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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 05:23:03 -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/2013/Mar/05/t1362479033zqgriuzt3tpwnkl.htm/, Retrieved Sat, 04 May 2024 15:37:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207361, Retrieved Sat, 04 May 2024 15:37:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten cons...] [2013-03-05 10:23:03] [efa64194dd516a5eefd4f5387836fbaf] [Current]
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Dataseries X:
6,94
6,98
7,05
7,07
7,08
7,10
7,12
7,13
7,18
7,20
7,21
7,22
7,26
7,29
7,32
7,36
7,41
7,48
7,48
7,51
7,51
7,51
7,51
7,54
7,58
7,64
7,63
7,71
7,77
7,85
7,88
7,89
7,94
8,02
8,08
8,15
8,17
8,17
8,25
8,33
8,41
8,43
8,48
8,52
8,56
8,63
8,70
8,72
8,73
8,82
8,83
8,81
8,82
8,83
8,84
8,83
8,82
8,87
8,87
8,87
8,86
8,95
8,94
8,96
8,96
9,01
9,01
8,96
8,96
8,94
8,93
8,89




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=207361&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=207361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207361&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 Mean8.101111111111110.083237399135542497.3253753149999
Geometric Mean8.07039084069182
Harmonic Mean8.03943131317448
Quadratic Mean8.13141575755552
Winsorized Mean ( 1 / 24 )8.101666666666670.083130033705709397.4577575097296
Winsorized Mean ( 2 / 24 )8.102222222222220.08256221209660198.1347521641294
Winsorized Mean ( 3 / 24 )8.103055555555560.082413856692886698.3215187435216
Winsorized Mean ( 4 / 24 )8.103611111111110.0823161644003198.4449551330236
Winsorized Mean ( 5 / 24 )8.1050.082074768386111298.7514209223347
Winsorized Mean ( 6 / 24 )8.105833333333330.081667564908349499.2540103580904
Winsorized Mean ( 7 / 24 )8.105833333333330.081361831669291799.6269770115403
Winsorized Mean ( 8 / 24 )8.111388888888890.0804394973686144100.838383558246
Winsorized Mean ( 9 / 24 )8.112638888888890.0798536398491998101.593852255317
Winsorized Mean ( 10 / 24 )8.108472222222220.0788420351037724102.84453225427
Winsorized Mean ( 11 / 24 )8.106944444444440.0781740061042973103.703837738959
Winsorized Mean ( 12 / 24 )8.113611111111110.0771216103557471105.205416143213
Winsorized Mean ( 13 / 24 )8.119027777777780.0762848113722275106.430462784543
Winsorized Mean ( 14 / 24 )8.122916666666670.0751301524575467108.117931362599
Winsorized Mean ( 15 / 24 )8.127083333333330.0733155755014657110.850706384633
Winsorized Mean ( 16 / 24 )8.135972222222220.0713966580081647113.954524612228
Winsorized Mean ( 17 / 24 )8.15250.0690792195663779118.016677825468
Winsorized Mean ( 18 / 24 )8.15250.0690792195663779118.016677825468
Winsorized Mean ( 19 / 24 )8.157777777777780.0676382321389228120.608973945718
Winsorized Mean ( 20 / 24 )8.157777777777780.0676382321389228120.608973945718
Winsorized Mean ( 21 / 24 )8.157777777777780.0676382321389228120.608973945718
Winsorized Mean ( 22 / 24 )8.154722222222220.0672177842920017121.317926618902
Winsorized Mean ( 23 / 24 )8.138750.0624637414387154130.29558928975
Winsorized Mean ( 24 / 24 )8.148750.0602319906979911135.2894019535
Trimmed Mean ( 1 / 24 )8.104714285714290.082961669272446997.6922759244191
Trimmed Mean ( 2 / 24 )8.107941176470590.082697487263085398.0433800929986
Trimmed Mean ( 3 / 24 )8.111060606060610.082659784881954298.125837342112
Trimmed Mean ( 4 / 24 )8.11406250.082596359896515898.237531413806
Trimmed Mean ( 5 / 24 )8.117096774193550.082468328647223398.4268373973752
Trimmed Mean ( 6 / 24 )8.120.082297517313295798.6664028890233
Trimmed Mean ( 7 / 24 )8.122931034482760.082105169384924598.9332473866649
Trimmed Mean ( 8 / 24 )8.126071428571430.081846656815724399.2840971729252
Trimmed Mean ( 9 / 24 )8.128518518518520.081638277445896499.5674917798882
Trimmed Mean ( 10 / 24 )8.130961538461540.081394918152237299.8951989023905
Trimmed Mean ( 11 / 24 )8.13420.0811776032246957100.202514941035
Trimmed Mean ( 12 / 24 )8.137916666666670.0809057537323375100.585141244584
Trimmed Mean ( 13 / 24 )8.141086956521740.0806376928807335100.95882788416
Trimmed Mean ( 14 / 24 )8.143863636363640.0803140084176282101.400288652211
Trimmed Mean ( 15 / 24 )8.146428571428570.0799686505275512101.870276885839
Trimmed Mean ( 16 / 24 )8.148750.079712775654622102.226398881238
Trimmed Mean ( 17 / 24 )8.150263157894740.0795725483251395102.425564210815
Trimmed Mean ( 18 / 24 )8.150.0796380701814291102.337989625225
Trimmed Mean ( 19 / 24 )8.149705882352940.0794359407313741102.594692116916
Trimmed Mean ( 20 / 24 )8.148750.0791929427248373102.897426457728
Trimmed Mean ( 21 / 24 )8.147666666666670.078511560512447103.776649113667
Trimmed Mean ( 22 / 24 )8.146428571428570.0771863242227168105.542382714359
Trimmed Mean ( 23 / 24 )8.145384615384620.0750245719116914108.569558050558
Trimmed Mean ( 24 / 24 )8.146250.0731085467059035111.42678068503
Median8.16
Midrange7.975
Midmean - Weighted Average at Xnp8.16769230769231
Midmean - Weighted Average at X(n+1)p8.16769230769231
Midmean - Empirical Distribution Function8.16769230769231
Midmean - Empirical Distribution Function - Averaging8.16769230769231
Midmean - Empirical Distribution Function - Interpolation8.16769230769231
Midmean - Closest Observation8.16769230769231
Midmean - True Basic - Statistics Graphics Toolkit8.16769230769231
Midmean - MS Excel (old versions)8.16769230769231
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.10111111111111 & 0.0832373991355424 & 97.3253753149999 \tabularnewline
Geometric Mean & 8.07039084069182 &  &  \tabularnewline
Harmonic Mean & 8.03943131317448 &  &  \tabularnewline
Quadratic Mean & 8.13141575755552 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.10166666666667 & 0.0831300337057093 & 97.4577575097296 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.10222222222222 & 0.082562212096601 & 98.1347521641294 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.10305555555556 & 0.0824138566928866 & 98.3215187435216 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.10361111111111 & 0.08231616440031 & 98.4449551330236 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.105 & 0.0820747683861112 & 98.7514209223347 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.10583333333333 & 0.0816675649083494 & 99.2540103580904 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.10583333333333 & 0.0813618316692917 & 99.6269770115403 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.11138888888889 & 0.0804394973686144 & 100.838383558246 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.11263888888889 & 0.0798536398491998 & 101.593852255317 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.10847222222222 & 0.0788420351037724 & 102.84453225427 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.10694444444444 & 0.0781740061042973 & 103.703837738959 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 8.11361111111111 & 0.0771216103557471 & 105.205416143213 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 8.11902777777778 & 0.0762848113722275 & 106.430462784543 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.12291666666667 & 0.0751301524575467 & 108.117931362599 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.12708333333333 & 0.0733155755014657 & 110.850706384633 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.13597222222222 & 0.0713966580081647 & 113.954524612228 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.1525 & 0.0690792195663779 & 118.016677825468 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.1525 & 0.0690792195663779 & 118.016677825468 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.15777777777778 & 0.0676382321389228 & 120.608973945718 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.15777777777778 & 0.0676382321389228 & 120.608973945718 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.15777777777778 & 0.0676382321389228 & 120.608973945718 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.15472222222222 & 0.0672177842920017 & 121.317926618902 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.13875 & 0.0624637414387154 & 130.29558928975 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.14875 & 0.0602319906979911 & 135.2894019535 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.10471428571429 & 0.0829616692724469 & 97.6922759244191 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.10794117647059 & 0.0826974872630853 & 98.0433800929986 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.11106060606061 & 0.0826597848819542 & 98.125837342112 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.1140625 & 0.0825963598965158 & 98.237531413806 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.11709677419355 & 0.0824683286472233 & 98.4268373973752 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.12 & 0.0822975173132957 & 98.6664028890233 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.12293103448276 & 0.0821051693849245 & 98.9332473866649 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.12607142857143 & 0.0818466568157243 & 99.2840971729252 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.12851851851852 & 0.0816382774458964 & 99.5674917798882 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.13096153846154 & 0.0813949181522372 & 99.8951989023905 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.1342 & 0.0811776032246957 & 100.202514941035 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.13791666666667 & 0.0809057537323375 & 100.585141244584 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.14108695652174 & 0.0806376928807335 & 100.95882788416 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.14386363636364 & 0.0803140084176282 & 101.400288652211 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.14642857142857 & 0.0799686505275512 & 101.870276885839 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.14875 & 0.079712775654622 & 102.226398881238 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.15026315789474 & 0.0795725483251395 & 102.425564210815 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.15 & 0.0796380701814291 & 102.337989625225 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.14970588235294 & 0.0794359407313741 & 102.594692116916 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.14875 & 0.0791929427248373 & 102.897426457728 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.14766666666667 & 0.078511560512447 & 103.776649113667 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.14642857142857 & 0.0771863242227168 & 105.542382714359 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.14538461538462 & 0.0750245719116914 & 108.569558050558 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.14625 & 0.0731085467059035 & 111.42678068503 \tabularnewline
Median & 8.16 &  &  \tabularnewline
Midrange & 7.975 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.16769230769231 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.16769230769231 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.16769230769231 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.16769230769231 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.16769230769231 &  &  \tabularnewline
Midmean - Closest Observation & 8.16769230769231 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.16769230769231 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.16769230769231 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207361&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]8.10111111111111[/C][C]0.0832373991355424[/C][C]97.3253753149999[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.07039084069182[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.03943131317448[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.13141575755552[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.10166666666667[/C][C]0.0831300337057093[/C][C]97.4577575097296[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.10222222222222[/C][C]0.082562212096601[/C][C]98.1347521641294[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.10305555555556[/C][C]0.0824138566928866[/C][C]98.3215187435216[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.10361111111111[/C][C]0.08231616440031[/C][C]98.4449551330236[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.105[/C][C]0.0820747683861112[/C][C]98.7514209223347[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.10583333333333[/C][C]0.0816675649083494[/C][C]99.2540103580904[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.10583333333333[/C][C]0.0813618316692917[/C][C]99.6269770115403[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.11138888888889[/C][C]0.0804394973686144[/C][C]100.838383558246[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.11263888888889[/C][C]0.0798536398491998[/C][C]101.593852255317[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.10847222222222[/C][C]0.0788420351037724[/C][C]102.84453225427[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.10694444444444[/C][C]0.0781740061042973[/C][C]103.703837738959[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]8.11361111111111[/C][C]0.0771216103557471[/C][C]105.205416143213[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]8.11902777777778[/C][C]0.0762848113722275[/C][C]106.430462784543[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.12291666666667[/C][C]0.0751301524575467[/C][C]108.117931362599[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.12708333333333[/C][C]0.0733155755014657[/C][C]110.850706384633[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.13597222222222[/C][C]0.0713966580081647[/C][C]113.954524612228[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.1525[/C][C]0.0690792195663779[/C][C]118.016677825468[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.1525[/C][C]0.0690792195663779[/C][C]118.016677825468[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.15777777777778[/C][C]0.0676382321389228[/C][C]120.608973945718[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.15777777777778[/C][C]0.0676382321389228[/C][C]120.608973945718[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.15777777777778[/C][C]0.0676382321389228[/C][C]120.608973945718[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.15472222222222[/C][C]0.0672177842920017[/C][C]121.317926618902[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.13875[/C][C]0.0624637414387154[/C][C]130.29558928975[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.14875[/C][C]0.0602319906979911[/C][C]135.2894019535[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.10471428571429[/C][C]0.0829616692724469[/C][C]97.6922759244191[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.10794117647059[/C][C]0.0826974872630853[/C][C]98.0433800929986[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.11106060606061[/C][C]0.0826597848819542[/C][C]98.125837342112[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.1140625[/C][C]0.0825963598965158[/C][C]98.237531413806[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.11709677419355[/C][C]0.0824683286472233[/C][C]98.4268373973752[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.12[/C][C]0.0822975173132957[/C][C]98.6664028890233[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.12293103448276[/C][C]0.0821051693849245[/C][C]98.9332473866649[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.12607142857143[/C][C]0.0818466568157243[/C][C]99.2840971729252[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.12851851851852[/C][C]0.0816382774458964[/C][C]99.5674917798882[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.13096153846154[/C][C]0.0813949181522372[/C][C]99.8951989023905[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.1342[/C][C]0.0811776032246957[/C][C]100.202514941035[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.13791666666667[/C][C]0.0809057537323375[/C][C]100.585141244584[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.14108695652174[/C][C]0.0806376928807335[/C][C]100.95882788416[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.14386363636364[/C][C]0.0803140084176282[/C][C]101.400288652211[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.14642857142857[/C][C]0.0799686505275512[/C][C]101.870276885839[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.14875[/C][C]0.079712775654622[/C][C]102.226398881238[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.15026315789474[/C][C]0.0795725483251395[/C][C]102.425564210815[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.15[/C][C]0.0796380701814291[/C][C]102.337989625225[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.14970588235294[/C][C]0.0794359407313741[/C][C]102.594692116916[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.14875[/C][C]0.0791929427248373[/C][C]102.897426457728[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.14766666666667[/C][C]0.078511560512447[/C][C]103.776649113667[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.14642857142857[/C][C]0.0771863242227168[/C][C]105.542382714359[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.14538461538462[/C][C]0.0750245719116914[/C][C]108.569558050558[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.14625[/C][C]0.0731085467059035[/C][C]111.42678068503[/C][/ROW]
[ROW][C]Median[/C][C]8.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.16769230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207361&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 Mean8.101111111111110.083237399135542497.3253753149999
Geometric Mean8.07039084069182
Harmonic Mean8.03943131317448
Quadratic Mean8.13141575755552
Winsorized Mean ( 1 / 24 )8.101666666666670.083130033705709397.4577575097296
Winsorized Mean ( 2 / 24 )8.102222222222220.08256221209660198.1347521641294
Winsorized Mean ( 3 / 24 )8.103055555555560.082413856692886698.3215187435216
Winsorized Mean ( 4 / 24 )8.103611111111110.0823161644003198.4449551330236
Winsorized Mean ( 5 / 24 )8.1050.082074768386111298.7514209223347
Winsorized Mean ( 6 / 24 )8.105833333333330.081667564908349499.2540103580904
Winsorized Mean ( 7 / 24 )8.105833333333330.081361831669291799.6269770115403
Winsorized Mean ( 8 / 24 )8.111388888888890.0804394973686144100.838383558246
Winsorized Mean ( 9 / 24 )8.112638888888890.0798536398491998101.593852255317
Winsorized Mean ( 10 / 24 )8.108472222222220.0788420351037724102.84453225427
Winsorized Mean ( 11 / 24 )8.106944444444440.0781740061042973103.703837738959
Winsorized Mean ( 12 / 24 )8.113611111111110.0771216103557471105.205416143213
Winsorized Mean ( 13 / 24 )8.119027777777780.0762848113722275106.430462784543
Winsorized Mean ( 14 / 24 )8.122916666666670.0751301524575467108.117931362599
Winsorized Mean ( 15 / 24 )8.127083333333330.0733155755014657110.850706384633
Winsorized Mean ( 16 / 24 )8.135972222222220.0713966580081647113.954524612228
Winsorized Mean ( 17 / 24 )8.15250.0690792195663779118.016677825468
Winsorized Mean ( 18 / 24 )8.15250.0690792195663779118.016677825468
Winsorized Mean ( 19 / 24 )8.157777777777780.0676382321389228120.608973945718
Winsorized Mean ( 20 / 24 )8.157777777777780.0676382321389228120.608973945718
Winsorized Mean ( 21 / 24 )8.157777777777780.0676382321389228120.608973945718
Winsorized Mean ( 22 / 24 )8.154722222222220.0672177842920017121.317926618902
Winsorized Mean ( 23 / 24 )8.138750.0624637414387154130.29558928975
Winsorized Mean ( 24 / 24 )8.148750.0602319906979911135.2894019535
Trimmed Mean ( 1 / 24 )8.104714285714290.082961669272446997.6922759244191
Trimmed Mean ( 2 / 24 )8.107941176470590.082697487263085398.0433800929986
Trimmed Mean ( 3 / 24 )8.111060606060610.082659784881954298.125837342112
Trimmed Mean ( 4 / 24 )8.11406250.082596359896515898.237531413806
Trimmed Mean ( 5 / 24 )8.117096774193550.082468328647223398.4268373973752
Trimmed Mean ( 6 / 24 )8.120.082297517313295798.6664028890233
Trimmed Mean ( 7 / 24 )8.122931034482760.082105169384924598.9332473866649
Trimmed Mean ( 8 / 24 )8.126071428571430.081846656815724399.2840971729252
Trimmed Mean ( 9 / 24 )8.128518518518520.081638277445896499.5674917798882
Trimmed Mean ( 10 / 24 )8.130961538461540.081394918152237299.8951989023905
Trimmed Mean ( 11 / 24 )8.13420.0811776032246957100.202514941035
Trimmed Mean ( 12 / 24 )8.137916666666670.0809057537323375100.585141244584
Trimmed Mean ( 13 / 24 )8.141086956521740.0806376928807335100.95882788416
Trimmed Mean ( 14 / 24 )8.143863636363640.0803140084176282101.400288652211
Trimmed Mean ( 15 / 24 )8.146428571428570.0799686505275512101.870276885839
Trimmed Mean ( 16 / 24 )8.148750.079712775654622102.226398881238
Trimmed Mean ( 17 / 24 )8.150263157894740.0795725483251395102.425564210815
Trimmed Mean ( 18 / 24 )8.150.0796380701814291102.337989625225
Trimmed Mean ( 19 / 24 )8.149705882352940.0794359407313741102.594692116916
Trimmed Mean ( 20 / 24 )8.148750.0791929427248373102.897426457728
Trimmed Mean ( 21 / 24 )8.147666666666670.078511560512447103.776649113667
Trimmed Mean ( 22 / 24 )8.146428571428570.0771863242227168105.542382714359
Trimmed Mean ( 23 / 24 )8.145384615384620.0750245719116914108.569558050558
Trimmed Mean ( 24 / 24 )8.146250.0731085467059035111.42678068503
Median8.16
Midrange7.975
Midmean - Weighted Average at Xnp8.16769230769231
Midmean - Weighted Average at X(n+1)p8.16769230769231
Midmean - Empirical Distribution Function8.16769230769231
Midmean - Empirical Distribution Function - Averaging8.16769230769231
Midmean - Empirical Distribution Function - Interpolation8.16769230769231
Midmean - Closest Observation8.16769230769231
Midmean - True Basic - Statistics Graphics Toolkit8.16769230769231
Midmean - MS Excel (old versions)8.16769230769231
Number of observations72



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')