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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 10:33:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331134438px2h9e2mmo43i2n.htm/, Retrieved Mon, 29 Apr 2024 05:03:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163622, Retrieved Mon, 29 Apr 2024 05:03:06 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave5Oefening2S...] [2012-03-07 15:33:12] [08dcc0ed4004cc7fccfdee3f5920290a] [Current]
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Dataseries X:
46,83
45,93
45,93
45,93
45,9
45,91
45,85
45,58
45,56
45,5
45,5
45,5
45,51
45,49
45,4
45,38
45,38
45,38
45,49
45,41
44,99
44,98
44,93
44,93
44,91
44,86
44,76
44,89
44,89
45
45,01
45,11
45,05
44,67
44,48
44,48
44,48
44,58
44,79
44,79
44,41
44,41
44,44
44,43
44,36
44,39
44,39
44,41
44,32
44,43
44,82
44,97
44,91
44,79
44,76
44,8
44,65
44,49
44,56
44,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163622&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163622&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean45.0180.06980351762946644.924518546047
Geometric Mean45.0148278966712
Harmonic Mean45.0116764253706
Quadratic Mean45.021192824417
Winsorized Mean ( 1 / 20 )45.00366666666670.0645072442244962697.652910269213
Winsorized Mean ( 2 / 20 )45.00466666666670.0643417195435666699.463225197042
Winsorized Mean ( 3 / 20 )45.00466666666670.0643417195435666699.463225197042
Winsorized Mean ( 4 / 20 )45.0040.0639116621984732704.159435882659
Winsorized Mean ( 5 / 20 )45.0040.063579302320927707.840419085364
Winsorized Mean ( 6 / 20 )44.9990.0624041411779556721.089965354671
Winsorized Mean ( 7 / 20 )44.96750.0557935181420447805.962798142917
Winsorized Mean ( 8 / 20 )44.96750.0548540049987856819.766943197594
Winsorized Mean ( 9 / 20 )44.960.053513818902778840.156821580641
Winsorized Mean ( 10 / 20 )44.960.0529459803588356849.167390900849
Winsorized Mean ( 11 / 20 )44.96733333333330.0517500875659986868.932507137983
Winsorized Mean ( 12 / 20 )44.96733333333330.0517500875659986868.932507137983
Winsorized Mean ( 13 / 20 )44.96516666666670.0513735030665208875.259890462281
Winsorized Mean ( 14 / 20 )44.96750.0510016201138482881.687677756538
Winsorized Mean ( 15 / 20 )44.9650.04484908781643261002.58449367001
Winsorized Mean ( 16 / 20 )44.96766666666670.04359052316709641031.59272703131
Winsorized Mean ( 17 / 20 )44.98183333333330.03973037067595751132.17753995318
Winsorized Mean ( 18 / 20 )44.98783333333330.03889003159472621156.79600886295
Winsorized Mean ( 19 / 20 )45.01633333333330.03514374570992051280.92018719069
Winsorized Mean ( 20 / 20 )44.92633333333330.02000418976830242245.84618790816
Trimmed Mean ( 1 / 20 )44.99879310344830.0637998598472438705.311786126005
Trimmed Mean ( 2 / 20 )44.99357142857140.062885398017815715.485197626086
Trimmed Mean ( 3 / 20 )44.98740740740740.0618174456667539727.746139009462
Trimmed Mean ( 4 / 20 )44.98076923076920.0604444612222405744.166931447784
Trimmed Mean ( 5 / 20 )44.97380.058852905534017764.172976540727
Trimmed Mean ( 6 / 20 )44.966250.0569135410291987790.079991278889
Trimmed Mean ( 7 / 20 )44.95913043478260.0547932663507763820.522911464387
Trimmed Mean ( 8 / 20 )44.95750.0540516206561863831.751193659251
Trimmed Mean ( 9 / 20 )44.95571428571430.0532684813938316843.945858965674
Trimmed Mean ( 10 / 20 )44.9550.0525173963851687856.002069681725
Trimmed Mean ( 11 / 20 )44.95421052631580.0515777135742354871.582073168357
Trimmed Mean ( 12 / 20 )44.95222222222220.0505322639526113889.574673804008
Trimmed Mean ( 13 / 20 )44.950.0490025282188176917.299609507467
Trimmed Mean ( 14 / 20 )44.94781250.0468949890175878958.477940641855
Trimmed Mean ( 15 / 20 )44.9450.04391410110502181023.47535003649
Trimmed Mean ( 16 / 20 )44.94214285714290.04167573597442331078.37670544617
Trimmed Mean ( 17 / 20 )44.93846153846150.03866897905076391162.13209248341
Trimmed Mean ( 18 / 20 )44.93208333333330.03542689536861721268.30428875617
Trimmed Mean ( 19 / 20 )44.92363636363640.03021958207017221486.57371433265
Trimmed Mean ( 20 / 20 )44.9090.02191970994813862048.79535843555
Median44.91
Midrange45.575
Midmean - Weighted Average at Xnp44.9303225806452
Midmean - Weighted Average at X(n+1)p44.945
Midmean - Empirical Distribution Function44.9303225806452
Midmean - Empirical Distribution Function - Averaging44.945
Midmean - Empirical Distribution Function - Interpolation44.945
Midmean - Closest Observation44.9303225806452
Midmean - True Basic - Statistics Graphics Toolkit44.945
Midmean - MS Excel (old versions)44.9642424242424
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 45.018 & 0.06980351762946 & 644.924518546047 \tabularnewline
Geometric Mean & 45.0148278966712 &  &  \tabularnewline
Harmonic Mean & 45.0116764253706 &  &  \tabularnewline
Quadratic Mean & 45.021192824417 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 45.0036666666667 & 0.0645072442244962 & 697.652910269213 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 45.0046666666667 & 0.0643417195435666 & 699.463225197042 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 45.0046666666667 & 0.0643417195435666 & 699.463225197042 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 45.004 & 0.0639116621984732 & 704.159435882659 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 45.004 & 0.063579302320927 & 707.840419085364 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 44.999 & 0.0624041411779556 & 721.089965354671 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 44.9675 & 0.0557935181420447 & 805.962798142917 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 44.9675 & 0.0548540049987856 & 819.766943197594 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 44.96 & 0.053513818902778 & 840.156821580641 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 44.96 & 0.0529459803588356 & 849.167390900849 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 44.9673333333333 & 0.0517500875659986 & 868.932507137983 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 44.9673333333333 & 0.0517500875659986 & 868.932507137983 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 44.9651666666667 & 0.0513735030665208 & 875.259890462281 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 44.9675 & 0.0510016201138482 & 881.687677756538 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 44.965 & 0.0448490878164326 & 1002.58449367001 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 44.9676666666667 & 0.0435905231670964 & 1031.59272703131 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 44.9818333333333 & 0.0397303706759575 & 1132.17753995318 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 44.9878333333333 & 0.0388900315947262 & 1156.79600886295 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 45.0163333333333 & 0.0351437457099205 & 1280.92018719069 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 44.9263333333333 & 0.0200041897683024 & 2245.84618790816 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 44.9987931034483 & 0.0637998598472438 & 705.311786126005 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 44.9935714285714 & 0.062885398017815 & 715.485197626086 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 44.9874074074074 & 0.0618174456667539 & 727.746139009462 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 44.9807692307692 & 0.0604444612222405 & 744.166931447784 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 44.9738 & 0.058852905534017 & 764.172976540727 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 44.96625 & 0.0569135410291987 & 790.079991278889 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 44.9591304347826 & 0.0547932663507763 & 820.522911464387 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 44.9575 & 0.0540516206561863 & 831.751193659251 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 44.9557142857143 & 0.0532684813938316 & 843.945858965674 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 44.955 & 0.0525173963851687 & 856.002069681725 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 44.9542105263158 & 0.0515777135742354 & 871.582073168357 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 44.9522222222222 & 0.0505322639526113 & 889.574673804008 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 44.95 & 0.0490025282188176 & 917.299609507467 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 44.9478125 & 0.0468949890175878 & 958.477940641855 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 44.945 & 0.0439141011050218 & 1023.47535003649 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 44.9421428571429 & 0.0416757359744233 & 1078.37670544617 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 44.9384615384615 & 0.0386689790507639 & 1162.13209248341 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 44.9320833333333 & 0.0354268953686172 & 1268.30428875617 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 44.9236363636364 & 0.0302195820701722 & 1486.57371433265 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 44.909 & 0.0219197099481386 & 2048.79535843555 \tabularnewline
Median & 44.91 &  &  \tabularnewline
Midrange & 45.575 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 44.9303225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 44.945 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 44.9303225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 44.945 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 44.945 &  &  \tabularnewline
Midmean - Closest Observation & 44.9303225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 44.945 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 44.9642424242424 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163622&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]45.018[/C][C]0.06980351762946[/C][C]644.924518546047[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]45.0148278966712[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]45.0116764253706[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]45.021192824417[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]45.0036666666667[/C][C]0.0645072442244962[/C][C]697.652910269213[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]45.0046666666667[/C][C]0.0643417195435666[/C][C]699.463225197042[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]45.0046666666667[/C][C]0.0643417195435666[/C][C]699.463225197042[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]45.004[/C][C]0.0639116621984732[/C][C]704.159435882659[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]45.004[/C][C]0.063579302320927[/C][C]707.840419085364[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]44.999[/C][C]0.0624041411779556[/C][C]721.089965354671[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]44.9675[/C][C]0.0557935181420447[/C][C]805.962798142917[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]44.9675[/C][C]0.0548540049987856[/C][C]819.766943197594[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]44.96[/C][C]0.053513818902778[/C][C]840.156821580641[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]44.96[/C][C]0.0529459803588356[/C][C]849.167390900849[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]44.9673333333333[/C][C]0.0517500875659986[/C][C]868.932507137983[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]44.9673333333333[/C][C]0.0517500875659986[/C][C]868.932507137983[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]44.9651666666667[/C][C]0.0513735030665208[/C][C]875.259890462281[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]44.9675[/C][C]0.0510016201138482[/C][C]881.687677756538[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]44.965[/C][C]0.0448490878164326[/C][C]1002.58449367001[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]44.9676666666667[/C][C]0.0435905231670964[/C][C]1031.59272703131[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]44.9818333333333[/C][C]0.0397303706759575[/C][C]1132.17753995318[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]44.9878333333333[/C][C]0.0388900315947262[/C][C]1156.79600886295[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]45.0163333333333[/C][C]0.0351437457099205[/C][C]1280.92018719069[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]44.9263333333333[/C][C]0.0200041897683024[/C][C]2245.84618790816[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]44.9987931034483[/C][C]0.0637998598472438[/C][C]705.311786126005[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]44.9935714285714[/C][C]0.062885398017815[/C][C]715.485197626086[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]44.9874074074074[/C][C]0.0618174456667539[/C][C]727.746139009462[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]44.9807692307692[/C][C]0.0604444612222405[/C][C]744.166931447784[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]44.9738[/C][C]0.058852905534017[/C][C]764.172976540727[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]44.96625[/C][C]0.0569135410291987[/C][C]790.079991278889[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]44.9591304347826[/C][C]0.0547932663507763[/C][C]820.522911464387[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]44.9575[/C][C]0.0540516206561863[/C][C]831.751193659251[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]44.9557142857143[/C][C]0.0532684813938316[/C][C]843.945858965674[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]44.955[/C][C]0.0525173963851687[/C][C]856.002069681725[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]44.9542105263158[/C][C]0.0515777135742354[/C][C]871.582073168357[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]44.9522222222222[/C][C]0.0505322639526113[/C][C]889.574673804008[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]44.95[/C][C]0.0490025282188176[/C][C]917.299609507467[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]44.9478125[/C][C]0.0468949890175878[/C][C]958.477940641855[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]44.945[/C][C]0.0439141011050218[/C][C]1023.47535003649[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]44.9421428571429[/C][C]0.0416757359744233[/C][C]1078.37670544617[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]44.9384615384615[/C][C]0.0386689790507639[/C][C]1162.13209248341[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]44.9320833333333[/C][C]0.0354268953686172[/C][C]1268.30428875617[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]44.9236363636364[/C][C]0.0302195820701722[/C][C]1486.57371433265[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]44.909[/C][C]0.0219197099481386[/C][C]2048.79535843555[/C][/ROW]
[ROW][C]Median[/C][C]44.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]45.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]44.9303225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]44.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]44.9303225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]44.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]44.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]44.9303225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]44.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]44.9642424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163622&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 Mean45.0180.06980351762946644.924518546047
Geometric Mean45.0148278966712
Harmonic Mean45.0116764253706
Quadratic Mean45.021192824417
Winsorized Mean ( 1 / 20 )45.00366666666670.0645072442244962697.652910269213
Winsorized Mean ( 2 / 20 )45.00466666666670.0643417195435666699.463225197042
Winsorized Mean ( 3 / 20 )45.00466666666670.0643417195435666699.463225197042
Winsorized Mean ( 4 / 20 )45.0040.0639116621984732704.159435882659
Winsorized Mean ( 5 / 20 )45.0040.063579302320927707.840419085364
Winsorized Mean ( 6 / 20 )44.9990.0624041411779556721.089965354671
Winsorized Mean ( 7 / 20 )44.96750.0557935181420447805.962798142917
Winsorized Mean ( 8 / 20 )44.96750.0548540049987856819.766943197594
Winsorized Mean ( 9 / 20 )44.960.053513818902778840.156821580641
Winsorized Mean ( 10 / 20 )44.960.0529459803588356849.167390900849
Winsorized Mean ( 11 / 20 )44.96733333333330.0517500875659986868.932507137983
Winsorized Mean ( 12 / 20 )44.96733333333330.0517500875659986868.932507137983
Winsorized Mean ( 13 / 20 )44.96516666666670.0513735030665208875.259890462281
Winsorized Mean ( 14 / 20 )44.96750.0510016201138482881.687677756538
Winsorized Mean ( 15 / 20 )44.9650.04484908781643261002.58449367001
Winsorized Mean ( 16 / 20 )44.96766666666670.04359052316709641031.59272703131
Winsorized Mean ( 17 / 20 )44.98183333333330.03973037067595751132.17753995318
Winsorized Mean ( 18 / 20 )44.98783333333330.03889003159472621156.79600886295
Winsorized Mean ( 19 / 20 )45.01633333333330.03514374570992051280.92018719069
Winsorized Mean ( 20 / 20 )44.92633333333330.02000418976830242245.84618790816
Trimmed Mean ( 1 / 20 )44.99879310344830.0637998598472438705.311786126005
Trimmed Mean ( 2 / 20 )44.99357142857140.062885398017815715.485197626086
Trimmed Mean ( 3 / 20 )44.98740740740740.0618174456667539727.746139009462
Trimmed Mean ( 4 / 20 )44.98076923076920.0604444612222405744.166931447784
Trimmed Mean ( 5 / 20 )44.97380.058852905534017764.172976540727
Trimmed Mean ( 6 / 20 )44.966250.0569135410291987790.079991278889
Trimmed Mean ( 7 / 20 )44.95913043478260.0547932663507763820.522911464387
Trimmed Mean ( 8 / 20 )44.95750.0540516206561863831.751193659251
Trimmed Mean ( 9 / 20 )44.95571428571430.0532684813938316843.945858965674
Trimmed Mean ( 10 / 20 )44.9550.0525173963851687856.002069681725
Trimmed Mean ( 11 / 20 )44.95421052631580.0515777135742354871.582073168357
Trimmed Mean ( 12 / 20 )44.95222222222220.0505322639526113889.574673804008
Trimmed Mean ( 13 / 20 )44.950.0490025282188176917.299609507467
Trimmed Mean ( 14 / 20 )44.94781250.0468949890175878958.477940641855
Trimmed Mean ( 15 / 20 )44.9450.04391410110502181023.47535003649
Trimmed Mean ( 16 / 20 )44.94214285714290.04167573597442331078.37670544617
Trimmed Mean ( 17 / 20 )44.93846153846150.03866897905076391162.13209248341
Trimmed Mean ( 18 / 20 )44.93208333333330.03542689536861721268.30428875617
Trimmed Mean ( 19 / 20 )44.92363636363640.03021958207017221486.57371433265
Trimmed Mean ( 20 / 20 )44.9090.02191970994813862048.79535843555
Median44.91
Midrange45.575
Midmean - Weighted Average at Xnp44.9303225806452
Midmean - Weighted Average at X(n+1)p44.945
Midmean - Empirical Distribution Function44.9303225806452
Midmean - Empirical Distribution Function - Averaging44.945
Midmean - Empirical Distribution Function - Interpolation44.945
Midmean - Closest Observation44.9303225806452
Midmean - True Basic - Statistics Graphics Toolkit44.945
Midmean - MS Excel (old versions)44.9642424242424
Number of observations60



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