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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 08 Mar 2012 13:32:24 -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/08/t1331231570k0rpfgsxnzkcxyv.htm/, Retrieved Sat, 04 May 2024 08:30:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163813, Retrieved Sat, 04 May 2024 08:30:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Gemi...] [2012-03-08 18:32:24] [189d488a4f2698cd6883783c0210c5ef] [Current]
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Dataseries X:
6.94
6.98
7.05
7.07
7.08
7.1
7.12
7.13
7.18
7.2
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
8.7
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163813&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163813&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163813&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.931833333333330.084175459629077694.2297596981978
Geometric Mean7.90558545066799
Harmonic Mean7.87952431674122
Quadratic Mean7.95814205703819
Winsorized Mean ( 1 / 20 )7.93250.084044857877167194.3841205799107
Winsorized Mean ( 2 / 20 )7.934833333333330.083611453972556394.9012719709165
Winsorized Mean ( 3 / 20 )7.934333333333330.083153036596939295.4184436076913
Winsorized Mean ( 4 / 20 )7.934333333333330.082913530162407695.6940720988709
Winsorized Mean ( 5 / 20 )7.9360.082625080664422196.0483177285078
Winsorized Mean ( 6 / 20 )7.9380.082285090740620196.4694810269122
Winsorized Mean ( 7 / 20 )7.9380.081875542867049296.9520289213819
Winsorized Mean ( 8 / 20 )7.944666666666670.080783055596845998.3457063856948
Winsorized Mean ( 9 / 20 )7.947666666666670.080305689502539998.9676661255153
Winsorized Mean ( 10 / 20 )7.947666666666670.079737339524848499.6730855835735
Winsorized Mean ( 11 / 20 )7.934833333333330.0768171545646212103.295069679498
Winsorized Mean ( 12 / 20 )7.940833333333330.075221440201005105.566090094978
Winsorized Mean ( 13 / 20 )7.9430.07347442769715108.105639593952
Winsorized Mean ( 14 / 20 )7.933666666666670.0696123108578901113.969304694723
Winsorized Mean ( 15 / 20 )7.926166666666670.0652024624620199121.56238226867
Winsorized Mean ( 16 / 20 )7.928833333333330.0615198703220711128.882477999775
Winsorized Mean ( 17 / 20 )7.937333333333330.056910012556581139.471649658167
Winsorized Mean ( 18 / 20 )7.922333333333330.0545134444966113145.328063682085
Winsorized Mean ( 19 / 20 )7.92550.0522215104932066151.766962026711
Winsorized Mean ( 20 / 20 )7.898833333333330.0480960031384186164.230555927917
Trimmed Mean ( 1 / 20 )7.932758620689650.083804641718644394.657747566324
Trimmed Mean ( 2 / 20 )7.933035714285710.083418410112157495.0993396256249
Trimmed Mean ( 3 / 20 )7.932037037037040.083123164588693195.4251089487033
Trimmed Mean ( 4 / 20 )7.931153846153850.082858369159853895.7194056143289
Trimmed Mean ( 5 / 20 )7.93020.082498974638031396.1248310635881
Trimmed Mean ( 6 / 20 )7.928750.082017785326897796.6711057656389
Trimmed Mean ( 7 / 20 )7.926739130434780.081381225118096797.4025534628149
Trimmed Mean ( 8 / 20 )7.924545454545450.080552042548380798.3779579491838
Trimmed Mean ( 9 / 20 )7.920952380952380.079632437787282199.4689174543569
Trimmed Mean ( 10 / 20 )7.91650.0784093057664027100.963781309133
Trimmed Mean ( 11 / 20 )7.911578947368420.0767980543663109103.017960710721
Trimmed Mean ( 12 / 20 )7.908055555555560.0752981580799244105.023227090916
Trimmed Mean ( 13 / 20 )7.903235294117650.0735158811080062107.503782516142
Trimmed Mean ( 14 / 20 )7.89750.0713634495766837110.665894752099
Trimmed Mean ( 15 / 20 )7.892333333333330.0693246292060721113.846023032779
Trimmed Mean ( 16 / 20 )7.88750.0675665946233396116.736680958543
Trimmed Mean ( 17 / 20 )7.881538461538460.0658943030283926119.608799233258
Trimmed Mean ( 18 / 20 )7.873333333333330.0645684297904469121.937816342844
Trimmed Mean ( 19 / 20 )7.865909090909090.0630318379350241124.792634144948
Trimmed Mean ( 20 / 20 )7.85650.0609368741533314128.928503622145
Median7.865
Midrange7.905
Midmean - Weighted Average at Xnp7.87387096774193
Midmean - Weighted Average at X(n+1)p7.89233333333333
Midmean - Empirical Distribution Function7.87387096774193
Midmean - Empirical Distribution Function - Averaging7.89233333333333
Midmean - Empirical Distribution Function - Interpolation7.89233333333333
Midmean - Closest Observation7.87387096774193
Midmean - True Basic - Statistics Graphics Toolkit7.89233333333333
Midmean - MS Excel (old versions)7.8975
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.93183333333333 & 0.0841754596290776 & 94.2297596981978 \tabularnewline
Geometric Mean & 7.90558545066799 &  &  \tabularnewline
Harmonic Mean & 7.87952431674122 &  &  \tabularnewline
Quadratic Mean & 7.95814205703819 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.9325 & 0.0840448578771671 & 94.3841205799107 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.93483333333333 & 0.0836114539725563 & 94.9012719709165 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.93433333333333 & 0.0831530365969392 & 95.4184436076913 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.93433333333333 & 0.0829135301624076 & 95.6940720988709 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.936 & 0.0826250806644221 & 96.0483177285078 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.938 & 0.0822850907406201 & 96.4694810269122 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.938 & 0.0818755428670492 & 96.9520289213819 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.94466666666667 & 0.0807830555968459 & 98.3457063856948 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.94766666666667 & 0.0803056895025399 & 98.9676661255153 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.94766666666667 & 0.0797373395248484 & 99.6730855835735 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.93483333333333 & 0.0768171545646212 & 103.295069679498 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.94083333333333 & 0.075221440201005 & 105.566090094978 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.943 & 0.07347442769715 & 108.105639593952 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.93366666666667 & 0.0696123108578901 & 113.969304694723 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.92616666666667 & 0.0652024624620199 & 121.56238226867 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.92883333333333 & 0.0615198703220711 & 128.882477999775 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.93733333333333 & 0.056910012556581 & 139.471649658167 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.92233333333333 & 0.0545134444966113 & 145.328063682085 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.9255 & 0.0522215104932066 & 151.766962026711 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.89883333333333 & 0.0480960031384186 & 164.230555927917 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.93275862068965 & 0.0838046417186443 & 94.657747566324 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.93303571428571 & 0.0834184101121574 & 95.0993396256249 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.93203703703704 & 0.0831231645886931 & 95.4251089487033 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.93115384615385 & 0.0828583691598538 & 95.7194056143289 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.9302 & 0.0824989746380313 & 96.1248310635881 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.92875 & 0.0820177853268977 & 96.6711057656389 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.92673913043478 & 0.0813812251180967 & 97.4025534628149 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.92454545454545 & 0.0805520425483807 & 98.3779579491838 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.92095238095238 & 0.0796324377872821 & 99.4689174543569 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.9165 & 0.0784093057664027 & 100.963781309133 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.91157894736842 & 0.0767980543663109 & 103.017960710721 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.90805555555556 & 0.0752981580799244 & 105.023227090916 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.90323529411765 & 0.0735158811080062 & 107.503782516142 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.8975 & 0.0713634495766837 & 110.665894752099 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.89233333333333 & 0.0693246292060721 & 113.846023032779 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.8875 & 0.0675665946233396 & 116.736680958543 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.88153846153846 & 0.0658943030283926 & 119.608799233258 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.87333333333333 & 0.0645684297904469 & 121.937816342844 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.86590909090909 & 0.0630318379350241 & 124.792634144948 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.8565 & 0.0609368741533314 & 128.928503622145 \tabularnewline
Median & 7.865 &  &  \tabularnewline
Midrange & 7.905 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.87387096774193 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.89233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.87387096774193 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.89233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.89233333333333 &  &  \tabularnewline
Midmean - Closest Observation & 7.87387096774193 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.89233333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.8975 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163813&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]7.93183333333333[/C][C]0.0841754596290776[/C][C]94.2297596981978[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.90558545066799[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.87952431674122[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.95814205703819[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.9325[/C][C]0.0840448578771671[/C][C]94.3841205799107[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.93483333333333[/C][C]0.0836114539725563[/C][C]94.9012719709165[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.93433333333333[/C][C]0.0831530365969392[/C][C]95.4184436076913[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.93433333333333[/C][C]0.0829135301624076[/C][C]95.6940720988709[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.936[/C][C]0.0826250806644221[/C][C]96.0483177285078[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.938[/C][C]0.0822850907406201[/C][C]96.4694810269122[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.938[/C][C]0.0818755428670492[/C][C]96.9520289213819[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.94466666666667[/C][C]0.0807830555968459[/C][C]98.3457063856948[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.94766666666667[/C][C]0.0803056895025399[/C][C]98.9676661255153[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.94766666666667[/C][C]0.0797373395248484[/C][C]99.6730855835735[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.93483333333333[/C][C]0.0768171545646212[/C][C]103.295069679498[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.94083333333333[/C][C]0.075221440201005[/C][C]105.566090094978[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.943[/C][C]0.07347442769715[/C][C]108.105639593952[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.93366666666667[/C][C]0.0696123108578901[/C][C]113.969304694723[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.92616666666667[/C][C]0.0652024624620199[/C][C]121.56238226867[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.92883333333333[/C][C]0.0615198703220711[/C][C]128.882477999775[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.93733333333333[/C][C]0.056910012556581[/C][C]139.471649658167[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.92233333333333[/C][C]0.0545134444966113[/C][C]145.328063682085[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.9255[/C][C]0.0522215104932066[/C][C]151.766962026711[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.89883333333333[/C][C]0.0480960031384186[/C][C]164.230555927917[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.93275862068965[/C][C]0.0838046417186443[/C][C]94.657747566324[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.93303571428571[/C][C]0.0834184101121574[/C][C]95.0993396256249[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.93203703703704[/C][C]0.0831231645886931[/C][C]95.4251089487033[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.93115384615385[/C][C]0.0828583691598538[/C][C]95.7194056143289[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.9302[/C][C]0.0824989746380313[/C][C]96.1248310635881[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.92875[/C][C]0.0820177853268977[/C][C]96.6711057656389[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.92673913043478[/C][C]0.0813812251180967[/C][C]97.4025534628149[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.92454545454545[/C][C]0.0805520425483807[/C][C]98.3779579491838[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.92095238095238[/C][C]0.0796324377872821[/C][C]99.4689174543569[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.9165[/C][C]0.0784093057664027[/C][C]100.963781309133[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.91157894736842[/C][C]0.0767980543663109[/C][C]103.017960710721[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.90805555555556[/C][C]0.0752981580799244[/C][C]105.023227090916[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.90323529411765[/C][C]0.0735158811080062[/C][C]107.503782516142[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.8975[/C][C]0.0713634495766837[/C][C]110.665894752099[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.89233333333333[/C][C]0.0693246292060721[/C][C]113.846023032779[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.8875[/C][C]0.0675665946233396[/C][C]116.736680958543[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.88153846153846[/C][C]0.0658943030283926[/C][C]119.608799233258[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.87333333333333[/C][C]0.0645684297904469[/C][C]121.937816342844[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.86590909090909[/C][C]0.0630318379350241[/C][C]124.792634144948[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.8565[/C][C]0.0609368741533314[/C][C]128.928503622145[/C][/ROW]
[ROW][C]Median[/C][C]7.865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.87387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.89233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.87387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.89233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.89233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.87387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.89233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.8975[/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=163813&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163813&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 Mean7.931833333333330.084175459629077694.2297596981978
Geometric Mean7.90558545066799
Harmonic Mean7.87952431674122
Quadratic Mean7.95814205703819
Winsorized Mean ( 1 / 20 )7.93250.084044857877167194.3841205799107
Winsorized Mean ( 2 / 20 )7.934833333333330.083611453972556394.9012719709165
Winsorized Mean ( 3 / 20 )7.934333333333330.083153036596939295.4184436076913
Winsorized Mean ( 4 / 20 )7.934333333333330.082913530162407695.6940720988709
Winsorized Mean ( 5 / 20 )7.9360.082625080664422196.0483177285078
Winsorized Mean ( 6 / 20 )7.9380.082285090740620196.4694810269122
Winsorized Mean ( 7 / 20 )7.9380.081875542867049296.9520289213819
Winsorized Mean ( 8 / 20 )7.944666666666670.080783055596845998.3457063856948
Winsorized Mean ( 9 / 20 )7.947666666666670.080305689502539998.9676661255153
Winsorized Mean ( 10 / 20 )7.947666666666670.079737339524848499.6730855835735
Winsorized Mean ( 11 / 20 )7.934833333333330.0768171545646212103.295069679498
Winsorized Mean ( 12 / 20 )7.940833333333330.075221440201005105.566090094978
Winsorized Mean ( 13 / 20 )7.9430.07347442769715108.105639593952
Winsorized Mean ( 14 / 20 )7.933666666666670.0696123108578901113.969304694723
Winsorized Mean ( 15 / 20 )7.926166666666670.0652024624620199121.56238226867
Winsorized Mean ( 16 / 20 )7.928833333333330.0615198703220711128.882477999775
Winsorized Mean ( 17 / 20 )7.937333333333330.056910012556581139.471649658167
Winsorized Mean ( 18 / 20 )7.922333333333330.0545134444966113145.328063682085
Winsorized Mean ( 19 / 20 )7.92550.0522215104932066151.766962026711
Winsorized Mean ( 20 / 20 )7.898833333333330.0480960031384186164.230555927917
Trimmed Mean ( 1 / 20 )7.932758620689650.083804641718644394.657747566324
Trimmed Mean ( 2 / 20 )7.933035714285710.083418410112157495.0993396256249
Trimmed Mean ( 3 / 20 )7.932037037037040.083123164588693195.4251089487033
Trimmed Mean ( 4 / 20 )7.931153846153850.082858369159853895.7194056143289
Trimmed Mean ( 5 / 20 )7.93020.082498974638031396.1248310635881
Trimmed Mean ( 6 / 20 )7.928750.082017785326897796.6711057656389
Trimmed Mean ( 7 / 20 )7.926739130434780.081381225118096797.4025534628149
Trimmed Mean ( 8 / 20 )7.924545454545450.080552042548380798.3779579491838
Trimmed Mean ( 9 / 20 )7.920952380952380.079632437787282199.4689174543569
Trimmed Mean ( 10 / 20 )7.91650.0784093057664027100.963781309133
Trimmed Mean ( 11 / 20 )7.911578947368420.0767980543663109103.017960710721
Trimmed Mean ( 12 / 20 )7.908055555555560.0752981580799244105.023227090916
Trimmed Mean ( 13 / 20 )7.903235294117650.0735158811080062107.503782516142
Trimmed Mean ( 14 / 20 )7.89750.0713634495766837110.665894752099
Trimmed Mean ( 15 / 20 )7.892333333333330.0693246292060721113.846023032779
Trimmed Mean ( 16 / 20 )7.88750.0675665946233396116.736680958543
Trimmed Mean ( 17 / 20 )7.881538461538460.0658943030283926119.608799233258
Trimmed Mean ( 18 / 20 )7.873333333333330.0645684297904469121.937816342844
Trimmed Mean ( 19 / 20 )7.865909090909090.0630318379350241124.792634144948
Trimmed Mean ( 20 / 20 )7.85650.0609368741533314128.928503622145
Median7.865
Midrange7.905
Midmean - Weighted Average at Xnp7.87387096774193
Midmean - Weighted Average at X(n+1)p7.89233333333333
Midmean - Empirical Distribution Function7.87387096774193
Midmean - Empirical Distribution Function - Averaging7.89233333333333
Midmean - Empirical Distribution Function - Interpolation7.89233333333333
Midmean - Closest Observation7.87387096774193
Midmean - True Basic - Statistics Graphics Toolkit7.89233333333333
Midmean - MS Excel (old versions)7.8975
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')