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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 15:01:05 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/10/t1197323200a53be8skh1jfy6l.htm/, Retrieved Mon, 06 May 2024 18:39:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3067, Retrieved Mon, 06 May 2024 18:39:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - consumpti...] [2007-12-10 22:01:05] [3463f71ebce131edf0c83e066f45702c] [Current]
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Dataseries X:
108,4
117
103,8
100,8
110,6
104,0
112,6
107,3
98,9
109,8
104,9
102,2
123,9
124,9
112,7
121,9
100,6
104,3
120,4
107,5
102,9
125,6
107,5
108,8
128,4
121,1
119,5
128,7
108,7
105,5
119,8
111,3
110,6
120,1
97,5
107,7
127,3
117,2
119,8
116,2
111,0
112,4
130,6
109,1
118,8
123,9
101,6
112,8
128,0
129,6
125,8
119,5
115,7
113,6
129,7
112,0
116,8
127,0
112,9
113,3
121,7




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=3067&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=3067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3067&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 Mean114.5327868852461.1465765658577699.8910934478789
Geometric Mean114.188285120846
Harmonic Mean113.844135347100
Quadratic Mean114.876618774160
Winsorized Mean ( 1 / 20 )114.5409836065571.13774385376124100.673788065652
Winsorized Mean ( 2 / 20 )114.5934426229511.12484818369069101.874585641383
Winsorized Mean ( 3 / 20 )114.5590163934431.11320778319897102.908925110315
Winsorized Mean ( 4 / 20 )114.5918032786891.09848951205653104.317612522451
Winsorized Mean ( 5 / 20 )114.6081967213111.08212575423972105.910238502578
Winsorized Mean ( 6 / 20 )114.6081967213111.05517277761125108.615573821727
Winsorized Mean ( 7 / 20 )114.6770491803281.02964101506547111.375758640536
Winsorized Mean ( 8 / 20 )114.5459016393440.994461640803711115.183831069411
Winsorized Mean ( 9 / 20 )114.5606557377050.981142633438384116.762488789454
Winsorized Mean ( 10 / 20 )114.5442622950820.942915849006107121.478775031535
Winsorized Mean ( 11 / 20 )114.4721311475410.892222408339338128.299995693455
Winsorized Mean ( 12 / 20 )114.8262295081970.835878849822818137.371856618380
Winsorized Mean ( 13 / 20 )114.4426229508200.755632615999869151.452730503681
Winsorized Mean ( 14 / 20 )114.3967213114750.748123215404292152.911604607343
Winsorized Mean ( 15 / 20 )114.2983606557380.716897885448125159.434646099271
Winsorized Mean ( 16 / 20 )114.2983606557380.660466352060201173.057053246097
Winsorized Mean ( 17 / 20 )114.2983606557380.635302482937584179.911717214187
Winsorized Mean ( 18 / 20 )114.2393442622950.617589526655497184.976168363716
Winsorized Mean ( 19 / 20 )114.3327868852460.60398368464681189.297806863945
Winsorized Mean ( 20 / 20 )114.4639344262300.556526271292486205.675707204975
Trimmed Mean ( 1 / 20 )114.5491525423731.11617503765212102.626513475277
Trimmed Mean ( 2 / 20 )114.5578947368421.08948594304970105.148575314493
Trimmed Mean ( 3 / 20 )114.5381818181821.06485480874041107.562252504326
Trimmed Mean ( 4 / 20 )114.5301886792451.03957114394408110.170611551148
Trimmed Mean ( 5 / 20 )114.5117647058821.01341065388249112.996408975152
Trimmed Mean ( 6 / 20 )114.4877551020410.985721327843466116.146168159427
Trimmed Mean ( 7 / 20 )114.4617021276600.958638378684506119.400291781276
Trimmed Mean ( 8 / 20 )114.420.93092004018182122.910663710336
Trimmed Mean ( 9 / 20 )114.3976744186050.904580985529143126.464823215012
Trimmed Mean ( 10 / 20 )114.3707317073170.873144331253703130.987200641958
Trimmed Mean ( 11 / 20 )114.3435897435900.841611740743008135.862636187374
Trimmed Mean ( 12 / 20 )114.3243243243240.812887979951131140.639703309670
Trimmed Mean ( 13 / 20 )114.2514285714290.788012833455316144.986761282114
Trimmed Mean ( 14 / 20 )114.2242424242420.775354639081544147.318706391630
Trimmed Mean ( 15 / 20 )114.20.757556910811511150.747750261649
Trimmed Mean ( 16 / 20 )114.1862068965520.739336744069512154.444111986156
Trimmed Mean ( 17 / 20 )114.1703703703700.727713799265513156.88911009466
Trimmed Mean ( 18 / 20 )114.1520.714915379607965159.672044071282
Trimmed Mean ( 19 / 20 )114.1391304347830.697418705660615163.659405043727
Trimmed Mean ( 20 / 20 )114.1095238095240.67021335486775170.258504968228
Median112.9
Midrange114.05
Midmean - Weighted Average at Xnp113.97
Midmean - Weighted Average at X(n+1)p114.2
Midmean - Empirical Distribution Function114.2
Midmean - Empirical Distribution Function - Averaging114.2
Midmean - Empirical Distribution Function - Interpolation114.2
Midmean - Closest Observation113.793939393939
Midmean - True Basic - Statistics Graphics Toolkit114.2
Midmean - MS Excel (old versions)114.2
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 114.532786885246 & 1.14657656585776 & 99.8910934478789 \tabularnewline
Geometric Mean & 114.188285120846 &  &  \tabularnewline
Harmonic Mean & 113.844135347100 &  &  \tabularnewline
Quadratic Mean & 114.876618774160 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 114.540983606557 & 1.13774385376124 & 100.673788065652 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 114.593442622951 & 1.12484818369069 & 101.874585641383 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 114.559016393443 & 1.11320778319897 & 102.908925110315 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.591803278689 & 1.09848951205653 & 104.317612522451 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 114.608196721311 & 1.08212575423972 & 105.910238502578 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 114.608196721311 & 1.05517277761125 & 108.615573821727 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 114.677049180328 & 1.02964101506547 & 111.375758640536 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 114.545901639344 & 0.994461640803711 & 115.183831069411 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 114.560655737705 & 0.981142633438384 & 116.762488789454 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 114.544262295082 & 0.942915849006107 & 121.478775031535 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.472131147541 & 0.892222408339338 & 128.299995693455 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 114.826229508197 & 0.835878849822818 & 137.371856618380 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 114.442622950820 & 0.755632615999869 & 151.452730503681 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 114.396721311475 & 0.748123215404292 & 152.911604607343 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 114.298360655738 & 0.716897885448125 & 159.434646099271 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 114.298360655738 & 0.660466352060201 & 173.057053246097 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.298360655738 & 0.635302482937584 & 179.911717214187 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.239344262295 & 0.617589526655497 & 184.976168363716 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.332786885246 & 0.60398368464681 & 189.297806863945 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.463934426230 & 0.556526271292486 & 205.675707204975 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 114.549152542373 & 1.11617503765212 & 102.626513475277 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 114.557894736842 & 1.08948594304970 & 105.148575314493 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 114.538181818182 & 1.06485480874041 & 107.562252504326 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 114.530188679245 & 1.03957114394408 & 110.170611551148 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 114.511764705882 & 1.01341065388249 & 112.996408975152 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.487755102041 & 0.985721327843466 & 116.146168159427 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 114.461702127660 & 0.958638378684506 & 119.400291781276 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 114.42 & 0.93092004018182 & 122.910663710336 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 114.397674418605 & 0.904580985529143 & 126.464823215012 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 114.370731707317 & 0.873144331253703 & 130.987200641958 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 114.343589743590 & 0.841611740743008 & 135.862636187374 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 114.324324324324 & 0.812887979951131 & 140.639703309670 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 114.251428571429 & 0.788012833455316 & 144.986761282114 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.224242424242 & 0.775354639081544 & 147.318706391630 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.2 & 0.757556910811511 & 150.747750261649 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.186206896552 & 0.739336744069512 & 154.444111986156 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.170370370370 & 0.727713799265513 & 156.88911009466 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.152 & 0.714915379607965 & 159.672044071282 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.139130434783 & 0.697418705660615 & 163.659405043727 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.109523809524 & 0.67021335486775 & 170.258504968228 \tabularnewline
Median & 112.9 &  &  \tabularnewline
Midrange & 114.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 113.97 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.2 &  &  \tabularnewline
Midmean - Closest Observation & 113.793939393939 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.2 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.2 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3067&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]114.532786885246[/C][C]1.14657656585776[/C][C]99.8910934478789[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.188285120846[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.844135347100[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.876618774160[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]114.540983606557[/C][C]1.13774385376124[/C][C]100.673788065652[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]114.593442622951[/C][C]1.12484818369069[/C][C]101.874585641383[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]114.559016393443[/C][C]1.11320778319897[/C][C]102.908925110315[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.591803278689[/C][C]1.09848951205653[/C][C]104.317612522451[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]114.608196721311[/C][C]1.08212575423972[/C][C]105.910238502578[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]114.608196721311[/C][C]1.05517277761125[/C][C]108.615573821727[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]114.677049180328[/C][C]1.02964101506547[/C][C]111.375758640536[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]114.545901639344[/C][C]0.994461640803711[/C][C]115.183831069411[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]114.560655737705[/C][C]0.981142633438384[/C][C]116.762488789454[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]114.544262295082[/C][C]0.942915849006107[/C][C]121.478775031535[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.472131147541[/C][C]0.892222408339338[/C][C]128.299995693455[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]114.826229508197[/C][C]0.835878849822818[/C][C]137.371856618380[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]114.442622950820[/C][C]0.755632615999869[/C][C]151.452730503681[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]114.396721311475[/C][C]0.748123215404292[/C][C]152.911604607343[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]114.298360655738[/C][C]0.716897885448125[/C][C]159.434646099271[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]114.298360655738[/C][C]0.660466352060201[/C][C]173.057053246097[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.298360655738[/C][C]0.635302482937584[/C][C]179.911717214187[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.239344262295[/C][C]0.617589526655497[/C][C]184.976168363716[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.332786885246[/C][C]0.60398368464681[/C][C]189.297806863945[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.463934426230[/C][C]0.556526271292486[/C][C]205.675707204975[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]114.549152542373[/C][C]1.11617503765212[/C][C]102.626513475277[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]114.557894736842[/C][C]1.08948594304970[/C][C]105.148575314493[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]114.538181818182[/C][C]1.06485480874041[/C][C]107.562252504326[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]114.530188679245[/C][C]1.03957114394408[/C][C]110.170611551148[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]114.511764705882[/C][C]1.01341065388249[/C][C]112.996408975152[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.487755102041[/C][C]0.985721327843466[/C][C]116.146168159427[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]114.461702127660[/C][C]0.958638378684506[/C][C]119.400291781276[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]114.42[/C][C]0.93092004018182[/C][C]122.910663710336[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]114.397674418605[/C][C]0.904580985529143[/C][C]126.464823215012[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]114.370731707317[/C][C]0.873144331253703[/C][C]130.987200641958[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]114.343589743590[/C][C]0.841611740743008[/C][C]135.862636187374[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]114.324324324324[/C][C]0.812887979951131[/C][C]140.639703309670[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]114.251428571429[/C][C]0.788012833455316[/C][C]144.986761282114[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.224242424242[/C][C]0.775354639081544[/C][C]147.318706391630[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.2[/C][C]0.757556910811511[/C][C]150.747750261649[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.186206896552[/C][C]0.739336744069512[/C][C]154.444111986156[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.170370370370[/C][C]0.727713799265513[/C][C]156.88911009466[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.152[/C][C]0.714915379607965[/C][C]159.672044071282[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.139130434783[/C][C]0.697418705660615[/C][C]163.659405043727[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.109523809524[/C][C]0.67021335486775[/C][C]170.258504968228[/C][/ROW]
[ROW][C]Median[/C][C]112.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]113.97[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.793939393939[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3067&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 Mean114.5327868852461.1465765658577699.8910934478789
Geometric Mean114.188285120846
Harmonic Mean113.844135347100
Quadratic Mean114.876618774160
Winsorized Mean ( 1 / 20 )114.5409836065571.13774385376124100.673788065652
Winsorized Mean ( 2 / 20 )114.5934426229511.12484818369069101.874585641383
Winsorized Mean ( 3 / 20 )114.5590163934431.11320778319897102.908925110315
Winsorized Mean ( 4 / 20 )114.5918032786891.09848951205653104.317612522451
Winsorized Mean ( 5 / 20 )114.6081967213111.08212575423972105.910238502578
Winsorized Mean ( 6 / 20 )114.6081967213111.05517277761125108.615573821727
Winsorized Mean ( 7 / 20 )114.6770491803281.02964101506547111.375758640536
Winsorized Mean ( 8 / 20 )114.5459016393440.994461640803711115.183831069411
Winsorized Mean ( 9 / 20 )114.5606557377050.981142633438384116.762488789454
Winsorized Mean ( 10 / 20 )114.5442622950820.942915849006107121.478775031535
Winsorized Mean ( 11 / 20 )114.4721311475410.892222408339338128.299995693455
Winsorized Mean ( 12 / 20 )114.8262295081970.835878849822818137.371856618380
Winsorized Mean ( 13 / 20 )114.4426229508200.755632615999869151.452730503681
Winsorized Mean ( 14 / 20 )114.3967213114750.748123215404292152.911604607343
Winsorized Mean ( 15 / 20 )114.2983606557380.716897885448125159.434646099271
Winsorized Mean ( 16 / 20 )114.2983606557380.660466352060201173.057053246097
Winsorized Mean ( 17 / 20 )114.2983606557380.635302482937584179.911717214187
Winsorized Mean ( 18 / 20 )114.2393442622950.617589526655497184.976168363716
Winsorized Mean ( 19 / 20 )114.3327868852460.60398368464681189.297806863945
Winsorized Mean ( 20 / 20 )114.4639344262300.556526271292486205.675707204975
Trimmed Mean ( 1 / 20 )114.5491525423731.11617503765212102.626513475277
Trimmed Mean ( 2 / 20 )114.5578947368421.08948594304970105.148575314493
Trimmed Mean ( 3 / 20 )114.5381818181821.06485480874041107.562252504326
Trimmed Mean ( 4 / 20 )114.5301886792451.03957114394408110.170611551148
Trimmed Mean ( 5 / 20 )114.5117647058821.01341065388249112.996408975152
Trimmed Mean ( 6 / 20 )114.4877551020410.985721327843466116.146168159427
Trimmed Mean ( 7 / 20 )114.4617021276600.958638378684506119.400291781276
Trimmed Mean ( 8 / 20 )114.420.93092004018182122.910663710336
Trimmed Mean ( 9 / 20 )114.3976744186050.904580985529143126.464823215012
Trimmed Mean ( 10 / 20 )114.3707317073170.873144331253703130.987200641958
Trimmed Mean ( 11 / 20 )114.3435897435900.841611740743008135.862636187374
Trimmed Mean ( 12 / 20 )114.3243243243240.812887979951131140.639703309670
Trimmed Mean ( 13 / 20 )114.2514285714290.788012833455316144.986761282114
Trimmed Mean ( 14 / 20 )114.2242424242420.775354639081544147.318706391630
Trimmed Mean ( 15 / 20 )114.20.757556910811511150.747750261649
Trimmed Mean ( 16 / 20 )114.1862068965520.739336744069512154.444111986156
Trimmed Mean ( 17 / 20 )114.1703703703700.727713799265513156.88911009466
Trimmed Mean ( 18 / 20 )114.1520.714915379607965159.672044071282
Trimmed Mean ( 19 / 20 )114.1391304347830.697418705660615163.659405043727
Trimmed Mean ( 20 / 20 )114.1095238095240.67021335486775170.258504968228
Median112.9
Midrange114.05
Midmean - Weighted Average at Xnp113.97
Midmean - Weighted Average at X(n+1)p114.2
Midmean - Empirical Distribution Function114.2
Midmean - Empirical Distribution Function - Averaging114.2
Midmean - Empirical Distribution Function - Interpolation114.2
Midmean - Closest Observation113.793939393939
Midmean - True Basic - Statistics Graphics Toolkit114.2
Midmean - MS Excel (old versions)114.2
Number of observations61



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')