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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 09:29:15 -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/20/t1256052747u56s6ngq0fmhhf9.htm/, Retrieved Thu, 02 May 2024 21:04:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48731, Retrieved Thu, 02 May 2024 21:04:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [WS3, part 1-3] [2009-10-20 14:26:04] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P   [Harrell-Davis Quantiles] [WS3 part 1 -3] [2009-10-20 14:31:26] [ed603017d2bee8fbd82b6d5ec04e12c3]
- RMPD      [Central Tendency] [WS part 2 Mediaan] [2009-10-20 15:29:15] [87085ce7f5378f281469a8b1f0969170] [Current]
-  M D        [Central Tendency] [Mediaan] [2009-12-04 12:32:51] [34b80aeb109c116fd63bf2eb7493a276]
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Dataseries X:
5.7
6.1
6
5.9
5.8
5.7
5.6
5.4
5.4
5.5
5.6
5.7
5.9
6.1
6
5.8
5.8
5.7
5.5
5.3
5.2
5.2
5
5.1
5.1
5.2
4.9
4.8
4.5
4.5
4.4
4.4
4.2
4.1
3.9
3.8
3.9
4.2
4.1
3.8
3.6
3.7
3.5
3.4
3.1
3.1
3.1
3.2
3.3
3.5
3.6
3.5
3.3
3.2
3.1
3.2
3
3
3.1
3.4




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=48731&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=48731&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48731&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 Mean4.511666666666670.13642099318762333.0716450690376
Geometric Mean4.38678192008681
Harmonic Mean4.26228366750416
Quadratic Mean4.63175632634821
Winsorized Mean ( 1 / 20 )4.511666666666670.13642099318762333.0716450690376
Winsorized Mean ( 2 / 20 )4.511666666666670.13517286832589633.3770136162919
Winsorized Mean ( 3 / 20 )4.511666666666670.13517286832589633.3770136162919
Winsorized Mean ( 4 / 20 )4.5050.13396232289267933.6288584933623
Winsorized Mean ( 5 / 20 )4.5050.13396232289267933.6288584933623
Winsorized Mean ( 6 / 20 )4.4950.13224324873564733.9903930293293
Winsorized Mean ( 7 / 20 )4.506666666666670.13020771468779634.6113644454361
Winsorized Mean ( 8 / 20 )4.506666666666670.13020771468779634.6113644454361
Winsorized Mean ( 9 / 20 )4.491666666666670.12774205264933735.1620047862914
Winsorized Mean ( 10 / 20 )4.508333333333330.12494725817640236.0818908644512
Winsorized Mean ( 11 / 20 )4.508333333333330.12494725817640236.0818908644512
Winsorized Mean ( 12 / 20 )4.528333333333330.12173630079117837.1978884186819
Winsorized Mean ( 13 / 20 )4.506666666666670.11827065261214738.1046909536018
Winsorized Mean ( 14 / 20 )4.530.11464265285271239.5140891045148
Winsorized Mean ( 15 / 20 )4.5050.11076072342264440.6732626944816
Winsorized Mean ( 16 / 20 )4.5050.11076072342264440.6732626944816
Winsorized Mean ( 17 / 20 )4.5050.10219138464687344.0839510646345
Winsorized Mean ( 18 / 20 )4.5050.10219138464687344.0839510646345
Winsorized Mean ( 19 / 20 )4.5050.092834370461500148.5272855043305
Winsorized Mean ( 20 / 20 )4.5050.083206400503481554.1424694823988
Trimmed Mean ( 1 / 20 )4.510344827586210.13591770167416533.1843812250361
Trimmed Mean ( 2 / 20 )4.508928571428570.13515928039193933.3601108140961
Trimmed Mean ( 3 / 20 )4.507407407407410.13486675495560833.4211897430989
Trimmed Mean ( 4 / 20 )4.505769230769230.13432175474369133.5445977411999
Trimmed Mean ( 5 / 20 )4.5060.13390249269905533.6513526311061
Trimmed Mean ( 6 / 20 )4.506250.13316943328329133.8384709531193
Trimmed Mean ( 7 / 20 )4.508695652173910.13252749553222434.0208319342881
Trimmed Mean ( 8 / 20 )4.509090909090910.13202033052714534.1545191644841
Trimmed Mean ( 9 / 20 )4.509523809523810.13109958994317934.3976957630326
Trimmed Mean ( 10 / 20 )4.51250.13024569976660434.6460574751125
Trimmed Mean ( 11 / 20 )4.513157894736840.12951221829977034.8473522729004
Trimmed Mean ( 12 / 20 )4.513888888888890.12818344851291535.2142881257723
Trimmed Mean ( 13 / 20 )4.511764705882350.12685449339084035.5664555924052
Trimmed Mean ( 14 / 20 )4.51250.12554317468376135.9438098595708
Trimmed Mean ( 15 / 20 )4.510.12423096769056136.303347577825
Trimmed Mean ( 16 / 20 )4.510714285714290.12294224627184636.6897012418361
Trimmed Mean ( 17 / 20 )4.511538461538460.12042577325433837.4632301675998
Trimmed Mean ( 18 / 20 )4.51250.11891912060882737.9459583698354
Trimmed Mean ( 19 / 20 )4.513636363636360.11571263378165039.007290873299
Trimmed Mean ( 20 / 20 )4.5150.11361870676220439.7381745371347
Median4.45
Midrange4.55
Midmean - Weighted Average at Xnp4.47741935483871
Midmean - Weighted Average at X(n+1)p4.47741935483871
Midmean - Empirical Distribution Function4.47741935483871
Midmean - Empirical Distribution Function - Averaging4.47741935483871
Midmean - Empirical Distribution Function - Interpolation4.47741935483871
Midmean - Closest Observation4.47741935483871
Midmean - True Basic - Statistics Graphics Toolkit4.47741935483871
Midmean - MS Excel (old versions)4.54545454545455
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.51166666666667 & 0.136420993187623 & 33.0716450690376 \tabularnewline
Geometric Mean & 4.38678192008681 &  &  \tabularnewline
Harmonic Mean & 4.26228366750416 &  &  \tabularnewline
Quadratic Mean & 4.63175632634821 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4.51166666666667 & 0.136420993187623 & 33.0716450690376 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4.51166666666667 & 0.135172868325896 & 33.3770136162919 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4.51166666666667 & 0.135172868325896 & 33.3770136162919 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4.505 & 0.133962322892679 & 33.6288584933623 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4.505 & 0.133962322892679 & 33.6288584933623 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4.495 & 0.132243248735647 & 33.9903930293293 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4.50666666666667 & 0.130207714687796 & 34.6113644454361 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4.50666666666667 & 0.130207714687796 & 34.6113644454361 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4.49166666666667 & 0.127742052649337 & 35.1620047862914 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4.50833333333333 & 0.124947258176402 & 36.0818908644512 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4.50833333333333 & 0.124947258176402 & 36.0818908644512 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4.52833333333333 & 0.121736300791178 & 37.1978884186819 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4.50666666666667 & 0.118270652612147 & 38.1046909536018 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4.53 & 0.114642652852712 & 39.5140891045148 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4.505 & 0.110760723422644 & 40.6732626944816 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4.505 & 0.110760723422644 & 40.6732626944816 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4.505 & 0.102191384646873 & 44.0839510646345 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4.505 & 0.102191384646873 & 44.0839510646345 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4.505 & 0.0928343704615001 & 48.5272855043305 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4.505 & 0.0832064005034815 & 54.1424694823988 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4.51034482758621 & 0.135917701674165 & 33.1843812250361 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4.50892857142857 & 0.135159280391939 & 33.3601108140961 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4.50740740740741 & 0.134866754955608 & 33.4211897430989 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4.50576923076923 & 0.134321754743691 & 33.5445977411999 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4.506 & 0.133902492699055 & 33.6513526311061 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4.50625 & 0.133169433283291 & 33.8384709531193 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4.50869565217391 & 0.132527495532224 & 34.0208319342881 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4.50909090909091 & 0.132020330527145 & 34.1545191644841 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4.50952380952381 & 0.131099589943179 & 34.3976957630326 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4.5125 & 0.130245699766604 & 34.6460574751125 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4.51315789473684 & 0.129512218299770 & 34.8473522729004 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4.51388888888889 & 0.128183448512915 & 35.2142881257723 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4.51176470588235 & 0.126854493390840 & 35.5664555924052 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4.5125 & 0.125543174683761 & 35.9438098595708 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4.51 & 0.124230967690561 & 36.303347577825 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4.51071428571429 & 0.122942246271846 & 36.6897012418361 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4.51153846153846 & 0.120425773254338 & 37.4632301675998 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4.5125 & 0.118919120608827 & 37.9459583698354 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4.51363636363636 & 0.115712633781650 & 39.007290873299 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4.515 & 0.113618706762204 & 39.7381745371347 \tabularnewline
Median & 4.45 &  &  \tabularnewline
Midrange & 4.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.47741935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.47741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.47741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.47741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.47741935483871 &  &  \tabularnewline
Midmean - Closest Observation & 4.47741935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.47741935483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.54545454545455 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48731&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]4.51166666666667[/C][C]0.136420993187623[/C][C]33.0716450690376[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.38678192008681[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.26228366750416[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.63175632634821[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4.51166666666667[/C][C]0.136420993187623[/C][C]33.0716450690376[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4.51166666666667[/C][C]0.135172868325896[/C][C]33.3770136162919[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4.51166666666667[/C][C]0.135172868325896[/C][C]33.3770136162919[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4.505[/C][C]0.133962322892679[/C][C]33.6288584933623[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4.505[/C][C]0.133962322892679[/C][C]33.6288584933623[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4.495[/C][C]0.132243248735647[/C][C]33.9903930293293[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4.50666666666667[/C][C]0.130207714687796[/C][C]34.6113644454361[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4.50666666666667[/C][C]0.130207714687796[/C][C]34.6113644454361[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4.49166666666667[/C][C]0.127742052649337[/C][C]35.1620047862914[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4.50833333333333[/C][C]0.124947258176402[/C][C]36.0818908644512[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4.50833333333333[/C][C]0.124947258176402[/C][C]36.0818908644512[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4.52833333333333[/C][C]0.121736300791178[/C][C]37.1978884186819[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4.50666666666667[/C][C]0.118270652612147[/C][C]38.1046909536018[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4.53[/C][C]0.114642652852712[/C][C]39.5140891045148[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4.505[/C][C]0.110760723422644[/C][C]40.6732626944816[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4.505[/C][C]0.110760723422644[/C][C]40.6732626944816[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4.505[/C][C]0.102191384646873[/C][C]44.0839510646345[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4.505[/C][C]0.102191384646873[/C][C]44.0839510646345[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4.505[/C][C]0.0928343704615001[/C][C]48.5272855043305[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4.505[/C][C]0.0832064005034815[/C][C]54.1424694823988[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4.51034482758621[/C][C]0.135917701674165[/C][C]33.1843812250361[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4.50892857142857[/C][C]0.135159280391939[/C][C]33.3601108140961[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4.50740740740741[/C][C]0.134866754955608[/C][C]33.4211897430989[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4.50576923076923[/C][C]0.134321754743691[/C][C]33.5445977411999[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4.506[/C][C]0.133902492699055[/C][C]33.6513526311061[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4.50625[/C][C]0.133169433283291[/C][C]33.8384709531193[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4.50869565217391[/C][C]0.132527495532224[/C][C]34.0208319342881[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4.50909090909091[/C][C]0.132020330527145[/C][C]34.1545191644841[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4.50952380952381[/C][C]0.131099589943179[/C][C]34.3976957630326[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4.5125[/C][C]0.130245699766604[/C][C]34.6460574751125[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4.51315789473684[/C][C]0.129512218299770[/C][C]34.8473522729004[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4.51388888888889[/C][C]0.128183448512915[/C][C]35.2142881257723[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4.51176470588235[/C][C]0.126854493390840[/C][C]35.5664555924052[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4.5125[/C][C]0.125543174683761[/C][C]35.9438098595708[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4.51[/C][C]0.124230967690561[/C][C]36.303347577825[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4.51071428571429[/C][C]0.122942246271846[/C][C]36.6897012418361[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4.51153846153846[/C][C]0.120425773254338[/C][C]37.4632301675998[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4.5125[/C][C]0.118919120608827[/C][C]37.9459583698354[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4.51363636363636[/C][C]0.115712633781650[/C][C]39.007290873299[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4.515[/C][C]0.113618706762204[/C][C]39.7381745371347[/C][/ROW]
[ROW][C]Median[/C][C]4.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.47741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.47741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.47741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.47741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.47741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.47741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.47741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.54545454545455[/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=48731&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48731&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 Mean4.511666666666670.13642099318762333.0716450690376
Geometric Mean4.38678192008681
Harmonic Mean4.26228366750416
Quadratic Mean4.63175632634821
Winsorized Mean ( 1 / 20 )4.511666666666670.13642099318762333.0716450690376
Winsorized Mean ( 2 / 20 )4.511666666666670.13517286832589633.3770136162919
Winsorized Mean ( 3 / 20 )4.511666666666670.13517286832589633.3770136162919
Winsorized Mean ( 4 / 20 )4.5050.13396232289267933.6288584933623
Winsorized Mean ( 5 / 20 )4.5050.13396232289267933.6288584933623
Winsorized Mean ( 6 / 20 )4.4950.13224324873564733.9903930293293
Winsorized Mean ( 7 / 20 )4.506666666666670.13020771468779634.6113644454361
Winsorized Mean ( 8 / 20 )4.506666666666670.13020771468779634.6113644454361
Winsorized Mean ( 9 / 20 )4.491666666666670.12774205264933735.1620047862914
Winsorized Mean ( 10 / 20 )4.508333333333330.12494725817640236.0818908644512
Winsorized Mean ( 11 / 20 )4.508333333333330.12494725817640236.0818908644512
Winsorized Mean ( 12 / 20 )4.528333333333330.12173630079117837.1978884186819
Winsorized Mean ( 13 / 20 )4.506666666666670.11827065261214738.1046909536018
Winsorized Mean ( 14 / 20 )4.530.11464265285271239.5140891045148
Winsorized Mean ( 15 / 20 )4.5050.11076072342264440.6732626944816
Winsorized Mean ( 16 / 20 )4.5050.11076072342264440.6732626944816
Winsorized Mean ( 17 / 20 )4.5050.10219138464687344.0839510646345
Winsorized Mean ( 18 / 20 )4.5050.10219138464687344.0839510646345
Winsorized Mean ( 19 / 20 )4.5050.092834370461500148.5272855043305
Winsorized Mean ( 20 / 20 )4.5050.083206400503481554.1424694823988
Trimmed Mean ( 1 / 20 )4.510344827586210.13591770167416533.1843812250361
Trimmed Mean ( 2 / 20 )4.508928571428570.13515928039193933.3601108140961
Trimmed Mean ( 3 / 20 )4.507407407407410.13486675495560833.4211897430989
Trimmed Mean ( 4 / 20 )4.505769230769230.13432175474369133.5445977411999
Trimmed Mean ( 5 / 20 )4.5060.13390249269905533.6513526311061
Trimmed Mean ( 6 / 20 )4.506250.13316943328329133.8384709531193
Trimmed Mean ( 7 / 20 )4.508695652173910.13252749553222434.0208319342881
Trimmed Mean ( 8 / 20 )4.509090909090910.13202033052714534.1545191644841
Trimmed Mean ( 9 / 20 )4.509523809523810.13109958994317934.3976957630326
Trimmed Mean ( 10 / 20 )4.51250.13024569976660434.6460574751125
Trimmed Mean ( 11 / 20 )4.513157894736840.12951221829977034.8473522729004
Trimmed Mean ( 12 / 20 )4.513888888888890.12818344851291535.2142881257723
Trimmed Mean ( 13 / 20 )4.511764705882350.12685449339084035.5664555924052
Trimmed Mean ( 14 / 20 )4.51250.12554317468376135.9438098595708
Trimmed Mean ( 15 / 20 )4.510.12423096769056136.303347577825
Trimmed Mean ( 16 / 20 )4.510714285714290.12294224627184636.6897012418361
Trimmed Mean ( 17 / 20 )4.511538461538460.12042577325433837.4632301675998
Trimmed Mean ( 18 / 20 )4.51250.11891912060882737.9459583698354
Trimmed Mean ( 19 / 20 )4.513636363636360.11571263378165039.007290873299
Trimmed Mean ( 20 / 20 )4.5150.11361870676220439.7381745371347
Median4.45
Midrange4.55
Midmean - Weighted Average at Xnp4.47741935483871
Midmean - Weighted Average at X(n+1)p4.47741935483871
Midmean - Empirical Distribution Function4.47741935483871
Midmean - Empirical Distribution Function - Averaging4.47741935483871
Midmean - Empirical Distribution Function - Interpolation4.47741935483871
Midmean - Closest Observation4.47741935483871
Midmean - True Basic - Statistics Graphics Toolkit4.47741935483871
Midmean - MS Excel (old versions)4.54545454545455
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')