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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 computationTue, 14 Mar 2017 19:47:44 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/14/t14895210072bi6n3rguwg7wqe.htm/, Retrieved Tue, 14 May 2024 22:23:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 22:23:43 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
93,09
93,02
93,23
92,7
92,68
93,11
93,02
93,29
93,2
92,86
93,04
92,8
93,11
93,42
94,01
94,47
94,07
94,33
94,43
95,37
95,83
95,46
96
95,35
96,85
97,84
98,38
98,9
99,51
99,95
99,93
101,4
101,7
101,65
102,33
101,56
101,91
102,29
102,44
102,84
103,2
103,23
103,16
103,31
103,04
102,57
102,88
101,91
102,59
103,27
103,59
104,35
104,6
105,08
104,93
105,15
104,67
104,55
109,82
109,25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.10866666666670.626798630774262158.11883083446
Geometric Mean98.9918383797891
Harmonic Mean98.8752314878607
Quadratic Mean99.2255386648686
Winsorized Mean ( 1 / 20 )99.09950.624055237351259158.799244151236
Winsorized Mean ( 2 / 20 )98.96616666666670.592366797903127167.069064331406
Winsorized Mean ( 3 / 20 )98.96566666666670.591223206135122167.391377130837
Winsorized Mean ( 4 / 20 )98.96633333333330.587638382147778168.413664491448
Winsorized Mean ( 5 / 20 )98.94466666666670.583974569268037169.433177185585
Winsorized Mean ( 6 / 20 )98.93966666666670.582472858496533169.861419675498
Winsorized Mean ( 7 / 20 )98.93966666666670.580515841458747170.434051236305
Winsorized Mean ( 8 / 20 )98.91566666666670.575742918081743171.805268567147
Winsorized Mean ( 9 / 20 )98.80166666666670.558325744108975176.960614317262
Winsorized Mean ( 10 / 20 )98.770.549077552074468179.883514863861
Winsorized Mean ( 11 / 20 )98.76816666666670.547107674446991180.527839911038
Winsorized Mean ( 12 / 20 )98.77216666666670.543939807013132181.586575193019
Winsorized Mean ( 13 / 20 )98.79383333333340.538248367033228183.546926259852
Winsorized Mean ( 14 / 20 )98.92216666666670.514143195537868192.401975802052
Winsorized Mean ( 15 / 20 )98.90716666666670.507551288308535194.871274972593
Winsorized Mean ( 16 / 20 )98.93383333333330.490582675102893201.66597467508
Winsorized Mean ( 17 / 20 )98.95083333333330.484545525994027204.213697217283
Winsorized Mean ( 18 / 20 )98.88783333333330.472563575471622209.258263789465
Winsorized Mean ( 19 / 20 )99.16016666666670.428591537181825231.362866655482
Winsorized Mean ( 20 / 20 )99.12350.42177696632466235.014019053142
Trimmed Mean ( 1 / 20 )99.03482758620690.611051241851399162.07286853087
Trimmed Mean ( 2 / 20 )98.96553571428570.594798226163242166.385055235731
Trimmed Mean ( 3 / 20 )98.96518518518520.59505185022339166.313549227739
Trimmed Mean ( 4 / 20 )98.9650.594954876167694166.340346073751
Trimmed Mean ( 5 / 20 )98.96460.595153090235047166.28427479208
Trimmed Mean ( 6 / 20 )98.96958333333330.595460290278919166.206857029837
Trimmed Mean ( 7 / 20 )98.97608695652170.595089850582877166.321248563687
Trimmed Mean ( 8 / 20 )98.98318181818180.593897950097264166.666986814774
Trimmed Mean ( 9 / 20 )98.99523809523810.592261972172123167.147719669005
Trimmed Mean ( 10 / 20 )99.02750.592822318474981167.044149509663
Trimmed Mean ( 11 / 20 )99.06815789473680.593876631208667166.816056885606
Trimmed Mean ( 12 / 20 )99.11361111111110.593661914472274166.95295536891
Trimmed Mean ( 13 / 20 )99.16382352941180.591926221300192167.527336956951
Trimmed Mean ( 14 / 20 )99.21718750.588660698722759168.547327374285
Trimmed Mean ( 15 / 20 )99.25933333333330.588232680003207168.741616553491
Trimmed Mean ( 16 / 20 )99.30964285714290.586151803780241169.426490231148
Trimmed Mean ( 17 / 20 )99.36384615384620.584572447815976169.976957561171
Trimmed Mean ( 18 / 20 )99.42458333333330.579864732841824171.461683565526
Trimmed Mean ( 19 / 20 )99.50590909090910.571496349532114174.114688873122
Trimmed Mean ( 20 / 20 )99.56050.571639136721393174.166696442487
Median99.94
Midrange101.25
Midmean - Weighted Average at Xnp99.09
Midmean - Weighted Average at X(n+1)p99.2593333333334
Midmean - Empirical Distribution Function99.09
Midmean - Empirical Distribution Function - Averaging99.2593333333334
Midmean - Empirical Distribution Function - Interpolation99.2593333333334
Midmean - Closest Observation99.09
Midmean - True Basic - Statistics Graphics Toolkit99.2593333333334
Midmean - MS Excel (old versions)99.2171875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.1086666666667 & 0.626798630774262 & 158.11883083446 \tabularnewline
Geometric Mean & 98.9918383797891 &  &  \tabularnewline
Harmonic Mean & 98.8752314878607 &  &  \tabularnewline
Quadratic Mean & 99.2255386648686 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.0995 & 0.624055237351259 & 158.799244151236 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 98.9661666666667 & 0.592366797903127 & 167.069064331406 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 98.9656666666667 & 0.591223206135122 & 167.391377130837 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 98.9663333333333 & 0.587638382147778 & 168.413664491448 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 98.9446666666667 & 0.583974569268037 & 169.433177185585 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 98.9396666666667 & 0.582472858496533 & 169.861419675498 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 98.9396666666667 & 0.580515841458747 & 170.434051236305 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 98.9156666666667 & 0.575742918081743 & 171.805268567147 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 98.8016666666667 & 0.558325744108975 & 176.960614317262 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 98.77 & 0.549077552074468 & 179.883514863861 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 98.7681666666667 & 0.547107674446991 & 180.527839911038 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 98.7721666666667 & 0.543939807013132 & 181.586575193019 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 98.7938333333334 & 0.538248367033228 & 183.546926259852 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 98.9221666666667 & 0.514143195537868 & 192.401975802052 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 98.9071666666667 & 0.507551288308535 & 194.871274972593 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 98.9338333333333 & 0.490582675102893 & 201.66597467508 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 98.9508333333333 & 0.484545525994027 & 204.213697217283 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 98.8878333333333 & 0.472563575471622 & 209.258263789465 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.1601666666667 & 0.428591537181825 & 231.362866655482 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 99.1235 & 0.42177696632466 & 235.014019053142 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.0348275862069 & 0.611051241851399 & 162.07286853087 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 98.9655357142857 & 0.594798226163242 & 166.385055235731 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 98.9651851851852 & 0.59505185022339 & 166.313549227739 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 98.965 & 0.594954876167694 & 166.340346073751 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 98.9646 & 0.595153090235047 & 166.28427479208 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 98.9695833333333 & 0.595460290278919 & 166.206857029837 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 98.9760869565217 & 0.595089850582877 & 166.321248563687 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 98.9831818181818 & 0.593897950097264 & 166.666986814774 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 98.9952380952381 & 0.592261972172123 & 167.147719669005 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.0275 & 0.592822318474981 & 167.044149509663 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.0681578947368 & 0.593876631208667 & 166.816056885606 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.1136111111111 & 0.593661914472274 & 166.95295536891 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.1638235294118 & 0.591926221300192 & 167.527336956951 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.2171875 & 0.588660698722759 & 168.547327374285 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.2593333333333 & 0.588232680003207 & 168.741616553491 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.3096428571429 & 0.586151803780241 & 169.426490231148 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.3638461538462 & 0.584572447815976 & 169.976957561171 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.4245833333333 & 0.579864732841824 & 171.461683565526 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.5059090909091 & 0.571496349532114 & 174.114688873122 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.5605 & 0.571639136721393 & 174.166696442487 \tabularnewline
Median & 99.94 &  &  \tabularnewline
Midrange & 101.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.09 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.2593333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.09 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.2593333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.2593333333334 &  &  \tabularnewline
Midmean - Closest Observation & 99.09 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.2593333333334 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.2171875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]99.1086666666667[/C][C]0.626798630774262[/C][C]158.11883083446[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.9918383797891[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.8752314878607[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.2255386648686[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.0995[/C][C]0.624055237351259[/C][C]158.799244151236[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]98.9661666666667[/C][C]0.592366797903127[/C][C]167.069064331406[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]98.9656666666667[/C][C]0.591223206135122[/C][C]167.391377130837[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]98.9663333333333[/C][C]0.587638382147778[/C][C]168.413664491448[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]98.9446666666667[/C][C]0.583974569268037[/C][C]169.433177185585[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]98.9396666666667[/C][C]0.582472858496533[/C][C]169.861419675498[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]98.9396666666667[/C][C]0.580515841458747[/C][C]170.434051236305[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]98.9156666666667[/C][C]0.575742918081743[/C][C]171.805268567147[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]98.8016666666667[/C][C]0.558325744108975[/C][C]176.960614317262[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]98.77[/C][C]0.549077552074468[/C][C]179.883514863861[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]98.7681666666667[/C][C]0.547107674446991[/C][C]180.527839911038[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]98.7721666666667[/C][C]0.543939807013132[/C][C]181.586575193019[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]98.7938333333334[/C][C]0.538248367033228[/C][C]183.546926259852[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]98.9221666666667[/C][C]0.514143195537868[/C][C]192.401975802052[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]98.9071666666667[/C][C]0.507551288308535[/C][C]194.871274972593[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]98.9338333333333[/C][C]0.490582675102893[/C][C]201.66597467508[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]98.9508333333333[/C][C]0.484545525994027[/C][C]204.213697217283[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]98.8878333333333[/C][C]0.472563575471622[/C][C]209.258263789465[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.1601666666667[/C][C]0.428591537181825[/C][C]231.362866655482[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]99.1235[/C][C]0.42177696632466[/C][C]235.014019053142[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.0348275862069[/C][C]0.611051241851399[/C][C]162.07286853087[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]98.9655357142857[/C][C]0.594798226163242[/C][C]166.385055235731[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]98.9651851851852[/C][C]0.59505185022339[/C][C]166.313549227739[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]98.965[/C][C]0.594954876167694[/C][C]166.340346073751[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]98.9646[/C][C]0.595153090235047[/C][C]166.28427479208[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]98.9695833333333[/C][C]0.595460290278919[/C][C]166.206857029837[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]98.9760869565217[/C][C]0.595089850582877[/C][C]166.321248563687[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]98.9831818181818[/C][C]0.593897950097264[/C][C]166.666986814774[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]98.9952380952381[/C][C]0.592261972172123[/C][C]167.147719669005[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.0275[/C][C]0.592822318474981[/C][C]167.044149509663[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.0681578947368[/C][C]0.593876631208667[/C][C]166.816056885606[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.1136111111111[/C][C]0.593661914472274[/C][C]166.95295536891[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.1638235294118[/C][C]0.591926221300192[/C][C]167.527336956951[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.2171875[/C][C]0.588660698722759[/C][C]168.547327374285[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.2593333333333[/C][C]0.588232680003207[/C][C]168.741616553491[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.3096428571429[/C][C]0.586151803780241[/C][C]169.426490231148[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.3638461538462[/C][C]0.584572447815976[/C][C]169.976957561171[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.4245833333333[/C][C]0.579864732841824[/C][C]171.461683565526[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.5059090909091[/C][C]0.571496349532114[/C][C]174.114688873122[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.5605[/C][C]0.571639136721393[/C][C]174.166696442487[/C][/ROW]
[ROW][C]Median[/C][C]99.94[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.2593333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.2593333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.2593333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.2593333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.2171875[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean99.10866666666670.626798630774262158.11883083446
Geometric Mean98.9918383797891
Harmonic Mean98.8752314878607
Quadratic Mean99.2255386648686
Winsorized Mean ( 1 / 20 )99.09950.624055237351259158.799244151236
Winsorized Mean ( 2 / 20 )98.96616666666670.592366797903127167.069064331406
Winsorized Mean ( 3 / 20 )98.96566666666670.591223206135122167.391377130837
Winsorized Mean ( 4 / 20 )98.96633333333330.587638382147778168.413664491448
Winsorized Mean ( 5 / 20 )98.94466666666670.583974569268037169.433177185585
Winsorized Mean ( 6 / 20 )98.93966666666670.582472858496533169.861419675498
Winsorized Mean ( 7 / 20 )98.93966666666670.580515841458747170.434051236305
Winsorized Mean ( 8 / 20 )98.91566666666670.575742918081743171.805268567147
Winsorized Mean ( 9 / 20 )98.80166666666670.558325744108975176.960614317262
Winsorized Mean ( 10 / 20 )98.770.549077552074468179.883514863861
Winsorized Mean ( 11 / 20 )98.76816666666670.547107674446991180.527839911038
Winsorized Mean ( 12 / 20 )98.77216666666670.543939807013132181.586575193019
Winsorized Mean ( 13 / 20 )98.79383333333340.538248367033228183.546926259852
Winsorized Mean ( 14 / 20 )98.92216666666670.514143195537868192.401975802052
Winsorized Mean ( 15 / 20 )98.90716666666670.507551288308535194.871274972593
Winsorized Mean ( 16 / 20 )98.93383333333330.490582675102893201.66597467508
Winsorized Mean ( 17 / 20 )98.95083333333330.484545525994027204.213697217283
Winsorized Mean ( 18 / 20 )98.88783333333330.472563575471622209.258263789465
Winsorized Mean ( 19 / 20 )99.16016666666670.428591537181825231.362866655482
Winsorized Mean ( 20 / 20 )99.12350.42177696632466235.014019053142
Trimmed Mean ( 1 / 20 )99.03482758620690.611051241851399162.07286853087
Trimmed Mean ( 2 / 20 )98.96553571428570.594798226163242166.385055235731
Trimmed Mean ( 3 / 20 )98.96518518518520.59505185022339166.313549227739
Trimmed Mean ( 4 / 20 )98.9650.594954876167694166.340346073751
Trimmed Mean ( 5 / 20 )98.96460.595153090235047166.28427479208
Trimmed Mean ( 6 / 20 )98.96958333333330.595460290278919166.206857029837
Trimmed Mean ( 7 / 20 )98.97608695652170.595089850582877166.321248563687
Trimmed Mean ( 8 / 20 )98.98318181818180.593897950097264166.666986814774
Trimmed Mean ( 9 / 20 )98.99523809523810.592261972172123167.147719669005
Trimmed Mean ( 10 / 20 )99.02750.592822318474981167.044149509663
Trimmed Mean ( 11 / 20 )99.06815789473680.593876631208667166.816056885606
Trimmed Mean ( 12 / 20 )99.11361111111110.593661914472274166.95295536891
Trimmed Mean ( 13 / 20 )99.16382352941180.591926221300192167.527336956951
Trimmed Mean ( 14 / 20 )99.21718750.588660698722759168.547327374285
Trimmed Mean ( 15 / 20 )99.25933333333330.588232680003207168.741616553491
Trimmed Mean ( 16 / 20 )99.30964285714290.586151803780241169.426490231148
Trimmed Mean ( 17 / 20 )99.36384615384620.584572447815976169.976957561171
Trimmed Mean ( 18 / 20 )99.42458333333330.579864732841824171.461683565526
Trimmed Mean ( 19 / 20 )99.50590909090910.571496349532114174.114688873122
Trimmed Mean ( 20 / 20 )99.56050.571639136721393174.166696442487
Median99.94
Midrange101.25
Midmean - Weighted Average at Xnp99.09
Midmean - Weighted Average at X(n+1)p99.2593333333334
Midmean - Empirical Distribution Function99.09
Midmean - Empirical Distribution Function - Averaging99.2593333333334
Midmean - Empirical Distribution Function - Interpolation99.2593333333334
Midmean - Closest Observation99.09
Midmean - True Basic - Statistics Graphics Toolkit99.2593333333334
Midmean - MS Excel (old versions)99.2171875
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')