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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, 16 Nov 2010 11:05:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t1289905527yig66ij1jfyr29x.htm/, Retrieved Mon, 29 Apr 2024 06:32:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95382, Retrieved Mon, 29 Apr 2024 06:32:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [ws 6 deel 1 vraag...] [2010-11-14 08:37:37] [05ab9592748364013445d860bb938e43]
-    D    [Central Tendency] [Hapiness tutorial] [2010-11-16 07:14:13] [05ab9592748364013445d860bb938e43]
-   PD        [Central Tendency] [Central Tendency ...] [2010-11-16 11:05:47] [c1f1b5e209adb4577289f490325e36f2] [Current]
-   PD          [Central Tendency] [Central Tendency ...] [2010-11-16 15:35:40] [717f3d787904f94c39256c5c1fc72d4c]
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Dataseries X:
1.3855
1.3431
1.3257
1.2978
1.2793
1.2945
1.289
1.2848
1.2694
1.2636
1.29
1.3559
1.3305
1.3482
1.3146
1.3027
1.3247
1.3267
1.3621
1.3479
1.4011
1.4135
1.3964
1.401
1.3955
1.4077
1.3975
1.3949
1.4138
1.421
1.4253
1.4169
1.4174
1.4346
1.4296
1.4311
1.4594
1.4722
1.4669
1.4571
1.4709
1.4893
1.4997
1.4713
1.4846
1.4914
1.4859
1.4957
1.4843
1.4619
1.434
1.4426
1.4318




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=95382&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=95382&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95382&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 Mean1.394949056603770.00962290017154272144.961397472353
Geometric Mean1.39320280266498
Harmonic Mean1.3914375497612
Quadratic Mean1.39667393521922
Winsorized Mean ( 1 / 17 )1.394983018867920.00957921095671931145.626088116310
Winsorized Mean ( 2 / 17 )1.395194339622640.0094557887351086147.54922922954
Winsorized Mean ( 3 / 17 )1.395386792452830.00936063114155155149.069733798050
Winsorized Mean ( 4 / 17 )1.395447169811320.00924059699524580151.012664065889
Winsorized Mean ( 5 / 17 )1.395418867924530.00919677092658503151.729218772950
Winsorized Mean ( 6 / 17 )1.395894339622640.00907956501354704153.740221865245
Winsorized Mean ( 7 / 17 )1.394732075471700.00869933341355754160.326315726452
Winsorized Mean ( 8 / 17 )1.395335849056600.00851946251904984163.782145403725
Winsorized Mean ( 9 / 17 )1.397288679245280.00809769299170662172.553921305283
Winsorized Mean ( 10 / 17 )1.398439622641510.00760118122534147183.976619052217
Winsorized Mean ( 11 / 17 )1.397609433962260.00738562045024367189.233855622266
Winsorized Mean ( 12 / 17 )1.397269811320750.00724919873701766192.748172868495
Winsorized Mean ( 13 / 17 )1.397637735849060.00698307783851815200.146377882227
Winsorized Mean ( 14 / 17 )1.397135849056600.00576879089887782242.188679317252
Winsorized Mean ( 15 / 17 )1.396230188679250.0051917635904658268.931773250095
Winsorized Mean ( 16 / 17 )1.396139622641510.0051498744750739271.101680128131
Winsorized Mean ( 17 / 17 )1.397903773584910.0046125325918068303.066427339286
Trimmed Mean ( 1 / 17 )1.395470588235290.00943433374898287147.914057883074
Trimmed Mean ( 2 / 17 )1.395997959183670.00924472661311982151.004785496038
Trimmed Mean ( 3 / 17 )1.396451063829790.00908088836563704153.779124640943
Trimmed Mean ( 4 / 17 )1.396868888888890.00891002319614152156.775000259685
Trimmed Mean ( 5 / 17 )1.397306976744190.00872931086429773160.070708726742
Trimmed Mean ( 6 / 17 )1.397795121951220.00849943107939635164.457492377301
Trimmed Mean ( 7 / 17 )1.398225641025640.00822728477792775169.949828985720
Trimmed Mean ( 8 / 17 )1.398940540540540.00797601082249344175.393510825655
Trimmed Mean ( 9 / 17 )1.399622857142860.00768186130031094182.198402499952
Trimmed Mean ( 10 / 17 )1.400039393939390.00740521153938677189.061363945227
Trimmed Mean ( 11 / 17 )1.400312903225810.00716618064158725195.405750044789
Trimmed Mean ( 12 / 17 )1.400762068965520.0068762323817846203.710693762501
Trimmed Mean ( 13 / 17 )1.401333333333330.00647821684163886216.314669235249
Trimmed Mean ( 14 / 17 )1.4019360.00596163814176383235.159526066978
Trimmed Mean ( 15 / 17 )1.402726086956520.00565739299934726247.945668105144
Trimmed Mean ( 16 / 17 )1.403819047619050.00537811977698534261.024132193267
Trimmed Mean ( 17 / 17 )1.405157894736840.00486956364022157288.559303985789
Median1.4077
Midrange1.38165
Midmean - Weighted Average at Xnp1.39918846153846
Midmean - Weighted Average at X(n+1)p1.40133333333333
Midmean - Empirical Distribution Function1.40133333333333
Midmean - Empirical Distribution Function - Averaging1.40133333333333
Midmean - Empirical Distribution Function - Interpolation1.40133333333333
Midmean - Closest Observation1.39866785714286
Midmean - True Basic - Statistics Graphics Toolkit1.40133333333333
Midmean - MS Excel (old versions)1.40133333333333
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.39494905660377 & 0.00962290017154272 & 144.961397472353 \tabularnewline
Geometric Mean & 1.39320280266498 &  &  \tabularnewline
Harmonic Mean & 1.3914375497612 &  &  \tabularnewline
Quadratic Mean & 1.39667393521922 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 1.39498301886792 & 0.00957921095671931 & 145.626088116310 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 1.39519433962264 & 0.0094557887351086 & 147.54922922954 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 1.39538679245283 & 0.00936063114155155 & 149.069733798050 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 1.39544716981132 & 0.00924059699524580 & 151.012664065889 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 1.39541886792453 & 0.00919677092658503 & 151.729218772950 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 1.39589433962264 & 0.00907956501354704 & 153.740221865245 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 1.39473207547170 & 0.00869933341355754 & 160.326315726452 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 1.39533584905660 & 0.00851946251904984 & 163.782145403725 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 1.39728867924528 & 0.00809769299170662 & 172.553921305283 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 1.39843962264151 & 0.00760118122534147 & 183.976619052217 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 1.39760943396226 & 0.00738562045024367 & 189.233855622266 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 1.39726981132075 & 0.00724919873701766 & 192.748172868495 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 1.39763773584906 & 0.00698307783851815 & 200.146377882227 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 1.39713584905660 & 0.00576879089887782 & 242.188679317252 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 1.39623018867925 & 0.0051917635904658 & 268.931773250095 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 1.39613962264151 & 0.0051498744750739 & 271.101680128131 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 1.39790377358491 & 0.0046125325918068 & 303.066427339286 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 1.39547058823529 & 0.00943433374898287 & 147.914057883074 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 1.39599795918367 & 0.00924472661311982 & 151.004785496038 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 1.39645106382979 & 0.00908088836563704 & 153.779124640943 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 1.39686888888889 & 0.00891002319614152 & 156.775000259685 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 1.39730697674419 & 0.00872931086429773 & 160.070708726742 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 1.39779512195122 & 0.00849943107939635 & 164.457492377301 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 1.39822564102564 & 0.00822728477792775 & 169.949828985720 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 1.39894054054054 & 0.00797601082249344 & 175.393510825655 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 1.39962285714286 & 0.00768186130031094 & 182.198402499952 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 1.40003939393939 & 0.00740521153938677 & 189.061363945227 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 1.40031290322581 & 0.00716618064158725 & 195.405750044789 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 1.40076206896552 & 0.0068762323817846 & 203.710693762501 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 1.40133333333333 & 0.00647821684163886 & 216.314669235249 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 1.401936 & 0.00596163814176383 & 235.159526066978 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 1.40272608695652 & 0.00565739299934726 & 247.945668105144 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 1.40381904761905 & 0.00537811977698534 & 261.024132193267 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 1.40515789473684 & 0.00486956364022157 & 288.559303985789 \tabularnewline
Median & 1.4077 &  &  \tabularnewline
Midrange & 1.38165 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.39918846153846 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.40133333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.40133333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.40133333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.40133333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.39866785714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.40133333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.40133333333333 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95382&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]1.39494905660377[/C][C]0.00962290017154272[/C][C]144.961397472353[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.39320280266498[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.3914375497612[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.39667393521922[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]1.39498301886792[/C][C]0.00957921095671931[/C][C]145.626088116310[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]1.39519433962264[/C][C]0.0094557887351086[/C][C]147.54922922954[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]1.39538679245283[/C][C]0.00936063114155155[/C][C]149.069733798050[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]1.39544716981132[/C][C]0.00924059699524580[/C][C]151.012664065889[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]1.39541886792453[/C][C]0.00919677092658503[/C][C]151.729218772950[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]1.39589433962264[/C][C]0.00907956501354704[/C][C]153.740221865245[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]1.39473207547170[/C][C]0.00869933341355754[/C][C]160.326315726452[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]1.39533584905660[/C][C]0.00851946251904984[/C][C]163.782145403725[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]1.39728867924528[/C][C]0.00809769299170662[/C][C]172.553921305283[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]1.39843962264151[/C][C]0.00760118122534147[/C][C]183.976619052217[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]1.39760943396226[/C][C]0.00738562045024367[/C][C]189.233855622266[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]1.39726981132075[/C][C]0.00724919873701766[/C][C]192.748172868495[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]1.39763773584906[/C][C]0.00698307783851815[/C][C]200.146377882227[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]1.39713584905660[/C][C]0.00576879089887782[/C][C]242.188679317252[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]1.39623018867925[/C][C]0.0051917635904658[/C][C]268.931773250095[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]1.39613962264151[/C][C]0.0051498744750739[/C][C]271.101680128131[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]1.39790377358491[/C][C]0.0046125325918068[/C][C]303.066427339286[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]1.39547058823529[/C][C]0.00943433374898287[/C][C]147.914057883074[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]1.39599795918367[/C][C]0.00924472661311982[/C][C]151.004785496038[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]1.39645106382979[/C][C]0.00908088836563704[/C][C]153.779124640943[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]1.39686888888889[/C][C]0.00891002319614152[/C][C]156.775000259685[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]1.39730697674419[/C][C]0.00872931086429773[/C][C]160.070708726742[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]1.39779512195122[/C][C]0.00849943107939635[/C][C]164.457492377301[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]1.39822564102564[/C][C]0.00822728477792775[/C][C]169.949828985720[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]1.39894054054054[/C][C]0.00797601082249344[/C][C]175.393510825655[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]1.39962285714286[/C][C]0.00768186130031094[/C][C]182.198402499952[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]1.40003939393939[/C][C]0.00740521153938677[/C][C]189.061363945227[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]1.40031290322581[/C][C]0.00716618064158725[/C][C]195.405750044789[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]1.40076206896552[/C][C]0.0068762323817846[/C][C]203.710693762501[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]1.40133333333333[/C][C]0.00647821684163886[/C][C]216.314669235249[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]1.401936[/C][C]0.00596163814176383[/C][C]235.159526066978[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]1.40272608695652[/C][C]0.00565739299934726[/C][C]247.945668105144[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]1.40381904761905[/C][C]0.00537811977698534[/C][C]261.024132193267[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]1.40515789473684[/C][C]0.00486956364022157[/C][C]288.559303985789[/C][/ROW]
[ROW][C]Median[/C][C]1.4077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.38165[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.39918846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.40133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.40133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.40133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.40133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.39866785714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.40133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.40133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]53[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95382&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95382&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 Mean1.394949056603770.00962290017154272144.961397472353
Geometric Mean1.39320280266498
Harmonic Mean1.3914375497612
Quadratic Mean1.39667393521922
Winsorized Mean ( 1 / 17 )1.394983018867920.00957921095671931145.626088116310
Winsorized Mean ( 2 / 17 )1.395194339622640.0094557887351086147.54922922954
Winsorized Mean ( 3 / 17 )1.395386792452830.00936063114155155149.069733798050
Winsorized Mean ( 4 / 17 )1.395447169811320.00924059699524580151.012664065889
Winsorized Mean ( 5 / 17 )1.395418867924530.00919677092658503151.729218772950
Winsorized Mean ( 6 / 17 )1.395894339622640.00907956501354704153.740221865245
Winsorized Mean ( 7 / 17 )1.394732075471700.00869933341355754160.326315726452
Winsorized Mean ( 8 / 17 )1.395335849056600.00851946251904984163.782145403725
Winsorized Mean ( 9 / 17 )1.397288679245280.00809769299170662172.553921305283
Winsorized Mean ( 10 / 17 )1.398439622641510.00760118122534147183.976619052217
Winsorized Mean ( 11 / 17 )1.397609433962260.00738562045024367189.233855622266
Winsorized Mean ( 12 / 17 )1.397269811320750.00724919873701766192.748172868495
Winsorized Mean ( 13 / 17 )1.397637735849060.00698307783851815200.146377882227
Winsorized Mean ( 14 / 17 )1.397135849056600.00576879089887782242.188679317252
Winsorized Mean ( 15 / 17 )1.396230188679250.0051917635904658268.931773250095
Winsorized Mean ( 16 / 17 )1.396139622641510.0051498744750739271.101680128131
Winsorized Mean ( 17 / 17 )1.397903773584910.0046125325918068303.066427339286
Trimmed Mean ( 1 / 17 )1.395470588235290.00943433374898287147.914057883074
Trimmed Mean ( 2 / 17 )1.395997959183670.00924472661311982151.004785496038
Trimmed Mean ( 3 / 17 )1.396451063829790.00908088836563704153.779124640943
Trimmed Mean ( 4 / 17 )1.396868888888890.00891002319614152156.775000259685
Trimmed Mean ( 5 / 17 )1.397306976744190.00872931086429773160.070708726742
Trimmed Mean ( 6 / 17 )1.397795121951220.00849943107939635164.457492377301
Trimmed Mean ( 7 / 17 )1.398225641025640.00822728477792775169.949828985720
Trimmed Mean ( 8 / 17 )1.398940540540540.00797601082249344175.393510825655
Trimmed Mean ( 9 / 17 )1.399622857142860.00768186130031094182.198402499952
Trimmed Mean ( 10 / 17 )1.400039393939390.00740521153938677189.061363945227
Trimmed Mean ( 11 / 17 )1.400312903225810.00716618064158725195.405750044789
Trimmed Mean ( 12 / 17 )1.400762068965520.0068762323817846203.710693762501
Trimmed Mean ( 13 / 17 )1.401333333333330.00647821684163886216.314669235249
Trimmed Mean ( 14 / 17 )1.4019360.00596163814176383235.159526066978
Trimmed Mean ( 15 / 17 )1.402726086956520.00565739299934726247.945668105144
Trimmed Mean ( 16 / 17 )1.403819047619050.00537811977698534261.024132193267
Trimmed Mean ( 17 / 17 )1.405157894736840.00486956364022157288.559303985789
Median1.4077
Midrange1.38165
Midmean - Weighted Average at Xnp1.39918846153846
Midmean - Weighted Average at X(n+1)p1.40133333333333
Midmean - Empirical Distribution Function1.40133333333333
Midmean - Empirical Distribution Function - Averaging1.40133333333333
Midmean - Empirical Distribution Function - Interpolation1.40133333333333
Midmean - Closest Observation1.39866785714286
Midmean - True Basic - Statistics Graphics Toolkit1.40133333333333
Midmean - MS Excel (old versions)1.40133333333333
Number of observations53



Parameters (Session):
par1 = 12 ;
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')