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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 01 Mar 2012 09:45:07 -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/01/t13306131163dz6mnwm8921axy.htm/, Retrieved Sat, 27 Apr 2024 22:36:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163375, Retrieved Sat, 27 Apr 2024 22:36:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-01 14:45:07] [a136497b64b0ea11fa49f30f9c72ef9a] [Current]
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Dataseries X:
2,58
2,59
2,6
2,6
2,61
2,62
2,64
2,65
2,66
2,67
2,68
2,69
2,69
2,71
2,72
2,73
2,73
2,74
2,74
2,74
2,74
2,74
2,75
2,75
2,75
2,75
2,77
2,78
2,79
2,8
2,82
2,83
2,84
2,87
2,89
2,9
2,9
2,91
2,92
2,92
2,92
2,92
2,94
2,95
2,95
2,97
2,99
3
3
3,01
3,03
3,03
3,04
3,04
3,05
3,05
3,09
3,09
3,09
3,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163375&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163375&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.83450.0198446295514403142.834613901587
Geometric Mean2.83041153722494
Harmonic Mean2.8263373216841
Quadratic Mean2.83859560346309
Winsorized Mean ( 1 / 20 )2.83450.0197718983939756143.360032684755
Winsorized Mean ( 2 / 20 )2.834833333333330.0197032958708247143.87609828927
Winsorized Mean ( 3 / 20 )2.834833333333330.0197032958708247143.87609828927
Winsorized Mean ( 4 / 20 )2.832833333333330.0190184146069529148.952128338694
Winsorized Mean ( 5 / 20 )2.833666666666670.0188556315175247150.282246661058
Winsorized Mean ( 6 / 20 )2.834666666666670.0182906024876082154.979403690346
Winsorized Mean ( 7 / 20 )2.835833333333330.018083753151939156.816635877894
Winsorized Mean ( 8 / 20 )2.835833333333330.0176024710429339161.104274872346
Winsorized Mean ( 9 / 20 )2.837333333333330.017352879027589163.507930230039
Winsorized Mean ( 10 / 20 )2.835666666666670.0164700835906802172.170751353762
Winsorized Mean ( 11 / 20 )2.835666666666670.0158548619620063178.851551874869
Winsorized Mean ( 12 / 20 )2.835666666666670.0158548619620063178.851551874869
Winsorized Mean ( 13 / 20 )2.837833333333330.0148211401672366191.471998868657
Winsorized Mean ( 14 / 20 )2.83550.0136882666568049207.148214678473
Winsorized Mean ( 15 / 20 )2.8330.0125218453180628226.244609164225
Winsorized Mean ( 16 / 20 )2.8330.0125218453180628226.244609164225
Winsorized Mean ( 17 / 20 )2.8330.0116887603553186242.369585300886
Winsorized Mean ( 18 / 20 )2.8270.0107836976771987262.154975466113
Winsorized Mean ( 19 / 20 )2.8270.0107836976771987262.154975466113
Winsorized Mean ( 20 / 20 )2.8270.0107836976771987262.154975466113
Trimmed Mean ( 1 / 20 )2.834310344827590.0195133039279731145.250151142497
Trimmed Mean ( 2 / 20 )2.834107142857140.0191859945971728147.717499267657
Trimmed Mean ( 3 / 20 )2.83370370370370.0188177776545421150.586522793765
Trimmed Mean ( 4 / 20 )2.833269230769230.0183516044026481154.388094283484
Trimmed Mean ( 5 / 20 )2.83340.0180285714285714157.161648177496
Trimmed Mean ( 6 / 20 )2.833333333333330.0176634548130825160.406520882586
Trimmed Mean ( 7 / 20 )2.833043478260870.0173591490174598163.201748853668
Trimmed Mean ( 8 / 20 )2.83250.0170098994929746166.520678218579
Trimmed Mean ( 9 / 20 )2.831904761904760.0166721411284508169.858492684671
Trimmed Mean ( 10 / 20 )2.8310.0162740945630211173.957450538155
Trimmed Mean ( 11 / 20 )2.830263157894740.0159635379438569177.295482232614
Trimmed Mean ( 12 / 20 )2.829444444444440.0156800573191192180.448603398561
Trimmed Mean ( 13 / 20 )2.828529411764710.0152585112740292185.373878287787
Trimmed Mean ( 14 / 20 )2.82718750.0149274750406326189.394890448947
Trimmed Mean ( 15 / 20 )2.8260.0147437888734486191.673932952825
Trimmed Mean ( 16 / 20 )2.8250.0147510200526131191.512179491585
Trimmed Mean ( 17 / 20 )2.823846153846150.014666308046539192.539672894197
Trimmed Mean ( 18 / 20 )2.82250.0146980477851874192.032305327276
Trimmed Mean ( 19 / 20 )2.821818181818180.0149260277570587189.053526346533
Trimmed Mean ( 20 / 20 )2.8210.0150944395478321186.890012779915
Median2.81
Midrange2.84
Midmean - Weighted Average at Xnp2.82258064516129
Midmean - Weighted Average at X(n+1)p2.826
Midmean - Empirical Distribution Function2.82258064516129
Midmean - Empirical Distribution Function - Averaging2.826
Midmean - Empirical Distribution Function - Interpolation2.826
Midmean - Closest Observation2.82258064516129
Midmean - True Basic - Statistics Graphics Toolkit2.826
Midmean - MS Excel (old versions)2.8271875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.8345 & 0.0198446295514403 & 142.834613901587 \tabularnewline
Geometric Mean & 2.83041153722494 &  &  \tabularnewline
Harmonic Mean & 2.8263373216841 &  &  \tabularnewline
Quadratic Mean & 2.83859560346309 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.8345 & 0.0197718983939756 & 143.360032684755 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.83483333333333 & 0.0197032958708247 & 143.87609828927 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.83483333333333 & 0.0197032958708247 & 143.87609828927 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.83283333333333 & 0.0190184146069529 & 148.952128338694 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.83366666666667 & 0.0188556315175247 & 150.282246661058 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.83466666666667 & 0.0182906024876082 & 154.979403690346 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.83583333333333 & 0.018083753151939 & 156.816635877894 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.83583333333333 & 0.0176024710429339 & 161.104274872346 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.83733333333333 & 0.017352879027589 & 163.507930230039 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.83566666666667 & 0.0164700835906802 & 172.170751353762 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.83566666666667 & 0.0158548619620063 & 178.851551874869 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.83566666666667 & 0.0158548619620063 & 178.851551874869 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.83783333333333 & 0.0148211401672366 & 191.471998868657 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.8355 & 0.0136882666568049 & 207.148214678473 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.833 & 0.0125218453180628 & 226.244609164225 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.833 & 0.0125218453180628 & 226.244609164225 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.833 & 0.0116887603553186 & 242.369585300886 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.827 & 0.0107836976771987 & 262.154975466113 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.827 & 0.0107836976771987 & 262.154975466113 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.827 & 0.0107836976771987 & 262.154975466113 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.83431034482759 & 0.0195133039279731 & 145.250151142497 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.83410714285714 & 0.0191859945971728 & 147.717499267657 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.8337037037037 & 0.0188177776545421 & 150.586522793765 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.83326923076923 & 0.0183516044026481 & 154.388094283484 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.8334 & 0.0180285714285714 & 157.161648177496 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.83333333333333 & 0.0176634548130825 & 160.406520882586 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.83304347826087 & 0.0173591490174598 & 163.201748853668 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.8325 & 0.0170098994929746 & 166.520678218579 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.83190476190476 & 0.0166721411284508 & 169.858492684671 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.831 & 0.0162740945630211 & 173.957450538155 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.83026315789474 & 0.0159635379438569 & 177.295482232614 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.82944444444444 & 0.0156800573191192 & 180.448603398561 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.82852941176471 & 0.0152585112740292 & 185.373878287787 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.8271875 & 0.0149274750406326 & 189.394890448947 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.826 & 0.0147437888734486 & 191.673932952825 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.825 & 0.0147510200526131 & 191.512179491585 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.82384615384615 & 0.014666308046539 & 192.539672894197 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.8225 & 0.0146980477851874 & 192.032305327276 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.82181818181818 & 0.0149260277570587 & 189.053526346533 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.821 & 0.0150944395478321 & 186.890012779915 \tabularnewline
Median & 2.81 &  &  \tabularnewline
Midrange & 2.84 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.82258064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.826 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.82258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.826 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.826 &  &  \tabularnewline
Midmean - Closest Observation & 2.82258064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.826 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.8271875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163375&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]2.8345[/C][C]0.0198446295514403[/C][C]142.834613901587[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.83041153722494[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.8263373216841[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.83859560346309[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.8345[/C][C]0.0197718983939756[/C][C]143.360032684755[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.83483333333333[/C][C]0.0197032958708247[/C][C]143.87609828927[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.83483333333333[/C][C]0.0197032958708247[/C][C]143.87609828927[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.83283333333333[/C][C]0.0190184146069529[/C][C]148.952128338694[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.83366666666667[/C][C]0.0188556315175247[/C][C]150.282246661058[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.83466666666667[/C][C]0.0182906024876082[/C][C]154.979403690346[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.83583333333333[/C][C]0.018083753151939[/C][C]156.816635877894[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.83583333333333[/C][C]0.0176024710429339[/C][C]161.104274872346[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.83733333333333[/C][C]0.017352879027589[/C][C]163.507930230039[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.83566666666667[/C][C]0.0164700835906802[/C][C]172.170751353762[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.83566666666667[/C][C]0.0158548619620063[/C][C]178.851551874869[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.83566666666667[/C][C]0.0158548619620063[/C][C]178.851551874869[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.83783333333333[/C][C]0.0148211401672366[/C][C]191.471998868657[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.8355[/C][C]0.0136882666568049[/C][C]207.148214678473[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.833[/C][C]0.0125218453180628[/C][C]226.244609164225[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.833[/C][C]0.0125218453180628[/C][C]226.244609164225[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.833[/C][C]0.0116887603553186[/C][C]242.369585300886[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.827[/C][C]0.0107836976771987[/C][C]262.154975466113[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.827[/C][C]0.0107836976771987[/C][C]262.154975466113[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.827[/C][C]0.0107836976771987[/C][C]262.154975466113[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.83431034482759[/C][C]0.0195133039279731[/C][C]145.250151142497[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.83410714285714[/C][C]0.0191859945971728[/C][C]147.717499267657[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.8337037037037[/C][C]0.0188177776545421[/C][C]150.586522793765[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.83326923076923[/C][C]0.0183516044026481[/C][C]154.388094283484[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.8334[/C][C]0.0180285714285714[/C][C]157.161648177496[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.83333333333333[/C][C]0.0176634548130825[/C][C]160.406520882586[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.83304347826087[/C][C]0.0173591490174598[/C][C]163.201748853668[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.8325[/C][C]0.0170098994929746[/C][C]166.520678218579[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.83190476190476[/C][C]0.0166721411284508[/C][C]169.858492684671[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.831[/C][C]0.0162740945630211[/C][C]173.957450538155[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.83026315789474[/C][C]0.0159635379438569[/C][C]177.295482232614[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.82944444444444[/C][C]0.0156800573191192[/C][C]180.448603398561[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.82852941176471[/C][C]0.0152585112740292[/C][C]185.373878287787[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.8271875[/C][C]0.0149274750406326[/C][C]189.394890448947[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.826[/C][C]0.0147437888734486[/C][C]191.673932952825[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.825[/C][C]0.0147510200526131[/C][C]191.512179491585[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.82384615384615[/C][C]0.014666308046539[/C][C]192.539672894197[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.8225[/C][C]0.0146980477851874[/C][C]192.032305327276[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.82181818181818[/C][C]0.0149260277570587[/C][C]189.053526346533[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.821[/C][C]0.0150944395478321[/C][C]186.890012779915[/C][/ROW]
[ROW][C]Median[/C][C]2.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.82258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.82258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.82258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.8271875[/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=163375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163375&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 Mean2.83450.0198446295514403142.834613901587
Geometric Mean2.83041153722494
Harmonic Mean2.8263373216841
Quadratic Mean2.83859560346309
Winsorized Mean ( 1 / 20 )2.83450.0197718983939756143.360032684755
Winsorized Mean ( 2 / 20 )2.834833333333330.0197032958708247143.87609828927
Winsorized Mean ( 3 / 20 )2.834833333333330.0197032958708247143.87609828927
Winsorized Mean ( 4 / 20 )2.832833333333330.0190184146069529148.952128338694
Winsorized Mean ( 5 / 20 )2.833666666666670.0188556315175247150.282246661058
Winsorized Mean ( 6 / 20 )2.834666666666670.0182906024876082154.979403690346
Winsorized Mean ( 7 / 20 )2.835833333333330.018083753151939156.816635877894
Winsorized Mean ( 8 / 20 )2.835833333333330.0176024710429339161.104274872346
Winsorized Mean ( 9 / 20 )2.837333333333330.017352879027589163.507930230039
Winsorized Mean ( 10 / 20 )2.835666666666670.0164700835906802172.170751353762
Winsorized Mean ( 11 / 20 )2.835666666666670.0158548619620063178.851551874869
Winsorized Mean ( 12 / 20 )2.835666666666670.0158548619620063178.851551874869
Winsorized Mean ( 13 / 20 )2.837833333333330.0148211401672366191.471998868657
Winsorized Mean ( 14 / 20 )2.83550.0136882666568049207.148214678473
Winsorized Mean ( 15 / 20 )2.8330.0125218453180628226.244609164225
Winsorized Mean ( 16 / 20 )2.8330.0125218453180628226.244609164225
Winsorized Mean ( 17 / 20 )2.8330.0116887603553186242.369585300886
Winsorized Mean ( 18 / 20 )2.8270.0107836976771987262.154975466113
Winsorized Mean ( 19 / 20 )2.8270.0107836976771987262.154975466113
Winsorized Mean ( 20 / 20 )2.8270.0107836976771987262.154975466113
Trimmed Mean ( 1 / 20 )2.834310344827590.0195133039279731145.250151142497
Trimmed Mean ( 2 / 20 )2.834107142857140.0191859945971728147.717499267657
Trimmed Mean ( 3 / 20 )2.83370370370370.0188177776545421150.586522793765
Trimmed Mean ( 4 / 20 )2.833269230769230.0183516044026481154.388094283484
Trimmed Mean ( 5 / 20 )2.83340.0180285714285714157.161648177496
Trimmed Mean ( 6 / 20 )2.833333333333330.0176634548130825160.406520882586
Trimmed Mean ( 7 / 20 )2.833043478260870.0173591490174598163.201748853668
Trimmed Mean ( 8 / 20 )2.83250.0170098994929746166.520678218579
Trimmed Mean ( 9 / 20 )2.831904761904760.0166721411284508169.858492684671
Trimmed Mean ( 10 / 20 )2.8310.0162740945630211173.957450538155
Trimmed Mean ( 11 / 20 )2.830263157894740.0159635379438569177.295482232614
Trimmed Mean ( 12 / 20 )2.829444444444440.0156800573191192180.448603398561
Trimmed Mean ( 13 / 20 )2.828529411764710.0152585112740292185.373878287787
Trimmed Mean ( 14 / 20 )2.82718750.0149274750406326189.394890448947
Trimmed Mean ( 15 / 20 )2.8260.0147437888734486191.673932952825
Trimmed Mean ( 16 / 20 )2.8250.0147510200526131191.512179491585
Trimmed Mean ( 17 / 20 )2.823846153846150.014666308046539192.539672894197
Trimmed Mean ( 18 / 20 )2.82250.0146980477851874192.032305327276
Trimmed Mean ( 19 / 20 )2.821818181818180.0149260277570587189.053526346533
Trimmed Mean ( 20 / 20 )2.8210.0150944395478321186.890012779915
Median2.81
Midrange2.84
Midmean - Weighted Average at Xnp2.82258064516129
Midmean - Weighted Average at X(n+1)p2.826
Midmean - Empirical Distribution Function2.82258064516129
Midmean - Empirical Distribution Function - Averaging2.826
Midmean - Empirical Distribution Function - Interpolation2.826
Midmean - Closest Observation2.82258064516129
Midmean - True Basic - Statistics Graphics Toolkit2.826
Midmean - MS Excel (old versions)2.8271875
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')