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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Nov 2007 15:04:33 -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/Nov/07/t11944728825mmisapemjxtcm4.htm/, Retrieved Tue, 30 Apr 2024 00:05:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=594, Retrieved Tue, 30 Apr 2024 00:05:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact267
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper stat] [2007-11-07 22:04:33] [0c12eff582f43eaf43ae2f09e879befe] [Current]
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Dataseries X:
0,98
1,00
0,97
1,04
1,02
1,03
1,04
1,00
1,04
1,12
1,21
1,09
1,02
1,03
1,00
1,12
1,05
1,08
1,04
1,09
1,11
0,99
1,20
1,15
1,03
0,98
1,02
1,13
1,03
1,07
1,07
1,09
1,11
1,03
1,20
1,09
1,02
1,08
1,15
1,23
1,14
1,09
1,11
1,17
1,14
1,14
1,28
1,14
1,05
1,09
1,08
1,29
1,19
1,19
1,24
1,23
1,23
1,16
1,39
1,18




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=594&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=594&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=594&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.104666666666670.011388036806120397.0023793805249
Geometric Mean1.10131838313748
Harmonic Mean1.09807946344639
Quadratic Mean1.10812454173707
Winsorized Mean ( 1 / 20 )1.103166666666670.0107527204984023102.594191565807
Winsorized Mean ( 2 / 20 )1.102833333333330.0106566646255580103.487664488230
Winsorized Mean ( 3 / 20 )1.101333333333330.0100435961177020109.655278888826
Winsorized Mean ( 4 / 20 )1.101333333333330.00976985640436739112.727688898376
Winsorized Mean ( 5 / 20 )1.101333333333330.00976985640436739112.727688898376
Winsorized Mean ( 6 / 20 )1.101333333333330.00976985640436739112.727688898376
Winsorized Mean ( 7 / 20 )1.101333333333330.00887918491025123124.035409158088
Winsorized Mean ( 8 / 20 )1.10.00860954666549352127.765147543566
Winsorized Mean ( 9 / 20 )1.10.00860954666549352127.765147543566
Winsorized Mean ( 10 / 20 )1.098333333333330.00828914839821367132.502554010256
Winsorized Mean ( 11 / 20 )1.100166666666670.00800597117081664137.418264841746
Winsorized Mean ( 12 / 20 )1.098166666666670.00763389581723507143.854028527260
Winsorized Mean ( 13 / 20 )1.0960.00724939116866955151.185109825043
Winsorized Mean ( 14 / 20 )1.093666666666670.00685592929356354159.521287317449
Winsorized Mean ( 15 / 20 )1.091166666666670.00645756100721925168.975045755943
Winsorized Mean ( 16 / 20 )1.093833333333330.00604171780613462181.046743398488
Winsorized Mean ( 17 / 20 )1.0910.00560820625522367194.536354468741
Winsorized Mean ( 18 / 20 )1.0910.00560820625522367194.536354468741
Winsorized Mean ( 19 / 20 )1.0910.00560820625522367194.536354468741
Winsorized Mean ( 20 / 20 )1.094333333333330.00510547876021417214.344899808657
Trimmed Mean ( 1 / 20 )1.102068965517240.0104228755720260105.735596467743
Trimmed Mean ( 2 / 20 )1.100892857142860.0100138760406783109.936737050750
Trimmed Mean ( 3 / 20 )1.099814814814810.00956967439968856114.927088308314
Trimmed Mean ( 4 / 20 )1.099230769230770.0093202052434618117.940618314375
Trimmed Mean ( 5 / 20 )1.09860.00911159834989426120.571600921451
Trimmed Mean ( 6 / 20 )1.097916666666670.0088423863016877124.165200343839
Trimmed Mean ( 7 / 20 )1.097173913043480.00849360682265213129.176442464626
Trimmed Mean ( 8 / 20 )1.096363636363640.00830885635838289131.951208334166
Trimmed Mean ( 9 / 20 )1.095714285714290.00813748625774502134.650216419280
Trimmed Mean ( 10 / 20 )1.0950.00790163890822007138.578845821577
Trimmed Mean ( 11 / 20 )1.094473684210530.00767120726014036142.672938834206
Trimmed Mean ( 12 / 20 )1.093611111111110.00742318095699425147.323784432426
Trimmed Mean ( 13 / 20 )1.092941176470590.00718397667129237152.135958464071
Trimmed Mean ( 14 / 20 )1.09250.00695608343640252157.056770521575
Trimmed Mean ( 15 / 20 )1.092333333333330.00674124947205222162.037221417471
Trimmed Mean ( 16 / 20 )1.09250.00653895530707593167.075618152304
Trimmed Mean ( 17 / 20 )1.092307692307690.00635628561849649171.846854887881
Trimmed Mean ( 18 / 20 )1.09250.00620454485128395176.080603200720
Trimmed Mean ( 19 / 20 )1.092727272727270.00592820750603024184.326758403065
Trimmed Mean ( 20 / 20 )1.0930.0054338122703562201.147913401938
Median1.09
Midrange1.18
Midmean - Weighted Average at Xnp1.085
Midmean - Weighted Average at X(n+1)p1.085
Midmean - Empirical Distribution Function1.085
Midmean - Empirical Distribution Function - Averaging1.085
Midmean - Empirical Distribution Function - Interpolation1.085
Midmean - Closest Observation1.085
Midmean - True Basic - Statistics Graphics Toolkit1.085
Midmean - MS Excel (old versions)1.08714285714286
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.10466666666667 & 0.0113880368061203 & 97.0023793805249 \tabularnewline
Geometric Mean & 1.10131838313748 &  &  \tabularnewline
Harmonic Mean & 1.09807946344639 &  &  \tabularnewline
Quadratic Mean & 1.10812454173707 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.10316666666667 & 0.0107527204984023 & 102.594191565807 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.10283333333333 & 0.0106566646255580 & 103.487664488230 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.10133333333333 & 0.0100435961177020 & 109.655278888826 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.10133333333333 & 0.00976985640436739 & 112.727688898376 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.10133333333333 & 0.00976985640436739 & 112.727688898376 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.10133333333333 & 0.00976985640436739 & 112.727688898376 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.10133333333333 & 0.00887918491025123 & 124.035409158088 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.1 & 0.00860954666549352 & 127.765147543566 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.1 & 0.00860954666549352 & 127.765147543566 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.09833333333333 & 0.00828914839821367 & 132.502554010256 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.10016666666667 & 0.00800597117081664 & 137.418264841746 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.09816666666667 & 0.00763389581723507 & 143.854028527260 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.096 & 0.00724939116866955 & 151.185109825043 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.09366666666667 & 0.00685592929356354 & 159.521287317449 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.09116666666667 & 0.00645756100721925 & 168.975045755943 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.09383333333333 & 0.00604171780613462 & 181.046743398488 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.091 & 0.00560820625522367 & 194.536354468741 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.091 & 0.00560820625522367 & 194.536354468741 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.091 & 0.00560820625522367 & 194.536354468741 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.09433333333333 & 0.00510547876021417 & 214.344899808657 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.10206896551724 & 0.0104228755720260 & 105.735596467743 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.10089285714286 & 0.0100138760406783 & 109.936737050750 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.09981481481481 & 0.00956967439968856 & 114.927088308314 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.09923076923077 & 0.0093202052434618 & 117.940618314375 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.0986 & 0.00911159834989426 & 120.571600921451 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.09791666666667 & 0.0088423863016877 & 124.165200343839 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.09717391304348 & 0.00849360682265213 & 129.176442464626 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.09636363636364 & 0.00830885635838289 & 131.951208334166 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.09571428571429 & 0.00813748625774502 & 134.650216419280 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.095 & 0.00790163890822007 & 138.578845821577 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.09447368421053 & 0.00767120726014036 & 142.672938834206 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.09361111111111 & 0.00742318095699425 & 147.323784432426 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.09294117647059 & 0.00718397667129237 & 152.135958464071 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.0925 & 0.00695608343640252 & 157.056770521575 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.09233333333333 & 0.00674124947205222 & 162.037221417471 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.0925 & 0.00653895530707593 & 167.075618152304 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.09230769230769 & 0.00635628561849649 & 171.846854887881 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.0925 & 0.00620454485128395 & 176.080603200720 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.09272727272727 & 0.00592820750603024 & 184.326758403065 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.093 & 0.0054338122703562 & 201.147913401938 \tabularnewline
Median & 1.09 &  &  \tabularnewline
Midrange & 1.18 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.085 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.085 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.085 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.085 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.085 &  &  \tabularnewline
Midmean - Closest Observation & 1.085 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.085 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.08714285714286 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=594&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]1.10466666666667[/C][C]0.0113880368061203[/C][C]97.0023793805249[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.10131838313748[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.09807946344639[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.10812454173707[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.10316666666667[/C][C]0.0107527204984023[/C][C]102.594191565807[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.10283333333333[/C][C]0.0106566646255580[/C][C]103.487664488230[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.10133333333333[/C][C]0.0100435961177020[/C][C]109.655278888826[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.10133333333333[/C][C]0.00976985640436739[/C][C]112.727688898376[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.10133333333333[/C][C]0.00976985640436739[/C][C]112.727688898376[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.10133333333333[/C][C]0.00976985640436739[/C][C]112.727688898376[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.10133333333333[/C][C]0.00887918491025123[/C][C]124.035409158088[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.1[/C][C]0.00860954666549352[/C][C]127.765147543566[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.1[/C][C]0.00860954666549352[/C][C]127.765147543566[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.09833333333333[/C][C]0.00828914839821367[/C][C]132.502554010256[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.10016666666667[/C][C]0.00800597117081664[/C][C]137.418264841746[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.09816666666667[/C][C]0.00763389581723507[/C][C]143.854028527260[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.096[/C][C]0.00724939116866955[/C][C]151.185109825043[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.09366666666667[/C][C]0.00685592929356354[/C][C]159.521287317449[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.09116666666667[/C][C]0.00645756100721925[/C][C]168.975045755943[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.09383333333333[/C][C]0.00604171780613462[/C][C]181.046743398488[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.091[/C][C]0.00560820625522367[/C][C]194.536354468741[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.091[/C][C]0.00560820625522367[/C][C]194.536354468741[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.091[/C][C]0.00560820625522367[/C][C]194.536354468741[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.09433333333333[/C][C]0.00510547876021417[/C][C]214.344899808657[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.10206896551724[/C][C]0.0104228755720260[/C][C]105.735596467743[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.10089285714286[/C][C]0.0100138760406783[/C][C]109.936737050750[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.09981481481481[/C][C]0.00956967439968856[/C][C]114.927088308314[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.09923076923077[/C][C]0.0093202052434618[/C][C]117.940618314375[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.0986[/C][C]0.00911159834989426[/C][C]120.571600921451[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.09791666666667[/C][C]0.0088423863016877[/C][C]124.165200343839[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.09717391304348[/C][C]0.00849360682265213[/C][C]129.176442464626[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.09636363636364[/C][C]0.00830885635838289[/C][C]131.951208334166[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.09571428571429[/C][C]0.00813748625774502[/C][C]134.650216419280[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.095[/C][C]0.00790163890822007[/C][C]138.578845821577[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.09447368421053[/C][C]0.00767120726014036[/C][C]142.672938834206[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.09361111111111[/C][C]0.00742318095699425[/C][C]147.323784432426[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.09294117647059[/C][C]0.00718397667129237[/C][C]152.135958464071[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.0925[/C][C]0.00695608343640252[/C][C]157.056770521575[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.09233333333333[/C][C]0.00674124947205222[/C][C]162.037221417471[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.0925[/C][C]0.00653895530707593[/C][C]167.075618152304[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.09230769230769[/C][C]0.00635628561849649[/C][C]171.846854887881[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.0925[/C][C]0.00620454485128395[/C][C]176.080603200720[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.09272727272727[/C][C]0.00592820750603024[/C][C]184.326758403065[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.093[/C][C]0.0054338122703562[/C][C]201.147913401938[/C][/ROW]
[ROW][C]Median[/C][C]1.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.18[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.08714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=594&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=594&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 Mean1.104666666666670.011388036806120397.0023793805249
Geometric Mean1.10131838313748
Harmonic Mean1.09807946344639
Quadratic Mean1.10812454173707
Winsorized Mean ( 1 / 20 )1.103166666666670.0107527204984023102.594191565807
Winsorized Mean ( 2 / 20 )1.102833333333330.0106566646255580103.487664488230
Winsorized Mean ( 3 / 20 )1.101333333333330.0100435961177020109.655278888826
Winsorized Mean ( 4 / 20 )1.101333333333330.00976985640436739112.727688898376
Winsorized Mean ( 5 / 20 )1.101333333333330.00976985640436739112.727688898376
Winsorized Mean ( 6 / 20 )1.101333333333330.00976985640436739112.727688898376
Winsorized Mean ( 7 / 20 )1.101333333333330.00887918491025123124.035409158088
Winsorized Mean ( 8 / 20 )1.10.00860954666549352127.765147543566
Winsorized Mean ( 9 / 20 )1.10.00860954666549352127.765147543566
Winsorized Mean ( 10 / 20 )1.098333333333330.00828914839821367132.502554010256
Winsorized Mean ( 11 / 20 )1.100166666666670.00800597117081664137.418264841746
Winsorized Mean ( 12 / 20 )1.098166666666670.00763389581723507143.854028527260
Winsorized Mean ( 13 / 20 )1.0960.00724939116866955151.185109825043
Winsorized Mean ( 14 / 20 )1.093666666666670.00685592929356354159.521287317449
Winsorized Mean ( 15 / 20 )1.091166666666670.00645756100721925168.975045755943
Winsorized Mean ( 16 / 20 )1.093833333333330.00604171780613462181.046743398488
Winsorized Mean ( 17 / 20 )1.0910.00560820625522367194.536354468741
Winsorized Mean ( 18 / 20 )1.0910.00560820625522367194.536354468741
Winsorized Mean ( 19 / 20 )1.0910.00560820625522367194.536354468741
Winsorized Mean ( 20 / 20 )1.094333333333330.00510547876021417214.344899808657
Trimmed Mean ( 1 / 20 )1.102068965517240.0104228755720260105.735596467743
Trimmed Mean ( 2 / 20 )1.100892857142860.0100138760406783109.936737050750
Trimmed Mean ( 3 / 20 )1.099814814814810.00956967439968856114.927088308314
Trimmed Mean ( 4 / 20 )1.099230769230770.0093202052434618117.940618314375
Trimmed Mean ( 5 / 20 )1.09860.00911159834989426120.571600921451
Trimmed Mean ( 6 / 20 )1.097916666666670.0088423863016877124.165200343839
Trimmed Mean ( 7 / 20 )1.097173913043480.00849360682265213129.176442464626
Trimmed Mean ( 8 / 20 )1.096363636363640.00830885635838289131.951208334166
Trimmed Mean ( 9 / 20 )1.095714285714290.00813748625774502134.650216419280
Trimmed Mean ( 10 / 20 )1.0950.00790163890822007138.578845821577
Trimmed Mean ( 11 / 20 )1.094473684210530.00767120726014036142.672938834206
Trimmed Mean ( 12 / 20 )1.093611111111110.00742318095699425147.323784432426
Trimmed Mean ( 13 / 20 )1.092941176470590.00718397667129237152.135958464071
Trimmed Mean ( 14 / 20 )1.09250.00695608343640252157.056770521575
Trimmed Mean ( 15 / 20 )1.092333333333330.00674124947205222162.037221417471
Trimmed Mean ( 16 / 20 )1.09250.00653895530707593167.075618152304
Trimmed Mean ( 17 / 20 )1.092307692307690.00635628561849649171.846854887881
Trimmed Mean ( 18 / 20 )1.09250.00620454485128395176.080603200720
Trimmed Mean ( 19 / 20 )1.092727272727270.00592820750603024184.326758403065
Trimmed Mean ( 20 / 20 )1.0930.0054338122703562201.147913401938
Median1.09
Midrange1.18
Midmean - Weighted Average at Xnp1.085
Midmean - Weighted Average at X(n+1)p1.085
Midmean - Empirical Distribution Function1.085
Midmean - Empirical Distribution Function - Averaging1.085
Midmean - Empirical Distribution Function - Interpolation1.085
Midmean - Closest Observation1.085
Midmean - True Basic - Statistics Graphics Toolkit1.085
Midmean - MS Excel (old versions)1.08714285714286
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')