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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 computationFri, 26 Dec 2008 10:43:23 -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/2008/Dec/26/t123031344730xsapicu92hprj.htm/, Retrieved Thu, 31 Oct 2024 23:08:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36634, Retrieved Thu, 31 Oct 2024 23:08:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsRobuustheidCentral tendency of electronics
Estimated Impact237
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [WS2 - Central ten...] [2007-10-20 14:57:18] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [paper robuustheid...] [2008-12-26 17:43:23] [3efbb18563b4564408d69b3c9a8e9a6e] [Current]
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Dataseries X:
105.5
106.4
117.9
89.7
88.5
106.4
61.4
92.3
95.5
92.5
89.6
84.3
76.3
80.7
96.3
81.0
82.9
90.3
74.8
70.1
86.7
86.4
89.9
88.1
78.8
81.1
85.4
82.6
80.3
81.2
68.0
67.4
91.3
94.9
82.8
88.6
73.1
76.7
93.2
84.9
83.8
93.5
91.9
69.6
87.0
90.2
82.7
91.4
74.6
76.1
87.1
78.4
81.3
99.3
71.0
73.2
95.6
84.0
90.8
93.6
80.9
84.4
97.3
83.5
88.8
100.7
69.4
74.6
96.6
96.6
93.1
91.8
85.7
79.1
91.3
84.2
85.8
90.0
76.6
81.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36634&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]6 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=36634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36634&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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean85.88251.1071642060299577.5697945546453
Geometric Mean85.3179405010884
Harmonic Mean84.7493592799855
Quadratic Mean86.4444503713223
Winsorized Mean ( 1 / 26 )85.813751.0437286248095582.2184502371567
Winsorized Mean ( 2 / 26 )85.828751.0404268138149282.4937889531056
Winsorized Mean ( 3 / 26 )85.84751.0210412515377584.0783855409451
Winsorized Mean ( 4 / 26 )85.61750.96586318546571388.6435069566478
Winsorized Mean ( 5 / 26 )85.561250.94261200145383890.7703804619871
Winsorized Mean ( 6 / 26 )85.478750.90244340218407694.7192364564094
Winsorized Mean ( 7 / 26 )85.601250.85671305505550299.9182275732384
Winsorized Mean ( 8 / 26 )85.611250.854870620439066100.145271054033
Winsorized Mean ( 9 / 26 )85.7350.82137215389242104.380212542766
Winsorized Mean ( 10 / 26 )85.64750.80742004933984106.075518028103
Winsorized Mean ( 11 / 26 )85.661250.800534816781723107.005027394526
Winsorized Mean ( 12 / 26 )85.766250.754037536733947113.742679670152
Winsorized Mean ( 13 / 26 )85.58750.71758291321754119.271931401262
Winsorized Mean ( 14 / 26 )85.62250.706567238596744121.180965268143
Winsorized Mean ( 15 / 26 )85.5850.695669470839585123.025378556155
Winsorized Mean ( 16 / 26 )85.9050.640052658039392134.215519490450
Winsorized Mean ( 17 / 26 )85.86250.609646543685641140.839804456062
Winsorized Mean ( 18 / 26 )85.8850.593634748974379144.676503773378
Winsorized Mean ( 19 / 26 )86.0750.540714190162454159.187610693441
Winsorized Mean ( 20 / 26 )86.150.523957675360921164.421677649167
Winsorized Mean ( 21 / 26 )86.09750.502890301222136171.205330050637
Winsorized Mean ( 22 / 26 )86.09750.495639131560632173.710053378761
Winsorized Mean ( 23 / 26 )86.126250.491908398613586175.085951455071
Winsorized Mean ( 24 / 26 )86.006250.468310131169181183.652336935947
Winsorized Mean ( 25 / 26 )85.881250.444274738773946193.306624268137
Winsorized Mean ( 26 / 26 )85.848750.440195561222797195.024115557924
Trimmed Mean ( 1 / 26 )85.78589743589741.0096021253007784.9700048029721
Trimmed Mean ( 2 / 26 )85.75657894736840.96961257505581688.4441695101075
Trimmed Mean ( 3 / 26 )85.71756756756760.92451966396811292.715786270744
Trimmed Mean ( 4 / 26 )85.66944444444440.88008668766920697.342052373646
Trimmed Mean ( 5 / 26 )85.68428571428570.848253926283044101.012542423169
Trimmed Mean ( 6 / 26 )85.71323529411770.817799957754504104.809537444178
Trimmed Mean ( 7 / 26 )85.7606060606060.792764125944187108.17922160449
Trimmed Mean ( 8 / 26 )85.78906250.774456149384165110.773298873304
Trimmed Mean ( 9 / 26 )85.81774193548390.752733513907152114.008132160925
Trimmed Mean ( 10 / 26 )85.830.733998029523672116.934918824918
Trimmed Mean ( 11 / 26 )85.85517241379310.714041912266386120.238281449455
Trimmed Mean ( 12 / 26 )85.8803571428570.69092174290852124.298240754927
Trimmed Mean ( 13 / 26 )85.89444444444440.672222222222222127.776859504132
Trimmed Mean ( 14 / 26 )85.93076923076920.65615509275104130.961064205857
Trimmed Mean ( 15 / 26 )85.9660.63803659289852134.735218883712
Trimmed Mean ( 16 / 26 )86.00833333333330.617094206784735139.376342198163
Trimmed Mean ( 17 / 26 )86.01956521739130.60229528416365142.819589459078
Trimmed Mean ( 18 / 26 )86.03636363636360.589182711506336146.02662630137
Trimmed Mean ( 19 / 26 )86.0523809523810.57504469447301149.644682890679
Trimmed Mean ( 20 / 26 )86.050.567348759921633151.670376457482
Trimmed Mean ( 21 / 26 )86.03947368421050.559700939675087153.724011494706
Trimmed Mean ( 22 / 26 )86.03333333333330.552986121700763155.579552464589
Trimmed Mean ( 23 / 26 )86.02647058823530.544152333046766158.092624737202
Trimmed Mean ( 24 / 26 )86.0156250.531414526231186161.861636733994
Trimmed Mean ( 25 / 26 )86.01666666666670.518687187491105165.835341109408
Trimmed Mean ( 26 / 26 )86.03214285714290.50586647263189170.068876890655
Median85.75
Midrange89.65
Midmean - Weighted Average at Xnp85.909756097561
Midmean - Weighted Average at X(n+1)p86.05
Midmean - Empirical Distribution Function85.909756097561
Midmean - Empirical Distribution Function - Averaging86.05
Midmean - Empirical Distribution Function - Interpolation86.05
Midmean - Closest Observation85.909756097561
Midmean - True Basic - Statistics Graphics Toolkit86.05
Midmean - MS Excel (old versions)86.052380952381
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 85.8825 & 1.10716420602995 & 77.5697945546453 \tabularnewline
Geometric Mean & 85.3179405010884 &  &  \tabularnewline
Harmonic Mean & 84.7493592799855 &  &  \tabularnewline
Quadratic Mean & 86.4444503713223 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 85.81375 & 1.04372862480955 & 82.2184502371567 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 85.82875 & 1.04042681381492 & 82.4937889531056 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 85.8475 & 1.02104125153775 & 84.0783855409451 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 85.6175 & 0.965863185465713 & 88.6435069566478 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 85.56125 & 0.942612001453838 & 90.7703804619871 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 85.47875 & 0.902443402184076 & 94.7192364564094 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 85.60125 & 0.856713055055502 & 99.9182275732384 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 85.61125 & 0.854870620439066 & 100.145271054033 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 85.735 & 0.82137215389242 & 104.380212542766 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 85.6475 & 0.80742004933984 & 106.075518028103 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 85.66125 & 0.800534816781723 & 107.005027394526 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 85.76625 & 0.754037536733947 & 113.742679670152 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 85.5875 & 0.71758291321754 & 119.271931401262 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 85.6225 & 0.706567238596744 & 121.180965268143 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 85.585 & 0.695669470839585 & 123.025378556155 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 85.905 & 0.640052658039392 & 134.215519490450 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 85.8625 & 0.609646543685641 & 140.839804456062 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 85.885 & 0.593634748974379 & 144.676503773378 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 86.075 & 0.540714190162454 & 159.187610693441 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 86.15 & 0.523957675360921 & 164.421677649167 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 86.0975 & 0.502890301222136 & 171.205330050637 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 86.0975 & 0.495639131560632 & 173.710053378761 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 86.12625 & 0.491908398613586 & 175.085951455071 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 86.00625 & 0.468310131169181 & 183.652336935947 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 85.88125 & 0.444274738773946 & 193.306624268137 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 85.84875 & 0.440195561222797 & 195.024115557924 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 85.7858974358974 & 1.00960212530077 & 84.9700048029721 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 85.7565789473684 & 0.969612575055816 & 88.4441695101075 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 85.7175675675676 & 0.924519663968112 & 92.715786270744 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 85.6694444444444 & 0.880086687669206 & 97.342052373646 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 85.6842857142857 & 0.848253926283044 & 101.012542423169 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 85.7132352941177 & 0.817799957754504 & 104.809537444178 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 85.760606060606 & 0.792764125944187 & 108.17922160449 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 85.7890625 & 0.774456149384165 & 110.773298873304 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 85.8177419354839 & 0.752733513907152 & 114.008132160925 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 85.83 & 0.733998029523672 & 116.934918824918 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 85.8551724137931 & 0.714041912266386 & 120.238281449455 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 85.880357142857 & 0.69092174290852 & 124.298240754927 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 85.8944444444444 & 0.672222222222222 & 127.776859504132 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 85.9307692307692 & 0.65615509275104 & 130.961064205857 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 85.966 & 0.63803659289852 & 134.735218883712 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 86.0083333333333 & 0.617094206784735 & 139.376342198163 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 86.0195652173913 & 0.60229528416365 & 142.819589459078 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 86.0363636363636 & 0.589182711506336 & 146.02662630137 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 86.052380952381 & 0.57504469447301 & 149.644682890679 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 86.05 & 0.567348759921633 & 151.670376457482 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 86.0394736842105 & 0.559700939675087 & 153.724011494706 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 86.0333333333333 & 0.552986121700763 & 155.579552464589 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 86.0264705882353 & 0.544152333046766 & 158.092624737202 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 86.015625 & 0.531414526231186 & 161.861636733994 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 86.0166666666667 & 0.518687187491105 & 165.835341109408 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 86.0321428571429 & 0.50586647263189 & 170.068876890655 \tabularnewline
Median & 85.75 &  &  \tabularnewline
Midrange & 89.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 85.909756097561 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 86.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 85.909756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 86.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 86.05 &  &  \tabularnewline
Midmean - Closest Observation & 85.909756097561 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 86.05 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 86.052380952381 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36634&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]85.8825[/C][C]1.10716420602995[/C][C]77.5697945546453[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]85.3179405010884[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]84.7493592799855[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]86.4444503713223[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]85.81375[/C][C]1.04372862480955[/C][C]82.2184502371567[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]85.82875[/C][C]1.04042681381492[/C][C]82.4937889531056[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]85.8475[/C][C]1.02104125153775[/C][C]84.0783855409451[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]85.6175[/C][C]0.965863185465713[/C][C]88.6435069566478[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]85.56125[/C][C]0.942612001453838[/C][C]90.7703804619871[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]85.47875[/C][C]0.902443402184076[/C][C]94.7192364564094[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]85.60125[/C][C]0.856713055055502[/C][C]99.9182275732384[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]85.61125[/C][C]0.854870620439066[/C][C]100.145271054033[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]85.735[/C][C]0.82137215389242[/C][C]104.380212542766[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]85.6475[/C][C]0.80742004933984[/C][C]106.075518028103[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]85.66125[/C][C]0.800534816781723[/C][C]107.005027394526[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]85.76625[/C][C]0.754037536733947[/C][C]113.742679670152[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]85.5875[/C][C]0.71758291321754[/C][C]119.271931401262[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]85.6225[/C][C]0.706567238596744[/C][C]121.180965268143[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]85.585[/C][C]0.695669470839585[/C][C]123.025378556155[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]85.905[/C][C]0.640052658039392[/C][C]134.215519490450[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]85.8625[/C][C]0.609646543685641[/C][C]140.839804456062[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]85.885[/C][C]0.593634748974379[/C][C]144.676503773378[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]86.075[/C][C]0.540714190162454[/C][C]159.187610693441[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]86.15[/C][C]0.523957675360921[/C][C]164.421677649167[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]86.0975[/C][C]0.502890301222136[/C][C]171.205330050637[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]86.0975[/C][C]0.495639131560632[/C][C]173.710053378761[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]86.12625[/C][C]0.491908398613586[/C][C]175.085951455071[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]86.00625[/C][C]0.468310131169181[/C][C]183.652336935947[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]85.88125[/C][C]0.444274738773946[/C][C]193.306624268137[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]85.84875[/C][C]0.440195561222797[/C][C]195.024115557924[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]85.7858974358974[/C][C]1.00960212530077[/C][C]84.9700048029721[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]85.7565789473684[/C][C]0.969612575055816[/C][C]88.4441695101075[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]85.7175675675676[/C][C]0.924519663968112[/C][C]92.715786270744[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]85.6694444444444[/C][C]0.880086687669206[/C][C]97.342052373646[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]85.6842857142857[/C][C]0.848253926283044[/C][C]101.012542423169[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]85.7132352941177[/C][C]0.817799957754504[/C][C]104.809537444178[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]85.760606060606[/C][C]0.792764125944187[/C][C]108.17922160449[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]85.7890625[/C][C]0.774456149384165[/C][C]110.773298873304[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]85.8177419354839[/C][C]0.752733513907152[/C][C]114.008132160925[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]85.83[/C][C]0.733998029523672[/C][C]116.934918824918[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]85.8551724137931[/C][C]0.714041912266386[/C][C]120.238281449455[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]85.880357142857[/C][C]0.69092174290852[/C][C]124.298240754927[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]85.8944444444444[/C][C]0.672222222222222[/C][C]127.776859504132[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]85.9307692307692[/C][C]0.65615509275104[/C][C]130.961064205857[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]85.966[/C][C]0.63803659289852[/C][C]134.735218883712[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]86.0083333333333[/C][C]0.617094206784735[/C][C]139.376342198163[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]86.0195652173913[/C][C]0.60229528416365[/C][C]142.819589459078[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]86.0363636363636[/C][C]0.589182711506336[/C][C]146.02662630137[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]86.052380952381[/C][C]0.57504469447301[/C][C]149.644682890679[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]86.05[/C][C]0.567348759921633[/C][C]151.670376457482[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]86.0394736842105[/C][C]0.559700939675087[/C][C]153.724011494706[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]86.0333333333333[/C][C]0.552986121700763[/C][C]155.579552464589[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]86.0264705882353[/C][C]0.544152333046766[/C][C]158.092624737202[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]86.015625[/C][C]0.531414526231186[/C][C]161.861636733994[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]86.0166666666667[/C][C]0.518687187491105[/C][C]165.835341109408[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]86.0321428571429[/C][C]0.50586647263189[/C][C]170.068876890655[/C][/ROW]
[ROW][C]Median[/C][C]85.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]89.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]85.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]86.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]85.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]86.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]86.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]85.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]86.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]86.052380952381[/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=36634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36634&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 Mean85.88251.1071642060299577.5697945546453
Geometric Mean85.3179405010884
Harmonic Mean84.7493592799855
Quadratic Mean86.4444503713223
Winsorized Mean ( 1 / 26 )85.813751.0437286248095582.2184502371567
Winsorized Mean ( 2 / 26 )85.828751.0404268138149282.4937889531056
Winsorized Mean ( 3 / 26 )85.84751.0210412515377584.0783855409451
Winsorized Mean ( 4 / 26 )85.61750.96586318546571388.6435069566478
Winsorized Mean ( 5 / 26 )85.561250.94261200145383890.7703804619871
Winsorized Mean ( 6 / 26 )85.478750.90244340218407694.7192364564094
Winsorized Mean ( 7 / 26 )85.601250.85671305505550299.9182275732384
Winsorized Mean ( 8 / 26 )85.611250.854870620439066100.145271054033
Winsorized Mean ( 9 / 26 )85.7350.82137215389242104.380212542766
Winsorized Mean ( 10 / 26 )85.64750.80742004933984106.075518028103
Winsorized Mean ( 11 / 26 )85.661250.800534816781723107.005027394526
Winsorized Mean ( 12 / 26 )85.766250.754037536733947113.742679670152
Winsorized Mean ( 13 / 26 )85.58750.71758291321754119.271931401262
Winsorized Mean ( 14 / 26 )85.62250.706567238596744121.180965268143
Winsorized Mean ( 15 / 26 )85.5850.695669470839585123.025378556155
Winsorized Mean ( 16 / 26 )85.9050.640052658039392134.215519490450
Winsorized Mean ( 17 / 26 )85.86250.609646543685641140.839804456062
Winsorized Mean ( 18 / 26 )85.8850.593634748974379144.676503773378
Winsorized Mean ( 19 / 26 )86.0750.540714190162454159.187610693441
Winsorized Mean ( 20 / 26 )86.150.523957675360921164.421677649167
Winsorized Mean ( 21 / 26 )86.09750.502890301222136171.205330050637
Winsorized Mean ( 22 / 26 )86.09750.495639131560632173.710053378761
Winsorized Mean ( 23 / 26 )86.126250.491908398613586175.085951455071
Winsorized Mean ( 24 / 26 )86.006250.468310131169181183.652336935947
Winsorized Mean ( 25 / 26 )85.881250.444274738773946193.306624268137
Winsorized Mean ( 26 / 26 )85.848750.440195561222797195.024115557924
Trimmed Mean ( 1 / 26 )85.78589743589741.0096021253007784.9700048029721
Trimmed Mean ( 2 / 26 )85.75657894736840.96961257505581688.4441695101075
Trimmed Mean ( 3 / 26 )85.71756756756760.92451966396811292.715786270744
Trimmed Mean ( 4 / 26 )85.66944444444440.88008668766920697.342052373646
Trimmed Mean ( 5 / 26 )85.68428571428570.848253926283044101.012542423169
Trimmed Mean ( 6 / 26 )85.71323529411770.817799957754504104.809537444178
Trimmed Mean ( 7 / 26 )85.7606060606060.792764125944187108.17922160449
Trimmed Mean ( 8 / 26 )85.78906250.774456149384165110.773298873304
Trimmed Mean ( 9 / 26 )85.81774193548390.752733513907152114.008132160925
Trimmed Mean ( 10 / 26 )85.830.733998029523672116.934918824918
Trimmed Mean ( 11 / 26 )85.85517241379310.714041912266386120.238281449455
Trimmed Mean ( 12 / 26 )85.8803571428570.69092174290852124.298240754927
Trimmed Mean ( 13 / 26 )85.89444444444440.672222222222222127.776859504132
Trimmed Mean ( 14 / 26 )85.93076923076920.65615509275104130.961064205857
Trimmed Mean ( 15 / 26 )85.9660.63803659289852134.735218883712
Trimmed Mean ( 16 / 26 )86.00833333333330.617094206784735139.376342198163
Trimmed Mean ( 17 / 26 )86.01956521739130.60229528416365142.819589459078
Trimmed Mean ( 18 / 26 )86.03636363636360.589182711506336146.02662630137
Trimmed Mean ( 19 / 26 )86.0523809523810.57504469447301149.644682890679
Trimmed Mean ( 20 / 26 )86.050.567348759921633151.670376457482
Trimmed Mean ( 21 / 26 )86.03947368421050.559700939675087153.724011494706
Trimmed Mean ( 22 / 26 )86.03333333333330.552986121700763155.579552464589
Trimmed Mean ( 23 / 26 )86.02647058823530.544152333046766158.092624737202
Trimmed Mean ( 24 / 26 )86.0156250.531414526231186161.861636733994
Trimmed Mean ( 25 / 26 )86.01666666666670.518687187491105165.835341109408
Trimmed Mean ( 26 / 26 )86.03214285714290.50586647263189170.068876890655
Median85.75
Midrange89.65
Midmean - Weighted Average at Xnp85.909756097561
Midmean - Weighted Average at X(n+1)p86.05
Midmean - Empirical Distribution Function85.909756097561
Midmean - Empirical Distribution Function - Averaging86.05
Midmean - Empirical Distribution Function - Interpolation86.05
Midmean - Closest Observation85.909756097561
Midmean - True Basic - Statistics Graphics Toolkit86.05
Midmean - MS Excel (old versions)86.052380952381
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')