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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 10 Oct 2015 17:43:53 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/10/t144449545758idezvhlc0i1en.htm/, Retrieved Tue, 14 May 2024 21:31:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282255, Retrieved Tue, 14 May 2024 21:31:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2015-10-01 20:32:13] [b63ade344763e232a60872be122cd067]
- RMPD  [Kernel Density Estimation] [] [2015-10-01 21:07:58] [b63ade344763e232a60872be122cd067]
- RMP     [Harrell-Davis Quantiles] [] [2015-10-10 16:31:21] [b63ade344763e232a60872be122cd067]
- RMP         [Central Tendency] [] [2015-10-10 16:43:53] [4b4e0ace64f044c9dde59b15676ee69f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104.93
105.68
106.93
107.29
107.25
106.74
106.44
106.6
107.26
107.35
107.22
106.99
106.87
107.68
108.9
109.48
109.57
109.03
109.58
109.76
110.15
110.2
109.86
109.58
109.52
110.35
111.61
112.06
111.9
111.36
112.09
112.24
112.7
113.36
112.9
112.74
112.7
113.66
114.87
114.97
115
114.57
115.54
115.39
115.46
115.13
114.56
114.62
114.37
114.86
115.82
116.35
115.95
115.64
116.58
116.5
116.48
116.34
115.65
115.42

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282255&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282255&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282255&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' @ jenkins.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.6766666666670.453227077112009246.403342400188
Geometric Mean111.622144121442
Harmonic Mean111.567382266529
Quadratic Mean111.7309149251
Winsorized Mean ( 1 / 20 )111.6878333333330.449992221631875248.19947537827
Winsorized Mean ( 2 / 20 )111.71250.444456096539818251.346535393945
Winsorized Mean ( 3 / 20 )111.7140.441697751810899252.919557643181
Winsorized Mean ( 4 / 20 )111.7226666666670.43976713577754254.049603932165
Winsorized Mean ( 5 / 20 )111.7010.432098590706329258.508133103161
Winsorized Mean ( 6 / 20 )111.6940.42882174664478260.467200821611
Winsorized Mean ( 7 / 20 )111.6811666666670.424317270944568263.202029033733
Winsorized Mean ( 8 / 20 )111.71050.418442661901765266.967281711408
Winsorized Mean ( 9 / 20 )111.70.415255417962117268.991071924292
Winsorized Mean ( 10 / 20 )111.6883333333330.412875418390476270.513400310271
Winsorized Mean ( 11 / 20 )111.68650.410743973275227271.912693226937
Winsorized Mean ( 12 / 20 )111.69250.407648737196441273.992017657537
Winsorized Mean ( 13 / 20 )111.7076666666670.386310694802798289.165348434608
Winsorized Mean ( 14 / 20 )111.9620.334227315318609334.987581410784
Winsorized Mean ( 15 / 20 )111.9870.32806549056811341.355623250932
Winsorized Mean ( 16 / 20 )112.0803333333330.306128731707182366.121574764633
Winsorized Mean ( 17 / 20 )112.0888333333330.304063821325055368.635876655337
Winsorized Mean ( 18 / 20 )112.0318333333330.290922018757806385.092313781173
Winsorized Mean ( 19 / 20 )112.0191666666670.288085860128584388.839516860244
Winsorized Mean ( 20 / 20 )112.0158333333330.28758583014238389.504007474484
Trimmed Mean ( 1 / 20 )111.7084482758620.445977369130335250.48008264118
Trimmed Mean ( 2 / 20 )111.7305357142860.440712632734908253.522425760581
Trimmed Mean ( 3 / 20 )111.7405555555560.437445607413778255.438741781354
Trimmed Mean ( 4 / 20 )111.7507692307690.434204413336186257.369031263727
Trimmed Mean ( 5 / 20 )111.75920.430385858200261259.672100908106
Trimmed Mean ( 6 / 20 )111.773750.427522305108457261.445423231531
Trimmed Mean ( 7 / 20 )111.7910869565220.424203285997753263.531874095652
Trimmed Mean ( 8 / 20 )111.81250.420492151623746265.908649110886
Trimmed Mean ( 9 / 20 )111.8307142857140.416540058746934268.475292921722
Trimmed Mean ( 10 / 20 )111.85250.411389102419769271.889798106195
Trimmed Mean ( 11 / 20 )111.8784210526320.404355118756811276.683578030622
Trimmed Mean ( 12 / 20 )111.90750.394665294198064283.550394841252
Trimmed Mean ( 13 / 20 )111.9391176470590.381532085414715293.393719496445
Trimmed Mean ( 14 / 20 )111.97250.368858854900773303.564625092494
Trimmed Mean ( 15 / 20 )111.9740.365718188094943306.175639180764
Trimmed Mean ( 16 / 20 )111.9721428571430.361359630164917309.863453219833
Trimmed Mean ( 17 / 20 )111.9565384615380.359710115042523311.241007076777
Trimmed Mean ( 18 / 20 )111.9370833333330.355414882677277314.947653542618
Trimmed Mean ( 19 / 20 )111.9227272727270.351012254086226318.857036954708
Trimmed Mean ( 20 / 20 )111.90750.34190555405658327.305300169184
Median112.075
Midrange110.755
Midmean - Weighted Average at Xnp111.874838709677
Midmean - Weighted Average at X(n+1)p111.974
Midmean - Empirical Distribution Function111.874838709677
Midmean - Empirical Distribution Function - Averaging111.974
Midmean - Empirical Distribution Function - Interpolation111.974
Midmean - Closest Observation111.874838709677
Midmean - True Basic - Statistics Graphics Toolkit111.974
Midmean - MS Excel (old versions)111.9725
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.676666666667 & 0.453227077112009 & 246.403342400188 \tabularnewline
Geometric Mean & 111.622144121442 &  &  \tabularnewline
Harmonic Mean & 111.567382266529 &  &  \tabularnewline
Quadratic Mean & 111.7309149251 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.687833333333 & 0.449992221631875 & 248.19947537827 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 111.7125 & 0.444456096539818 & 251.346535393945 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 111.714 & 0.441697751810899 & 252.919557643181 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 111.722666666667 & 0.43976713577754 & 254.049603932165 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.701 & 0.432098590706329 & 258.508133103161 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.694 & 0.42882174664478 & 260.467200821611 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.681166666667 & 0.424317270944568 & 263.202029033733 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.7105 & 0.418442661901765 & 266.967281711408 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.7 & 0.415255417962117 & 268.991071924292 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.688333333333 & 0.412875418390476 & 270.513400310271 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.6865 & 0.410743973275227 & 271.912693226937 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.6925 & 0.407648737196441 & 273.992017657537 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.707666666667 & 0.386310694802798 & 289.165348434608 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.962 & 0.334227315318609 & 334.987581410784 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.987 & 0.32806549056811 & 341.355623250932 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 112.080333333333 & 0.306128731707182 & 366.121574764633 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 112.088833333333 & 0.304063821325055 & 368.635876655337 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 112.031833333333 & 0.290922018757806 & 385.092313781173 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 112.019166666667 & 0.288085860128584 & 388.839516860244 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 112.015833333333 & 0.28758583014238 & 389.504007474484 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 111.708448275862 & 0.445977369130335 & 250.48008264118 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 111.730535714286 & 0.440712632734908 & 253.522425760581 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 111.740555555556 & 0.437445607413778 & 255.438741781354 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.750769230769 & 0.434204413336186 & 257.369031263727 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.7592 & 0.430385858200261 & 259.672100908106 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.77375 & 0.427522305108457 & 261.445423231531 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.791086956522 & 0.424203285997753 & 263.531874095652 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.8125 & 0.420492151623746 & 265.908649110886 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.830714285714 & 0.416540058746934 & 268.475292921722 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.8525 & 0.411389102419769 & 271.889798106195 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.878421052632 & 0.404355118756811 & 276.683578030622 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.9075 & 0.394665294198064 & 283.550394841252 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.939117647059 & 0.381532085414715 & 293.393719496445 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.9725 & 0.368858854900773 & 303.564625092494 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.974 & 0.365718188094943 & 306.175639180764 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.972142857143 & 0.361359630164917 & 309.863453219833 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.956538461538 & 0.359710115042523 & 311.241007076777 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.937083333333 & 0.355414882677277 & 314.947653542618 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.922727272727 & 0.351012254086226 & 318.857036954708 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111.9075 & 0.34190555405658 & 327.305300169184 \tabularnewline
Median & 112.075 &  &  \tabularnewline
Midrange & 110.755 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.874838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.974 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.874838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.974 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.974 &  &  \tabularnewline
Midmean - Closest Observation & 111.874838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.974 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.9725 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282255&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]111.676666666667[/C][C]0.453227077112009[/C][C]246.403342400188[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.622144121442[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.567382266529[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.7309149251[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.687833333333[/C][C]0.449992221631875[/C][C]248.19947537827[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]111.7125[/C][C]0.444456096539818[/C][C]251.346535393945[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]111.714[/C][C]0.441697751810899[/C][C]252.919557643181[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]111.722666666667[/C][C]0.43976713577754[/C][C]254.049603932165[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.701[/C][C]0.432098590706329[/C][C]258.508133103161[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.694[/C][C]0.42882174664478[/C][C]260.467200821611[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.681166666667[/C][C]0.424317270944568[/C][C]263.202029033733[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.7105[/C][C]0.418442661901765[/C][C]266.967281711408[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.7[/C][C]0.415255417962117[/C][C]268.991071924292[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.688333333333[/C][C]0.412875418390476[/C][C]270.513400310271[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.6865[/C][C]0.410743973275227[/C][C]271.912693226937[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.6925[/C][C]0.407648737196441[/C][C]273.992017657537[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.707666666667[/C][C]0.386310694802798[/C][C]289.165348434608[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.962[/C][C]0.334227315318609[/C][C]334.987581410784[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.987[/C][C]0.32806549056811[/C][C]341.355623250932[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]112.080333333333[/C][C]0.306128731707182[/C][C]366.121574764633[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]112.088833333333[/C][C]0.304063821325055[/C][C]368.635876655337[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]112.031833333333[/C][C]0.290922018757806[/C][C]385.092313781173[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]112.019166666667[/C][C]0.288085860128584[/C][C]388.839516860244[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]112.015833333333[/C][C]0.28758583014238[/C][C]389.504007474484[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]111.708448275862[/C][C]0.445977369130335[/C][C]250.48008264118[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]111.730535714286[/C][C]0.440712632734908[/C][C]253.522425760581[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]111.740555555556[/C][C]0.437445607413778[/C][C]255.438741781354[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.750769230769[/C][C]0.434204413336186[/C][C]257.369031263727[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.7592[/C][C]0.430385858200261[/C][C]259.672100908106[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.77375[/C][C]0.427522305108457[/C][C]261.445423231531[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.791086956522[/C][C]0.424203285997753[/C][C]263.531874095652[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.8125[/C][C]0.420492151623746[/C][C]265.908649110886[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.830714285714[/C][C]0.416540058746934[/C][C]268.475292921722[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.8525[/C][C]0.411389102419769[/C][C]271.889798106195[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.878421052632[/C][C]0.404355118756811[/C][C]276.683578030622[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.9075[/C][C]0.394665294198064[/C][C]283.550394841252[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.939117647059[/C][C]0.381532085414715[/C][C]293.393719496445[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.9725[/C][C]0.368858854900773[/C][C]303.564625092494[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.974[/C][C]0.365718188094943[/C][C]306.175639180764[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.972142857143[/C][C]0.361359630164917[/C][C]309.863453219833[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.956538461538[/C][C]0.359710115042523[/C][C]311.241007076777[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.937083333333[/C][C]0.355414882677277[/C][C]314.947653542618[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.922727272727[/C][C]0.351012254086226[/C][C]318.857036954708[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111.9075[/C][C]0.34190555405658[/C][C]327.305300169184[/C][/ROW]
[ROW][C]Median[/C][C]112.075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.755[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.874838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.874838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.874838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.974[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.9725[/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=282255&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282255&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 Mean111.6766666666670.453227077112009246.403342400188
Geometric Mean111.622144121442
Harmonic Mean111.567382266529
Quadratic Mean111.7309149251
Winsorized Mean ( 1 / 20 )111.6878333333330.449992221631875248.19947537827
Winsorized Mean ( 2 / 20 )111.71250.444456096539818251.346535393945
Winsorized Mean ( 3 / 20 )111.7140.441697751810899252.919557643181
Winsorized Mean ( 4 / 20 )111.7226666666670.43976713577754254.049603932165
Winsorized Mean ( 5 / 20 )111.7010.432098590706329258.508133103161
Winsorized Mean ( 6 / 20 )111.6940.42882174664478260.467200821611
Winsorized Mean ( 7 / 20 )111.6811666666670.424317270944568263.202029033733
Winsorized Mean ( 8 / 20 )111.71050.418442661901765266.967281711408
Winsorized Mean ( 9 / 20 )111.70.415255417962117268.991071924292
Winsorized Mean ( 10 / 20 )111.6883333333330.412875418390476270.513400310271
Winsorized Mean ( 11 / 20 )111.68650.410743973275227271.912693226937
Winsorized Mean ( 12 / 20 )111.69250.407648737196441273.992017657537
Winsorized Mean ( 13 / 20 )111.7076666666670.386310694802798289.165348434608
Winsorized Mean ( 14 / 20 )111.9620.334227315318609334.987581410784
Winsorized Mean ( 15 / 20 )111.9870.32806549056811341.355623250932
Winsorized Mean ( 16 / 20 )112.0803333333330.306128731707182366.121574764633
Winsorized Mean ( 17 / 20 )112.0888333333330.304063821325055368.635876655337
Winsorized Mean ( 18 / 20 )112.0318333333330.290922018757806385.092313781173
Winsorized Mean ( 19 / 20 )112.0191666666670.288085860128584388.839516860244
Winsorized Mean ( 20 / 20 )112.0158333333330.28758583014238389.504007474484
Trimmed Mean ( 1 / 20 )111.7084482758620.445977369130335250.48008264118
Trimmed Mean ( 2 / 20 )111.7305357142860.440712632734908253.522425760581
Trimmed Mean ( 3 / 20 )111.7405555555560.437445607413778255.438741781354
Trimmed Mean ( 4 / 20 )111.7507692307690.434204413336186257.369031263727
Trimmed Mean ( 5 / 20 )111.75920.430385858200261259.672100908106
Trimmed Mean ( 6 / 20 )111.773750.427522305108457261.445423231531
Trimmed Mean ( 7 / 20 )111.7910869565220.424203285997753263.531874095652
Trimmed Mean ( 8 / 20 )111.81250.420492151623746265.908649110886
Trimmed Mean ( 9 / 20 )111.8307142857140.416540058746934268.475292921722
Trimmed Mean ( 10 / 20 )111.85250.411389102419769271.889798106195
Trimmed Mean ( 11 / 20 )111.8784210526320.404355118756811276.683578030622
Trimmed Mean ( 12 / 20 )111.90750.394665294198064283.550394841252
Trimmed Mean ( 13 / 20 )111.9391176470590.381532085414715293.393719496445
Trimmed Mean ( 14 / 20 )111.97250.368858854900773303.564625092494
Trimmed Mean ( 15 / 20 )111.9740.365718188094943306.175639180764
Trimmed Mean ( 16 / 20 )111.9721428571430.361359630164917309.863453219833
Trimmed Mean ( 17 / 20 )111.9565384615380.359710115042523311.241007076777
Trimmed Mean ( 18 / 20 )111.9370833333330.355414882677277314.947653542618
Trimmed Mean ( 19 / 20 )111.9227272727270.351012254086226318.857036954708
Trimmed Mean ( 20 / 20 )111.90750.34190555405658327.305300169184
Median112.075
Midrange110.755
Midmean - Weighted Average at Xnp111.874838709677
Midmean - Weighted Average at X(n+1)p111.974
Midmean - Empirical Distribution Function111.874838709677
Midmean - Empirical Distribution Function - Averaging111.974
Midmean - Empirical Distribution Function - Interpolation111.974
Midmean - Closest Observation111.874838709677
Midmean - True Basic - Statistics Graphics Toolkit111.974
Midmean - MS Excel (old versions)111.9725
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')