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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 03:53:21 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/13/t1197542339ijyhs9vuqob7tcj.htm/, Retrieved Sun, 05 May 2024 09:16:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3425, Retrieved Sun, 05 May 2024 09:16:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrale tendens ...] [2007-12-13 10:53:21] [2cdb7403ed3391afb545b8c0d20da37e] [Current]
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Dataseries X:
0
6
1
0
-1
-2
0
-1
3
1
-3
0
-2
-1
1
0
1
-2
-2
0
-1
-3
1
0
-2
0
-3
-4
0
2
1
1
-1
-1
-1
1
2
0
-1
-2
1
-1
2
2
0
-4
-2
-1
-5
-1
-2
8
-4
0
0
-4
-3
-1
0
-5




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3425&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3425&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3425&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.5333333333333330.296368478338907-1.79956160089147
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.33809038890002
Winsorized Mean ( 1 / 20 )-0.5666666666666670.281608241190828-2.01225171632201
Winsorized Mean ( 2 / 20 )-0.6333333333333330.240017262404924-2.63869909600444
Winsorized Mean ( 3 / 20 )-0.6833333333333330.228593917040068-2.98928922598391
Winsorized Mean ( 4 / 20 )-0.6833333333333330.228593917040068-2.98928922598391
Winsorized Mean ( 5 / 20 )-0.6833333333333330.228593917040068-2.98928922598391
Winsorized Mean ( 6 / 20 )-0.5833333333333330.206246611568354-2.82832929422458
Winsorized Mean ( 7 / 20 )-0.70.184574636963396-3.79250373462103
Winsorized Mean ( 8 / 20 )-0.70.184574636963396-3.79250373462103
Winsorized Mean ( 9 / 20 )-0.70.184574636963396-3.79250373462103
Winsorized Mean ( 10 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 11 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 12 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 13 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 14 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 15 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 16 / 20 )-0.80.113496061307005-7.04870275485609
Winsorized Mean ( 17 / 20 )-0.80.113496061307005-7.04870275485609
Winsorized Mean ( 18 / 20 )-0.50.0650944554904119-7.68114574786861
Winsorized Mean ( 19 / 20 )-0.50.0650944554904119-7.68114574786861
Winsorized Mean ( 20 / 20 )-0.50.0650944554904119-7.68114574786861
Trimmed Mean ( 1 / 20 )-0.6034482758620690.256718148181651-2.35062569645476
Trimmed Mean ( 2 / 20 )-0.6428571428571430.224228216635275-2.86697701343627
Trimmed Mean ( 3 / 20 )-0.6481481481481480.213384112482872-3.03747144342892
Trimmed Mean ( 4 / 20 )-0.6346153846153850.205557855092504-3.08728355007304
Trimmed Mean ( 5 / 20 )-0.620.195646495037371-3.16898086971387
Trimmed Mean ( 6 / 20 )-0.6041666666666670.182912759049684-3.30303183772193
Trimmed Mean ( 7 / 20 )-0.6086956521739130.174395466162218-3.4903181004013
Trimmed Mean ( 8 / 20 )-0.5909090909090910.169934018466955-3.47728545608422
Trimmed Mean ( 9 / 20 )-0.5714285714285710.163948297644858-3.48541936474625
Trimmed Mean ( 10 / 20 )-0.550.155868123087666-3.52862400024320
Trimmed Mean ( 11 / 20 )-0.5526315789473680.154115511633664-3.58582710519746
Trimmed Mean ( 12 / 20 )-0.5555555555555560.151418920859833-3.66899692852671
Trimmed Mean ( 13 / 20 )-0.5588235294117650.147414898683918-3.79082124263421
Trimmed Mean ( 14 / 20 )-0.56250.141546042890872-3.97397192116259
Trimmed Mean ( 15 / 20 )-0.5666666666666670.132901599873900-4.26380620853574
Trimmed Mean ( 16 / 20 )-0.5714285714285710.119838641829694-4.76831648543416
Trimmed Mean ( 17 / 20 )-0.5384615384615380.114095361339933-4.71939903724269
Trimmed Mean ( 18 / 20 )-0.50.104257207028537-4.79583152331272
Trimmed Mean ( 19 / 20 )-0.50.109108945117996-4.58257569495584
Trimmed Mean ( 20 / 20 )-0.50.114707866935281-4.35889894354067
Median-0.5
Midrange1.5
Midmean - Weighted Average at Xnp-0.441860465116279
Midmean - Weighted Average at X(n+1)p-0.441860465116279
Midmean - Empirical Distribution Function-0.441860465116279
Midmean - Empirical Distribution Function - Averaging-0.441860465116279
Midmean - Empirical Distribution Function - Interpolation-0.441860465116279
Midmean - Closest Observation-0.441860465116279
Midmean - True Basic - Statistics Graphics Toolkit-0.441860465116279
Midmean - MS Excel (old versions)-0.441860465116279
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.533333333333333 & 0.296368478338907 & -1.79956160089147 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.33809038890002 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -0.566666666666667 & 0.281608241190828 & -2.01225171632201 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -0.633333333333333 & 0.240017262404924 & -2.63869909600444 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -0.683333333333333 & 0.228593917040068 & -2.98928922598391 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -0.683333333333333 & 0.228593917040068 & -2.98928922598391 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -0.683333333333333 & 0.228593917040068 & -2.98928922598391 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -0.583333333333333 & 0.206246611568354 & -2.82832929422458 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -0.7 & 0.184574636963396 & -3.79250373462103 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -0.7 & 0.184574636963396 & -3.79250373462103 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -0.7 & 0.184574636963396 & -3.79250373462103 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -0.533333333333333 & 0.153060430196384 & -3.48446252665723 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -0.533333333333333 & 0.153060430196384 & -3.48446252665723 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -0.533333333333333 & 0.153060430196384 & -3.48446252665723 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -0.533333333333333 & 0.153060430196384 & -3.48446252665723 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -0.533333333333333 & 0.153060430196384 & -3.48446252665723 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -0.533333333333333 & 0.153060430196384 & -3.48446252665723 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -0.8 & 0.113496061307005 & -7.04870275485609 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -0.8 & 0.113496061307005 & -7.04870275485609 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -0.5 & 0.0650944554904119 & -7.68114574786861 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -0.5 & 0.0650944554904119 & -7.68114574786861 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -0.5 & 0.0650944554904119 & -7.68114574786861 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -0.603448275862069 & 0.256718148181651 & -2.35062569645476 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -0.642857142857143 & 0.224228216635275 & -2.86697701343627 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -0.648148148148148 & 0.213384112482872 & -3.03747144342892 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -0.634615384615385 & 0.205557855092504 & -3.08728355007304 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -0.62 & 0.195646495037371 & -3.16898086971387 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -0.604166666666667 & 0.182912759049684 & -3.30303183772193 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -0.608695652173913 & 0.174395466162218 & -3.4903181004013 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -0.590909090909091 & 0.169934018466955 & -3.47728545608422 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -0.571428571428571 & 0.163948297644858 & -3.48541936474625 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -0.55 & 0.155868123087666 & -3.52862400024320 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -0.552631578947368 & 0.154115511633664 & -3.58582710519746 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -0.555555555555556 & 0.151418920859833 & -3.66899692852671 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -0.558823529411765 & 0.147414898683918 & -3.79082124263421 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -0.5625 & 0.141546042890872 & -3.97397192116259 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -0.566666666666667 & 0.132901599873900 & -4.26380620853574 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -0.571428571428571 & 0.119838641829694 & -4.76831648543416 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -0.538461538461538 & 0.114095361339933 & -4.71939903724269 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -0.5 & 0.104257207028537 & -4.79583152331272 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -0.5 & 0.109108945117996 & -4.58257569495584 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -0.5 & 0.114707866935281 & -4.35889894354067 \tabularnewline
Median & -0.5 &  &  \tabularnewline
Midrange & 1.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.441860465116279 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.441860465116279 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.441860465116279 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.441860465116279 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.441860465116279 &  &  \tabularnewline
Midmean - Closest Observation & -0.441860465116279 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.441860465116279 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.441860465116279 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3425&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]-0.533333333333333[/C][C]0.296368478338907[/C][C]-1.79956160089147[/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]2.33809038890002[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-0.566666666666667[/C][C]0.281608241190828[/C][C]-2.01225171632201[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-0.633333333333333[/C][C]0.240017262404924[/C][C]-2.63869909600444[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-0.683333333333333[/C][C]0.228593917040068[/C][C]-2.98928922598391[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-0.683333333333333[/C][C]0.228593917040068[/C][C]-2.98928922598391[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-0.683333333333333[/C][C]0.228593917040068[/C][C]-2.98928922598391[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-0.583333333333333[/C][C]0.206246611568354[/C][C]-2.82832929422458[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-0.7[/C][C]0.184574636963396[/C][C]-3.79250373462103[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-0.7[/C][C]0.184574636963396[/C][C]-3.79250373462103[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-0.7[/C][C]0.184574636963396[/C][C]-3.79250373462103[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-0.533333333333333[/C][C]0.153060430196384[/C][C]-3.48446252665723[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-0.533333333333333[/C][C]0.153060430196384[/C][C]-3.48446252665723[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-0.533333333333333[/C][C]0.153060430196384[/C][C]-3.48446252665723[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-0.533333333333333[/C][C]0.153060430196384[/C][C]-3.48446252665723[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-0.533333333333333[/C][C]0.153060430196384[/C][C]-3.48446252665723[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-0.533333333333333[/C][C]0.153060430196384[/C][C]-3.48446252665723[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-0.8[/C][C]0.113496061307005[/C][C]-7.04870275485609[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-0.8[/C][C]0.113496061307005[/C][C]-7.04870275485609[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-0.5[/C][C]0.0650944554904119[/C][C]-7.68114574786861[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-0.5[/C][C]0.0650944554904119[/C][C]-7.68114574786861[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-0.5[/C][C]0.0650944554904119[/C][C]-7.68114574786861[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-0.603448275862069[/C][C]0.256718148181651[/C][C]-2.35062569645476[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-0.642857142857143[/C][C]0.224228216635275[/C][C]-2.86697701343627[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-0.648148148148148[/C][C]0.213384112482872[/C][C]-3.03747144342892[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-0.634615384615385[/C][C]0.205557855092504[/C][C]-3.08728355007304[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-0.62[/C][C]0.195646495037371[/C][C]-3.16898086971387[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-0.604166666666667[/C][C]0.182912759049684[/C][C]-3.30303183772193[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-0.608695652173913[/C][C]0.174395466162218[/C][C]-3.4903181004013[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-0.590909090909091[/C][C]0.169934018466955[/C][C]-3.47728545608422[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-0.571428571428571[/C][C]0.163948297644858[/C][C]-3.48541936474625[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-0.55[/C][C]0.155868123087666[/C][C]-3.52862400024320[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-0.552631578947368[/C][C]0.154115511633664[/C][C]-3.58582710519746[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-0.555555555555556[/C][C]0.151418920859833[/C][C]-3.66899692852671[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-0.558823529411765[/C][C]0.147414898683918[/C][C]-3.79082124263421[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-0.5625[/C][C]0.141546042890872[/C][C]-3.97397192116259[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-0.566666666666667[/C][C]0.132901599873900[/C][C]-4.26380620853574[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-0.571428571428571[/C][C]0.119838641829694[/C][C]-4.76831648543416[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-0.538461538461538[/C][C]0.114095361339933[/C][C]-4.71939903724269[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-0.5[/C][C]0.104257207028537[/C][C]-4.79583152331272[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-0.5[/C][C]0.109108945117996[/C][C]-4.58257569495584[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-0.5[/C][C]0.114707866935281[/C][C]-4.35889894354067[/C][/ROW]
[ROW][C]Median[/C][C]-0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.441860465116279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.441860465116279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.441860465116279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.441860465116279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.441860465116279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.441860465116279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.441860465116279[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.441860465116279[/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=3425&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3425&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 Mean-0.5333333333333330.296368478338907-1.79956160089147
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.33809038890002
Winsorized Mean ( 1 / 20 )-0.5666666666666670.281608241190828-2.01225171632201
Winsorized Mean ( 2 / 20 )-0.6333333333333330.240017262404924-2.63869909600444
Winsorized Mean ( 3 / 20 )-0.6833333333333330.228593917040068-2.98928922598391
Winsorized Mean ( 4 / 20 )-0.6833333333333330.228593917040068-2.98928922598391
Winsorized Mean ( 5 / 20 )-0.6833333333333330.228593917040068-2.98928922598391
Winsorized Mean ( 6 / 20 )-0.5833333333333330.206246611568354-2.82832929422458
Winsorized Mean ( 7 / 20 )-0.70.184574636963396-3.79250373462103
Winsorized Mean ( 8 / 20 )-0.70.184574636963396-3.79250373462103
Winsorized Mean ( 9 / 20 )-0.70.184574636963396-3.79250373462103
Winsorized Mean ( 10 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 11 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 12 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 13 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 14 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 15 / 20 )-0.5333333333333330.153060430196384-3.48446252665723
Winsorized Mean ( 16 / 20 )-0.80.113496061307005-7.04870275485609
Winsorized Mean ( 17 / 20 )-0.80.113496061307005-7.04870275485609
Winsorized Mean ( 18 / 20 )-0.50.0650944554904119-7.68114574786861
Winsorized Mean ( 19 / 20 )-0.50.0650944554904119-7.68114574786861
Winsorized Mean ( 20 / 20 )-0.50.0650944554904119-7.68114574786861
Trimmed Mean ( 1 / 20 )-0.6034482758620690.256718148181651-2.35062569645476
Trimmed Mean ( 2 / 20 )-0.6428571428571430.224228216635275-2.86697701343627
Trimmed Mean ( 3 / 20 )-0.6481481481481480.213384112482872-3.03747144342892
Trimmed Mean ( 4 / 20 )-0.6346153846153850.205557855092504-3.08728355007304
Trimmed Mean ( 5 / 20 )-0.620.195646495037371-3.16898086971387
Trimmed Mean ( 6 / 20 )-0.6041666666666670.182912759049684-3.30303183772193
Trimmed Mean ( 7 / 20 )-0.6086956521739130.174395466162218-3.4903181004013
Trimmed Mean ( 8 / 20 )-0.5909090909090910.169934018466955-3.47728545608422
Trimmed Mean ( 9 / 20 )-0.5714285714285710.163948297644858-3.48541936474625
Trimmed Mean ( 10 / 20 )-0.550.155868123087666-3.52862400024320
Trimmed Mean ( 11 / 20 )-0.5526315789473680.154115511633664-3.58582710519746
Trimmed Mean ( 12 / 20 )-0.5555555555555560.151418920859833-3.66899692852671
Trimmed Mean ( 13 / 20 )-0.5588235294117650.147414898683918-3.79082124263421
Trimmed Mean ( 14 / 20 )-0.56250.141546042890872-3.97397192116259
Trimmed Mean ( 15 / 20 )-0.5666666666666670.132901599873900-4.26380620853574
Trimmed Mean ( 16 / 20 )-0.5714285714285710.119838641829694-4.76831648543416
Trimmed Mean ( 17 / 20 )-0.5384615384615380.114095361339933-4.71939903724269
Trimmed Mean ( 18 / 20 )-0.50.104257207028537-4.79583152331272
Trimmed Mean ( 19 / 20 )-0.50.109108945117996-4.58257569495584
Trimmed Mean ( 20 / 20 )-0.50.114707866935281-4.35889894354067
Median-0.5
Midrange1.5
Midmean - Weighted Average at Xnp-0.441860465116279
Midmean - Weighted Average at X(n+1)p-0.441860465116279
Midmean - Empirical Distribution Function-0.441860465116279
Midmean - Empirical Distribution Function - Averaging-0.441860465116279
Midmean - Empirical Distribution Function - Interpolation-0.441860465116279
Midmean - Closest Observation-0.441860465116279
Midmean - True Basic - Statistics Graphics Toolkit-0.441860465116279
Midmean - MS Excel (old versions)-0.441860465116279
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')