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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 27 Oct 2008 14:18:10 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/27/t1225138734q3v10g1fb72losb.htm/, Retrieved Sun, 19 May 2024 14:39:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19568, Retrieved Sun, 19 May 2024 14:39:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [invoer vanuit vs] [2008-10-13 19:11:39] [57ce5bd741080980f0f51979adb31ad8]
F   PD  [Univariate Data Series] [Totale productie ...] [2008-10-19 13:44:22] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD      [Central Tendency] [central tend produ] [2008-10-27 20:18:10] [a8228479d4547a92e2d3f176a5299609] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
89.9
109.8
111.7
98.6
96.9
95.1
97
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1
115.9
95.7

Tables (Output of Computation)





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=19568&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=19568&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19568&T=0

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


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

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






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.0951.1608014594445590.5365849990307
Geometric Mean104.704283922727
Harmonic Mean104.300419825972
Quadratic Mean105.472551721605
Winsorized Mean ( 1 / 20 )105.111.1225543410399293.6346652961382
Winsorized Mean ( 2 / 20 )105.1266666666671.0935761753184496.1310871975194
Winsorized Mean ( 3 / 20 )105.2466666666671.0600913154001599.2807554761824
Winsorized Mean ( 4 / 20 )105.3733333333331.01125269594989104.200793486493
Winsorized Mean ( 5 / 20 )105.4983333333330.966373884163095109.169271916633
Winsorized Mean ( 6 / 20 )105.5083333333330.949734698806336111.092427670528
Winsorized Mean ( 7 / 20 )105.4966666666670.922667977040969114.338710448149
Winsorized Mean ( 8 / 20 )105.470.91814200740556114.873297539268
Winsorized Mean ( 9 / 20 )105.4250.900300091212529117.099843739895
Winsorized Mean ( 10 / 20 )105.5416666666670.86860590839889121.506963798131
Winsorized Mean ( 11 / 20 )105.450.847870379710814124.370425625632
Winsorized Mean ( 12 / 20 )105.450.841328314829195125.337514667396
Winsorized Mean ( 13 / 20 )105.4716666666670.81660414265443129.158867996706
Winsorized Mean ( 14 / 20 )105.6116666666670.786079780840071134.352351047372
Winsorized Mean ( 15 / 20 )105.7116666666670.762189426114403138.694743123870
Winsorized Mean ( 16 / 20 )105.7650.737183619775654143.471717442918
Winsorized Mean ( 17 / 20 )105.8216666666670.659194387911953160.531807623340
Winsorized Mean ( 18 / 20 )105.8816666666670.623433592649967169.836319240685
Winsorized Mean ( 19 / 20 )105.7233333333330.581437759500755181.830869436673
Winsorized Mean ( 20 / 20 )105.590.562298049120924187.782974109683
Trimmed Mean ( 1 / 20 )105.2137931034481.0839433294295397.0657692582706
Trimmed Mean ( 2 / 20 )105.3251.03611176877912101.654090971390
Trimmed Mean ( 3 / 20 )105.4351851851850.996342568787167105.822222685446
Trimmed Mean ( 4 / 20 )105.5076923076920.963331661239446109.523746133231
Trimmed Mean ( 5 / 20 )105.5480.941333140621668112.126085277625
Trimmed Mean ( 6 / 20 )105.5604166666670.928263552692069113.718152954007
Trimmed Mean ( 7 / 20 )105.5717391304350.915701273165064115.290588999110
Trimmed Mean ( 8 / 20 )105.5863636363640.90602044900063116.538609865626
Trimmed Mean ( 9 / 20 )105.6071428571430.8932863080075118.223174261679
Trimmed Mean ( 10 / 20 )105.63750.879865137538936120.061013322426
Trimmed Mean ( 11 / 20 )105.6526315789470.868819254366669121.604845942282
Trimmed Mean ( 12 / 20 )105.6833333333330.857363066950886123.265553890937
Trimmed Mean ( 13 / 20 )105.7176470588240.841360312981828125.650860193482
Trimmed Mean ( 14 / 20 )105.7531250.823936073200934128.351128734001
Trimmed Mean ( 15 / 20 )105.7733333333330.806010942758685131.230641821449
Trimmed Mean ( 16 / 20 )105.7821428571430.784911506679712134.769514724808
Trimmed Mean ( 17 / 20 )105.7846153846150.759183616336397139.339960858352
Trimmed Mean ( 18 / 20 )105.7791666666670.744763827137543142.030483775270
Trimmed Mean ( 19 / 20 )105.7636363636360.730757344631971144.731540696182
Trimmed Mean ( 20 / 20 )105.770.719469834048143147.011028113407
Median105.6
Midrange101.65
Midmean - Weighted Average at Xnp105.525806451613
Midmean - Weighted Average at X(n+1)p105.773333333333
Midmean - Empirical Distribution Function105.525806451613
Midmean - Empirical Distribution Function - Averaging105.773333333333
Midmean - Empirical Distribution Function - Interpolation105.773333333333
Midmean - Closest Observation105.525806451613
Midmean - True Basic - Statistics Graphics Toolkit105.773333333333
Midmean - MS Excel (old versions)105.753125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.095 & 1.16080145944455 & 90.5365849990307 \tabularnewline
Geometric Mean & 104.704283922727 &  &  \tabularnewline
Harmonic Mean & 104.300419825972 &  &  \tabularnewline
Quadratic Mean & 105.472551721605 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 105.11 & 1.12255434103992 & 93.6346652961382 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 105.126666666667 & 1.09357617531844 & 96.1310871975194 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 105.246666666667 & 1.06009131540015 & 99.2807554761824 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 105.373333333333 & 1.01125269594989 & 104.200793486493 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 105.498333333333 & 0.966373884163095 & 109.169271916633 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.508333333333 & 0.949734698806336 & 111.092427670528 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 105.496666666667 & 0.922667977040969 & 114.338710448149 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 105.47 & 0.91814200740556 & 114.873297539268 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.425 & 0.900300091212529 & 117.099843739895 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.541666666667 & 0.86860590839889 & 121.506963798131 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 105.45 & 0.847870379710814 & 124.370425625632 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 105.45 & 0.841328314829195 & 125.337514667396 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.471666666667 & 0.81660414265443 & 129.158867996706 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 105.611666666667 & 0.786079780840071 & 134.352351047372 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 105.711666666667 & 0.762189426114403 & 138.694743123870 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.765 & 0.737183619775654 & 143.471717442918 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.821666666667 & 0.659194387911953 & 160.531807623340 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 105.881666666667 & 0.623433592649967 & 169.836319240685 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.723333333333 & 0.581437759500755 & 181.830869436673 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.59 & 0.562298049120924 & 187.782974109683 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 105.213793103448 & 1.08394332942953 & 97.0657692582706 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 105.325 & 1.03611176877912 & 101.654090971390 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 105.435185185185 & 0.996342568787167 & 105.822222685446 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 105.507692307692 & 0.963331661239446 & 109.523746133231 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.548 & 0.941333140621668 & 112.126085277625 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.560416666667 & 0.928263552692069 & 113.718152954007 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.571739130435 & 0.915701273165064 & 115.290588999110 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.586363636364 & 0.90602044900063 & 116.538609865626 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.607142857143 & 0.8932863080075 & 118.223174261679 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.6375 & 0.879865137538936 & 120.061013322426 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.652631578947 & 0.868819254366669 & 121.604845942282 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.683333333333 & 0.857363066950886 & 123.265553890937 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.717647058824 & 0.841360312981828 & 125.650860193482 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.753125 & 0.823936073200934 & 128.351128734001 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.773333333333 & 0.806010942758685 & 131.230641821449 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.782142857143 & 0.784911506679712 & 134.769514724808 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.784615384615 & 0.759183616336397 & 139.339960858352 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.779166666667 & 0.744763827137543 & 142.030483775270 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 105.763636363636 & 0.730757344631971 & 144.731540696182 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 105.77 & 0.719469834048143 & 147.011028113407 \tabularnewline
Median & 105.6 &  &  \tabularnewline
Midrange & 101.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.525806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.773333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.525806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.773333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.773333333333 &  &  \tabularnewline
Midmean - Closest Observation & 105.525806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.773333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.753125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19568&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]105.095[/C][C]1.16080145944455[/C][C]90.5365849990307[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.704283922727[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.300419825972[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.472551721605[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]105.11[/C][C]1.12255434103992[/C][C]93.6346652961382[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]105.126666666667[/C][C]1.09357617531844[/C][C]96.1310871975194[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]105.246666666667[/C][C]1.06009131540015[/C][C]99.2807554761824[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]105.373333333333[/C][C]1.01125269594989[/C][C]104.200793486493[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]105.498333333333[/C][C]0.966373884163095[/C][C]109.169271916633[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.508333333333[/C][C]0.949734698806336[/C][C]111.092427670528[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]105.496666666667[/C][C]0.922667977040969[/C][C]114.338710448149[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]105.47[/C][C]0.91814200740556[/C][C]114.873297539268[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.425[/C][C]0.900300091212529[/C][C]117.099843739895[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.541666666667[/C][C]0.86860590839889[/C][C]121.506963798131[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]105.45[/C][C]0.847870379710814[/C][C]124.370425625632[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]105.45[/C][C]0.841328314829195[/C][C]125.337514667396[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.471666666667[/C][C]0.81660414265443[/C][C]129.158867996706[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]105.611666666667[/C][C]0.786079780840071[/C][C]134.352351047372[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]105.711666666667[/C][C]0.762189426114403[/C][C]138.694743123870[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.765[/C][C]0.737183619775654[/C][C]143.471717442918[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.821666666667[/C][C]0.659194387911953[/C][C]160.531807623340[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]105.881666666667[/C][C]0.623433592649967[/C][C]169.836319240685[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.723333333333[/C][C]0.581437759500755[/C][C]181.830869436673[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.59[/C][C]0.562298049120924[/C][C]187.782974109683[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]105.213793103448[/C][C]1.08394332942953[/C][C]97.0657692582706[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]105.325[/C][C]1.03611176877912[/C][C]101.654090971390[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]105.435185185185[/C][C]0.996342568787167[/C][C]105.822222685446[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]105.507692307692[/C][C]0.963331661239446[/C][C]109.523746133231[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.548[/C][C]0.941333140621668[/C][C]112.126085277625[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.560416666667[/C][C]0.928263552692069[/C][C]113.718152954007[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.571739130435[/C][C]0.915701273165064[/C][C]115.290588999110[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.586363636364[/C][C]0.90602044900063[/C][C]116.538609865626[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.607142857143[/C][C]0.8932863080075[/C][C]118.223174261679[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.6375[/C][C]0.879865137538936[/C][C]120.061013322426[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.652631578947[/C][C]0.868819254366669[/C][C]121.604845942282[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.683333333333[/C][C]0.857363066950886[/C][C]123.265553890937[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.717647058824[/C][C]0.841360312981828[/C][C]125.650860193482[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.753125[/C][C]0.823936073200934[/C][C]128.351128734001[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.773333333333[/C][C]0.806010942758685[/C][C]131.230641821449[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.782142857143[/C][C]0.784911506679712[/C][C]134.769514724808[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.784615384615[/C][C]0.759183616336397[/C][C]139.339960858352[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.779166666667[/C][C]0.744763827137543[/C][C]142.030483775270[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]105.763636363636[/C][C]0.730757344631971[/C][C]144.731540696182[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]105.77[/C][C]0.719469834048143[/C][C]147.011028113407[/C][/ROW]
[ROW][C]Median[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.773333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.773333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.773333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.773333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.753125[/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=19568&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19568&T=1

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


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.0951.1608014594445590.5365849990307
Geometric Mean104.704283922727
Harmonic Mean104.300419825972
Quadratic Mean105.472551721605
Winsorized Mean ( 1 / 20 )105.111.1225543410399293.6346652961382
Winsorized Mean ( 2 / 20 )105.1266666666671.0935761753184496.1310871975194
Winsorized Mean ( 3 / 20 )105.2466666666671.0600913154001599.2807554761824
Winsorized Mean ( 4 / 20 )105.3733333333331.01125269594989104.200793486493
Winsorized Mean ( 5 / 20 )105.4983333333330.966373884163095109.169271916633
Winsorized Mean ( 6 / 20 )105.5083333333330.949734698806336111.092427670528
Winsorized Mean ( 7 / 20 )105.4966666666670.922667977040969114.338710448149
Winsorized Mean ( 8 / 20 )105.470.91814200740556114.873297539268
Winsorized Mean ( 9 / 20 )105.4250.900300091212529117.099843739895
Winsorized Mean ( 10 / 20 )105.5416666666670.86860590839889121.506963798131
Winsorized Mean ( 11 / 20 )105.450.847870379710814124.370425625632
Winsorized Mean ( 12 / 20 )105.450.841328314829195125.337514667396
Winsorized Mean ( 13 / 20 )105.4716666666670.81660414265443129.158867996706
Winsorized Mean ( 14 / 20 )105.6116666666670.786079780840071134.352351047372
Winsorized Mean ( 15 / 20 )105.7116666666670.762189426114403138.694743123870
Winsorized Mean ( 16 / 20 )105.7650.737183619775654143.471717442918
Winsorized Mean ( 17 / 20 )105.8216666666670.659194387911953160.531807623340
Winsorized Mean ( 18 / 20 )105.8816666666670.623433592649967169.836319240685
Winsorized Mean ( 19 / 20 )105.7233333333330.581437759500755181.830869436673
Winsorized Mean ( 20 / 20 )105.590.562298049120924187.782974109683
Trimmed Mean ( 1 / 20 )105.2137931034481.0839433294295397.0657692582706
Trimmed Mean ( 2 / 20 )105.3251.03611176877912101.654090971390
Trimmed Mean ( 3 / 20 )105.4351851851850.996342568787167105.822222685446
Trimmed Mean ( 4 / 20 )105.5076923076920.963331661239446109.523746133231
Trimmed Mean ( 5 / 20 )105.5480.941333140621668112.126085277625
Trimmed Mean ( 6 / 20 )105.5604166666670.928263552692069113.718152954007
Trimmed Mean ( 7 / 20 )105.5717391304350.915701273165064115.290588999110
Trimmed Mean ( 8 / 20 )105.5863636363640.90602044900063116.538609865626
Trimmed Mean ( 9 / 20 )105.6071428571430.8932863080075118.223174261679
Trimmed Mean ( 10 / 20 )105.63750.879865137538936120.061013322426
Trimmed Mean ( 11 / 20 )105.6526315789470.868819254366669121.604845942282
Trimmed Mean ( 12 / 20 )105.6833333333330.857363066950886123.265553890937
Trimmed Mean ( 13 / 20 )105.7176470588240.841360312981828125.650860193482
Trimmed Mean ( 14 / 20 )105.7531250.823936073200934128.351128734001
Trimmed Mean ( 15 / 20 )105.7733333333330.806010942758685131.230641821449
Trimmed Mean ( 16 / 20 )105.7821428571430.784911506679712134.769514724808
Trimmed Mean ( 17 / 20 )105.7846153846150.759183616336397139.339960858352
Trimmed Mean ( 18 / 20 )105.7791666666670.744763827137543142.030483775270
Trimmed Mean ( 19 / 20 )105.7636363636360.730757344631971144.731540696182
Trimmed Mean ( 20 / 20 )105.770.719469834048143147.011028113407
Median105.6
Midrange101.65
Midmean - Weighted Average at Xnp105.525806451613
Midmean - Weighted Average at X(n+1)p105.773333333333
Midmean - Empirical Distribution Function105.525806451613
Midmean - Empirical Distribution Function - Averaging105.773333333333
Midmean - Empirical Distribution Function - Interpolation105.773333333333
Midmean - Closest Observation105.525806451613
Midmean - True Basic - Statistics Graphics Toolkit105.773333333333
Midmean - MS Excel (old versions)105.753125
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0 ; par2 = 12 ;
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')