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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 computationWed, 21 Oct 2009 09:23:57 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/21/t1256138708ydbkc4j2j7y64qk.htm/, Retrieved Thu, 02 May 2024 03:24:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49417, Retrieved Thu, 02 May 2024 03:24:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsworkshop 3 deel 2.4 central tendency
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3 deel 2...] [2009-10-21 15:23:57] [6198946fb53eb5eb18db46bb758f7fde] [Current]
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Dataseries X:
0,92705025
0,921070695
0,949104768
0,928945683
0,922979649
0,906730594
0,914614988
0,909161955
0,903639
0,903768494
0,900103806
0,915456756
0,948106005
0,93403488
0,931332588
0,923751291
0,9228621
0,934802157
0,942641343
0,960760531
0,982820498
1,003007225
1,031049528
1,08088491
1,082222064
1,08401642
1,0767526
1,078429482
1,080280055
1,08004402
1,091126624
1,083699255
1,06503446
1,05183308
1,034373004
1,0342178
1,009174176
1,01661552
1,030036554
1,05131403
1,066615344
1,063020192
1,067798
1,080772623
1,069072968
1,072696102
1,056834175
1,056627752
1,029580945
1,071080968
1,064087256
1,05000896
1,05544213
1,049496917
1,051364638
1,062857412
1,06406726
1,081659085
1,093903324
1,06348812
1,071258266
1,078983234
1,067478475
1,069441751
1,069204092
1,073095034
1,074490134
1,071738855
1,0829616
1,096770604
1,11241925
1,124652816
1,117678166
1,11727848
1,110210378
1,134913325
1,162971484
1,16872056
1,195685888
1,210769175




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49417&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49417&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.03786305720.00838056667646941123.841632346183
Geometric Mean1.03512986679879
Harmonic Mean1.03233736710047
Quadratic Mean1.04053265370589
Winsorized Mean ( 1 / 26 )1.03771870603750.00832419241742798124.662988792147
Winsorized Mean ( 2 / 26 )1.03704781018750.00817371578114256126.875932312212
Winsorized Mean ( 3 / 26 )1.03694329858750.00810776666628423127.895059301544
Winsorized Mean ( 4 / 26 )1.03566195868750.00783200186789263132.234641430974
Winsorized Mean ( 5 / 26 )1.03536149143750.00766440548095406135.086993245642
Winsorized Mean ( 6 / 26 )1.03490152528750.00757705844667917136.583547899260
Winsorized Mean ( 7 / 26 )1.0353577724250.00747566499362757138.497079966473
Winsorized Mean ( 8 / 26 )1.0350509899250.00737510919001126140.343819089060
Winsorized Mean ( 9 / 26 )1.03481571608750.00733990544975841140.984883684239
Winsorized Mean ( 10 / 26 )1.03323219958750.00711684749056702145.181163563922
Winsorized Mean ( 11 / 26 )1.033291555450.00698507679759298147.928445941506
Winsorized Mean ( 12 / 26 )1.03315936540.00688539848781328150.050772984109
Winsorized Mean ( 13 / 26 )1.03239182931250.00669313395252256154.246401855353
Winsorized Mean ( 14 / 26 )1.03280922653750.00659771138329946156.540528455338
Winsorized Mean ( 15 / 26 )1.03281478066250.00655702228604912157.512775709172
Winsorized Mean ( 16 / 26 )1.03423471066250.00624883045490018165.508524855476
Winsorized Mean ( 17 / 26 )1.03527631830.00602306247077022171.885369498353
Winsorized Mean ( 18 / 26 )1.03532685060.00596500882886122173.566692071042
Winsorized Mean ( 19 / 26 )1.038068426150.00546088562280001190.091589140031
Winsorized Mean ( 20 / 26 )1.04346027590.00447964093665931232.933909358851
Winsorized Mean ( 21 / 26 )1.048697332550.00358908359818983292.190834752056
Winsorized Mean ( 22 / 26 )1.0501015279250.00328628723992296319.540396581285
Winsorized Mean ( 23 / 26 )1.0520817106250.00293591246657695358.349141059933
Winsorized Mean ( 24 / 26 )1.0554682735250.00230119017456342458.661906865322
Winsorized Mean ( 25 / 26 )1.05490363071250.00219959662742122479.589583636185
Winsorized Mean ( 26 / 26 )1.05477943976250.00210194536890781501.811062915765
Trimmed Mean ( 1 / 26 )1.037412456346150.00810959993337186127.923999318030
Trimmed Mean ( 2 / 26 )1.037090088250.0078587814927764131.965762020902
Trimmed Mean ( 3 / 26 )1.037112941256760.00765960954027958135.400236239575
Trimmed Mean ( 4 / 26 )1.0371757718750.00745478106211656139.128937957103
Trimmed Mean ( 5 / 26 )1.037608289928570.00731061514413391141.931734809095
Trimmed Mean ( 6 / 26 )1.038136948397060.00718830958369952144.420177833072
Trimmed Mean ( 7 / 26 )1.038790569227270.0070630075589171147.074820543805
Trimmed Mean ( 8 / 26 )1.039403568656250.00693594729134831149.857478004882
Trimmed Mean ( 9 / 26 )1.040105597483870.00680282733923732152.893134812456
Trimmed Mean ( 10 / 26 )1.040889283616670.00664590943165523156.621045519939
Trimmed Mean ( 11 / 26 )1.041945433137930.00649459707526196160.432652105043
Trimmed Mean ( 12 / 26 )1.043069313357140.00633161337687618164.739893494849
Trimmed Mean ( 13 / 26 )1.044292763722220.00614467417022796169.950876936975
Trimmed Mean ( 14 / 26 )1.045701158326920.00594150333920654175.999422810485
Trimmed Mean ( 15 / 26 )1.047174521960.00569990060607613183.718032002822
Trimmed Mean ( 16 / 26 )1.048770048770830.00539105785057195194.538822962096
Trimmed Mean ( 17 / 26 )1.050349976826090.00506337150943691207.440827691290
Trimmed Mean ( 18 / 26 )1.051962132818180.00468464582807249224.555317824531
Trimmed Mean ( 19 / 26 )1.053722480142860.00417220352715794252.557784701515
Trimmed Mean ( 20 / 26 )1.05537027530.00362444484698701291.181220808844
Trimmed Mean ( 21 / 26 )1.056623959447370.00321684354885635328.466070357391
Trimmed Mean ( 22 / 26 )1.057462755944440.00296819403781052356.26469916518
Trimmed Mean ( 23 / 26 )1.058250053058820.00271734856678972389.442144446357
Trimmed Mean ( 24 / 26 )1.05892052506250.00248580657341059425.98669437487
Trimmed Mean ( 25 / 26 )1.059304108566670.00238447866585479444.249774064103
Trimmed Mean ( 26 / 26 )1.059807020321430.00225735295201755469.491055607501
Median1.06377769
Midrange1.0554364905
Midmean - Weighted Average at Xnp1.05306272056098
Midmean - Weighted Average at X(n+1)p1.0553702753
Midmean - Empirical Distribution Function1.05306272056098
Midmean - Empirical Distribution Function - Averaging1.0553702753
Midmean - Empirical Distribution Function - Interpolation1.0553702753
Midmean - Closest Observation1.05306272056098
Midmean - True Basic - Statistics Graphics Toolkit1.0553702753
Midmean - MS Excel (old versions)1.05372248014286
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.0378630572 & 0.00838056667646941 & 123.841632346183 \tabularnewline
Geometric Mean & 1.03512986679879 &  &  \tabularnewline
Harmonic Mean & 1.03233736710047 &  &  \tabularnewline
Quadratic Mean & 1.04053265370589 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 1.0377187060375 & 0.00832419241742798 & 124.662988792147 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 1.0370478101875 & 0.00817371578114256 & 126.875932312212 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 1.0369432985875 & 0.00810776666628423 & 127.895059301544 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 1.0356619586875 & 0.00783200186789263 & 132.234641430974 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 1.0353614914375 & 0.00766440548095406 & 135.086993245642 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 1.0349015252875 & 0.00757705844667917 & 136.583547899260 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 1.035357772425 & 0.00747566499362757 & 138.497079966473 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 1.035050989925 & 0.00737510919001126 & 140.343819089060 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 1.0348157160875 & 0.00733990544975841 & 140.984883684239 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 1.0332321995875 & 0.00711684749056702 & 145.181163563922 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 1.03329155545 & 0.00698507679759298 & 147.928445941506 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 1.0331593654 & 0.00688539848781328 & 150.050772984109 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 1.0323918293125 & 0.00669313395252256 & 154.246401855353 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 1.0328092265375 & 0.00659771138329946 & 156.540528455338 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 1.0328147806625 & 0.00655702228604912 & 157.512775709172 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 1.0342347106625 & 0.00624883045490018 & 165.508524855476 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 1.0352763183 & 0.00602306247077022 & 171.885369498353 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 1.0353268506 & 0.00596500882886122 & 173.566692071042 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 1.03806842615 & 0.00546088562280001 & 190.091589140031 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 1.0434602759 & 0.00447964093665931 & 232.933909358851 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 1.04869733255 & 0.00358908359818983 & 292.190834752056 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 1.050101527925 & 0.00328628723992296 & 319.540396581285 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 1.052081710625 & 0.00293591246657695 & 358.349141059933 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 1.055468273525 & 0.00230119017456342 & 458.661906865322 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 1.0549036307125 & 0.00219959662742122 & 479.589583636185 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 1.0547794397625 & 0.00210194536890781 & 501.811062915765 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 1.03741245634615 & 0.00810959993337186 & 127.923999318030 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 1.03709008825 & 0.0078587814927764 & 131.965762020902 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 1.03711294125676 & 0.00765960954027958 & 135.400236239575 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 1.037175771875 & 0.00745478106211656 & 139.128937957103 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 1.03760828992857 & 0.00731061514413391 & 141.931734809095 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 1.03813694839706 & 0.00718830958369952 & 144.420177833072 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 1.03879056922727 & 0.0070630075589171 & 147.074820543805 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 1.03940356865625 & 0.00693594729134831 & 149.857478004882 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 1.04010559748387 & 0.00680282733923732 & 152.893134812456 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 1.04088928361667 & 0.00664590943165523 & 156.621045519939 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 1.04194543313793 & 0.00649459707526196 & 160.432652105043 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 1.04306931335714 & 0.00633161337687618 & 164.739893494849 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 1.04429276372222 & 0.00614467417022796 & 169.950876936975 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 1.04570115832692 & 0.00594150333920654 & 175.999422810485 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 1.04717452196 & 0.00569990060607613 & 183.718032002822 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 1.04877004877083 & 0.00539105785057195 & 194.538822962096 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 1.05034997682609 & 0.00506337150943691 & 207.440827691290 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 1.05196213281818 & 0.00468464582807249 & 224.555317824531 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 1.05372248014286 & 0.00417220352715794 & 252.557784701515 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 1.0553702753 & 0.00362444484698701 & 291.181220808844 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 1.05662395944737 & 0.00321684354885635 & 328.466070357391 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 1.05746275594444 & 0.00296819403781052 & 356.26469916518 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 1.05825005305882 & 0.00271734856678972 & 389.442144446357 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 1.0589205250625 & 0.00248580657341059 & 425.98669437487 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 1.05930410856667 & 0.00238447866585479 & 444.249774064103 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 1.05980702032143 & 0.00225735295201755 & 469.491055607501 \tabularnewline
Median & 1.06377769 &  &  \tabularnewline
Midrange & 1.0554364905 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.05306272056098 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.0553702753 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.05306272056098 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.0553702753 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.0553702753 &  &  \tabularnewline
Midmean - Closest Observation & 1.05306272056098 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.0553702753 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.05372248014286 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49417&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]1.0378630572[/C][C]0.00838056667646941[/C][C]123.841632346183[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.03512986679879[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.03233736710047[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.04053265370589[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]1.0377187060375[/C][C]0.00832419241742798[/C][C]124.662988792147[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]1.0370478101875[/C][C]0.00817371578114256[/C][C]126.875932312212[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]1.0369432985875[/C][C]0.00810776666628423[/C][C]127.895059301544[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]1.0356619586875[/C][C]0.00783200186789263[/C][C]132.234641430974[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]1.0353614914375[/C][C]0.00766440548095406[/C][C]135.086993245642[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]1.0349015252875[/C][C]0.00757705844667917[/C][C]136.583547899260[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]1.035357772425[/C][C]0.00747566499362757[/C][C]138.497079966473[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]1.035050989925[/C][C]0.00737510919001126[/C][C]140.343819089060[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]1.0348157160875[/C][C]0.00733990544975841[/C][C]140.984883684239[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]1.0332321995875[/C][C]0.00711684749056702[/C][C]145.181163563922[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]1.03329155545[/C][C]0.00698507679759298[/C][C]147.928445941506[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]1.0331593654[/C][C]0.00688539848781328[/C][C]150.050772984109[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]1.0323918293125[/C][C]0.00669313395252256[/C][C]154.246401855353[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]1.0328092265375[/C][C]0.00659771138329946[/C][C]156.540528455338[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]1.0328147806625[/C][C]0.00655702228604912[/C][C]157.512775709172[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]1.0342347106625[/C][C]0.00624883045490018[/C][C]165.508524855476[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]1.0352763183[/C][C]0.00602306247077022[/C][C]171.885369498353[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]1.0353268506[/C][C]0.00596500882886122[/C][C]173.566692071042[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]1.03806842615[/C][C]0.00546088562280001[/C][C]190.091589140031[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]1.0434602759[/C][C]0.00447964093665931[/C][C]232.933909358851[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]1.04869733255[/C][C]0.00358908359818983[/C][C]292.190834752056[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]1.050101527925[/C][C]0.00328628723992296[/C][C]319.540396581285[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]1.052081710625[/C][C]0.00293591246657695[/C][C]358.349141059933[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]1.055468273525[/C][C]0.00230119017456342[/C][C]458.661906865322[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]1.0549036307125[/C][C]0.00219959662742122[/C][C]479.589583636185[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]1.0547794397625[/C][C]0.00210194536890781[/C][C]501.811062915765[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]1.03741245634615[/C][C]0.00810959993337186[/C][C]127.923999318030[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]1.03709008825[/C][C]0.0078587814927764[/C][C]131.965762020902[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]1.03711294125676[/C][C]0.00765960954027958[/C][C]135.400236239575[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]1.037175771875[/C][C]0.00745478106211656[/C][C]139.128937957103[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]1.03760828992857[/C][C]0.00731061514413391[/C][C]141.931734809095[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]1.03813694839706[/C][C]0.00718830958369952[/C][C]144.420177833072[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]1.03879056922727[/C][C]0.0070630075589171[/C][C]147.074820543805[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]1.03940356865625[/C][C]0.00693594729134831[/C][C]149.857478004882[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]1.04010559748387[/C][C]0.00680282733923732[/C][C]152.893134812456[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]1.04088928361667[/C][C]0.00664590943165523[/C][C]156.621045519939[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]1.04194543313793[/C][C]0.00649459707526196[/C][C]160.432652105043[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]1.04306931335714[/C][C]0.00633161337687618[/C][C]164.739893494849[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]1.04429276372222[/C][C]0.00614467417022796[/C][C]169.950876936975[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]1.04570115832692[/C][C]0.00594150333920654[/C][C]175.999422810485[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]1.04717452196[/C][C]0.00569990060607613[/C][C]183.718032002822[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]1.04877004877083[/C][C]0.00539105785057195[/C][C]194.538822962096[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]1.05034997682609[/C][C]0.00506337150943691[/C][C]207.440827691290[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]1.05196213281818[/C][C]0.00468464582807249[/C][C]224.555317824531[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]1.05372248014286[/C][C]0.00417220352715794[/C][C]252.557784701515[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]1.0553702753[/C][C]0.00362444484698701[/C][C]291.181220808844[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]1.05662395944737[/C][C]0.00321684354885635[/C][C]328.466070357391[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]1.05746275594444[/C][C]0.00296819403781052[/C][C]356.26469916518[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]1.05825005305882[/C][C]0.00271734856678972[/C][C]389.442144446357[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]1.0589205250625[/C][C]0.00248580657341059[/C][C]425.98669437487[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]1.05930410856667[/C][C]0.00238447866585479[/C][C]444.249774064103[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]1.05980702032143[/C][C]0.00225735295201755[/C][C]469.491055607501[/C][/ROW]
[ROW][C]Median[/C][C]1.06377769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.0554364905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.05306272056098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.0553702753[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.05306272056098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.0553702753[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.0553702753[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.05306272056098[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.0553702753[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.05372248014286[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49417&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 Mean1.03786305720.00838056667646941123.841632346183
Geometric Mean1.03512986679879
Harmonic Mean1.03233736710047
Quadratic Mean1.04053265370589
Winsorized Mean ( 1 / 26 )1.03771870603750.00832419241742798124.662988792147
Winsorized Mean ( 2 / 26 )1.03704781018750.00817371578114256126.875932312212
Winsorized Mean ( 3 / 26 )1.03694329858750.00810776666628423127.895059301544
Winsorized Mean ( 4 / 26 )1.03566195868750.00783200186789263132.234641430974
Winsorized Mean ( 5 / 26 )1.03536149143750.00766440548095406135.086993245642
Winsorized Mean ( 6 / 26 )1.03490152528750.00757705844667917136.583547899260
Winsorized Mean ( 7 / 26 )1.0353577724250.00747566499362757138.497079966473
Winsorized Mean ( 8 / 26 )1.0350509899250.00737510919001126140.343819089060
Winsorized Mean ( 9 / 26 )1.03481571608750.00733990544975841140.984883684239
Winsorized Mean ( 10 / 26 )1.03323219958750.00711684749056702145.181163563922
Winsorized Mean ( 11 / 26 )1.033291555450.00698507679759298147.928445941506
Winsorized Mean ( 12 / 26 )1.03315936540.00688539848781328150.050772984109
Winsorized Mean ( 13 / 26 )1.03239182931250.00669313395252256154.246401855353
Winsorized Mean ( 14 / 26 )1.03280922653750.00659771138329946156.540528455338
Winsorized Mean ( 15 / 26 )1.03281478066250.00655702228604912157.512775709172
Winsorized Mean ( 16 / 26 )1.03423471066250.00624883045490018165.508524855476
Winsorized Mean ( 17 / 26 )1.03527631830.00602306247077022171.885369498353
Winsorized Mean ( 18 / 26 )1.03532685060.00596500882886122173.566692071042
Winsorized Mean ( 19 / 26 )1.038068426150.00546088562280001190.091589140031
Winsorized Mean ( 20 / 26 )1.04346027590.00447964093665931232.933909358851
Winsorized Mean ( 21 / 26 )1.048697332550.00358908359818983292.190834752056
Winsorized Mean ( 22 / 26 )1.0501015279250.00328628723992296319.540396581285
Winsorized Mean ( 23 / 26 )1.0520817106250.00293591246657695358.349141059933
Winsorized Mean ( 24 / 26 )1.0554682735250.00230119017456342458.661906865322
Winsorized Mean ( 25 / 26 )1.05490363071250.00219959662742122479.589583636185
Winsorized Mean ( 26 / 26 )1.05477943976250.00210194536890781501.811062915765
Trimmed Mean ( 1 / 26 )1.037412456346150.00810959993337186127.923999318030
Trimmed Mean ( 2 / 26 )1.037090088250.0078587814927764131.965762020902
Trimmed Mean ( 3 / 26 )1.037112941256760.00765960954027958135.400236239575
Trimmed Mean ( 4 / 26 )1.0371757718750.00745478106211656139.128937957103
Trimmed Mean ( 5 / 26 )1.037608289928570.00731061514413391141.931734809095
Trimmed Mean ( 6 / 26 )1.038136948397060.00718830958369952144.420177833072
Trimmed Mean ( 7 / 26 )1.038790569227270.0070630075589171147.074820543805
Trimmed Mean ( 8 / 26 )1.039403568656250.00693594729134831149.857478004882
Trimmed Mean ( 9 / 26 )1.040105597483870.00680282733923732152.893134812456
Trimmed Mean ( 10 / 26 )1.040889283616670.00664590943165523156.621045519939
Trimmed Mean ( 11 / 26 )1.041945433137930.00649459707526196160.432652105043
Trimmed Mean ( 12 / 26 )1.043069313357140.00633161337687618164.739893494849
Trimmed Mean ( 13 / 26 )1.044292763722220.00614467417022796169.950876936975
Trimmed Mean ( 14 / 26 )1.045701158326920.00594150333920654175.999422810485
Trimmed Mean ( 15 / 26 )1.047174521960.00569990060607613183.718032002822
Trimmed Mean ( 16 / 26 )1.048770048770830.00539105785057195194.538822962096
Trimmed Mean ( 17 / 26 )1.050349976826090.00506337150943691207.440827691290
Trimmed Mean ( 18 / 26 )1.051962132818180.00468464582807249224.555317824531
Trimmed Mean ( 19 / 26 )1.053722480142860.00417220352715794252.557784701515
Trimmed Mean ( 20 / 26 )1.05537027530.00362444484698701291.181220808844
Trimmed Mean ( 21 / 26 )1.056623959447370.00321684354885635328.466070357391
Trimmed Mean ( 22 / 26 )1.057462755944440.00296819403781052356.26469916518
Trimmed Mean ( 23 / 26 )1.058250053058820.00271734856678972389.442144446357
Trimmed Mean ( 24 / 26 )1.05892052506250.00248580657341059425.98669437487
Trimmed Mean ( 25 / 26 )1.059304108566670.00238447866585479444.249774064103
Trimmed Mean ( 26 / 26 )1.059807020321430.00225735295201755469.491055607501
Median1.06377769
Midrange1.0554364905
Midmean - Weighted Average at Xnp1.05306272056098
Midmean - Weighted Average at X(n+1)p1.0553702753
Midmean - Empirical Distribution Function1.05306272056098
Midmean - Empirical Distribution Function - Averaging1.0553702753
Midmean - Empirical Distribution Function - Interpolation1.0553702753
Midmean - Closest Observation1.05306272056098
Midmean - True Basic - Statistics Graphics Toolkit1.0553702753
Midmean - MS Excel (old versions)1.05372248014286
Number of observations80



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')