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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 02 Jan 2012 08:59:16 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/02/t1325512865ozpwz1g07jp8bom.htm/, Retrieved Sat, 04 May 2024 12:21:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160921, Retrieved Sat, 04 May 2024 12:21:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [decielen] [2012-01-02 13:39:09] [da1dd7ba20267c8dec1286cd318791a0]
- RMPD    [Central Tendency] [eigen cijfers cen...] [2012-01-02 13:59:16] [5f178b5bce8a01d64692a8a5c649399b] [Current]
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Dataseries X:
123,46
123,24
123,86
124,28
124,78
125,19
125,46
127,60
127,80
126,63
127,06
126,77
127,05
128,23
128,60
128,97
129,34
129,71
130,08
130,45
128,82
132,19
131,56
131,93
132,30
130,67
133,05
132,42
133,79
134,16
134,53
136,90
135,27
136,64
136,01
136,38
136,75
138,12
137,50
137,87
138,24
138,61
138,98
140,35
139,72
143,09
140,46
141,83
143,20
140,57
141,95
141,32
142,69
143,06
144,43
143,80
144,17
144,54
146,91
145,28
144,65
145,02
144,40
146,77
146,14
147,51
148,88
148,25
147,62
150,99
148,36
149,73
150,10




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=160921&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=160921&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160921&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 Mean136.8087671232880.929836750724925147.132028301342
Geometric Mean136.580544662455
Harmonic Mean136.351881132991
Quadratic Mean137.036089047265
Winsorized Mean ( 1 / 24 )136.7995890410960.926723587292017147.616388443115
Winsorized Mean ( 2 / 24 )136.8004109589040.922563627516935148.282900906358
Winsorized Mean ( 3 / 24 )136.7827397260270.912623821591598149.878555095659
Winsorized Mean ( 4 / 24 )136.7816438356160.902323970059752151.588174950687
Winsorized Mean ( 5 / 24 )136.8021917808220.89586211054077152.704517995793
Winsorized Mean ( 6 / 24 )136.7726027397260.882875323394505154.917233629159
Winsorized Mean ( 7 / 24 )136.8742465753420.861818586137055158.820253794777
Winsorized Mean ( 8 / 24 )136.8238356164380.848222750957043161.306491086287
Winsorized Mean ( 9 / 24 )136.8410958904110.839743418667257162.955842044692
Winsorized Mean ( 10 / 24 )136.7561643835620.825620624227501165.640441106372
Winsorized Mean ( 11 / 24 )136.7079452054790.792515189558713172.498832838271
Winsorized Mean ( 12 / 24 )136.6980821917810.780916134933598175.048351643297
Winsorized Mean ( 13 / 24 )136.7087671232880.759253442133377180.056828901768
Winsorized Mean ( 14 / 24 )136.7586301369860.74529340843223183.496363431774
Winsorized Mean ( 15 / 24 )136.7812328767120.735185289839199186.050013196849
Winsorized Mean ( 16 / 24 )136.8075342465750.729308897565226187.585170979406
Winsorized Mean ( 17 / 24 )136.8401369863010.708826889374339193.051560314093
Winsorized Mean ( 18 / 24 )136.8401369863010.682488354201484200.50179046118
Winsorized Mean ( 19 / 24 )136.7802739726030.646739715211195211.491997097993
Winsorized Mean ( 20 / 24 )136.8515068493150.628114422072813217.876714878951
Winsorized Mean ( 21 / 24 )136.9061643835620.618008001595169221.528142079369
Winsorized Mean ( 22 / 24 )137.0628767123290.565647938688294242.311281165755
Winsorized Mean ( 23 / 24 )136.9463013698630.5181710131711264.287846847665
Winsorized Mean ( 24 / 24 )136.9923287671230.50144974453257273.192538755447
Trimmed Mean ( 1 / 24 )136.800140845070.91478956014727149.542743823013
Trimmed Mean ( 2 / 24 )136.8007246376810.900441407309948151.926292512881
Trimmed Mean ( 3 / 24 )136.8008955223880.885791704622218154.43912469324
Trimmed Mean ( 4 / 24 )136.8076923076920.872515670159887156.796831262208
Trimmed Mean ( 5 / 24 )136.8152380952380.85999067789107159.089210630453
Trimmed Mean ( 6 / 24 )136.8183606557380.846547865476316161.619166777718
Trimmed Mean ( 7 / 24 )136.8277966101690.833479292147167164.164602407434
Trimmed Mean ( 8 / 24 )136.8192982456140.822443782678937166.357021752847
Trimmed Mean ( 9 / 24 )136.8185454545450.811595693832794168.5796838182
Trimmed Mean ( 10 / 24 )136.8150943396230.799547569029444171.115640443632
Trimmed Mean ( 11 / 24 )136.8235294117650.787083513197555173.836101401634
Trimmed Mean ( 12 / 24 )136.8391836734690.777863583685712175.916685834669
Trimmed Mean ( 13 / 24 )136.8574468085110.767783459157518178.250058888587
Trimmed Mean ( 14 / 24 )136.8760.758556670409154180.442681924043
Trimmed Mean ( 15 / 24 )136.890232558140.748594289027786182.863046866042
Trimmed Mean ( 16 / 24 )136.9031707317070.736706119967858185.831455747484
Trimmed Mean ( 17 / 24 )136.9143589743590.721252639806637189.828572427915
Trimmed Mean ( 18 / 24 )136.9229729729730.704408241505187194.380140528161
Trimmed Mean ( 19 / 24 )136.9325714285710.686975265643707199.326785514269
Trimmed Mean ( 20 / 24 )136.9503030303030.670929009483685204.120407814373
Trimmed Mean ( 21 / 24 )136.9619354838710.652043837063624210.050195552277
Trimmed Mean ( 22 / 24 )136.9686206896550.62641342132669218.655309778592
Trimmed Mean ( 23 / 24 )136.9570370370370.604626939868277226.514943358088
Trimmed Mean ( 24 / 24 )136.95840.586560505546245233.49407044113
Median136.9
Midrange137.115
Midmean - Weighted Average at Xnp136.731944444444
Midmean - Weighted Average at X(n+1)p136.922972972973
Midmean - Empirical Distribution Function136.922972972973
Midmean - Empirical Distribution Function - Averaging136.922972972973
Midmean - Empirical Distribution Function - Interpolation136.922972972973
Midmean - Closest Observation136.723421052632
Midmean - True Basic - Statistics Graphics Toolkit136.922972972973
Midmean - MS Excel (old versions)136.922972972973
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 136.808767123288 & 0.929836750724925 & 147.132028301342 \tabularnewline
Geometric Mean & 136.580544662455 &  &  \tabularnewline
Harmonic Mean & 136.351881132991 &  &  \tabularnewline
Quadratic Mean & 137.036089047265 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 136.799589041096 & 0.926723587292017 & 147.616388443115 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 136.800410958904 & 0.922563627516935 & 148.282900906358 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 136.782739726027 & 0.912623821591598 & 149.878555095659 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 136.781643835616 & 0.902323970059752 & 151.588174950687 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 136.802191780822 & 0.89586211054077 & 152.704517995793 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 136.772602739726 & 0.882875323394505 & 154.917233629159 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 136.874246575342 & 0.861818586137055 & 158.820253794777 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 136.823835616438 & 0.848222750957043 & 161.306491086287 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 136.841095890411 & 0.839743418667257 & 162.955842044692 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 136.756164383562 & 0.825620624227501 & 165.640441106372 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 136.707945205479 & 0.792515189558713 & 172.498832838271 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 136.698082191781 & 0.780916134933598 & 175.048351643297 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 136.708767123288 & 0.759253442133377 & 180.056828901768 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 136.758630136986 & 0.74529340843223 & 183.496363431774 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 136.781232876712 & 0.735185289839199 & 186.050013196849 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 136.807534246575 & 0.729308897565226 & 187.585170979406 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 136.840136986301 & 0.708826889374339 & 193.051560314093 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 136.840136986301 & 0.682488354201484 & 200.50179046118 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 136.780273972603 & 0.646739715211195 & 211.491997097993 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 136.851506849315 & 0.628114422072813 & 217.876714878951 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 136.906164383562 & 0.618008001595169 & 221.528142079369 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 137.062876712329 & 0.565647938688294 & 242.311281165755 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 136.946301369863 & 0.5181710131711 & 264.287846847665 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 136.992328767123 & 0.50144974453257 & 273.192538755447 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 136.80014084507 & 0.91478956014727 & 149.542743823013 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 136.800724637681 & 0.900441407309948 & 151.926292512881 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 136.800895522388 & 0.885791704622218 & 154.43912469324 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 136.807692307692 & 0.872515670159887 & 156.796831262208 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 136.815238095238 & 0.85999067789107 & 159.089210630453 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 136.818360655738 & 0.846547865476316 & 161.619166777718 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 136.827796610169 & 0.833479292147167 & 164.164602407434 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 136.819298245614 & 0.822443782678937 & 166.357021752847 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 136.818545454545 & 0.811595693832794 & 168.5796838182 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 136.815094339623 & 0.799547569029444 & 171.115640443632 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 136.823529411765 & 0.787083513197555 & 173.836101401634 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 136.839183673469 & 0.777863583685712 & 175.916685834669 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 136.857446808511 & 0.767783459157518 & 178.250058888587 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 136.876 & 0.758556670409154 & 180.442681924043 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 136.89023255814 & 0.748594289027786 & 182.863046866042 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 136.903170731707 & 0.736706119967858 & 185.831455747484 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 136.914358974359 & 0.721252639806637 & 189.828572427915 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 136.922972972973 & 0.704408241505187 & 194.380140528161 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 136.932571428571 & 0.686975265643707 & 199.326785514269 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 136.950303030303 & 0.670929009483685 & 204.120407814373 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 136.961935483871 & 0.652043837063624 & 210.050195552277 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 136.968620689655 & 0.62641342132669 & 218.655309778592 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 136.957037037037 & 0.604626939868277 & 226.514943358088 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 136.9584 & 0.586560505546245 & 233.49407044113 \tabularnewline
Median & 136.9 &  &  \tabularnewline
Midrange & 137.115 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 136.731944444444 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 136.922972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 136.922972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 136.922972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 136.922972972973 &  &  \tabularnewline
Midmean - Closest Observation & 136.723421052632 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 136.922972972973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 136.922972972973 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160921&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]136.808767123288[/C][C]0.929836750724925[/C][C]147.132028301342[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]136.580544662455[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]136.351881132991[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]137.036089047265[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]136.799589041096[/C][C]0.926723587292017[/C][C]147.616388443115[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]136.800410958904[/C][C]0.922563627516935[/C][C]148.282900906358[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]136.782739726027[/C][C]0.912623821591598[/C][C]149.878555095659[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]136.781643835616[/C][C]0.902323970059752[/C][C]151.588174950687[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]136.802191780822[/C][C]0.89586211054077[/C][C]152.704517995793[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]136.772602739726[/C][C]0.882875323394505[/C][C]154.917233629159[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]136.874246575342[/C][C]0.861818586137055[/C][C]158.820253794777[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]136.823835616438[/C][C]0.848222750957043[/C][C]161.306491086287[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]136.841095890411[/C][C]0.839743418667257[/C][C]162.955842044692[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]136.756164383562[/C][C]0.825620624227501[/C][C]165.640441106372[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]136.707945205479[/C][C]0.792515189558713[/C][C]172.498832838271[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]136.698082191781[/C][C]0.780916134933598[/C][C]175.048351643297[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]136.708767123288[/C][C]0.759253442133377[/C][C]180.056828901768[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]136.758630136986[/C][C]0.74529340843223[/C][C]183.496363431774[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]136.781232876712[/C][C]0.735185289839199[/C][C]186.050013196849[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]136.807534246575[/C][C]0.729308897565226[/C][C]187.585170979406[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]136.840136986301[/C][C]0.708826889374339[/C][C]193.051560314093[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]136.840136986301[/C][C]0.682488354201484[/C][C]200.50179046118[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]136.780273972603[/C][C]0.646739715211195[/C][C]211.491997097993[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]136.851506849315[/C][C]0.628114422072813[/C][C]217.876714878951[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]136.906164383562[/C][C]0.618008001595169[/C][C]221.528142079369[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]137.062876712329[/C][C]0.565647938688294[/C][C]242.311281165755[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]136.946301369863[/C][C]0.5181710131711[/C][C]264.287846847665[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]136.992328767123[/C][C]0.50144974453257[/C][C]273.192538755447[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]136.80014084507[/C][C]0.91478956014727[/C][C]149.542743823013[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]136.800724637681[/C][C]0.900441407309948[/C][C]151.926292512881[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]136.800895522388[/C][C]0.885791704622218[/C][C]154.43912469324[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]136.807692307692[/C][C]0.872515670159887[/C][C]156.796831262208[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]136.815238095238[/C][C]0.85999067789107[/C][C]159.089210630453[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]136.818360655738[/C][C]0.846547865476316[/C][C]161.619166777718[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]136.827796610169[/C][C]0.833479292147167[/C][C]164.164602407434[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]136.819298245614[/C][C]0.822443782678937[/C][C]166.357021752847[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]136.818545454545[/C][C]0.811595693832794[/C][C]168.5796838182[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]136.815094339623[/C][C]0.799547569029444[/C][C]171.115640443632[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]136.823529411765[/C][C]0.787083513197555[/C][C]173.836101401634[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]136.839183673469[/C][C]0.777863583685712[/C][C]175.916685834669[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]136.857446808511[/C][C]0.767783459157518[/C][C]178.250058888587[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]136.876[/C][C]0.758556670409154[/C][C]180.442681924043[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]136.89023255814[/C][C]0.748594289027786[/C][C]182.863046866042[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]136.903170731707[/C][C]0.736706119967858[/C][C]185.831455747484[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]136.914358974359[/C][C]0.721252639806637[/C][C]189.828572427915[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]136.922972972973[/C][C]0.704408241505187[/C][C]194.380140528161[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]136.932571428571[/C][C]0.686975265643707[/C][C]199.326785514269[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]136.950303030303[/C][C]0.670929009483685[/C][C]204.120407814373[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]136.961935483871[/C][C]0.652043837063624[/C][C]210.050195552277[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]136.968620689655[/C][C]0.62641342132669[/C][C]218.655309778592[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]136.957037037037[/C][C]0.604626939868277[/C][C]226.514943358088[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]136.9584[/C][C]0.586560505546245[/C][C]233.49407044113[/C][/ROW]
[ROW][C]Median[/C][C]136.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]137.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]136.731944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]136.922972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]136.922972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]136.922972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]136.922972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]136.723421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]136.922972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]136.922972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160921&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160921&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 Mean136.8087671232880.929836750724925147.132028301342
Geometric Mean136.580544662455
Harmonic Mean136.351881132991
Quadratic Mean137.036089047265
Winsorized Mean ( 1 / 24 )136.7995890410960.926723587292017147.616388443115
Winsorized Mean ( 2 / 24 )136.8004109589040.922563627516935148.282900906358
Winsorized Mean ( 3 / 24 )136.7827397260270.912623821591598149.878555095659
Winsorized Mean ( 4 / 24 )136.7816438356160.902323970059752151.588174950687
Winsorized Mean ( 5 / 24 )136.8021917808220.89586211054077152.704517995793
Winsorized Mean ( 6 / 24 )136.7726027397260.882875323394505154.917233629159
Winsorized Mean ( 7 / 24 )136.8742465753420.861818586137055158.820253794777
Winsorized Mean ( 8 / 24 )136.8238356164380.848222750957043161.306491086287
Winsorized Mean ( 9 / 24 )136.8410958904110.839743418667257162.955842044692
Winsorized Mean ( 10 / 24 )136.7561643835620.825620624227501165.640441106372
Winsorized Mean ( 11 / 24 )136.7079452054790.792515189558713172.498832838271
Winsorized Mean ( 12 / 24 )136.6980821917810.780916134933598175.048351643297
Winsorized Mean ( 13 / 24 )136.7087671232880.759253442133377180.056828901768
Winsorized Mean ( 14 / 24 )136.7586301369860.74529340843223183.496363431774
Winsorized Mean ( 15 / 24 )136.7812328767120.735185289839199186.050013196849
Winsorized Mean ( 16 / 24 )136.8075342465750.729308897565226187.585170979406
Winsorized Mean ( 17 / 24 )136.8401369863010.708826889374339193.051560314093
Winsorized Mean ( 18 / 24 )136.8401369863010.682488354201484200.50179046118
Winsorized Mean ( 19 / 24 )136.7802739726030.646739715211195211.491997097993
Winsorized Mean ( 20 / 24 )136.8515068493150.628114422072813217.876714878951
Winsorized Mean ( 21 / 24 )136.9061643835620.618008001595169221.528142079369
Winsorized Mean ( 22 / 24 )137.0628767123290.565647938688294242.311281165755
Winsorized Mean ( 23 / 24 )136.9463013698630.5181710131711264.287846847665
Winsorized Mean ( 24 / 24 )136.9923287671230.50144974453257273.192538755447
Trimmed Mean ( 1 / 24 )136.800140845070.91478956014727149.542743823013
Trimmed Mean ( 2 / 24 )136.8007246376810.900441407309948151.926292512881
Trimmed Mean ( 3 / 24 )136.8008955223880.885791704622218154.43912469324
Trimmed Mean ( 4 / 24 )136.8076923076920.872515670159887156.796831262208
Trimmed Mean ( 5 / 24 )136.8152380952380.85999067789107159.089210630453
Trimmed Mean ( 6 / 24 )136.8183606557380.846547865476316161.619166777718
Trimmed Mean ( 7 / 24 )136.8277966101690.833479292147167164.164602407434
Trimmed Mean ( 8 / 24 )136.8192982456140.822443782678937166.357021752847
Trimmed Mean ( 9 / 24 )136.8185454545450.811595693832794168.5796838182
Trimmed Mean ( 10 / 24 )136.8150943396230.799547569029444171.115640443632
Trimmed Mean ( 11 / 24 )136.8235294117650.787083513197555173.836101401634
Trimmed Mean ( 12 / 24 )136.8391836734690.777863583685712175.916685834669
Trimmed Mean ( 13 / 24 )136.8574468085110.767783459157518178.250058888587
Trimmed Mean ( 14 / 24 )136.8760.758556670409154180.442681924043
Trimmed Mean ( 15 / 24 )136.890232558140.748594289027786182.863046866042
Trimmed Mean ( 16 / 24 )136.9031707317070.736706119967858185.831455747484
Trimmed Mean ( 17 / 24 )136.9143589743590.721252639806637189.828572427915
Trimmed Mean ( 18 / 24 )136.9229729729730.704408241505187194.380140528161
Trimmed Mean ( 19 / 24 )136.9325714285710.686975265643707199.326785514269
Trimmed Mean ( 20 / 24 )136.9503030303030.670929009483685204.120407814373
Trimmed Mean ( 21 / 24 )136.9619354838710.652043837063624210.050195552277
Trimmed Mean ( 22 / 24 )136.9686206896550.62641342132669218.655309778592
Trimmed Mean ( 23 / 24 )136.9570370370370.604626939868277226.514943358088
Trimmed Mean ( 24 / 24 )136.95840.586560505546245233.49407044113
Median136.9
Midrange137.115
Midmean - Weighted Average at Xnp136.731944444444
Midmean - Weighted Average at X(n+1)p136.922972972973
Midmean - Empirical Distribution Function136.922972972973
Midmean - Empirical Distribution Function - Averaging136.922972972973
Midmean - Empirical Distribution Function - Interpolation136.922972972973
Midmean - Closest Observation136.723421052632
Midmean - True Basic - Statistics Graphics Toolkit136.922972972973
Midmean - MS Excel (old versions)136.922972972973
Number of observations73



Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
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')