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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 20 Dec 2007 11:17:31 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/20/t1198173793x4ew57azborn54p.htm/, Retrieved Mon, 29 Apr 2024 15:58:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4753, Retrieved Mon, 29 Apr 2024 15:58:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTinne Van der Eycken Central Tendency
Estimated Impact212
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper: Residu's] [2007-12-20 18:17:31] [c8635c97647ba59406cb570a9fab7b02] [Current]
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Dataseries X:
0.0963998702089473
3.68776849361799
-2.21255748827435
-7.20539944007456
-7.023891220501
-7.61148340355811
-3.99320973953091
6.89080433018175
4.29343380939718
7.62272567916079
-11.6843627244492
-0.535869903617174
4.04039602192003
2.32019809603990
9.33968250429729
-2.53778924222572
-1.01815086767597
12.8776109208021
-8.42487576488816
2.83410372215247
-0.471503171874632
-4.91856672164707
7.16052036556875
6.998877306551
1.22749287747846
1.66434155208273
-4.36846797387122
-2.09547670954011
4.81586323198283
-4.48888699863318
-8.48643331579231
2.89866303275703
5.27231601243985
-2.56938765772798
2.36292159333768
-6.05726375617971
4.66991235080987
0.262121137580347
5.3112374408186
-7.91592347989297
6.18741413248122
0.747779670353935
-1.40792915135314
4.52258059154915
0.456098235973329
13.4046188187457
4.19387306989446
2.69556495773171
8.39583369915604
4.06972911185789
1.66853211858185
1.26029425179894
-1.31856162906204
3.42176579549080
4.38702403425957
3.14027069254159




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4753&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4753&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.050942485164860.7251271420917981.44932167637964
Geometric MeanNaN
Harmonic Mean3.38124142866431
Quadratic Mean5.47941562377107
Winsorized Mean ( 1 / 18 )1.098637512141880.7060489530909371.55603589146656
Winsorized Mean ( 2 / 18 )0.9744814097990040.6719136312543521.45030754619430
Winsorized Mean ( 3 / 18 )0.9511833819340370.654123934279021.45413327977738
Winsorized Mean ( 4 / 18 )0.9177071002440090.6378034555314111.43885564163240
Winsorized Mean ( 5 / 18 )0.9126962654128940.6213694187680741.46884645083178
Winsorized Mean ( 6 / 18 )0.9148246754724450.6136279771901021.49084577215917
Winsorized Mean ( 7 / 18 )1.022143986466450.5836184025177591.75139094664745
Winsorized Mean ( 8 / 18 )1.084330677442470.5309164343399642.04237542352688
Winsorized Mean ( 9 / 18 )1.012572236052490.4933122629066492.0525989564628
Winsorized Mean ( 10 / 18 )1.027125378263780.4878697432733622.10532707228835
Winsorized Mean ( 11 / 18 )1.011176449562280.4592993938889512.20156277804007
Winsorized Mean ( 12 / 18 )1.285005992554420.3971458353011593.23560233630547
Winsorized Mean ( 13 / 18 )1.258139323467630.3906015394123223.22103012026159
Winsorized Mean ( 14 / 18 )1.305558122633080.3712773713441363.51639562062877
Winsorized Mean ( 15 / 18 )1.311850235277330.3621249671070453.6226450933706
Winsorized Mean ( 16 / 18 )1.479846469187110.3251225392456424.55165757692681
Winsorized Mean ( 17 / 18 )1.469289336907240.3150612108240574.66350438082887
Winsorized Mean ( 18 / 18 )1.556421445587020.2982908579244335.21779801237258
Trimmed Mean ( 1 / 18 )1.058009686572880.6751785879612361.56700716734463
Trimmed Mean ( 2 / 18 )1.014256643652420.6363160910827151.59395095906914
Trimmed Mean ( 3 / 18 )1.036530774610340.6112400235638661.69578354599032
Trimmed Mean ( 4 / 18 )1.069721427317790.5883760795737441.81809129305998
Trimmed Mean ( 5 / 18 )1.115986657296760.5657677864403331.97251714226833
Trimmed Mean ( 6 / 18 )1.167733302503570.5424346229225642.15276321450865
Trimmed Mean ( 7 / 18 )1.223935219621590.5142880747652072.37986311500684
Trimmed Mean ( 8 / 18 )1.264293466252620.4871826343019632.59511192976758
Trimmed Mean ( 9 / 18 )1.297444506296600.467853178621592.77318732795444
Trimmed Mean ( 10 / 18 )1.346681688807920.4525721149358612.97561790566522
Trimmed Mean ( 11 / 18 )1.399314492897550.4325311921346783.23517590949103
Trimmed Mean ( 12 / 18 )1.461063727064520.4127910124951523.53947562528795
Trimmed Mean ( 13 / 18 )1.488450485766090.4046702925640143.67818076374025
Trimmed Mean ( 14 / 18 )1.523882972273550.3934278118103803.87334836665796
Trimmed Mean ( 15 / 18 )1.557471410679780.3819583105905164.0775952963869
Trimmed Mean ( 16 / 18 )1.595679149075710.3660535272150244.3591415747741
Trimmed Mean ( 17 / 18 )1.614107075421630.3548842765569324.54826314392287
Trimmed Mean ( 18 / 18 )1.637959408824000.3385090863703344.83874576717284
Median1.66643683533229
Midrange0.86012804714825
Midmean - Weighted Average at Xnp1.38382530970461
Midmean - Weighted Average at X(n+1)p1.52388297227355
Midmean - Empirical Distribution Function1.38382530970461
Midmean - Empirical Distribution Function - Averaging1.52388297227355
Midmean - Empirical Distribution Function - Interpolation1.52388297227355
Midmean - Closest Observation1.38382530970461
Midmean - True Basic - Statistics Graphics Toolkit1.52388297227355
Midmean - MS Excel (old versions)1.48845048576609
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.05094248516486 & 0.725127142091798 & 1.44932167637964 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 3.38124142866431 &  &  \tabularnewline
Quadratic Mean & 5.47941562377107 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 1.09863751214188 & 0.706048953090937 & 1.55603589146656 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 0.974481409799004 & 0.671913631254352 & 1.45030754619430 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 0.951183381934037 & 0.65412393427902 & 1.45413327977738 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 0.917707100244009 & 0.637803455531411 & 1.43885564163240 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 0.912696265412894 & 0.621369418768074 & 1.46884645083178 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 0.914824675472445 & 0.613627977190102 & 1.49084577215917 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 1.02214398646645 & 0.583618402517759 & 1.75139094664745 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 1.08433067744247 & 0.530916434339964 & 2.04237542352688 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 1.01257223605249 & 0.493312262906649 & 2.0525989564628 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 1.02712537826378 & 0.487869743273362 & 2.10532707228835 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 1.01117644956228 & 0.459299393888951 & 2.20156277804007 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 1.28500599255442 & 0.397145835301159 & 3.23560233630547 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 1.25813932346763 & 0.390601539412322 & 3.22103012026159 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 1.30555812263308 & 0.371277371344136 & 3.51639562062877 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 1.31185023527733 & 0.362124967107045 & 3.6226450933706 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 1.47984646918711 & 0.325122539245642 & 4.55165757692681 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 1.46928933690724 & 0.315061210824057 & 4.66350438082887 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 1.55642144558702 & 0.298290857924433 & 5.21779801237258 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 1.05800968657288 & 0.675178587961236 & 1.56700716734463 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 1.01425664365242 & 0.636316091082715 & 1.59395095906914 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 1.03653077461034 & 0.611240023563866 & 1.69578354599032 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 1.06972142731779 & 0.588376079573744 & 1.81809129305998 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 1.11598665729676 & 0.565767786440333 & 1.97251714226833 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 1.16773330250357 & 0.542434622922564 & 2.15276321450865 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 1.22393521962159 & 0.514288074765207 & 2.37986311500684 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 1.26429346625262 & 0.487182634301963 & 2.59511192976758 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 1.29744450629660 & 0.46785317862159 & 2.77318732795444 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 1.34668168880792 & 0.452572114935861 & 2.97561790566522 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 1.39931449289755 & 0.432531192134678 & 3.23517590949103 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 1.46106372706452 & 0.412791012495152 & 3.53947562528795 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 1.48845048576609 & 0.404670292564014 & 3.67818076374025 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 1.52388297227355 & 0.393427811810380 & 3.87334836665796 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 1.55747141067978 & 0.381958310590516 & 4.0775952963869 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 1.59567914907571 & 0.366053527215024 & 4.3591415747741 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 1.61410707542163 & 0.354884276556932 & 4.54826314392287 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 1.63795940882400 & 0.338509086370334 & 4.83874576717284 \tabularnewline
Median & 1.66643683533229 &  &  \tabularnewline
Midrange & 0.86012804714825 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.38382530970461 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.52388297227355 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.38382530970461 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.52388297227355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.52388297227355 &  &  \tabularnewline
Midmean - Closest Observation & 1.38382530970461 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.52388297227355 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.48845048576609 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4753&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]1.05094248516486[/C][C]0.725127142091798[/C][C]1.44932167637964[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.38124142866431[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.47941562377107[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]1.09863751214188[/C][C]0.706048953090937[/C][C]1.55603589146656[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]0.974481409799004[/C][C]0.671913631254352[/C][C]1.45030754619430[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]0.951183381934037[/C][C]0.65412393427902[/C][C]1.45413327977738[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]0.917707100244009[/C][C]0.637803455531411[/C][C]1.43885564163240[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]0.912696265412894[/C][C]0.621369418768074[/C][C]1.46884645083178[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]0.914824675472445[/C][C]0.613627977190102[/C][C]1.49084577215917[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]1.02214398646645[/C][C]0.583618402517759[/C][C]1.75139094664745[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]1.08433067744247[/C][C]0.530916434339964[/C][C]2.04237542352688[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]1.01257223605249[/C][C]0.493312262906649[/C][C]2.0525989564628[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]1.02712537826378[/C][C]0.487869743273362[/C][C]2.10532707228835[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]1.01117644956228[/C][C]0.459299393888951[/C][C]2.20156277804007[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]1.28500599255442[/C][C]0.397145835301159[/C][C]3.23560233630547[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]1.25813932346763[/C][C]0.390601539412322[/C][C]3.22103012026159[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]1.30555812263308[/C][C]0.371277371344136[/C][C]3.51639562062877[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]1.31185023527733[/C][C]0.362124967107045[/C][C]3.6226450933706[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]1.47984646918711[/C][C]0.325122539245642[/C][C]4.55165757692681[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]1.46928933690724[/C][C]0.315061210824057[/C][C]4.66350438082887[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]1.55642144558702[/C][C]0.298290857924433[/C][C]5.21779801237258[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]1.05800968657288[/C][C]0.675178587961236[/C][C]1.56700716734463[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]1.01425664365242[/C][C]0.636316091082715[/C][C]1.59395095906914[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]1.03653077461034[/C][C]0.611240023563866[/C][C]1.69578354599032[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]1.06972142731779[/C][C]0.588376079573744[/C][C]1.81809129305998[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]1.11598665729676[/C][C]0.565767786440333[/C][C]1.97251714226833[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]1.16773330250357[/C][C]0.542434622922564[/C][C]2.15276321450865[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]1.22393521962159[/C][C]0.514288074765207[/C][C]2.37986311500684[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]1.26429346625262[/C][C]0.487182634301963[/C][C]2.59511192976758[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]1.29744450629660[/C][C]0.46785317862159[/C][C]2.77318732795444[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]1.34668168880792[/C][C]0.452572114935861[/C][C]2.97561790566522[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]1.39931449289755[/C][C]0.432531192134678[/C][C]3.23517590949103[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]1.46106372706452[/C][C]0.412791012495152[/C][C]3.53947562528795[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]1.48845048576609[/C][C]0.404670292564014[/C][C]3.67818076374025[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]1.52388297227355[/C][C]0.393427811810380[/C][C]3.87334836665796[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]1.55747141067978[/C][C]0.381958310590516[/C][C]4.0775952963869[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]1.59567914907571[/C][C]0.366053527215024[/C][C]4.3591415747741[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]1.61410707542163[/C][C]0.354884276556932[/C][C]4.54826314392287[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]1.63795940882400[/C][C]0.338509086370334[/C][C]4.83874576717284[/C][/ROW]
[ROW][C]Median[/C][C]1.66643683533229[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.86012804714825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.38382530970461[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.52388297227355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.38382530970461[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.52388297227355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.52388297227355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.38382530970461[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.52388297227355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.48845048576609[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4753&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 Mean1.050942485164860.7251271420917981.44932167637964
Geometric MeanNaN
Harmonic Mean3.38124142866431
Quadratic Mean5.47941562377107
Winsorized Mean ( 1 / 18 )1.098637512141880.7060489530909371.55603589146656
Winsorized Mean ( 2 / 18 )0.9744814097990040.6719136312543521.45030754619430
Winsorized Mean ( 3 / 18 )0.9511833819340370.654123934279021.45413327977738
Winsorized Mean ( 4 / 18 )0.9177071002440090.6378034555314111.43885564163240
Winsorized Mean ( 5 / 18 )0.9126962654128940.6213694187680741.46884645083178
Winsorized Mean ( 6 / 18 )0.9148246754724450.6136279771901021.49084577215917
Winsorized Mean ( 7 / 18 )1.022143986466450.5836184025177591.75139094664745
Winsorized Mean ( 8 / 18 )1.084330677442470.5309164343399642.04237542352688
Winsorized Mean ( 9 / 18 )1.012572236052490.4933122629066492.0525989564628
Winsorized Mean ( 10 / 18 )1.027125378263780.4878697432733622.10532707228835
Winsorized Mean ( 11 / 18 )1.011176449562280.4592993938889512.20156277804007
Winsorized Mean ( 12 / 18 )1.285005992554420.3971458353011593.23560233630547
Winsorized Mean ( 13 / 18 )1.258139323467630.3906015394123223.22103012026159
Winsorized Mean ( 14 / 18 )1.305558122633080.3712773713441363.51639562062877
Winsorized Mean ( 15 / 18 )1.311850235277330.3621249671070453.6226450933706
Winsorized Mean ( 16 / 18 )1.479846469187110.3251225392456424.55165757692681
Winsorized Mean ( 17 / 18 )1.469289336907240.3150612108240574.66350438082887
Winsorized Mean ( 18 / 18 )1.556421445587020.2982908579244335.21779801237258
Trimmed Mean ( 1 / 18 )1.058009686572880.6751785879612361.56700716734463
Trimmed Mean ( 2 / 18 )1.014256643652420.6363160910827151.59395095906914
Trimmed Mean ( 3 / 18 )1.036530774610340.6112400235638661.69578354599032
Trimmed Mean ( 4 / 18 )1.069721427317790.5883760795737441.81809129305998
Trimmed Mean ( 5 / 18 )1.115986657296760.5657677864403331.97251714226833
Trimmed Mean ( 6 / 18 )1.167733302503570.5424346229225642.15276321450865
Trimmed Mean ( 7 / 18 )1.223935219621590.5142880747652072.37986311500684
Trimmed Mean ( 8 / 18 )1.264293466252620.4871826343019632.59511192976758
Trimmed Mean ( 9 / 18 )1.297444506296600.467853178621592.77318732795444
Trimmed Mean ( 10 / 18 )1.346681688807920.4525721149358612.97561790566522
Trimmed Mean ( 11 / 18 )1.399314492897550.4325311921346783.23517590949103
Trimmed Mean ( 12 / 18 )1.461063727064520.4127910124951523.53947562528795
Trimmed Mean ( 13 / 18 )1.488450485766090.4046702925640143.67818076374025
Trimmed Mean ( 14 / 18 )1.523882972273550.3934278118103803.87334836665796
Trimmed Mean ( 15 / 18 )1.557471410679780.3819583105905164.0775952963869
Trimmed Mean ( 16 / 18 )1.595679149075710.3660535272150244.3591415747741
Trimmed Mean ( 17 / 18 )1.614107075421630.3548842765569324.54826314392287
Trimmed Mean ( 18 / 18 )1.637959408824000.3385090863703344.83874576717284
Median1.66643683533229
Midrange0.86012804714825
Midmean - Weighted Average at Xnp1.38382530970461
Midmean - Weighted Average at X(n+1)p1.52388297227355
Midmean - Empirical Distribution Function1.38382530970461
Midmean - Empirical Distribution Function - Averaging1.52388297227355
Midmean - Empirical Distribution Function - Interpolation1.52388297227355
Midmean - Closest Observation1.38382530970461
Midmean - True Basic - Statistics Graphics Toolkit1.52388297227355
Midmean - MS Excel (old versions)1.48845048576609
Number of observations56



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')