202.961798939724 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 566293.384615385 & 2681.7442022666 & 211.166070252620 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 566284.75 & 2537.26011449101 & 223.187503230665 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 566266.181818182 & 2328.81862795045 & 243.155982617909 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 566144.35 & 2109.54229667181 & 268.373073577713 \tabularnewline
Median & 565603 &  &  \tabularnewline
Midrange & 549120.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 565155.161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 566207.333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 565155.161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 566207.333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 566207.333333333 &  &  \tabularnewline
Midmean - Closest Observation & 565155.161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 566207.333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 566041.875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18121&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]563109.933333333[/C][C]5154.20041527574[/C][C]109.252626588679[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]561688.82708944[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]560238.16314564[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]564499.936361378[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]563236.116666667[/C][C]5111.25724951046[/C][C]110.195219917881[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]563577.45[/C][C]4981.29796522144[/C][C]113.138674685755[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]563442.7[/C][C]4899.87198006983[/C][C]114.991310444803[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]563790.766666667[/C][C]4793.32350633309[/C][C]117.620011651992[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]564503.266666667[/C][C]4624.58697076908[/C][C]122.065661265483[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]564036.366666667[/C][C]4442.39238620088[/C][C]126.966804737622[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]564117.566666667[/C][C]4403.09973546286[/C][C]128.118280429404[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]564441.166666667[/C][C]4297.18788161801[/C][C]131.351288846635[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]564756.616666667[/C][C]4203.50754244284[/C][C]134.353658454116[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]563985.783333333[/C][C]3527.05450502366[/C][C]159.902769444032[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]563887.516666667[/C][C]3439.91406306825[/C][C]163.924884845438[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]564139.316666667[/C][C]3391.21079442950[/C][C]166.353361930004[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]564585[/C][C]3223.84908075428[/C][C]175.127614803825[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]564883.666666667[/C][C]3124.05946485093[/C][C]180.817194109851[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]565621.166666667[/C][C]2991.03099188966[/C][C]189.105752565045[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]566275.033333333[/C][C]2671.08317043311[/C][C]212.002022101585[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]566352.1[/C][C]2589.19900181831[/C][C]218.736412149962[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]566407.3[/C][C]2516.41394734785[/C][C]225.085105968738[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]567037.783333333[/C][C]2251.21438729542[/C][C]251.880845526473[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]566475.45[/C][C]2013.33462062082[/C][C]281.361798579376[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]563592.327586207[/C][C]4947.19639880419[/C][C]113.921559233516[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]563973.982142857[/C][C]4744.40771565817[/C][C]118.871314596667[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]564194.277777778[/C][C]4581.22281473829[/C][C]123.15364272672[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]564483.346153846[/C][C]4417.10685061809[/C][C]127.794813493103[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]564691.12[/C][C]4253.94614922691[/C][C]132.745244107668[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]564738.083333333[/C][C]4107.38086647672[/C][C]137.493478616158[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]564890.630434783[/C][C]3977.82525724273[/C][C]142.009915947475[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]565041.227272727[/C][C]3820.93725964444[/C][C]147.880268341624[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]565148.380952381[/C][C]3646.77772694252[/C][C]154.971984384199[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]565213.675[/C][C]3443.14714703537[/C][C]164.156119638007[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]565407.552631579[/C][C]3365.94052739994[/C][C]167.979067968956[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]565637.861111111[/C][C]3279.91588746022[/C][C]172.454989859240[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]565858.235294118[/C][C]3170.57997389616[/C][C]178.471522545689[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]566041.875[/C][C]3063.1617431039[/C][C]184.790070675938[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]566207.333333333[/C][C]2935.7788300036[/C][C]192.864437724908[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]566291.071428571[/C][C]2790.13624429270[/C][C]202.961798939724[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]566293.384615385[/C][C]2681.7442022666[/C][C]211.166070252620[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]566284.75[/C][C]2537.26011449101[/C][C]223.187503230665[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]566266.181818182[/C][C]2328.81862795045[/C][C]243.155982617909[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]566144.35[/C][C]2109.54229667181[/C][C]268.373073577713[/C][/ROW]
[ROW][C]Median[/C][C]565603[/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]565155.161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]566207.333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]565155.161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]566207.333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]566207.333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]565155.161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]566207.333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]566041.875[/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=18121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18121&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 Mean563109.9333333335154.20041527574109.252626588679
Geometric Mean561688.82708944
Harmonic Mean560238.16314564
Quadratic Mean564499.936361378
Winsorized Mean ( 1 / 20 )563236.1166666675111.25724951046110.195219917881
Winsorized Mean ( 2 / 20 )563577.454981.29796522144113.138674685755
Winsorized Mean ( 3 / 20 )563442.74899.87198006983114.991310444803
Winsorized Mean ( 4 / 20 )563790.7666666674793.32350633309117.620011651992
Winsorized Mean ( 5 / 20 )564503.2666666674624.58697076908122.065661265483
Winsorized Mean ( 6 / 20 )564036.3666666674442.39238620088126.966804737622
Winsorized Mean ( 7 / 20 )564117.5666666674403.09973546286128.118280429404
Winsorized Mean ( 8 / 20 )564441.1666666674297.18788161801131.351288846635
Winsorized Mean ( 9 / 20 )564756.6166666674203.50754244284134.353658454116
Winsorized Mean ( 10 / 20 )563985.7833333333527.05450502366159.902769444032
Winsorized Mean ( 11 / 20 )563887.5166666673439.91406306825163.924884845438
Winsorized Mean ( 12 / 20 )564139.3166666673391.21079442950166.353361930004
Winsorized Mean ( 13 / 20 )5645853223.84908075428175.127614803825
Winsorized Mean ( 14 / 20 )564883.6666666673124.05946485093180.817194109851
Winsorized Mean ( 15 / 20 )565621.1666666672991.03099188966189.105752565045
Winsorized Mean ( 16 / 20 )566275.0333333332671.08317043311212.002022101585
Winsorized Mean ( 17 / 20 )566352.12589.19900181831218.736412149962
Winsorized Mean ( 18 / 20 )566407.32516.41394734785225.085105968738
Winsorized Mean ( 19 / 20 )567037.7833333332251.21438729542251.880845526473
Winsorized Mean ( 20 / 20 )566475.452013.33462062082281.361798579376
Trimmed Mean ( 1 / 20 )563592.3275862074947.19639880419113.921559233516
Trimmed Mean ( 2 / 20 )563973.9821428574744.40771565817118.871314596667
Trimmed Mean ( 3 / 20 )564194.2777777784581.22281473829123.15364272672
Trimmed Mean ( 4 / 20 )564483.3461538464417.10685061809127.794813493103
Trimmed Mean ( 5 / 20 )564691.124253.94614922691132.745244107668
Trimmed Mean ( 6 / 20 )564738.0833333334107.38086647672137.493478616158
Trimmed Mean ( 7 / 20 )564890.6304347833977.82525724273142.009915947475
Trimmed Mean ( 8 / 20 )565041.2272727273820.93725964444147.880268341624
Trimmed Mean ( 9 / 20 )565148.3809523813646.77772694252154.971984384199
Trimmed Mean ( 10 / 20 )565213.6753443.14714703537164.156119638007
Trimmed Mean ( 11 / 20 )565407.5526315793365.94052739994167.979067968956
Trimmed Mean ( 12 / 20 )565637.8611111113279.91588746022172.454989859240
Trimmed Mean ( 13 / 20 )565858.2352941183170.57997389616178.471522545689
Trimmed Mean ( 14 / 20 )566041.8753063.1617431039184.790070675938
Trimmed Mean ( 15 / 20 )566207.3333333332935.7788300036192.864437724908
Trimmed Mean ( 16 / 20 )566291.0714285712790.13624429270202.961798939724
Trimmed Mean ( 17 / 20 )566293.3846153852681.7442022666211.166070252620
Trimmed Mean ( 18 / 20 )566284.752537.26011449101223.187503230665
Trimmed Mean ( 19 / 20 )566266.1818181822328.81862795045243.155982617909
Trimmed Mean ( 20 / 20 )566144.352109.54229667181268.373073577713
Median565603
Midrange549120.5
Midmean - Weighted Average at Xnp565155.161290323
Midmean - Weighted Average at X(n+1)p566207.333333333
Midmean - Empirical Distribution Function565155.161290323
Midmean - Empirical Distribution Function - Averaging566207.333333333
Midmean - Empirical Distribution Function - Interpolation566207.333333333
Midmean - Closest Observation565155.161290323
Midmean - True Basic - Statistics Graphics Toolkit566207.333333333
Midmean - MS Excel (old versions)566041.875
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')