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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 computationTue, 16 Nov 2010 22:16:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t1289945678kjj81c9ds60c9fm.htm/, Retrieved Sun, 05 May 2024 03:27:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=96458, Retrieved Sun, 05 May 2024 03:27:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [] [2010-11-16 22:16:22] [6ff6d3268c67efbfcd6d6506b34b66fb] [Current]
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Dataseries X:
188,7
189,0
 191,0 
192,5 
194,2 
195,6
 197,7
 197,5 
199,9 
201,0
 202,4 
203,4 
204,1
 206,3 
207,3 
206,7 
208,0 
208,6 
208,6 
209,9 
210,3 
211,2 
213,1 
214,5 
214,7 
216,8 
217,3 
217,7 
219,0
 220,9 
220,5 
223,8 
224,8 
226,1 
228,0 
228,0 
229,9 
229,1 
225,8 
223,7 
218,8 
 214,1
  210,2
  204,1
  198,6
  193,6
  188,3
  184,7
  180,5
  176,9
  177,2
  178,7
  180,0
  181,4
  185,0
  187,5
  190,7
  194,9
  197,9
  201,3
  204,7 




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96458&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]1 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=96458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96458&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean204.5360655737701.90353285698809107.450767042394
Geometric Mean203.999816399049
Harmonic Mean203.459391302009
Quadratic Mean205.066838763989
Winsorized Mean ( 1 / 20 )204.5278688524591.89947811519266107.675822751827
Winsorized Mean ( 2 / 20 )204.5409836065571.88030978881356108.780470549812
Winsorized Mean ( 3 / 20 )204.6049180327871.86596116580501109.651219855112
Winsorized Mean ( 4 / 20 )204.5131147540981.83353174595962111.540536565437
Winsorized Mean ( 5 / 20 )204.5622950819671.81281136603398112.842570890044
Winsorized Mean ( 6 / 20 )204.7885245901641.72762368518124118.537692176106
Winsorized Mean ( 7 / 20 )204.7081967213111.69913558074669120.477847112914
Winsorized Mean ( 8 / 20 )205.0229508196721.63565196212902125.346317900544
Winsorized Mean ( 9 / 20 )204.7278688524591.53903335489290133.023672425024
Winsorized Mean ( 10 / 20 )204.7278688524591.51599510349199135.045204553024
Winsorized Mean ( 11 / 20 )204.5114754098361.46061050631273140.017803874436
Winsorized Mean ( 12 / 20 )204.8065573770491.39628873595917146.679230522016
Winsorized Mean ( 13 / 20 )204.6360655737711.34697603596292151.922573312509
Winsorized Mean ( 14 / 20 )204.8885245901641.27516440247402160.676163946114
Winsorized Mean ( 15 / 20 )205.0360655737711.21206375237404169.162773139755
Winsorized Mean ( 16 / 20 )204.6426229508201.10062937537915185.932365179989
Winsorized Mean ( 17 / 20 )204.7819672131151.06157041159779192.904742799768
Winsorized Mean ( 18 / 20 )204.8704918032791.01179206988894202.482800468843
Winsorized Mean ( 19 / 20 )205.1508196721310.876152240404106234.149740434961
Winsorized Mean ( 20 / 20 )204.5934426229510.774998215589199263.992146701147
Trimmed Mean ( 1 / 20 )204.5745762711861.86124552670986109.912729586415
Trimmed Mean ( 2 / 20 )204.6245614035091.81400200180218112.802831088509
Trimmed Mean ( 3 / 20 )204.6709090909091.76812341831838115.756008302614
Trimmed Mean ( 4 / 20 )204.6962264150941.71775278119453119.165125887759
Trimmed Mean ( 5 / 20 )204.7509803921571.66725410639363122.807303102132
Trimmed Mean ( 6 / 20 )204.7979591836731.61043179287081127.169595191978
Trimmed Mean ( 7 / 20 )204.81.56509687068120130.854520149198
Trimmed Mean ( 8 / 20 )204.8177777777781.51471332384155135.218839468796
Trimmed Mean ( 9 / 20 )204.7813953488371.46693439547984139.598196061013
Trimmed Mean ( 10 / 20 )204.7902439024391.43026436613983143.183490234852
Trimmed Mean ( 11 / 20 )204.81.3865509787722147.704630507961
Trimmed Mean ( 12 / 20 )204.8432432432431.34170536310678152.673790293958
Trimmed Mean ( 13 / 20 )204.8485714285711.29738179415619157.893823045208
Trimmed Mean ( 14 / 20 )204.8787878787881.2484972601619164.100310362091
Trimmed Mean ( 15 / 20 )204.8774193548391.19969269969769170.774915448318
Trimmed Mean ( 16 / 20 )204.8551724137931.14748156672893178.525893882343
Trimmed Mean ( 17 / 20 )204.8851851851851.10598866708907185.250709416795
Trimmed Mean ( 18 / 20 )204.91.05399240983984194.403676997195
Trimmed Mean ( 19 / 20 )204.9043478260870.989479806257254207.082900055480
Trimmed Mean ( 20 / 20 )204.8666666666670.94287638268008217.278394527545
Median204.7
Midrange203.4
Midmean - Weighted Average at Xnp204.48
Midmean - Weighted Average at X(n+1)p204.877419354839
Midmean - Empirical Distribution Function204.877419354839
Midmean - Empirical Distribution Function - Averaging204.877419354839
Midmean - Empirical Distribution Function - Interpolation204.877419354839
Midmean - Closest Observation204.490625
Midmean - True Basic - Statistics Graphics Toolkit204.877419354839
Midmean - MS Excel (old versions)204.877419354839
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 204.536065573770 & 1.90353285698809 & 107.450767042394 \tabularnewline
Geometric Mean & 203.999816399049 &  &  \tabularnewline
Harmonic Mean & 203.459391302009 &  &  \tabularnewline
Quadratic Mean & 205.066838763989 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 204.527868852459 & 1.89947811519266 & 107.675822751827 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 204.540983606557 & 1.88030978881356 & 108.780470549812 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 204.604918032787 & 1.86596116580501 & 109.651219855112 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 204.513114754098 & 1.83353174595962 & 111.540536565437 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 204.562295081967 & 1.81281136603398 & 112.842570890044 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 204.788524590164 & 1.72762368518124 & 118.537692176106 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 204.708196721311 & 1.69913558074669 & 120.477847112914 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 205.022950819672 & 1.63565196212902 & 125.346317900544 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 204.727868852459 & 1.53903335489290 & 133.023672425024 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 204.727868852459 & 1.51599510349199 & 135.045204553024 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 204.511475409836 & 1.46061050631273 & 140.017803874436 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 204.806557377049 & 1.39628873595917 & 146.679230522016 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 204.636065573771 & 1.34697603596292 & 151.922573312509 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 204.888524590164 & 1.27516440247402 & 160.676163946114 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 205.036065573771 & 1.21206375237404 & 169.162773139755 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 204.642622950820 & 1.10062937537915 & 185.932365179989 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 204.781967213115 & 1.06157041159779 & 192.904742799768 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 204.870491803279 & 1.01179206988894 & 202.482800468843 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 205.150819672131 & 0.876152240404106 & 234.149740434961 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 204.593442622951 & 0.774998215589199 & 263.992146701147 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 204.574576271186 & 1.86124552670986 & 109.912729586415 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 204.624561403509 & 1.81400200180218 & 112.802831088509 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 204.670909090909 & 1.76812341831838 & 115.756008302614 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 204.696226415094 & 1.71775278119453 & 119.165125887759 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 204.750980392157 & 1.66725410639363 & 122.807303102132 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 204.797959183673 & 1.61043179287081 & 127.169595191978 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 204.8 & 1.56509687068120 & 130.854520149198 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 204.817777777778 & 1.51471332384155 & 135.218839468796 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 204.781395348837 & 1.46693439547984 & 139.598196061013 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 204.790243902439 & 1.43026436613983 & 143.183490234852 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 204.8 & 1.3865509787722 & 147.704630507961 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 204.843243243243 & 1.34170536310678 & 152.673790293958 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 204.848571428571 & 1.29738179415619 & 157.893823045208 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 204.878787878788 & 1.2484972601619 & 164.100310362091 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 204.877419354839 & 1.19969269969769 & 170.774915448318 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 204.855172413793 & 1.14748156672893 & 178.525893882343 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 204.885185185185 & 1.10598866708907 & 185.250709416795 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 204.9 & 1.05399240983984 & 194.403676997195 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 204.904347826087 & 0.989479806257254 & 207.082900055480 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 204.866666666667 & 0.94287638268008 & 217.278394527545 \tabularnewline
Median & 204.7 &  &  \tabularnewline
Midrange & 203.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 204.48 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 204.877419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 204.877419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 204.877419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 204.877419354839 &  &  \tabularnewline
Midmean - Closest Observation & 204.490625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 204.877419354839 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 204.877419354839 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96458&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]204.536065573770[/C][C]1.90353285698809[/C][C]107.450767042394[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]203.999816399049[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]203.459391302009[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]205.066838763989[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]204.527868852459[/C][C]1.89947811519266[/C][C]107.675822751827[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]204.540983606557[/C][C]1.88030978881356[/C][C]108.780470549812[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]204.604918032787[/C][C]1.86596116580501[/C][C]109.651219855112[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]204.513114754098[/C][C]1.83353174595962[/C][C]111.540536565437[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]204.562295081967[/C][C]1.81281136603398[/C][C]112.842570890044[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]204.788524590164[/C][C]1.72762368518124[/C][C]118.537692176106[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]204.708196721311[/C][C]1.69913558074669[/C][C]120.477847112914[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]205.022950819672[/C][C]1.63565196212902[/C][C]125.346317900544[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]204.727868852459[/C][C]1.53903335489290[/C][C]133.023672425024[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]204.727868852459[/C][C]1.51599510349199[/C][C]135.045204553024[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]204.511475409836[/C][C]1.46061050631273[/C][C]140.017803874436[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]204.806557377049[/C][C]1.39628873595917[/C][C]146.679230522016[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]204.636065573771[/C][C]1.34697603596292[/C][C]151.922573312509[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]204.888524590164[/C][C]1.27516440247402[/C][C]160.676163946114[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]205.036065573771[/C][C]1.21206375237404[/C][C]169.162773139755[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]204.642622950820[/C][C]1.10062937537915[/C][C]185.932365179989[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]204.781967213115[/C][C]1.06157041159779[/C][C]192.904742799768[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]204.870491803279[/C][C]1.01179206988894[/C][C]202.482800468843[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]205.150819672131[/C][C]0.876152240404106[/C][C]234.149740434961[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]204.593442622951[/C][C]0.774998215589199[/C][C]263.992146701147[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]204.574576271186[/C][C]1.86124552670986[/C][C]109.912729586415[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]204.624561403509[/C][C]1.81400200180218[/C][C]112.802831088509[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]204.670909090909[/C][C]1.76812341831838[/C][C]115.756008302614[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]204.696226415094[/C][C]1.71775278119453[/C][C]119.165125887759[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]204.750980392157[/C][C]1.66725410639363[/C][C]122.807303102132[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]204.797959183673[/C][C]1.61043179287081[/C][C]127.169595191978[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]204.8[/C][C]1.56509687068120[/C][C]130.854520149198[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]204.817777777778[/C][C]1.51471332384155[/C][C]135.218839468796[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]204.781395348837[/C][C]1.46693439547984[/C][C]139.598196061013[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]204.790243902439[/C][C]1.43026436613983[/C][C]143.183490234852[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]204.8[/C][C]1.3865509787722[/C][C]147.704630507961[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]204.843243243243[/C][C]1.34170536310678[/C][C]152.673790293958[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]204.848571428571[/C][C]1.29738179415619[/C][C]157.893823045208[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]204.878787878788[/C][C]1.2484972601619[/C][C]164.100310362091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]204.877419354839[/C][C]1.19969269969769[/C][C]170.774915448318[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]204.855172413793[/C][C]1.14748156672893[/C][C]178.525893882343[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]204.885185185185[/C][C]1.10598866708907[/C][C]185.250709416795[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]204.9[/C][C]1.05399240983984[/C][C]194.403676997195[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]204.904347826087[/C][C]0.989479806257254[/C][C]207.082900055480[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]204.866666666667[/C][C]0.94287638268008[/C][C]217.278394527545[/C][/ROW]
[ROW][C]Median[/C][C]204.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]203.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]204.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]204.877419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]204.877419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]204.877419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]204.877419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]204.490625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]204.877419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]204.877419354839[/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=96458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96458&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 Mean204.5360655737701.90353285698809107.450767042394
Geometric Mean203.999816399049
Harmonic Mean203.459391302009
Quadratic Mean205.066838763989
Winsorized Mean ( 1 / 20 )204.5278688524591.89947811519266107.675822751827
Winsorized Mean ( 2 / 20 )204.5409836065571.88030978881356108.780470549812
Winsorized Mean ( 3 / 20 )204.6049180327871.86596116580501109.651219855112
Winsorized Mean ( 4 / 20 )204.5131147540981.83353174595962111.540536565437
Winsorized Mean ( 5 / 20 )204.5622950819671.81281136603398112.842570890044
Winsorized Mean ( 6 / 20 )204.7885245901641.72762368518124118.537692176106
Winsorized Mean ( 7 / 20 )204.7081967213111.69913558074669120.477847112914
Winsorized Mean ( 8 / 20 )205.0229508196721.63565196212902125.346317900544
Winsorized Mean ( 9 / 20 )204.7278688524591.53903335489290133.023672425024
Winsorized Mean ( 10 / 20 )204.7278688524591.51599510349199135.045204553024
Winsorized Mean ( 11 / 20 )204.5114754098361.46061050631273140.017803874436
Winsorized Mean ( 12 / 20 )204.8065573770491.39628873595917146.679230522016
Winsorized Mean ( 13 / 20 )204.6360655737711.34697603596292151.922573312509
Winsorized Mean ( 14 / 20 )204.8885245901641.27516440247402160.676163946114
Winsorized Mean ( 15 / 20 )205.0360655737711.21206375237404169.162773139755
Winsorized Mean ( 16 / 20 )204.6426229508201.10062937537915185.932365179989
Winsorized Mean ( 17 / 20 )204.7819672131151.06157041159779192.904742799768
Winsorized Mean ( 18 / 20 )204.8704918032791.01179206988894202.482800468843
Winsorized Mean ( 19 / 20 )205.1508196721310.876152240404106234.149740434961
Winsorized Mean ( 20 / 20 )204.5934426229510.774998215589199263.992146701147
Trimmed Mean ( 1 / 20 )204.5745762711861.86124552670986109.912729586415
Trimmed Mean ( 2 / 20 )204.6245614035091.81400200180218112.802831088509
Trimmed Mean ( 3 / 20 )204.6709090909091.76812341831838115.756008302614
Trimmed Mean ( 4 / 20 )204.6962264150941.71775278119453119.165125887759
Trimmed Mean ( 5 / 20 )204.7509803921571.66725410639363122.807303102132
Trimmed Mean ( 6 / 20 )204.7979591836731.61043179287081127.169595191978
Trimmed Mean ( 7 / 20 )204.81.56509687068120130.854520149198
Trimmed Mean ( 8 / 20 )204.8177777777781.51471332384155135.218839468796
Trimmed Mean ( 9 / 20 )204.7813953488371.46693439547984139.598196061013
Trimmed Mean ( 10 / 20 )204.7902439024391.43026436613983143.183490234852
Trimmed Mean ( 11 / 20 )204.81.3865509787722147.704630507961
Trimmed Mean ( 12 / 20 )204.8432432432431.34170536310678152.673790293958
Trimmed Mean ( 13 / 20 )204.8485714285711.29738179415619157.893823045208
Trimmed Mean ( 14 / 20 )204.8787878787881.2484972601619164.100310362091
Trimmed Mean ( 15 / 20 )204.8774193548391.19969269969769170.774915448318
Trimmed Mean ( 16 / 20 )204.8551724137931.14748156672893178.525893882343
Trimmed Mean ( 17 / 20 )204.8851851851851.10598866708907185.250709416795
Trimmed Mean ( 18 / 20 )204.91.05399240983984194.403676997195
Trimmed Mean ( 19 / 20 )204.9043478260870.989479806257254207.082900055480
Trimmed Mean ( 20 / 20 )204.8666666666670.94287638268008217.278394527545
Median204.7
Midrange203.4
Midmean - Weighted Average at Xnp204.48
Midmean - Weighted Average at X(n+1)p204.877419354839
Midmean - Empirical Distribution Function204.877419354839
Midmean - Empirical Distribution Function - Averaging204.877419354839
Midmean - Empirical Distribution Function - Interpolation204.877419354839
Midmean - Closest Observation204.490625
Midmean - True Basic - Statistics Graphics Toolkit204.877419354839
Midmean - MS Excel (old versions)204.877419354839
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')