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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 09:39:00 -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/20/t1224517186l2hxbymw3b6vba2.htm/, Retrieved Tue, 28 May 2024 23:17:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17501, Retrieved Tue, 28 May 2024 23:17:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentral tendency, reeks 2
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Industriele produ...] [2008-10-13 18:27:09] [6743688719638b0cb1c0a6e0bf433315]
-   PD  [Univariate Data Series] [Reeks 2 Productie...] [2008-10-20 05:44:53] [6743688719638b0cb1c0a6e0bf433315]
- RMPD      [Central Tendency] [Central tendency ...] [2008-10-20 15:39:00] [9b05d7ef5dbcfba4217d280d9092f628] [Current]
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Dataseries X:
117.8
113.5
121.2
130.4
115.2
117.9
110.7
107.6
124.3
115.1
112.5
127.9
117.4
119.3
130.4
126
125.4
130.5
115.9
108.7
124
119.4
118.6
131.3
111.1
124.8
132.3
126.7
131.7
130.9
122.1
113.2
133.6
119.2
129.4
131.4
117.1
130.5
132.3
140.8
137.5
128.6
126.7
120.8
139.3
128.6
131.3
136.3
128.8
133.2
136.3
151.1
145
134.4
135.7
128.7
129.2
138.6
132.7
132.5
135.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17501&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17501&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17501&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean126.5344262295081.18706803531618106.594080933032
Geometric Mean126.197997406916
Harmonic Mean125.859163549160
Quadratic Mean126.868076569557
Winsorized Mean ( 1 / 20 )126.4524590163931.15162894031043109.803127196775
Winsorized Mean ( 2 / 20 )126.3803278688521.10183855211627114.699497150574
Winsorized Mean ( 3 / 20 )126.3262295081971.08177374491512116.77694166825
Winsorized Mean ( 4 / 20 )126.3721311475411.05187090968536120.140342302405
Winsorized Mean ( 5 / 20 )126.3393442622951.02247497514642123.562284978371
Winsorized Mean ( 6 / 20 )126.2508196721310.995488794322651126.822944057381
Winsorized Mean ( 7 / 20 )126.4344262295080.957754903352438132.011254431534
Winsorized Mean ( 8 / 20 )126.3688524590160.941912775954359134.161947565663
Winsorized Mean ( 9 / 20 )126.3983606557380.909730314338628138.940473526629
Winsorized Mean ( 10 / 20 )126.4639344262300.851998719780476148.432070952893
Winsorized Mean ( 11 / 20 )126.3737704918030.820312154497353154.055708913930
Winsorized Mean ( 12 / 20 )126.3737704918030.794650494157821159.030632235038
Winsorized Mean ( 13 / 20 )126.2885245901640.775844677573694162.775524844879
Winsorized Mean ( 14 / 20 )126.4032786885250.740952596188475170.595635049737
Winsorized Mean ( 15 / 20 )126.5016393442620.708602456634163178.522721957726
Winsorized Mean ( 16 / 20 )126.5278688524590.704106344223395179.699941479742
Winsorized Mean ( 17 / 20 )126.3885245901640.676959202266752186.700356782153
Winsorized Mean ( 18 / 20 )126.7131147540980.595559503709009212.763147871804
Winsorized Mean ( 19 / 20 )126.8065573770490.570968254658388222.090381282087
Winsorized Mean ( 20 / 20 )127.1016393442620.523290825968225242.889103031934
Trimmed Mean ( 1 / 20 )126.4389830508471.10718660036393114.198440451941
Trimmed Mean ( 2 / 20 )126.4245614035091.05246244464086120.122634348867
Trimmed Mean ( 3 / 20 )126.4490909090911.01864064938241124.135131447734
Trimmed Mean ( 4 / 20 )126.4962264150940.98628093817109128.255775326716
Trimmed Mean ( 5 / 20 )126.5333333333330.957618232772623132.133379464776
Trimmed Mean ( 6 / 20 )126.5816326530610.93137705027218135.908043489014
Trimmed Mean ( 7 / 20 )126.6531914893620.905951394079759139.801309779994
Trimmed Mean ( 8 / 20 )126.6955555555560.884158879842074143.295010030534
Trimmed Mean ( 9 / 20 )126.7534883720930.859597299656687147.456824751214
Trimmed Mean ( 10 / 20 )126.8121951219510.83563321340219151.755809951174
Trimmed Mean ( 11 / 20 )126.8666666666670.818628698781527154.974614077785
Trimmed Mean ( 12 / 20 )126.9405405405410.802590208596409158.163579845483
Trimmed Mean ( 13 / 20 )127.0228571428570.78592754936135161.621586170477
Trimmed Mean ( 14 / 20 )127.1272727272730.765759584364984166.014602132201
Trimmed Mean ( 15 / 20 )127.2290322580650.745829891360647170.587199215032
Trimmed Mean ( 16 / 20 )127.3310344827590.725029359831471175.621901039092
Trimmed Mean ( 17 / 20 )127.4444444444440.693176620465877183.855659123053
Trimmed Mean ( 18 / 20 )127.5960.650524916253534196.143140427032
Trimmed Mean ( 19 / 20 )127.7260869565220.617377386693879206.884945431041
Trimmed Mean ( 20 / 20 )127.8666666666670.571311495943173223.812521846025
Median128.6
Midrange129.35
Midmean - Weighted Average at Xnp127.229032258065
Midmean - Weighted Average at X(n+1)p127.229032258065
Midmean - Empirical Distribution Function127.229032258065
Midmean - Empirical Distribution Function - Averaging127.229032258065
Midmean - Empirical Distribution Function - Interpolation127.229032258065
Midmean - Closest Observation126.959375
Midmean - True Basic - Statistics Graphics Toolkit127.229032258065
Midmean - MS Excel (old versions)127.229032258065
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 126.534426229508 & 1.18706803531618 & 106.594080933032 \tabularnewline
Geometric Mean & 126.197997406916 &  &  \tabularnewline
Harmonic Mean & 125.859163549160 &  &  \tabularnewline
Quadratic Mean & 126.868076569557 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 126.452459016393 & 1.15162894031043 & 109.803127196775 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 126.380327868852 & 1.10183855211627 & 114.699497150574 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 126.326229508197 & 1.08177374491512 & 116.77694166825 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 126.372131147541 & 1.05187090968536 & 120.140342302405 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 126.339344262295 & 1.02247497514642 & 123.562284978371 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 126.250819672131 & 0.995488794322651 & 126.822944057381 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 126.434426229508 & 0.957754903352438 & 132.011254431534 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 126.368852459016 & 0.941912775954359 & 134.161947565663 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 126.398360655738 & 0.909730314338628 & 138.940473526629 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 126.463934426230 & 0.851998719780476 & 148.432070952893 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 126.373770491803 & 0.820312154497353 & 154.055708913930 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 126.373770491803 & 0.794650494157821 & 159.030632235038 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 126.288524590164 & 0.775844677573694 & 162.775524844879 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 126.403278688525 & 0.740952596188475 & 170.595635049737 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 126.501639344262 & 0.708602456634163 & 178.522721957726 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 126.527868852459 & 0.704106344223395 & 179.699941479742 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 126.388524590164 & 0.676959202266752 & 186.700356782153 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 126.713114754098 & 0.595559503709009 & 212.763147871804 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 126.806557377049 & 0.570968254658388 & 222.090381282087 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 127.101639344262 & 0.523290825968225 & 242.889103031934 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 126.438983050847 & 1.10718660036393 & 114.198440451941 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 126.424561403509 & 1.05246244464086 & 120.122634348867 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 126.449090909091 & 1.01864064938241 & 124.135131447734 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 126.496226415094 & 0.98628093817109 & 128.255775326716 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 126.533333333333 & 0.957618232772623 & 132.133379464776 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 126.581632653061 & 0.93137705027218 & 135.908043489014 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 126.653191489362 & 0.905951394079759 & 139.801309779994 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 126.695555555556 & 0.884158879842074 & 143.295010030534 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 126.753488372093 & 0.859597299656687 & 147.456824751214 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 126.812195121951 & 0.83563321340219 & 151.755809951174 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 126.866666666667 & 0.818628698781527 & 154.974614077785 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 126.940540540541 & 0.802590208596409 & 158.163579845483 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 127.022857142857 & 0.78592754936135 & 161.621586170477 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 127.127272727273 & 0.765759584364984 & 166.014602132201 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 127.229032258065 & 0.745829891360647 & 170.587199215032 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 127.331034482759 & 0.725029359831471 & 175.621901039092 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 127.444444444444 & 0.693176620465877 & 183.855659123053 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 127.596 & 0.650524916253534 & 196.143140427032 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 127.726086956522 & 0.617377386693879 & 206.884945431041 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 127.866666666667 & 0.571311495943173 & 223.812521846025 \tabularnewline
Median & 128.6 &  &  \tabularnewline
Midrange & 129.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 127.229032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 127.229032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 127.229032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 127.229032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 127.229032258065 &  &  \tabularnewline
Midmean - Closest Observation & 126.959375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 127.229032258065 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 127.229032258065 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17501&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]126.534426229508[/C][C]1.18706803531618[/C][C]106.594080933032[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]126.197997406916[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]125.859163549160[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]126.868076569557[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]126.452459016393[/C][C]1.15162894031043[/C][C]109.803127196775[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]126.380327868852[/C][C]1.10183855211627[/C][C]114.699497150574[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]126.326229508197[/C][C]1.08177374491512[/C][C]116.77694166825[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]126.372131147541[/C][C]1.05187090968536[/C][C]120.140342302405[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]126.339344262295[/C][C]1.02247497514642[/C][C]123.562284978371[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]126.250819672131[/C][C]0.995488794322651[/C][C]126.822944057381[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]126.434426229508[/C][C]0.957754903352438[/C][C]132.011254431534[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]126.368852459016[/C][C]0.941912775954359[/C][C]134.161947565663[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]126.398360655738[/C][C]0.909730314338628[/C][C]138.940473526629[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]126.463934426230[/C][C]0.851998719780476[/C][C]148.432070952893[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]126.373770491803[/C][C]0.820312154497353[/C][C]154.055708913930[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]126.373770491803[/C][C]0.794650494157821[/C][C]159.030632235038[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]126.288524590164[/C][C]0.775844677573694[/C][C]162.775524844879[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]126.403278688525[/C][C]0.740952596188475[/C][C]170.595635049737[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]126.501639344262[/C][C]0.708602456634163[/C][C]178.522721957726[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]126.527868852459[/C][C]0.704106344223395[/C][C]179.699941479742[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]126.388524590164[/C][C]0.676959202266752[/C][C]186.700356782153[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]126.713114754098[/C][C]0.595559503709009[/C][C]212.763147871804[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]126.806557377049[/C][C]0.570968254658388[/C][C]222.090381282087[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]127.101639344262[/C][C]0.523290825968225[/C][C]242.889103031934[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]126.438983050847[/C][C]1.10718660036393[/C][C]114.198440451941[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]126.424561403509[/C][C]1.05246244464086[/C][C]120.122634348867[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]126.449090909091[/C][C]1.01864064938241[/C][C]124.135131447734[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]126.496226415094[/C][C]0.98628093817109[/C][C]128.255775326716[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]126.533333333333[/C][C]0.957618232772623[/C][C]132.133379464776[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]126.581632653061[/C][C]0.93137705027218[/C][C]135.908043489014[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]126.653191489362[/C][C]0.905951394079759[/C][C]139.801309779994[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]126.695555555556[/C][C]0.884158879842074[/C][C]143.295010030534[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]126.753488372093[/C][C]0.859597299656687[/C][C]147.456824751214[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]126.812195121951[/C][C]0.83563321340219[/C][C]151.755809951174[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]126.866666666667[/C][C]0.818628698781527[/C][C]154.974614077785[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]126.940540540541[/C][C]0.802590208596409[/C][C]158.163579845483[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]127.022857142857[/C][C]0.78592754936135[/C][C]161.621586170477[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]127.127272727273[/C][C]0.765759584364984[/C][C]166.014602132201[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]127.229032258065[/C][C]0.745829891360647[/C][C]170.587199215032[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]127.331034482759[/C][C]0.725029359831471[/C][C]175.621901039092[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]127.444444444444[/C][C]0.693176620465877[/C][C]183.855659123053[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]127.596[/C][C]0.650524916253534[/C][C]196.143140427032[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]127.726086956522[/C][C]0.617377386693879[/C][C]206.884945431041[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]127.866666666667[/C][C]0.571311495943173[/C][C]223.812521846025[/C][/ROW]
[ROW][C]Median[/C][C]128.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]129.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]127.229032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]127.229032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]127.229032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]127.229032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]127.229032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]126.959375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]127.229032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]127.229032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17501&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17501&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 Mean126.5344262295081.18706803531618106.594080933032
Geometric Mean126.197997406916
Harmonic Mean125.859163549160
Quadratic Mean126.868076569557
Winsorized Mean ( 1 / 20 )126.4524590163931.15162894031043109.803127196775
Winsorized Mean ( 2 / 20 )126.3803278688521.10183855211627114.699497150574
Winsorized Mean ( 3 / 20 )126.3262295081971.08177374491512116.77694166825
Winsorized Mean ( 4 / 20 )126.3721311475411.05187090968536120.140342302405
Winsorized Mean ( 5 / 20 )126.3393442622951.02247497514642123.562284978371
Winsorized Mean ( 6 / 20 )126.2508196721310.995488794322651126.822944057381
Winsorized Mean ( 7 / 20 )126.4344262295080.957754903352438132.011254431534
Winsorized Mean ( 8 / 20 )126.3688524590160.941912775954359134.161947565663
Winsorized Mean ( 9 / 20 )126.3983606557380.909730314338628138.940473526629
Winsorized Mean ( 10 / 20 )126.4639344262300.851998719780476148.432070952893
Winsorized Mean ( 11 / 20 )126.3737704918030.820312154497353154.055708913930
Winsorized Mean ( 12 / 20 )126.3737704918030.794650494157821159.030632235038
Winsorized Mean ( 13 / 20 )126.2885245901640.775844677573694162.775524844879
Winsorized Mean ( 14 / 20 )126.4032786885250.740952596188475170.595635049737
Winsorized Mean ( 15 / 20 )126.5016393442620.708602456634163178.522721957726
Winsorized Mean ( 16 / 20 )126.5278688524590.704106344223395179.699941479742
Winsorized Mean ( 17 / 20 )126.3885245901640.676959202266752186.700356782153
Winsorized Mean ( 18 / 20 )126.7131147540980.595559503709009212.763147871804
Winsorized Mean ( 19 / 20 )126.8065573770490.570968254658388222.090381282087
Winsorized Mean ( 20 / 20 )127.1016393442620.523290825968225242.889103031934
Trimmed Mean ( 1 / 20 )126.4389830508471.10718660036393114.198440451941
Trimmed Mean ( 2 / 20 )126.4245614035091.05246244464086120.122634348867
Trimmed Mean ( 3 / 20 )126.4490909090911.01864064938241124.135131447734
Trimmed Mean ( 4 / 20 )126.4962264150940.98628093817109128.255775326716
Trimmed Mean ( 5 / 20 )126.5333333333330.957618232772623132.133379464776
Trimmed Mean ( 6 / 20 )126.5816326530610.93137705027218135.908043489014
Trimmed Mean ( 7 / 20 )126.6531914893620.905951394079759139.801309779994
Trimmed Mean ( 8 / 20 )126.6955555555560.884158879842074143.295010030534
Trimmed Mean ( 9 / 20 )126.7534883720930.859597299656687147.456824751214
Trimmed Mean ( 10 / 20 )126.8121951219510.83563321340219151.755809951174
Trimmed Mean ( 11 / 20 )126.8666666666670.818628698781527154.974614077785
Trimmed Mean ( 12 / 20 )126.9405405405410.802590208596409158.163579845483
Trimmed Mean ( 13 / 20 )127.0228571428570.78592754936135161.621586170477
Trimmed Mean ( 14 / 20 )127.1272727272730.765759584364984166.014602132201
Trimmed Mean ( 15 / 20 )127.2290322580650.745829891360647170.587199215032
Trimmed Mean ( 16 / 20 )127.3310344827590.725029359831471175.621901039092
Trimmed Mean ( 17 / 20 )127.4444444444440.693176620465877183.855659123053
Trimmed Mean ( 18 / 20 )127.5960.650524916253534196.143140427032
Trimmed Mean ( 19 / 20 )127.7260869565220.617377386693879206.884945431041
Trimmed Mean ( 20 / 20 )127.8666666666670.571311495943173223.812521846025
Median128.6
Midrange129.35
Midmean - Weighted Average at Xnp127.229032258065
Midmean - Weighted Average at X(n+1)p127.229032258065
Midmean - Empirical Distribution Function127.229032258065
Midmean - Empirical Distribution Function - Averaging127.229032258065
Midmean - Empirical Distribution Function - Interpolation127.229032258065
Midmean - Closest Observation126.959375
Midmean - True Basic - Statistics Graphics Toolkit127.229032258065
Midmean - MS Excel (old versions)127.229032258065
Number of observations61



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')