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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, 19 Oct 2009 02:42:13 -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/2009/Oct/19/t12559423121rzagmv8e5m7hu7.htm/, Retrieved Mon, 29 Apr 2024 18:33:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47613, Retrieved Mon, 29 Apr 2024 18:33:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Omzetindex van de...] [2009-10-12 07:10:37] [83058a88a37d754675a5cd22dab372fc]
- RMPD    [Central Tendency] [WS 3 Part 2 vgl 1.2] [2009-10-19 08:42:13] [eba9f01697e64705b70041e6f338cb22] [Current]
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Dataseries X:
108.0
101.2
119.9
94.8
95.3
118.0
115.9
111.4
108.2
108.8
109.5
124.8
115.3
109.5
124.2
92.9
98.4
120.9
111.7
116.1
109.4
111.7
114.3
133.7
114.3
126.5
131.0
104.0
108.9
128.5
132.4
128.0
116.4
120.9
118.6
133.1
121.1
127.6
135.4
114.9
114.3
128.9
138.9
129.4
115.0
128.0
127.0
128.8
137.9
128.4
135.9
122.2
113.1
136.2
138.0
115.2
111.0
99.2
102.4
112.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47613&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]4 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=47613&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47613&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean118.31.5246338821422977.5923986641137
Geometric Mean117.709335825588
Harmonic Mean117.107885972521
Quadratic Mean118.878240229236
Winsorized Mean ( 1 / 20 )118.3166666666671.5126176784153478.2198095097093
Winsorized Mean ( 2 / 20 )118.331.5075296888326578.492649847333
Winsorized Mean ( 3 / 20 )118.41.4511246369159481.591888792981
Winsorized Mean ( 4 / 20 )118.4333333333331.4346925627217882.5496252023858
Winsorized Mean ( 5 / 20 )118.5583333333331.3895133718486385.3236361270866
Winsorized Mean ( 6 / 20 )118.5083333333331.3305563418764889.0667532095645
Winsorized Mean ( 7 / 20 )118.6251.2798230478852692.6885948772471
Winsorized Mean ( 8 / 20 )119.0651.16693094262632102.032601631104
Winsorized Mean ( 9 / 20 )118.8851.12253452377294105.907655829076
Winsorized Mean ( 10 / 20 )118.7183333333331.05930499458989112.071909355336
Winsorized Mean ( 11 / 20 )118.6451.04090742952299113.982277996008
Winsorized Mean ( 12 / 20 )118.7251.02189760617888116.180916054732
Winsorized Mean ( 13 / 20 )118.6816666666671.00775101082146117.768839120215
Winsorized Mean ( 14 / 20 )118.6583333333331.00390562633713118.196701184227
Winsorized Mean ( 15 / 20 )118.9333333333330.9312972140738127.707171820132
Winsorized Mean ( 16 / 20 )119.040.916056396753987129.948331152770
Winsorized Mean ( 17 / 20 )119.0116666666670.88538699019725134.417681741803
Winsorized Mean ( 18 / 20 )118.8316666666670.85603042499215138.817106492163
Winsorized Mean ( 19 / 20 )118.990.786559769621127151.279031290039
Winsorized Mean ( 20 / 20 )118.5566666666670.678259515132794174.795434522514
Trimmed Mean ( 1 / 20 )118.3827586206901.471532936391880.448595945779
Trimmed Mean ( 2 / 20 )118.4535714285711.4208077186177883.3705855313117
Trimmed Mean ( 3 / 20 )118.5222222222221.3612221321256187.0704489921455
Trimmed Mean ( 4 / 20 )118.5692307692311.3149492545122190.1701950568539
Trimmed Mean ( 5 / 20 )118.611.2632877417149893.8899318685545
Trimmed Mean ( 6 / 20 )118.6229166666671.2140074879107397.7118492661141
Trimmed Mean ( 7 / 20 )118.6478260869571.17015932327181101.394591084582
Trimmed Mean ( 8 / 20 )118.6522727272731.12884760709589105.109203387090
Trimmed Mean ( 9 / 20 )118.5785714285711.10648776093115107.166636284150
Trimmed Mean ( 10 / 20 )118.52751.08785832587681108.954904495002
Trimmed Mean ( 11 / 20 )118.4973684210531.07780192815355109.943548369836
Trimmed Mean ( 12 / 20 )118.4751.06642389350339111.095597840357
Trimmed Mean ( 13 / 20 )118.4382352941181.05293930929240112.483439690091
Trimmed Mean ( 14 / 20 )118.4031251.03505575250142114.392992564753
Trimmed Mean ( 15 / 20 )118.3666666666671.00774396188730117.457083488737
Trimmed Mean ( 16 / 20 )118.2857142857140.986867663537699119.859752888940
Trimmed Mean ( 17 / 20 )118.1769230769230.956102789651143123.602738488027
Trimmed Mean ( 18 / 20 )118.0541666666670.915921551579251128.891133157764
Trimmed Mean ( 19 / 20 )117.9363636363640.860849913625974136.999913422313
Trimmed Mean ( 20 / 20 )117.770.796475790096928147.863879184159
Median116.25
Midrange115.9
Midmean - Weighted Average at Xnp117.8125
Midmean - Weighted Average at X(n+1)p118.366666666667
Midmean - Empirical Distribution Function117.8125
Midmean - Empirical Distribution Function - Averaging118.366666666667
Midmean - Empirical Distribution Function - Interpolation118.366666666667
Midmean - Closest Observation117.8125
Midmean - True Basic - Statistics Graphics Toolkit118.366666666667
Midmean - MS Excel (old versions)118.133333333333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 118.3 & 1.52463388214229 & 77.5923986641137 \tabularnewline
Geometric Mean & 117.709335825588 &  &  \tabularnewline
Harmonic Mean & 117.107885972521 &  &  \tabularnewline
Quadratic Mean & 118.878240229236 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 118.316666666667 & 1.51261767841534 & 78.2198095097093 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 118.33 & 1.50752968883265 & 78.492649847333 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 118.4 & 1.45112463691594 & 81.591888792981 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 118.433333333333 & 1.43469256272178 & 82.5496252023858 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 118.558333333333 & 1.38951337184863 & 85.3236361270866 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 118.508333333333 & 1.33055634187648 & 89.0667532095645 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 118.625 & 1.27982304788526 & 92.6885948772471 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 119.065 & 1.16693094262632 & 102.032601631104 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 118.885 & 1.12253452377294 & 105.907655829076 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 118.718333333333 & 1.05930499458989 & 112.071909355336 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 118.645 & 1.04090742952299 & 113.982277996008 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 118.725 & 1.02189760617888 & 116.180916054732 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 118.681666666667 & 1.00775101082146 & 117.768839120215 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 118.658333333333 & 1.00390562633713 & 118.196701184227 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 118.933333333333 & 0.9312972140738 & 127.707171820132 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 119.04 & 0.916056396753987 & 129.948331152770 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 119.011666666667 & 0.88538699019725 & 134.417681741803 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 118.831666666667 & 0.85603042499215 & 138.817106492163 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 118.99 & 0.786559769621127 & 151.279031290039 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 118.556666666667 & 0.678259515132794 & 174.795434522514 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 118.382758620690 & 1.4715329363918 & 80.448595945779 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 118.453571428571 & 1.42080771861778 & 83.3705855313117 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 118.522222222222 & 1.36122213212561 & 87.0704489921455 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 118.569230769231 & 1.31494925451221 & 90.1701950568539 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 118.61 & 1.26328774171498 & 93.8899318685545 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 118.622916666667 & 1.21400748791073 & 97.7118492661141 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 118.647826086957 & 1.17015932327181 & 101.394591084582 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 118.652272727273 & 1.12884760709589 & 105.109203387090 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 118.578571428571 & 1.10648776093115 & 107.166636284150 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 118.5275 & 1.08785832587681 & 108.954904495002 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 118.497368421053 & 1.07780192815355 & 109.943548369836 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 118.475 & 1.06642389350339 & 111.095597840357 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 118.438235294118 & 1.05293930929240 & 112.483439690091 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 118.403125 & 1.03505575250142 & 114.392992564753 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 118.366666666667 & 1.00774396188730 & 117.457083488737 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 118.285714285714 & 0.986867663537699 & 119.859752888940 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 118.176923076923 & 0.956102789651143 & 123.602738488027 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 118.054166666667 & 0.915921551579251 & 128.891133157764 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 117.936363636364 & 0.860849913625974 & 136.999913422313 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 117.77 & 0.796475790096928 & 147.863879184159 \tabularnewline
Median & 116.25 &  &  \tabularnewline
Midrange & 115.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 117.8125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 118.366666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 117.8125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 118.366666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 118.366666666667 &  &  \tabularnewline
Midmean - Closest Observation & 117.8125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 118.366666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.133333333333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47613&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]118.3[/C][C]1.52463388214229[/C][C]77.5923986641137[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]117.709335825588[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]117.107885972521[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]118.878240229236[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]118.316666666667[/C][C]1.51261767841534[/C][C]78.2198095097093[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]118.33[/C][C]1.50752968883265[/C][C]78.492649847333[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]118.4[/C][C]1.45112463691594[/C][C]81.591888792981[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]118.433333333333[/C][C]1.43469256272178[/C][C]82.5496252023858[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]118.558333333333[/C][C]1.38951337184863[/C][C]85.3236361270866[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]118.508333333333[/C][C]1.33055634187648[/C][C]89.0667532095645[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]118.625[/C][C]1.27982304788526[/C][C]92.6885948772471[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]119.065[/C][C]1.16693094262632[/C][C]102.032601631104[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]118.885[/C][C]1.12253452377294[/C][C]105.907655829076[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]118.718333333333[/C][C]1.05930499458989[/C][C]112.071909355336[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]118.645[/C][C]1.04090742952299[/C][C]113.982277996008[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]118.725[/C][C]1.02189760617888[/C][C]116.180916054732[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]118.681666666667[/C][C]1.00775101082146[/C][C]117.768839120215[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]118.658333333333[/C][C]1.00390562633713[/C][C]118.196701184227[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]118.933333333333[/C][C]0.9312972140738[/C][C]127.707171820132[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]119.04[/C][C]0.916056396753987[/C][C]129.948331152770[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]119.011666666667[/C][C]0.88538699019725[/C][C]134.417681741803[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]118.831666666667[/C][C]0.85603042499215[/C][C]138.817106492163[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]118.99[/C][C]0.786559769621127[/C][C]151.279031290039[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]118.556666666667[/C][C]0.678259515132794[/C][C]174.795434522514[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]118.382758620690[/C][C]1.4715329363918[/C][C]80.448595945779[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]118.453571428571[/C][C]1.42080771861778[/C][C]83.3705855313117[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]118.522222222222[/C][C]1.36122213212561[/C][C]87.0704489921455[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]118.569230769231[/C][C]1.31494925451221[/C][C]90.1701950568539[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]118.61[/C][C]1.26328774171498[/C][C]93.8899318685545[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]118.622916666667[/C][C]1.21400748791073[/C][C]97.7118492661141[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]118.647826086957[/C][C]1.17015932327181[/C][C]101.394591084582[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]118.652272727273[/C][C]1.12884760709589[/C][C]105.109203387090[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]118.578571428571[/C][C]1.10648776093115[/C][C]107.166636284150[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]118.5275[/C][C]1.08785832587681[/C][C]108.954904495002[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]118.497368421053[/C][C]1.07780192815355[/C][C]109.943548369836[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]118.475[/C][C]1.06642389350339[/C][C]111.095597840357[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]118.438235294118[/C][C]1.05293930929240[/C][C]112.483439690091[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]118.403125[/C][C]1.03505575250142[/C][C]114.392992564753[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]118.366666666667[/C][C]1.00774396188730[/C][C]117.457083488737[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]118.285714285714[/C][C]0.986867663537699[/C][C]119.859752888940[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]118.176923076923[/C][C]0.956102789651143[/C][C]123.602738488027[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]118.054166666667[/C][C]0.915921551579251[/C][C]128.891133157764[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]117.936363636364[/C][C]0.860849913625974[/C][C]136.999913422313[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]117.77[/C][C]0.796475790096928[/C][C]147.863879184159[/C][/ROW]
[ROW][C]Median[/C][C]116.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]115.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]117.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]118.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]117.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]118.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]118.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]117.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]118.366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.133333333333[/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=47613&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47613&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 Mean118.31.5246338821422977.5923986641137
Geometric Mean117.709335825588
Harmonic Mean117.107885972521
Quadratic Mean118.878240229236
Winsorized Mean ( 1 / 20 )118.3166666666671.5126176784153478.2198095097093
Winsorized Mean ( 2 / 20 )118.331.5075296888326578.492649847333
Winsorized Mean ( 3 / 20 )118.41.4511246369159481.591888792981
Winsorized Mean ( 4 / 20 )118.4333333333331.4346925627217882.5496252023858
Winsorized Mean ( 5 / 20 )118.5583333333331.3895133718486385.3236361270866
Winsorized Mean ( 6 / 20 )118.5083333333331.3305563418764889.0667532095645
Winsorized Mean ( 7 / 20 )118.6251.2798230478852692.6885948772471
Winsorized Mean ( 8 / 20 )119.0651.16693094262632102.032601631104
Winsorized Mean ( 9 / 20 )118.8851.12253452377294105.907655829076
Winsorized Mean ( 10 / 20 )118.7183333333331.05930499458989112.071909355336
Winsorized Mean ( 11 / 20 )118.6451.04090742952299113.982277996008
Winsorized Mean ( 12 / 20 )118.7251.02189760617888116.180916054732
Winsorized Mean ( 13 / 20 )118.6816666666671.00775101082146117.768839120215
Winsorized Mean ( 14 / 20 )118.6583333333331.00390562633713118.196701184227
Winsorized Mean ( 15 / 20 )118.9333333333330.9312972140738127.707171820132
Winsorized Mean ( 16 / 20 )119.040.916056396753987129.948331152770
Winsorized Mean ( 17 / 20 )119.0116666666670.88538699019725134.417681741803
Winsorized Mean ( 18 / 20 )118.8316666666670.85603042499215138.817106492163
Winsorized Mean ( 19 / 20 )118.990.786559769621127151.279031290039
Winsorized Mean ( 20 / 20 )118.5566666666670.678259515132794174.795434522514
Trimmed Mean ( 1 / 20 )118.3827586206901.471532936391880.448595945779
Trimmed Mean ( 2 / 20 )118.4535714285711.4208077186177883.3705855313117
Trimmed Mean ( 3 / 20 )118.5222222222221.3612221321256187.0704489921455
Trimmed Mean ( 4 / 20 )118.5692307692311.3149492545122190.1701950568539
Trimmed Mean ( 5 / 20 )118.611.2632877417149893.8899318685545
Trimmed Mean ( 6 / 20 )118.6229166666671.2140074879107397.7118492661141
Trimmed Mean ( 7 / 20 )118.6478260869571.17015932327181101.394591084582
Trimmed Mean ( 8 / 20 )118.6522727272731.12884760709589105.109203387090
Trimmed Mean ( 9 / 20 )118.5785714285711.10648776093115107.166636284150
Trimmed Mean ( 10 / 20 )118.52751.08785832587681108.954904495002
Trimmed Mean ( 11 / 20 )118.4973684210531.07780192815355109.943548369836
Trimmed Mean ( 12 / 20 )118.4751.06642389350339111.095597840357
Trimmed Mean ( 13 / 20 )118.4382352941181.05293930929240112.483439690091
Trimmed Mean ( 14 / 20 )118.4031251.03505575250142114.392992564753
Trimmed Mean ( 15 / 20 )118.3666666666671.00774396188730117.457083488737
Trimmed Mean ( 16 / 20 )118.2857142857140.986867663537699119.859752888940
Trimmed Mean ( 17 / 20 )118.1769230769230.956102789651143123.602738488027
Trimmed Mean ( 18 / 20 )118.0541666666670.915921551579251128.891133157764
Trimmed Mean ( 19 / 20 )117.9363636363640.860849913625974136.999913422313
Trimmed Mean ( 20 / 20 )117.770.796475790096928147.863879184159
Median116.25
Midrange115.9
Midmean - Weighted Average at Xnp117.8125
Midmean - Weighted Average at X(n+1)p118.366666666667
Midmean - Empirical Distribution Function117.8125
Midmean - Empirical Distribution Function - Averaging118.366666666667
Midmean - Empirical Distribution Function - Interpolation118.366666666667
Midmean - Closest Observation117.8125
Midmean - True Basic - Statistics Graphics Toolkit118.366666666667
Midmean - MS Excel (old versions)118.133333333333
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')