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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Oct 2009 13:36:24 -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/2009/Oct/21/t1256153844eas77lerpqhrb1j.htm/, Retrieved Thu, 02 May 2024 05:48:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49600, Retrieved Thu, 02 May 2024 05:48:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [part 2,2] [2009-10-21 17:53:57] [35f0fff14d789f48983afb62e692bd0d]
-   PD  [Univariate Data Series] [part 2,3] [2009-10-21 17:58:12] [35f0fff14d789f48983afb62e692bd0d]
- RMPD      [Central Tendency] [part 3,1] [2009-10-21 19:36:24] [2210215221105fab636491031ce54076] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.00
2.90
2.50
1.80
1.50
1.60
1.90
2.40
2.90
3.10
2.90
3.20
3.00
3.00
3.50
3.40
3.20
3.10
2.60
2.40
2.50
2.80
2.70
3.40
3.40
2.20
2.90
2.20
2.00
2.20
2.00
1.90
2.10
1.80
1.40
1.70
1.50
0.80
0.60
0.00
-0.20
-0.30
-0.60
-1.00
-1.10
-1.20
-0.80
0.60
1.20
0.80
0.80
0.00
0.30
0.50
0.60
0.40
0.10
-0.30
-0.40
0.00
0.50

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49600&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]3 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=49600&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49600&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.539344262295080.1744668488798318.82313328966781
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.04839001153205
Winsorized Mean ( 1 / 20 )1.539344262295080.1737449718346968.85979171679075
Winsorized Mean ( 2 / 20 )1.542622950819670.1729281574254628.92060017169037
Winsorized Mean ( 3 / 20 )1.552459016393440.1705921310521799.1004139922409
Winsorized Mean ( 4 / 20 )1.552459016393440.1653875487971889.38679500170351
Winsorized Mean ( 5 / 20 )1.568852459016390.1619475220879239.68741255679507
Winsorized Mean ( 6 / 20 )1.568852459016390.1583649548568499.9065633582539
Winsorized Mean ( 7 / 20 )1.568852459016390.1583649548568499.9065633582539
Winsorized Mean ( 8 / 20 )1.568852459016390.15374275910101310.2043990116349
Winsorized Mean ( 9 / 20 )1.598360655737710.14825933200346310.7808434999584
Winsorized Mean ( 10 / 20 )1.598360655737710.14825933200346310.7808434999584
Winsorized Mean ( 11 / 20 )1.580327868852460.14547490858577310.8632332834269
Winsorized Mean ( 12 / 20 )1.60.14196128156818311.2706787535694
Winsorized Mean ( 13 / 20 )1.642622950819670.13466126327673712.1981846215417
Winsorized Mean ( 14 / 20 )1.665573770491800.13090448789205912.7235803547484
Winsorized Mean ( 15 / 20 )1.665573770491800.12316156801343513.5234862413420
Winsorized Mean ( 16 / 20 )1.639344262295080.11920223639402313.7526300838537
Winsorized Mean ( 17 / 20 )1.639344262295080.11071744889223814.8065574008182
Winsorized Mean ( 18 / 20 )1.609836065573770.10652752839613815.1119254319630
Winsorized Mean ( 19 / 20 )1.609836065573770.10652752839613815.1119254319630
Winsorized Mean ( 20 / 20 )1.642622950819670.091778392411424217.8977089014168
Trimmed Mean ( 1 / 20 )1.552542372881360.170986684061259.07990222399547
Trimmed Mean ( 2 / 20 )1.566666666666670.1675290969627559.35160933276543
Trimmed Mean ( 3 / 20 )1.580.1637399597250919.64944661433116
Trimmed Mean ( 4 / 20 )1.590566037735850.1601039246792619.93458493239475
Trimmed Mean ( 5 / 20 )1.601960784313730.15749236386290310.1716727403256
Trimmed Mean ( 6 / 20 )1.610204081632650.15524407209752510.3720809424602
Trimmed Mean ( 7 / 20 )1.619148936170210.15330579556996810.5615637696570
Trimmed Mean ( 8 / 20 )1.628888888888890.15064246997384410.8129459718213
Trimmed Mean ( 9 / 20 )1.639534883720930.14826943893268911.0578072967906
Trimmed Mean ( 10 / 20 )1.646341463414630.14642477303461711.2435992168170
Trimmed Mean ( 11 / 20 )1.653846153846150.14373305938300111.5063727227791
Trimmed Mean ( 12 / 20 )1.664864864864860.14058095976871411.8427478913498
Trimmed Mean ( 13 / 20 )1.674285714285710.13703602281378212.2178510431589
Trimmed Mean ( 14 / 20 )1.678787878787880.13397743872129312.5303774636279
Trimmed Mean ( 15 / 20 )1.680645161290320.13045984467183812.8824709665863
Trimmed Mean ( 16 / 20 )1.682758620689660.12740967683679413.2074632199656
Trimmed Mean ( 17 / 20 )1.688888888888890.12372809695177813.6500029540349
Trimmed Mean ( 18 / 20 )1.6960.12062061736425214.0606144874751
Trimmed Mean ( 19 / 20 )1.708695652173910.11659074117610914.6555003848285
Trimmed Mean ( 20 / 20 )1.723809523809520.10930620204265015.7704639956012
Median1.8
Midrange1.15
Midmean - Weighted Average at Xnp1.64333333333333
Midmean - Weighted Average at X(n+1)p1.68064516129032
Midmean - Empirical Distribution Function1.68064516129032
Midmean - Empirical Distribution Function - Averaging1.68064516129032
Midmean - Empirical Distribution Function - Interpolation1.68064516129032
Midmean - Closest Observation1.640625
Midmean - True Basic - Statistics Graphics Toolkit1.68064516129032
Midmean - MS Excel (old versions)1.68064516129032
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.53934426229508 & 0.174466848879831 & 8.82313328966781 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.04839001153205 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.53934426229508 & 0.173744971834696 & 8.85979171679075 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.54262295081967 & 0.172928157425462 & 8.92060017169037 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.55245901639344 & 0.170592131052179 & 9.1004139922409 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.55245901639344 & 0.165387548797188 & 9.38679500170351 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.56885245901639 & 0.161947522087923 & 9.68741255679507 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.56885245901639 & 0.158364954856849 & 9.9065633582539 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.56885245901639 & 0.158364954856849 & 9.9065633582539 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.56885245901639 & 0.153742759101013 & 10.2043990116349 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.59836065573771 & 0.148259332003463 & 10.7808434999584 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.59836065573771 & 0.148259332003463 & 10.7808434999584 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.58032786885246 & 0.145474908585773 & 10.8632332834269 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.6 & 0.141961281568183 & 11.2706787535694 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.64262295081967 & 0.134661263276737 & 12.1981846215417 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.66557377049180 & 0.130904487892059 & 12.7235803547484 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.66557377049180 & 0.123161568013435 & 13.5234862413420 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.63934426229508 & 0.119202236394023 & 13.7526300838537 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.63934426229508 & 0.110717448892238 & 14.8065574008182 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.60983606557377 & 0.106527528396138 & 15.1119254319630 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.60983606557377 & 0.106527528396138 & 15.1119254319630 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.64262295081967 & 0.0917783924114242 & 17.8977089014168 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.55254237288136 & 0.17098668406125 & 9.07990222399547 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.56666666666667 & 0.167529096962755 & 9.35160933276543 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.58 & 0.163739959725091 & 9.64944661433116 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.59056603773585 & 0.160103924679261 & 9.93458493239475 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.60196078431373 & 0.157492363862903 & 10.1716727403256 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.61020408163265 & 0.155244072097525 & 10.3720809424602 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.61914893617021 & 0.153305795569968 & 10.5615637696570 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.62888888888889 & 0.150642469973844 & 10.8129459718213 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.63953488372093 & 0.148269438932689 & 11.0578072967906 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.64634146341463 & 0.146424773034617 & 11.2435992168170 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.65384615384615 & 0.143733059383001 & 11.5063727227791 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.66486486486486 & 0.140580959768714 & 11.8427478913498 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.67428571428571 & 0.137036022813782 & 12.2178510431589 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.67878787878788 & 0.133977438721293 & 12.5303774636279 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.68064516129032 & 0.130459844671838 & 12.8824709665863 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.68275862068966 & 0.127409676836794 & 13.2074632199656 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.68888888888889 & 0.123728096951778 & 13.6500029540349 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.696 & 0.120620617364252 & 14.0606144874751 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.70869565217391 & 0.116590741176109 & 14.6555003848285 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.72380952380952 & 0.109306202042650 & 15.7704639956012 \tabularnewline
Median & 1.8 &  &  \tabularnewline
Midrange & 1.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.64333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.68064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.68064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.68064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.68064516129032 &  &  \tabularnewline
Midmean - Closest Observation & 1.640625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.68064516129032 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.68064516129032 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49600&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]1.53934426229508[/C][C]0.174466848879831[/C][C]8.82313328966781[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.04839001153205[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.53934426229508[/C][C]0.173744971834696[/C][C]8.85979171679075[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.54262295081967[/C][C]0.172928157425462[/C][C]8.92060017169037[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.55245901639344[/C][C]0.170592131052179[/C][C]9.1004139922409[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.55245901639344[/C][C]0.165387548797188[/C][C]9.38679500170351[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.56885245901639[/C][C]0.161947522087923[/C][C]9.68741255679507[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.56885245901639[/C][C]0.158364954856849[/C][C]9.9065633582539[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.56885245901639[/C][C]0.158364954856849[/C][C]9.9065633582539[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.56885245901639[/C][C]0.153742759101013[/C][C]10.2043990116349[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.59836065573771[/C][C]0.148259332003463[/C][C]10.7808434999584[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.59836065573771[/C][C]0.148259332003463[/C][C]10.7808434999584[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.58032786885246[/C][C]0.145474908585773[/C][C]10.8632332834269[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.6[/C][C]0.141961281568183[/C][C]11.2706787535694[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.64262295081967[/C][C]0.134661263276737[/C][C]12.1981846215417[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.66557377049180[/C][C]0.130904487892059[/C][C]12.7235803547484[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.66557377049180[/C][C]0.123161568013435[/C][C]13.5234862413420[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.63934426229508[/C][C]0.119202236394023[/C][C]13.7526300838537[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.63934426229508[/C][C]0.110717448892238[/C][C]14.8065574008182[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.60983606557377[/C][C]0.106527528396138[/C][C]15.1119254319630[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.60983606557377[/C][C]0.106527528396138[/C][C]15.1119254319630[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.64262295081967[/C][C]0.0917783924114242[/C][C]17.8977089014168[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.55254237288136[/C][C]0.17098668406125[/C][C]9.07990222399547[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.56666666666667[/C][C]0.167529096962755[/C][C]9.35160933276543[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.58[/C][C]0.163739959725091[/C][C]9.64944661433116[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.59056603773585[/C][C]0.160103924679261[/C][C]9.93458493239475[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.60196078431373[/C][C]0.157492363862903[/C][C]10.1716727403256[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.61020408163265[/C][C]0.155244072097525[/C][C]10.3720809424602[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.61914893617021[/C][C]0.153305795569968[/C][C]10.5615637696570[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.62888888888889[/C][C]0.150642469973844[/C][C]10.8129459718213[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.63953488372093[/C][C]0.148269438932689[/C][C]11.0578072967906[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.64634146341463[/C][C]0.146424773034617[/C][C]11.2435992168170[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.65384615384615[/C][C]0.143733059383001[/C][C]11.5063727227791[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.66486486486486[/C][C]0.140580959768714[/C][C]11.8427478913498[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.67428571428571[/C][C]0.137036022813782[/C][C]12.2178510431589[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.67878787878788[/C][C]0.133977438721293[/C][C]12.5303774636279[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.68064516129032[/C][C]0.130459844671838[/C][C]12.8824709665863[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.68275862068966[/C][C]0.127409676836794[/C][C]13.2074632199656[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.68888888888889[/C][C]0.123728096951778[/C][C]13.6500029540349[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.696[/C][C]0.120620617364252[/C][C]14.0606144874751[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.70869565217391[/C][C]0.116590741176109[/C][C]14.6555003848285[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.72380952380952[/C][C]0.109306202042650[/C][C]15.7704639956012[/C][/ROW]
[ROW][C]Median[/C][C]1.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.64333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.68064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.68064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.68064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.68064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.640625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.68064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.68064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49600&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49600&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.539344262295080.1744668488798318.82313328966781
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.04839001153205
Winsorized Mean ( 1 / 20 )1.539344262295080.1737449718346968.85979171679075
Winsorized Mean ( 2 / 20 )1.542622950819670.1729281574254628.92060017169037
Winsorized Mean ( 3 / 20 )1.552459016393440.1705921310521799.1004139922409
Winsorized Mean ( 4 / 20 )1.552459016393440.1653875487971889.38679500170351
Winsorized Mean ( 5 / 20 )1.568852459016390.1619475220879239.68741255679507
Winsorized Mean ( 6 / 20 )1.568852459016390.1583649548568499.9065633582539
Winsorized Mean ( 7 / 20 )1.568852459016390.1583649548568499.9065633582539
Winsorized Mean ( 8 / 20 )1.568852459016390.15374275910101310.2043990116349
Winsorized Mean ( 9 / 20 )1.598360655737710.14825933200346310.7808434999584
Winsorized Mean ( 10 / 20 )1.598360655737710.14825933200346310.7808434999584
Winsorized Mean ( 11 / 20 )1.580327868852460.14547490858577310.8632332834269
Winsorized Mean ( 12 / 20 )1.60.14196128156818311.2706787535694
Winsorized Mean ( 13 / 20 )1.642622950819670.13466126327673712.1981846215417
Winsorized Mean ( 14 / 20 )1.665573770491800.13090448789205912.7235803547484
Winsorized Mean ( 15 / 20 )1.665573770491800.12316156801343513.5234862413420
Winsorized Mean ( 16 / 20 )1.639344262295080.11920223639402313.7526300838537
Winsorized Mean ( 17 / 20 )1.639344262295080.11071744889223814.8065574008182
Winsorized Mean ( 18 / 20 )1.609836065573770.10652752839613815.1119254319630
Winsorized Mean ( 19 / 20 )1.609836065573770.10652752839613815.1119254319630
Winsorized Mean ( 20 / 20 )1.642622950819670.091778392411424217.8977089014168
Trimmed Mean ( 1 / 20 )1.552542372881360.170986684061259.07990222399547
Trimmed Mean ( 2 / 20 )1.566666666666670.1675290969627559.35160933276543
Trimmed Mean ( 3 / 20 )1.580.1637399597250919.64944661433116
Trimmed Mean ( 4 / 20 )1.590566037735850.1601039246792619.93458493239475
Trimmed Mean ( 5 / 20 )1.601960784313730.15749236386290310.1716727403256
Trimmed Mean ( 6 / 20 )1.610204081632650.15524407209752510.3720809424602
Trimmed Mean ( 7 / 20 )1.619148936170210.15330579556996810.5615637696570
Trimmed Mean ( 8 / 20 )1.628888888888890.15064246997384410.8129459718213
Trimmed Mean ( 9 / 20 )1.639534883720930.14826943893268911.0578072967906
Trimmed Mean ( 10 / 20 )1.646341463414630.14642477303461711.2435992168170
Trimmed Mean ( 11 / 20 )1.653846153846150.14373305938300111.5063727227791
Trimmed Mean ( 12 / 20 )1.664864864864860.14058095976871411.8427478913498
Trimmed Mean ( 13 / 20 )1.674285714285710.13703602281378212.2178510431589
Trimmed Mean ( 14 / 20 )1.678787878787880.13397743872129312.5303774636279
Trimmed Mean ( 15 / 20 )1.680645161290320.13045984467183812.8824709665863
Trimmed Mean ( 16 / 20 )1.682758620689660.12740967683679413.2074632199656
Trimmed Mean ( 17 / 20 )1.688888888888890.12372809695177813.6500029540349
Trimmed Mean ( 18 / 20 )1.6960.12062061736425214.0606144874751
Trimmed Mean ( 19 / 20 )1.708695652173910.11659074117610914.6555003848285
Trimmed Mean ( 20 / 20 )1.723809523809520.10930620204265015.7704639956012
Median1.8
Midrange1.15
Midmean - Weighted Average at Xnp1.64333333333333
Midmean - Weighted Average at X(n+1)p1.68064516129032
Midmean - Empirical Distribution Function1.68064516129032
Midmean - Empirical Distribution Function - Averaging1.68064516129032
Midmean - Empirical Distribution Function - Interpolation1.68064516129032
Midmean - Closest Observation1.640625
Midmean - True Basic - Statistics Graphics Toolkit1.68064516129032
Midmean - MS Excel (old versions)1.68064516129032
Number of observations61


Figures (Output of Computation)

Input Parameters & R Code

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')