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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 11:34:51 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t12245242013wzd3m99jd11g42.htm/, Retrieved Sun, 19 May 2024 16:09:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17751, Retrieved Sun, 19 May 2024 16:09:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordswerkzoekenden central tendency
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Totaal % werkzoek...] [2008-10-13 16:48:54] [b635de6fc42b001d22cbe6e730fec936]
- RMP     [Central Tendency] [Totaal % werkzoek...] [2008-10-20 17:34:51] [f4b2017b314c03698059f43b95818e67] [Current]
- RMP       [Histogram] [Histogram totaal ...] [2008-10-21 07:13:38] [b635de6fc42b001d22cbe6e730fec936]
- RMPD      [Back to Back Histogram] [Histogram kolom 4...] [2008-10-21 07:41:23] [b635de6fc42b001d22cbe6e730fec936]
- RMP         [Bivariate Kernel Density Estimation] [Bivariate Kernel ...] [2008-11-10 12:05:17] [b635de6fc42b001d22cbe6e730fec936]
- RMPD      [Univariate Explorative Data Analysis] [Univariate EDA-mo...] [2008-10-27 09:49:38] [b635de6fc42b001d22cbe6e730fec936]
- RMP         [Tukey lambda PPCC Plot] [Tukey - Lambda pp...] [2008-10-27 10:02:06] [b635de6fc42b001d22cbe6e730fec936]
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Dataseries X:
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17751&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17751&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.980.09513000322781683.8852068667506
Geometric Mean7.94502457156984
Harmonic Mean7.90848389482875
Quadratic Mean8.01338463655236
Winsorized Mean ( 1 / 20 )7.980.09513000322781683.8852068667506
Winsorized Mean ( 2 / 20 )7.980.088483775524518990.186025095513
Winsorized Mean ( 3 / 20 )7.9850.085132830741474293.7946022756876
Winsorized Mean ( 4 / 20 )7.9850.085132830741474293.7946022756876
Winsorized Mean ( 5 / 20 )7.993333333333330.083221393743723396.0490202549173
Winsorized Mean ( 6 / 20 )7.993333333333330.0794709436531517100.581834893266
Winsorized Mean ( 7 / 20 )7.993333333333330.0794709436531517100.581834893266
Winsorized Mean ( 8 / 20 )7.993333333333330.0794709436531517100.581834893266
Winsorized Mean ( 9 / 20 )8.008333333333330.0763685557598887104.864276319595
Winsorized Mean ( 10 / 20 )8.008333333333330.0706023985550957113.428629865654
Winsorized Mean ( 11 / 20 )8.008333333333330.0706023985550957113.428629865654
Winsorized Mean ( 12 / 20 )8.008333333333330.0706023985550957113.428629865654
Winsorized Mean ( 13 / 20 )8.030.0664813809370672120.785697992666
Winsorized Mean ( 14 / 20 )8.030.0664813809370672120.785697992666
Winsorized Mean ( 15 / 20 )8.0550.0538582047109748149.559385486881
Winsorized Mean ( 16 / 20 )8.0550.0538582047109748149.559385486881
Winsorized Mean ( 17 / 20 )8.0550.0538582047109748149.559385486881
Winsorized Mean ( 18 / 20 )8.1150.0437523203581612185.475877246504
Winsorized Mean ( 19 / 20 )8.146666666666670.0293495076106366277.574219463710
Winsorized Mean ( 20 / 20 )8.146666666666670.0293495076106366277.574219463710
Trimmed Mean ( 1 / 20 )7.987931034482760.090574478489813788.1918523591732
Trimmed Mean ( 2 / 20 )7.996428571428570.084897351530221594.1893760794413
Trimmed Mean ( 3 / 20 )8.005555555555560.082391604103459597.1647007321637
Trimmed Mean ( 4 / 20 )8.013461538461540.08086209916332899.1003402258415
Trimmed Mean ( 5 / 20 )8.0220.0788845707993907101.692890240863
Trimmed Mean ( 6 / 20 )8.029166666666670.077009620687853104.261864880645
Trimmed Mean ( 7 / 20 )8.036956521739130.0757161426481099106.145879077475
Trimmed Mean ( 8 / 20 )8.045454545454540.0739589156174432108.782754293886
Trimmed Mean ( 9 / 20 )8.05476190476190.0715842283832243112.521460197083
Trimmed Mean ( 10 / 20 )8.06250.0693086278715421116.327508531019
Trimmed Mean ( 11 / 20 )8.071052631578950.067773773837335119.088139476347
Trimmed Mean ( 12 / 20 )8.080555555555560.0655646348299753123.245642662548
Trimmed Mean ( 13 / 20 )8.091176470588240.062389674042052129.687750334047
Trimmed Mean ( 14 / 20 )8.10.0592289162160598136.757525166461
Trimmed Mean ( 15 / 20 )8.110.0545303880271432148.724413916936
Trimmed Mean ( 16 / 20 )8.117857142857140.0522138387635674155.473287065065
Trimmed Mean ( 17 / 20 )8.126923076923080.0485347432441457167.445473772097
Trimmed Mean ( 18 / 20 )8.13750.0424829462800979191.547449330561
Trimmed Mean ( 19 / 20 )8.140909090909090.0381720251304283213.268985941741
Trimmed Mean ( 20 / 20 )8.140.037975061068521214.35120236706
Median8.1
Midrange7.75
Midmean - Weighted Average at Xnp8.059375
Midmean - Weighted Average at X(n+1)p8.11
Midmean - Empirical Distribution Function8.059375
Midmean - Empirical Distribution Function - Averaging8.11
Midmean - Empirical Distribution Function - Interpolation8.11
Midmean - Closest Observation8.059375
Midmean - True Basic - Statistics Graphics Toolkit8.11
Midmean - MS Excel (old versions)8.13243243243243
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.98 & 0.095130003227816 & 83.8852068667506 \tabularnewline
Geometric Mean & 7.94502457156984 &  &  \tabularnewline
Harmonic Mean & 7.90848389482875 &  &  \tabularnewline
Quadratic Mean & 8.01338463655236 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.98 & 0.095130003227816 & 83.8852068667506 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.98 & 0.0884837755245189 & 90.186025095513 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.985 & 0.0851328307414742 & 93.7946022756876 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.985 & 0.0851328307414742 & 93.7946022756876 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.99333333333333 & 0.0832213937437233 & 96.0490202549173 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.99333333333333 & 0.0794709436531517 & 100.581834893266 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.99333333333333 & 0.0794709436531517 & 100.581834893266 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.99333333333333 & 0.0794709436531517 & 100.581834893266 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.00833333333333 & 0.0763685557598887 & 104.864276319595 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.00833333333333 & 0.0706023985550957 & 113.428629865654 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.00833333333333 & 0.0706023985550957 & 113.428629865654 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.00833333333333 & 0.0706023985550957 & 113.428629865654 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.03 & 0.0664813809370672 & 120.785697992666 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.03 & 0.0664813809370672 & 120.785697992666 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.055 & 0.0538582047109748 & 149.559385486881 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.055 & 0.0538582047109748 & 149.559385486881 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.055 & 0.0538582047109748 & 149.559385486881 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.115 & 0.0437523203581612 & 185.475877246504 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.14666666666667 & 0.0293495076106366 & 277.574219463710 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.14666666666667 & 0.0293495076106366 & 277.574219463710 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.98793103448276 & 0.0905744784898137 & 88.1918523591732 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.99642857142857 & 0.0848973515302215 & 94.1893760794413 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.00555555555556 & 0.0823916041034595 & 97.1647007321637 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.01346153846154 & 0.080862099163328 & 99.1003402258415 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.022 & 0.0788845707993907 & 101.692890240863 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.02916666666667 & 0.077009620687853 & 104.261864880645 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.03695652173913 & 0.0757161426481099 & 106.145879077475 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.04545454545454 & 0.0739589156174432 & 108.782754293886 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.0547619047619 & 0.0715842283832243 & 112.521460197083 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.0625 & 0.0693086278715421 & 116.327508531019 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.07105263157895 & 0.067773773837335 & 119.088139476347 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.08055555555556 & 0.0655646348299753 & 123.245642662548 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.09117647058824 & 0.062389674042052 & 129.687750334047 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.1 & 0.0592289162160598 & 136.757525166461 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.11 & 0.0545303880271432 & 148.724413916936 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.11785714285714 & 0.0522138387635674 & 155.473287065065 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.12692307692308 & 0.0485347432441457 & 167.445473772097 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.1375 & 0.0424829462800979 & 191.547449330561 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.14090909090909 & 0.0381720251304283 & 213.268985941741 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.14 & 0.037975061068521 & 214.35120236706 \tabularnewline
Median & 8.1 &  &  \tabularnewline
Midrange & 7.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.059375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.11 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.059375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.11 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.11 &  &  \tabularnewline
Midmean - Closest Observation & 8.059375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.11 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.13243243243243 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17751&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]7.98[/C][C]0.095130003227816[/C][C]83.8852068667506[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.94502457156984[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.90848389482875[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.01338463655236[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.98[/C][C]0.095130003227816[/C][C]83.8852068667506[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.98[/C][C]0.0884837755245189[/C][C]90.186025095513[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.985[/C][C]0.0851328307414742[/C][C]93.7946022756876[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.985[/C][C]0.0851328307414742[/C][C]93.7946022756876[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.99333333333333[/C][C]0.0832213937437233[/C][C]96.0490202549173[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.99333333333333[/C][C]0.0794709436531517[/C][C]100.581834893266[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.99333333333333[/C][C]0.0794709436531517[/C][C]100.581834893266[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.99333333333333[/C][C]0.0794709436531517[/C][C]100.581834893266[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.00833333333333[/C][C]0.0763685557598887[/C][C]104.864276319595[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.00833333333333[/C][C]0.0706023985550957[/C][C]113.428629865654[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.00833333333333[/C][C]0.0706023985550957[/C][C]113.428629865654[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.00833333333333[/C][C]0.0706023985550957[/C][C]113.428629865654[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.03[/C][C]0.0664813809370672[/C][C]120.785697992666[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.03[/C][C]0.0664813809370672[/C][C]120.785697992666[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.055[/C][C]0.0538582047109748[/C][C]149.559385486881[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.055[/C][C]0.0538582047109748[/C][C]149.559385486881[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.055[/C][C]0.0538582047109748[/C][C]149.559385486881[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.115[/C][C]0.0437523203581612[/C][C]185.475877246504[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.14666666666667[/C][C]0.0293495076106366[/C][C]277.574219463710[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.14666666666667[/C][C]0.0293495076106366[/C][C]277.574219463710[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.98793103448276[/C][C]0.0905744784898137[/C][C]88.1918523591732[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.99642857142857[/C][C]0.0848973515302215[/C][C]94.1893760794413[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.00555555555556[/C][C]0.0823916041034595[/C][C]97.1647007321637[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.01346153846154[/C][C]0.080862099163328[/C][C]99.1003402258415[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.022[/C][C]0.0788845707993907[/C][C]101.692890240863[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.02916666666667[/C][C]0.077009620687853[/C][C]104.261864880645[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.03695652173913[/C][C]0.0757161426481099[/C][C]106.145879077475[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.04545454545454[/C][C]0.0739589156174432[/C][C]108.782754293886[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.0547619047619[/C][C]0.0715842283832243[/C][C]112.521460197083[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.0625[/C][C]0.0693086278715421[/C][C]116.327508531019[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.07105263157895[/C][C]0.067773773837335[/C][C]119.088139476347[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.08055555555556[/C][C]0.0655646348299753[/C][C]123.245642662548[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.09117647058824[/C][C]0.062389674042052[/C][C]129.687750334047[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.1[/C][C]0.0592289162160598[/C][C]136.757525166461[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.11[/C][C]0.0545303880271432[/C][C]148.724413916936[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.11785714285714[/C][C]0.0522138387635674[/C][C]155.473287065065[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.12692307692308[/C][C]0.0485347432441457[/C][C]167.445473772097[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.1375[/C][C]0.0424829462800979[/C][C]191.547449330561[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.14090909090909[/C][C]0.0381720251304283[/C][C]213.268985941741[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.14[/C][C]0.037975061068521[/C][C]214.35120236706[/C][/ROW]
[ROW][C]Median[/C][C]8.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.059375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.059375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.059375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.13243243243243[/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=17751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17751&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 Mean7.980.09513000322781683.8852068667506
Geometric Mean7.94502457156984
Harmonic Mean7.90848389482875
Quadratic Mean8.01338463655236
Winsorized Mean ( 1 / 20 )7.980.09513000322781683.8852068667506
Winsorized Mean ( 2 / 20 )7.980.088483775524518990.186025095513
Winsorized Mean ( 3 / 20 )7.9850.085132830741474293.7946022756876
Winsorized Mean ( 4 / 20 )7.9850.085132830741474293.7946022756876
Winsorized Mean ( 5 / 20 )7.993333333333330.083221393743723396.0490202549173
Winsorized Mean ( 6 / 20 )7.993333333333330.0794709436531517100.581834893266
Winsorized Mean ( 7 / 20 )7.993333333333330.0794709436531517100.581834893266
Winsorized Mean ( 8 / 20 )7.993333333333330.0794709436531517100.581834893266
Winsorized Mean ( 9 / 20 )8.008333333333330.0763685557598887104.864276319595
Winsorized Mean ( 10 / 20 )8.008333333333330.0706023985550957113.428629865654
Winsorized Mean ( 11 / 20 )8.008333333333330.0706023985550957113.428629865654
Winsorized Mean ( 12 / 20 )8.008333333333330.0706023985550957113.428629865654
Winsorized Mean ( 13 / 20 )8.030.0664813809370672120.785697992666
Winsorized Mean ( 14 / 20 )8.030.0664813809370672120.785697992666
Winsorized Mean ( 15 / 20 )8.0550.0538582047109748149.559385486881
Winsorized Mean ( 16 / 20 )8.0550.0538582047109748149.559385486881
Winsorized Mean ( 17 / 20 )8.0550.0538582047109748149.559385486881
Winsorized Mean ( 18 / 20 )8.1150.0437523203581612185.475877246504
Winsorized Mean ( 19 / 20 )8.146666666666670.0293495076106366277.574219463710
Winsorized Mean ( 20 / 20 )8.146666666666670.0293495076106366277.574219463710
Trimmed Mean ( 1 / 20 )7.987931034482760.090574478489813788.1918523591732
Trimmed Mean ( 2 / 20 )7.996428571428570.084897351530221594.1893760794413
Trimmed Mean ( 3 / 20 )8.005555555555560.082391604103459597.1647007321637
Trimmed Mean ( 4 / 20 )8.013461538461540.08086209916332899.1003402258415
Trimmed Mean ( 5 / 20 )8.0220.0788845707993907101.692890240863
Trimmed Mean ( 6 / 20 )8.029166666666670.077009620687853104.261864880645
Trimmed Mean ( 7 / 20 )8.036956521739130.0757161426481099106.145879077475
Trimmed Mean ( 8 / 20 )8.045454545454540.0739589156174432108.782754293886
Trimmed Mean ( 9 / 20 )8.05476190476190.0715842283832243112.521460197083
Trimmed Mean ( 10 / 20 )8.06250.0693086278715421116.327508531019
Trimmed Mean ( 11 / 20 )8.071052631578950.067773773837335119.088139476347
Trimmed Mean ( 12 / 20 )8.080555555555560.0655646348299753123.245642662548
Trimmed Mean ( 13 / 20 )8.091176470588240.062389674042052129.687750334047
Trimmed Mean ( 14 / 20 )8.10.0592289162160598136.757525166461
Trimmed Mean ( 15 / 20 )8.110.0545303880271432148.724413916936
Trimmed Mean ( 16 / 20 )8.117857142857140.0522138387635674155.473287065065
Trimmed Mean ( 17 / 20 )8.126923076923080.0485347432441457167.445473772097
Trimmed Mean ( 18 / 20 )8.13750.0424829462800979191.547449330561
Trimmed Mean ( 19 / 20 )8.140909090909090.0381720251304283213.268985941741
Trimmed Mean ( 20 / 20 )8.140.037975061068521214.35120236706
Median8.1
Midrange7.75
Midmean - Weighted Average at Xnp8.059375
Midmean - Weighted Average at X(n+1)p8.11
Midmean - Empirical Distribution Function8.059375
Midmean - Empirical Distribution Function - Averaging8.11
Midmean - Empirical Distribution Function - Interpolation8.11
Midmean - Closest Observation8.059375
Midmean - True Basic - Statistics Graphics Toolkit8.11
Midmean - MS Excel (old versions)8.13243243243243
Number of observations60



Parameters (Session):
par1 = grey ; par2 = grey ; par3 = TRUE ; par4 = Female ; par5 = Male ;
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')