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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 21 Oct 2008 01:30:49 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/21/t1224574280qqcfgd6govr2yqo.htm/, Retrieved Sun, 19 May 2024 20:58:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18358, Retrieved Sun, 19 May 2024 20:58:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [] [2008-10-21 07:26:01] [e3dae385761e8d86216d332d70171419]
F    D    [Central Tendency] [] [2008-10-21 07:30:49] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
Feedback Forum
2008-10-24 11:46:18 [c4ccf1f44d59ce687616256b9e80d6b0] [reply
Deze tijdreeks is minder gevoelig voor outliers. De mediaan, mid-range en mean schommelen ongeveer rond dezelfde waarden.
2008-10-24 16:15:51 [Jan Van Riet] [reply
Hier ga ik niet mee akkoord: op de grafiek van de winsorized mean is duidelijk te zien dat een groot aantal waarden niet binnen het betrouwbaarheidsinterval liggen, dus deze tijdreeks is zeer moeilijk te gebruiken.

Post a new message
Dataseries X:
4,85
4,83
4,83
4,88
4,91
4,93
4,93
4,95
4,95
4,88
4,78
4,61
4,46
4,42
4,43
4,41
4,4
4,36
4,36
4,38
4,4
4,37
4,32
4,18
4,04
4
3,97
3,94
3,93
3,89
3,89
3,88
3,9
3,9
3,95
4,02
4,07
4,17
4,27
4,32
4,38
4,45
4,71
4,96
4,95
4,78
4,78
4,68
4,65
4,64
4,74
4,76
4,61
4,75
4,73
4,68
4,68
4,75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18358&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18358&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18358&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.476551724137930.046358340005770596.5641074201688
Geometric Mean4.4625767179218
Harmonic Mean4.44833821567469
Quadratic Mean4.49021311221455
Winsorized Mean ( 1 / 19 )4.476551724137930.046288471662399696.7098623775531
Winsorized Mean ( 2 / 19 )4.476551724137930.046288471662399696.7098623775531
Winsorized Mean ( 3 / 19 )4.477068965517240.046174272462360496.9602492203161
Winsorized Mean ( 4 / 19 )4.475689655172410.045930661376741297.4444852526955
Winsorized Mean ( 5 / 19 )4.478275862068970.045372117362322698.7010552385585
Winsorized Mean ( 6 / 19 )4.477241379310350.044797584078034599.9438132983082
Winsorized Mean ( 7 / 19 )4.474827586206900.0439443919212166101.829320888758
Winsorized Mean ( 8 / 19 )4.477586206896550.0433721569846598103.236419818369
Winsorized Mean ( 9 / 19 )4.477586206896550.0416821945741185107.422036019111
Winsorized Mean ( 10 / 19 )4.477586206896550.0404596326236459110.667989710804
Winsorized Mean ( 11 / 19 )4.481379310344830.0397134688149412112.842807341443
Winsorized Mean ( 12 / 19 )4.477241379310350.0369666492680003121.115693955687
Winsorized Mean ( 13 / 19 )4.499655172413790.0328141345141168137.125517373558
Winsorized Mean ( 14 / 19 )4.502068965517240.0323908737237233138.991896418648
Winsorized Mean ( 15 / 19 )4.52017241379310.027722035913969163.053407326242
Winsorized Mean ( 16 / 19 )4.531206896551720.0251926366322460179.862352746035
Winsorized Mean ( 17 / 19 )4.531206896551720.0251926366322460179.862352746035
Winsorized Mean ( 18 / 19 )4.540517241379310.0229474035158262197.866274423938
Winsorized Mean ( 19 / 19 )4.537241379310350.0224508512112974202.09663039534
Trimmed Mean ( 1 / 19 )4.478571428571430.045992255539093697.3766425689783
Trimmed Mean ( 2 / 19 )4.480740740740740.045581001114534698.3028154533435
Trimmed Mean ( 3 / 19 )4.483076923076920.045026838369688199.5645505080568
Trimmed Mean ( 4 / 19 )4.48540.0443476157240518101.141852313097
Trimmed Mean ( 5 / 19 )4.488333333333330.043544561561779103.074486740795
Trimmed Mean ( 6 / 19 )4.490869565217390.0426793754702104105.223413317094
Trimmed Mean ( 7 / 19 )4.493863636363640.0417067380509051107.749103535229
Trimmed Mean ( 8 / 19 )4.497619047619050.0406506454282011110.640778276520
Trimmed Mean ( 9 / 19 )4.501250.0393898781414718114.274280916367
Trimmed Mean ( 10 / 19 )4.505263157894740.0381558100180996118.075416450539
Trimmed Mean ( 11 / 19 )4.509722222222220.0367887278093054122.584348270981
Trimmed Mean ( 12 / 19 )4.514117647058820.0350886771887372128.648840843387
Trimmed Mean ( 13 / 19 )4.51968750.0334883356408158134.963037532727
Trimmed Mean ( 14 / 19 )4.522666666666670.0325574058292349138.913606642626
Trimmed Mean ( 15 / 19 )4.525714285714290.0312500944820945144.822419282841
Trimmed Mean ( 16 / 19 )4.526538461538460.0308342582088485146.802249331864
Trimmed Mean ( 17 / 19 )4.525833333333330.0308509546200143146.699944590928
Trimmed Mean ( 18 / 19 )4.5250.0306053640999141147.849899293069
Trimmed Mean ( 19 / 19 )4.52250.0307440623278878147.101575314517
Median4.455
Midrange4.42
Midmean - Weighted Average at Xnp4.51379310344828
Midmean - Weighted Average at X(n+1)p4.53875
Midmean - Empirical Distribution Function4.53875
Midmean - Empirical Distribution Function - Averaging4.53875
Midmean - Empirical Distribution Function - Interpolation4.52571428571429
Midmean - Closest Observation4.53875
Midmean - True Basic - Statistics Graphics Toolkit4.53875
Midmean - MS Excel (old versions)4.53875
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.47655172413793 & 0.0463583400057705 & 96.5641074201688 \tabularnewline
Geometric Mean & 4.4625767179218 &  &  \tabularnewline
Harmonic Mean & 4.44833821567469 &  &  \tabularnewline
Quadratic Mean & 4.49021311221455 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 4.47655172413793 & 0.0462884716623996 & 96.7098623775531 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 4.47655172413793 & 0.0462884716623996 & 96.7098623775531 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 4.47706896551724 & 0.0461742724623604 & 96.9602492203161 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 4.47568965517241 & 0.0459306613767412 & 97.4444852526955 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 4.47827586206897 & 0.0453721173623226 & 98.7010552385585 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 4.47724137931035 & 0.0447975840780345 & 99.9438132983082 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 4.47482758620690 & 0.0439443919212166 & 101.829320888758 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 4.47758620689655 & 0.0433721569846598 & 103.236419818369 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 4.47758620689655 & 0.0416821945741185 & 107.422036019111 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 4.47758620689655 & 0.0404596326236459 & 110.667989710804 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 4.48137931034483 & 0.0397134688149412 & 112.842807341443 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 4.47724137931035 & 0.0369666492680003 & 121.115693955687 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 4.49965517241379 & 0.0328141345141168 & 137.125517373558 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 4.50206896551724 & 0.0323908737237233 & 138.991896418648 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 4.5201724137931 & 0.027722035913969 & 163.053407326242 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 4.53120689655172 & 0.0251926366322460 & 179.862352746035 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 4.53120689655172 & 0.0251926366322460 & 179.862352746035 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 4.54051724137931 & 0.0229474035158262 & 197.866274423938 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 4.53724137931035 & 0.0224508512112974 & 202.09663039534 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 4.47857142857143 & 0.0459922555390936 & 97.3766425689783 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 4.48074074074074 & 0.0455810011145346 & 98.3028154533435 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 4.48307692307692 & 0.0450268383696881 & 99.5645505080568 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 4.4854 & 0.0443476157240518 & 101.141852313097 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 4.48833333333333 & 0.043544561561779 & 103.074486740795 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 4.49086956521739 & 0.0426793754702104 & 105.223413317094 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 4.49386363636364 & 0.0417067380509051 & 107.749103535229 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 4.49761904761905 & 0.0406506454282011 & 110.640778276520 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 4.50125 & 0.0393898781414718 & 114.274280916367 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 4.50526315789474 & 0.0381558100180996 & 118.075416450539 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 4.50972222222222 & 0.0367887278093054 & 122.584348270981 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 4.51411764705882 & 0.0350886771887372 & 128.648840843387 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 4.5196875 & 0.0334883356408158 & 134.963037532727 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 4.52266666666667 & 0.0325574058292349 & 138.913606642626 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 4.52571428571429 & 0.0312500944820945 & 144.822419282841 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 4.52653846153846 & 0.0308342582088485 & 146.802249331864 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 4.52583333333333 & 0.0308509546200143 & 146.699944590928 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 4.525 & 0.0306053640999141 & 147.849899293069 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 4.5225 & 0.0307440623278878 & 147.101575314517 \tabularnewline
Median & 4.455 &  &  \tabularnewline
Midrange & 4.42 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.51379310344828 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.53875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.53875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.53875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.52571428571429 &  &  \tabularnewline
Midmean - Closest Observation & 4.53875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.53875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.53875 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18358&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]4.47655172413793[/C][C]0.0463583400057705[/C][C]96.5641074201688[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.4625767179218[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.44833821567469[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.49021311221455[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]4.47655172413793[/C][C]0.0462884716623996[/C][C]96.7098623775531[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]4.47655172413793[/C][C]0.0462884716623996[/C][C]96.7098623775531[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]4.47706896551724[/C][C]0.0461742724623604[/C][C]96.9602492203161[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]4.47568965517241[/C][C]0.0459306613767412[/C][C]97.4444852526955[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]4.47827586206897[/C][C]0.0453721173623226[/C][C]98.7010552385585[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]4.47724137931035[/C][C]0.0447975840780345[/C][C]99.9438132983082[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]4.47482758620690[/C][C]0.0439443919212166[/C][C]101.829320888758[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]4.47758620689655[/C][C]0.0433721569846598[/C][C]103.236419818369[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]4.47758620689655[/C][C]0.0416821945741185[/C][C]107.422036019111[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]4.47758620689655[/C][C]0.0404596326236459[/C][C]110.667989710804[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]4.48137931034483[/C][C]0.0397134688149412[/C][C]112.842807341443[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]4.47724137931035[/C][C]0.0369666492680003[/C][C]121.115693955687[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]4.49965517241379[/C][C]0.0328141345141168[/C][C]137.125517373558[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]4.50206896551724[/C][C]0.0323908737237233[/C][C]138.991896418648[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]4.5201724137931[/C][C]0.027722035913969[/C][C]163.053407326242[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]4.53120689655172[/C][C]0.0251926366322460[/C][C]179.862352746035[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]4.53120689655172[/C][C]0.0251926366322460[/C][C]179.862352746035[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]4.54051724137931[/C][C]0.0229474035158262[/C][C]197.866274423938[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]4.53724137931035[/C][C]0.0224508512112974[/C][C]202.09663039534[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]4.47857142857143[/C][C]0.0459922555390936[/C][C]97.3766425689783[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]4.48074074074074[/C][C]0.0455810011145346[/C][C]98.3028154533435[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]4.48307692307692[/C][C]0.0450268383696881[/C][C]99.5645505080568[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]4.4854[/C][C]0.0443476157240518[/C][C]101.141852313097[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]4.48833333333333[/C][C]0.043544561561779[/C][C]103.074486740795[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]4.49086956521739[/C][C]0.0426793754702104[/C][C]105.223413317094[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]4.49386363636364[/C][C]0.0417067380509051[/C][C]107.749103535229[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]4.49761904761905[/C][C]0.0406506454282011[/C][C]110.640778276520[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]4.50125[/C][C]0.0393898781414718[/C][C]114.274280916367[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]4.50526315789474[/C][C]0.0381558100180996[/C][C]118.075416450539[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]4.50972222222222[/C][C]0.0367887278093054[/C][C]122.584348270981[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]4.51411764705882[/C][C]0.0350886771887372[/C][C]128.648840843387[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]4.5196875[/C][C]0.0334883356408158[/C][C]134.963037532727[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]4.52266666666667[/C][C]0.0325574058292349[/C][C]138.913606642626[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]4.52571428571429[/C][C]0.0312500944820945[/C][C]144.822419282841[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]4.52653846153846[/C][C]0.0308342582088485[/C][C]146.802249331864[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]4.52583333333333[/C][C]0.0308509546200143[/C][C]146.699944590928[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]4.525[/C][C]0.0306053640999141[/C][C]147.849899293069[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]4.5225[/C][C]0.0307440623278878[/C][C]147.101575314517[/C][/ROW]
[ROW][C]Median[/C][C]4.455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.51379310344828[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.53875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.53875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.53875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.52571428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.53875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.53875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.53875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18358&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18358&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 Mean4.476551724137930.046358340005770596.5641074201688
Geometric Mean4.4625767179218
Harmonic Mean4.44833821567469
Quadratic Mean4.49021311221455
Winsorized Mean ( 1 / 19 )4.476551724137930.046288471662399696.7098623775531
Winsorized Mean ( 2 / 19 )4.476551724137930.046288471662399696.7098623775531
Winsorized Mean ( 3 / 19 )4.477068965517240.046174272462360496.9602492203161
Winsorized Mean ( 4 / 19 )4.475689655172410.045930661376741297.4444852526955
Winsorized Mean ( 5 / 19 )4.478275862068970.045372117362322698.7010552385585
Winsorized Mean ( 6 / 19 )4.477241379310350.044797584078034599.9438132983082
Winsorized Mean ( 7 / 19 )4.474827586206900.0439443919212166101.829320888758
Winsorized Mean ( 8 / 19 )4.477586206896550.0433721569846598103.236419818369
Winsorized Mean ( 9 / 19 )4.477586206896550.0416821945741185107.422036019111
Winsorized Mean ( 10 / 19 )4.477586206896550.0404596326236459110.667989710804
Winsorized Mean ( 11 / 19 )4.481379310344830.0397134688149412112.842807341443
Winsorized Mean ( 12 / 19 )4.477241379310350.0369666492680003121.115693955687
Winsorized Mean ( 13 / 19 )4.499655172413790.0328141345141168137.125517373558
Winsorized Mean ( 14 / 19 )4.502068965517240.0323908737237233138.991896418648
Winsorized Mean ( 15 / 19 )4.52017241379310.027722035913969163.053407326242
Winsorized Mean ( 16 / 19 )4.531206896551720.0251926366322460179.862352746035
Winsorized Mean ( 17 / 19 )4.531206896551720.0251926366322460179.862352746035
Winsorized Mean ( 18 / 19 )4.540517241379310.0229474035158262197.866274423938
Winsorized Mean ( 19 / 19 )4.537241379310350.0224508512112974202.09663039534
Trimmed Mean ( 1 / 19 )4.478571428571430.045992255539093697.3766425689783
Trimmed Mean ( 2 / 19 )4.480740740740740.045581001114534698.3028154533435
Trimmed Mean ( 3 / 19 )4.483076923076920.045026838369688199.5645505080568
Trimmed Mean ( 4 / 19 )4.48540.0443476157240518101.141852313097
Trimmed Mean ( 5 / 19 )4.488333333333330.043544561561779103.074486740795
Trimmed Mean ( 6 / 19 )4.490869565217390.0426793754702104105.223413317094
Trimmed Mean ( 7 / 19 )4.493863636363640.0417067380509051107.749103535229
Trimmed Mean ( 8 / 19 )4.497619047619050.0406506454282011110.640778276520
Trimmed Mean ( 9 / 19 )4.501250.0393898781414718114.274280916367
Trimmed Mean ( 10 / 19 )4.505263157894740.0381558100180996118.075416450539
Trimmed Mean ( 11 / 19 )4.509722222222220.0367887278093054122.584348270981
Trimmed Mean ( 12 / 19 )4.514117647058820.0350886771887372128.648840843387
Trimmed Mean ( 13 / 19 )4.51968750.0334883356408158134.963037532727
Trimmed Mean ( 14 / 19 )4.522666666666670.0325574058292349138.913606642626
Trimmed Mean ( 15 / 19 )4.525714285714290.0312500944820945144.822419282841
Trimmed Mean ( 16 / 19 )4.526538461538460.0308342582088485146.802249331864
Trimmed Mean ( 17 / 19 )4.525833333333330.0308509546200143146.699944590928
Trimmed Mean ( 18 / 19 )4.5250.0306053640999141147.849899293069
Trimmed Mean ( 19 / 19 )4.52250.0307440623278878147.101575314517
Median4.455
Midrange4.42
Midmean - Weighted Average at Xnp4.51379310344828
Midmean - Weighted Average at X(n+1)p4.53875
Midmean - Empirical Distribution Function4.53875
Midmean - Empirical Distribution Function - Averaging4.53875
Midmean - Empirical Distribution Function - Interpolation4.52571428571429
Midmean - Closest Observation4.53875
Midmean - True Basic - Statistics Graphics Toolkit4.53875
Midmean - MS Excel (old versions)4.53875
Number of observations58



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')