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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 19 Dec 2009 04:41:24 -0700
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/Dec/19/t1261223217nvh8wzwoggg7tl1.htm/, Retrieved Sat, 04 May 2024 04:24:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69525, Retrieved Sat, 04 May 2024 04:24:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentral Tendency
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Central tendency ...] [2009-12-17 14:38:34] [35f0fff14d789f48983afb62e692bd0d]
-    D    [Central Tendency] [Central Tendency ...] [2009-12-19 11:41:24] [8b8f95c5f2993a04d1b74eff1a82c018] [Current]
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Dataseries X:
7.5
7.2
7
6.9
7
6.9
6.9
6.9
6.8
7
6.8
6.8
6.7
6.4
6.2
6.1
6.2
6.5
6.6
6.5
6.2
6.2
6.6
7.1
7.3
7.4
7.4
7.4
7.4
7.3
7.3
7.4
7.6
7.6
7.6
7.6
7.8
7.9
8.1
8.2
8.2
8.1
8.1
8.1
8.1
8.1
8.2
8.3
8.4
8.5
8.6
8.5
8.3
7.8
7.8
8
8.6
8.9
8.9
8.3
8.3
8.3
8.4
8.5
8.4
8.6
8.5
8.5
8.4
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.6
8.4
8.1
8
8
8
8
7.9
7.8
7.8
7.9
8.1
8
7.6
7.3
7
6.8
7
7.1
7.2
7.1
6.9
6.7
6.7
6.6
6.9
7.3
7.4
7.3
7
6.9
7.1
7.5
7.7
7.9
7.8
7.7
7.8
7.8
7.9
8
8.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69525&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69525&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69525&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.636134453781510.0644317252521407118.515132473933
Geometric Mean7.60324224414912
Harmonic Mean7.56958163667955
Quadratic Mean7.6681432021101
Winsorized Mean ( 1 / 39 )7.636974789915970.064267209705234118.831591179133
Winsorized Mean ( 2 / 39 )7.631932773109240.0635211932566545120.147818103365
Winsorized Mean ( 3 / 39 )7.631932773109240.0635211932566545120.147818103365
Winsorized Mean ( 4 / 39 )7.631932773109240.0635211932566545120.147818103365
Winsorized Mean ( 5 / 39 )7.640336134453780.0620051333238768123.2210258229
Winsorized Mean ( 6 / 39 )7.640336134453780.0605406883290668126.201672715133
Winsorized Mean ( 7 / 39 )7.640336134453780.0605406883290668126.201672715133
Winsorized Mean ( 8 / 39 )7.647058823529410.0595025613412543128.516464689186
Winsorized Mean ( 9 / 39 )7.647058823529410.0595025613412543128.516464689186
Winsorized Mean ( 10 / 39 )7.647058823529410.0595025613412543128.516464689186
Winsorized Mean ( 11 / 39 )7.65630252100840.0581688804417584131.621968015600
Winsorized Mean ( 12 / 39 )7.65630252100840.0581688804417584131.621968015600
Winsorized Mean ( 13 / 39 )7.65630252100840.0581688804417584131.621968015600
Winsorized Mean ( 14 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 15 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 16 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 17 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 18 / 39 )7.683193277310920.0546814176729923140.508304361424
Winsorized Mean ( 19 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 20 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 21 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 22 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 23 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 24 / 39 )7.647058823529410.0504335784283544151.626338281603
Winsorized Mean ( 25 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 26 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 27 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 28 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 29 / 39 )7.64369747899160.0452349679936483168.977625452612
Winsorized Mean ( 30 / 39 )7.64369747899160.0452349679936483168.977625452612
Winsorized Mean ( 31 / 39 )7.669747899159660.0421700665903578181.876589706723
Winsorized Mean ( 32 / 39 )7.642857142857140.0394119180682192193.922486330858
Winsorized Mean ( 33 / 39 )7.642857142857140.0394119180682192193.922486330858
Winsorized Mean ( 34 / 39 )7.642857142857140.0394119180682192193.922486330858
Winsorized Mean ( 35 / 39 )7.672268907563030.0360593516379148212.767799726493
Winsorized Mean ( 36 / 39 )7.672268907563030.0360593516379148212.767799726493
Winsorized Mean ( 37 / 39 )7.703361344537820.0327040127064016235.547894800993
Winsorized Mean ( 38 / 39 )7.703361344537820.0327040127064016235.547894800993
Winsorized Mean ( 39 / 39 )7.703361344537810.0327040127064016235.547894800993
Trimmed Mean ( 1 / 39 )7.638461538461540.0632740444931607120.720298499129
Trimmed Mean ( 2 / 39 )7.640.0621727128590694122.883490982902
Trimmed Mean ( 3 / 39 )7.644247787610620.0613782140998175124.543340006260
Trimmed Mean ( 4 / 39 )7.648648648648650.0604902827545297126.444253528901
Trimmed Mean ( 5 / 39 )7.653211009174310.0594968255596971128.632257892404
Trimmed Mean ( 6 / 39 )7.656074766355140.0587919525729941130.223175643803
Trimmed Mean ( 7 / 39 )7.659047619047620.0583298571140343131.305784001395
Trimmed Mean ( 8 / 39 )7.66213592233010.0578028530175635132.556362226652
Trimmed Mean ( 9 / 39 )7.664356435643560.0573953487337519133.536194216666
Trimmed Mean ( 10 / 39 )7.666666666666670.056925995422607134.677779628637
Trimmed Mean ( 11 / 39 )7.669072164948450.0563867814767394136.008333231647
Trimmed Mean ( 12 / 39 )7.670526315789470.0559729914914983137.039777782014
Trimmed Mean ( 13 / 39 )7.672043010752690.0554923054064414138.254176945082
Trimmed Mean ( 14 / 39 )7.673626373626370.0549355303099912139.684214029163
Trimmed Mean ( 15 / 39 )7.674157303370790.0545088594229086140.787339610807
Trimmed Mean ( 16 / 39 )7.674712643678160.0540084836664699142.101983293467
Trimmed Mean ( 17 / 39 )7.675294117647060.0534235725296331143.668679465225
Trimmed Mean ( 18 / 39 )7.675903614457830.0527412069886702145.539020677072
Trimmed Mean ( 19 / 39 )7.675308641975310.0521906188118869147.062993631859
Trimmed Mean ( 20 / 39 )7.67594936708860.0517846134087366148.228380243032
Trimmed Mean ( 21 / 39 )7.676623376623380.0512954566058997149.655035446950
Trimmed Mean ( 22 / 39 )7.677333333333330.0507093229636862151.398853004431
Trimmed Mean ( 23 / 39 )7.678082191780820.0500093817432104153.532835722834
Trimmed Mean ( 24 / 39 )7.678873239436620.0491749021129467156.154316724403
Trimmed Mean ( 25 / 39 )7.681159420289860.0484752757011268158.455198226161
Trimmed Mean ( 26 / 39 )7.68208955223880.047976954984271160.120406865282
Trimmed Mean ( 27 / 39 )7.683076923076920.0473616015541614162.221645192694
Trimmed Mean ( 28 / 39 )7.684126984126980.046605531010491164.875859528288
Trimmed Mean ( 29 / 39 )7.685245901639340.0456786150999819168.246035586188
Trimmed Mean ( 30 / 39 )7.688135593220340.0449094644658914171.191878697629
Trimmed Mean ( 31 / 39 )7.691228070175440.0439497820737175.000368768107
Trimmed Mean ( 32 / 39 )7.692727272727270.043255917284983177.842194908162
Trimmed Mean ( 33 / 39 )7.696226415094340.0427605361914107179.984329023458
Trimmed Mean ( 34 / 39 )7.70.042101651031852182.890689825313
Trimmed Mean ( 35 / 39 )7.704081632653060.0412350966350546186.833116964341
Trimmed Mean ( 36 / 39 )7.70638297872340.0407383582479655189.167735523762
Trimmed Mean ( 37 / 39 )7.708888888888890.0400532754082801192.465879764112
Trimmed Mean ( 38 / 39 )7.70930232558140.0397687046874545193.853493247251
Trimmed Mean ( 39 / 39 )7.709756097560980.0393243048484572196.055750439119
Median7.8
Midrange7.5
Midmean - Weighted Average at Xnp7.64307692307692
Midmean - Weighted Average at X(n+1)p7.64307692307692
Midmean - Empirical Distribution Function7.64307692307692
Midmean - Empirical Distribution Function - Averaging7.64307692307692
Midmean - Empirical Distribution Function - Interpolation7.64307692307692
Midmean - Closest Observation7.64307692307692
Midmean - True Basic - Statistics Graphics Toolkit7.64307692307692
Midmean - MS Excel (old versions)7.64307692307692
Number of observations119

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.63613445378151 & 0.0644317252521407 & 118.515132473933 \tabularnewline
Geometric Mean & 7.60324224414912 &  &  \tabularnewline
Harmonic Mean & 7.56958163667955 &  &  \tabularnewline
Quadratic Mean & 7.6681432021101 &  &  \tabularnewline
Winsorized Mean ( 1 / 39 ) & 7.63697478991597 & 0.064267209705234 & 118.831591179133 \tabularnewline
Winsorized Mean ( 2 / 39 ) & 7.63193277310924 & 0.0635211932566545 & 120.147818103365 \tabularnewline
Winsorized Mean ( 3 / 39 ) & 7.63193277310924 & 0.0635211932566545 & 120.147818103365 \tabularnewline
Winsorized Mean ( 4 / 39 ) & 7.63193277310924 & 0.0635211932566545 & 120.147818103365 \tabularnewline
Winsorized Mean ( 5 / 39 ) & 7.64033613445378 & 0.0620051333238768 & 123.2210258229 \tabularnewline
Winsorized Mean ( 6 / 39 ) & 7.64033613445378 & 0.0605406883290668 & 126.201672715133 \tabularnewline
Winsorized Mean ( 7 / 39 ) & 7.64033613445378 & 0.0605406883290668 & 126.201672715133 \tabularnewline
Winsorized Mean ( 8 / 39 ) & 7.64705882352941 & 0.0595025613412543 & 128.516464689186 \tabularnewline
Winsorized Mean ( 9 / 39 ) & 7.64705882352941 & 0.0595025613412543 & 128.516464689186 \tabularnewline
Winsorized Mean ( 10 / 39 ) & 7.64705882352941 & 0.0595025613412543 & 128.516464689186 \tabularnewline
Winsorized Mean ( 11 / 39 ) & 7.6563025210084 & 0.0581688804417584 & 131.621968015600 \tabularnewline
Winsorized Mean ( 12 / 39 ) & 7.6563025210084 & 0.0581688804417584 & 131.621968015600 \tabularnewline
Winsorized Mean ( 13 / 39 ) & 7.6563025210084 & 0.0581688804417584 & 131.621968015600 \tabularnewline
Winsorized Mean ( 14 / 39 ) & 7.66806722689076 & 0.0565838082048242 & 135.516987459268 \tabularnewline
Winsorized Mean ( 15 / 39 ) & 7.66806722689076 & 0.0565838082048242 & 135.516987459268 \tabularnewline
Winsorized Mean ( 16 / 39 ) & 7.66806722689076 & 0.0565838082048242 & 135.516987459268 \tabularnewline
Winsorized Mean ( 17 / 39 ) & 7.66806722689076 & 0.0565838082048242 & 135.516987459268 \tabularnewline
Winsorized Mean ( 18 / 39 ) & 7.68319327731092 & 0.0546814176729923 & 140.508304361424 \tabularnewline
Winsorized Mean ( 19 / 39 ) & 7.6672268907563 & 0.0527293687805989 & 145.407143458493 \tabularnewline
Winsorized Mean ( 20 / 39 ) & 7.6672268907563 & 0.0527293687805989 & 145.407143458493 \tabularnewline
Winsorized Mean ( 21 / 39 ) & 7.6672268907563 & 0.0527293687805989 & 145.407143458493 \tabularnewline
Winsorized Mean ( 22 / 39 ) & 7.6672268907563 & 0.0527293687805989 & 145.407143458493 \tabularnewline
Winsorized Mean ( 23 / 39 ) & 7.6672268907563 & 0.0527293687805989 & 145.407143458493 \tabularnewline
Winsorized Mean ( 24 / 39 ) & 7.64705882352941 & 0.0504335784283544 & 151.626338281603 \tabularnewline
Winsorized Mean ( 25 / 39 ) & 7.66806722689076 & 0.0478706652177604 & 160.183009615790 \tabularnewline
Winsorized Mean ( 26 / 39 ) & 7.66806722689076 & 0.0478706652177604 & 160.183009615790 \tabularnewline
Winsorized Mean ( 27 / 39 ) & 7.66806722689076 & 0.0478706652177604 & 160.183009615790 \tabularnewline
Winsorized Mean ( 28 / 39 ) & 7.66806722689076 & 0.0478706652177604 & 160.183009615790 \tabularnewline
Winsorized Mean ( 29 / 39 ) & 7.6436974789916 & 0.0452349679936483 & 168.977625452612 \tabularnewline
Winsorized Mean ( 30 / 39 ) & 7.6436974789916 & 0.0452349679936483 & 168.977625452612 \tabularnewline
Winsorized Mean ( 31 / 39 ) & 7.66974789915966 & 0.0421700665903578 & 181.876589706723 \tabularnewline
Winsorized Mean ( 32 / 39 ) & 7.64285714285714 & 0.0394119180682192 & 193.922486330858 \tabularnewline
Winsorized Mean ( 33 / 39 ) & 7.64285714285714 & 0.0394119180682192 & 193.922486330858 \tabularnewline
Winsorized Mean ( 34 / 39 ) & 7.64285714285714 & 0.0394119180682192 & 193.922486330858 \tabularnewline
Winsorized Mean ( 35 / 39 ) & 7.67226890756303 & 0.0360593516379148 & 212.767799726493 \tabularnewline
Winsorized Mean ( 36 / 39 ) & 7.67226890756303 & 0.0360593516379148 & 212.767799726493 \tabularnewline
Winsorized Mean ( 37 / 39 ) & 7.70336134453782 & 0.0327040127064016 & 235.547894800993 \tabularnewline
Winsorized Mean ( 38 / 39 ) & 7.70336134453782 & 0.0327040127064016 & 235.547894800993 \tabularnewline
Winsorized Mean ( 39 / 39 ) & 7.70336134453781 & 0.0327040127064016 & 235.547894800993 \tabularnewline
Trimmed Mean ( 1 / 39 ) & 7.63846153846154 & 0.0632740444931607 & 120.720298499129 \tabularnewline
Trimmed Mean ( 2 / 39 ) & 7.64 & 0.0621727128590694 & 122.883490982902 \tabularnewline
Trimmed Mean ( 3 / 39 ) & 7.64424778761062 & 0.0613782140998175 & 124.543340006260 \tabularnewline
Trimmed Mean ( 4 / 39 ) & 7.64864864864865 & 0.0604902827545297 & 126.444253528901 \tabularnewline
Trimmed Mean ( 5 / 39 ) & 7.65321100917431 & 0.0594968255596971 & 128.632257892404 \tabularnewline
Trimmed Mean ( 6 / 39 ) & 7.65607476635514 & 0.0587919525729941 & 130.223175643803 \tabularnewline
Trimmed Mean ( 7 / 39 ) & 7.65904761904762 & 0.0583298571140343 & 131.305784001395 \tabularnewline
Trimmed Mean ( 8 / 39 ) & 7.6621359223301 & 0.0578028530175635 & 132.556362226652 \tabularnewline
Trimmed Mean ( 9 / 39 ) & 7.66435643564356 & 0.0573953487337519 & 133.536194216666 \tabularnewline
Trimmed Mean ( 10 / 39 ) & 7.66666666666667 & 0.056925995422607 & 134.677779628637 \tabularnewline
Trimmed Mean ( 11 / 39 ) & 7.66907216494845 & 0.0563867814767394 & 136.008333231647 \tabularnewline
Trimmed Mean ( 12 / 39 ) & 7.67052631578947 & 0.0559729914914983 & 137.039777782014 \tabularnewline
Trimmed Mean ( 13 / 39 ) & 7.67204301075269 & 0.0554923054064414 & 138.254176945082 \tabularnewline
Trimmed Mean ( 14 / 39 ) & 7.67362637362637 & 0.0549355303099912 & 139.684214029163 \tabularnewline
Trimmed Mean ( 15 / 39 ) & 7.67415730337079 & 0.0545088594229086 & 140.787339610807 \tabularnewline
Trimmed Mean ( 16 / 39 ) & 7.67471264367816 & 0.0540084836664699 & 142.101983293467 \tabularnewline
Trimmed Mean ( 17 / 39 ) & 7.67529411764706 & 0.0534235725296331 & 143.668679465225 \tabularnewline
Trimmed Mean ( 18 / 39 ) & 7.67590361445783 & 0.0527412069886702 & 145.539020677072 \tabularnewline
Trimmed Mean ( 19 / 39 ) & 7.67530864197531 & 0.0521906188118869 & 147.062993631859 \tabularnewline
Trimmed Mean ( 20 / 39 ) & 7.6759493670886 & 0.0517846134087366 & 148.228380243032 \tabularnewline
Trimmed Mean ( 21 / 39 ) & 7.67662337662338 & 0.0512954566058997 & 149.655035446950 \tabularnewline
Trimmed Mean ( 22 / 39 ) & 7.67733333333333 & 0.0507093229636862 & 151.398853004431 \tabularnewline
Trimmed Mean ( 23 / 39 ) & 7.67808219178082 & 0.0500093817432104 & 153.532835722834 \tabularnewline
Trimmed Mean ( 24 / 39 ) & 7.67887323943662 & 0.0491749021129467 & 156.154316724403 \tabularnewline
Trimmed Mean ( 25 / 39 ) & 7.68115942028986 & 0.0484752757011268 & 158.455198226161 \tabularnewline
Trimmed Mean ( 26 / 39 ) & 7.6820895522388 & 0.047976954984271 & 160.120406865282 \tabularnewline
Trimmed Mean ( 27 / 39 ) & 7.68307692307692 & 0.0473616015541614 & 162.221645192694 \tabularnewline
Trimmed Mean ( 28 / 39 ) & 7.68412698412698 & 0.046605531010491 & 164.875859528288 \tabularnewline
Trimmed Mean ( 29 / 39 ) & 7.68524590163934 & 0.0456786150999819 & 168.246035586188 \tabularnewline
Trimmed Mean ( 30 / 39 ) & 7.68813559322034 & 0.0449094644658914 & 171.191878697629 \tabularnewline
Trimmed Mean ( 31 / 39 ) & 7.69122807017544 & 0.0439497820737 & 175.000368768107 \tabularnewline
Trimmed Mean ( 32 / 39 ) & 7.69272727272727 & 0.043255917284983 & 177.842194908162 \tabularnewline
Trimmed Mean ( 33 / 39 ) & 7.69622641509434 & 0.0427605361914107 & 179.984329023458 \tabularnewline
Trimmed Mean ( 34 / 39 ) & 7.7 & 0.042101651031852 & 182.890689825313 \tabularnewline
Trimmed Mean ( 35 / 39 ) & 7.70408163265306 & 0.0412350966350546 & 186.833116964341 \tabularnewline
Trimmed Mean ( 36 / 39 ) & 7.7063829787234 & 0.0407383582479655 & 189.167735523762 \tabularnewline
Trimmed Mean ( 37 / 39 ) & 7.70888888888889 & 0.0400532754082801 & 192.465879764112 \tabularnewline
Trimmed Mean ( 38 / 39 ) & 7.7093023255814 & 0.0397687046874545 & 193.853493247251 \tabularnewline
Trimmed Mean ( 39 / 39 ) & 7.70975609756098 & 0.0393243048484572 & 196.055750439119 \tabularnewline
Median & 7.8 &  &  \tabularnewline
Midrange & 7.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.64307692307692 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.64307692307692 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.64307692307692 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.64307692307692 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.64307692307692 &  &  \tabularnewline
Midmean - Closest Observation & 7.64307692307692 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.64307692307692 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.64307692307692 &  &  \tabularnewline
Number of observations & 119 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69525&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]7.63613445378151[/C][C]0.0644317252521407[/C][C]118.515132473933[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.60324224414912[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.56958163667955[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.6681432021101[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 39 )[/C][C]7.63697478991597[/C][C]0.064267209705234[/C][C]118.831591179133[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 39 )[/C][C]7.63193277310924[/C][C]0.0635211932566545[/C][C]120.147818103365[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 39 )[/C][C]7.63193277310924[/C][C]0.0635211932566545[/C][C]120.147818103365[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 39 )[/C][C]7.63193277310924[/C][C]0.0635211932566545[/C][C]120.147818103365[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 39 )[/C][C]7.64033613445378[/C][C]0.0620051333238768[/C][C]123.2210258229[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 39 )[/C][C]7.64033613445378[/C][C]0.0605406883290668[/C][C]126.201672715133[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 39 )[/C][C]7.64033613445378[/C][C]0.0605406883290668[/C][C]126.201672715133[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 39 )[/C][C]7.64705882352941[/C][C]0.0595025613412543[/C][C]128.516464689186[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 39 )[/C][C]7.64705882352941[/C][C]0.0595025613412543[/C][C]128.516464689186[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 39 )[/C][C]7.64705882352941[/C][C]0.0595025613412543[/C][C]128.516464689186[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 39 )[/C][C]7.6563025210084[/C][C]0.0581688804417584[/C][C]131.621968015600[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 39 )[/C][C]7.6563025210084[/C][C]0.0581688804417584[/C][C]131.621968015600[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 39 )[/C][C]7.6563025210084[/C][C]0.0581688804417584[/C][C]131.621968015600[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 39 )[/C][C]7.66806722689076[/C][C]0.0565838082048242[/C][C]135.516987459268[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 39 )[/C][C]7.66806722689076[/C][C]0.0565838082048242[/C][C]135.516987459268[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 39 )[/C][C]7.66806722689076[/C][C]0.0565838082048242[/C][C]135.516987459268[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 39 )[/C][C]7.66806722689076[/C][C]0.0565838082048242[/C][C]135.516987459268[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 39 )[/C][C]7.68319327731092[/C][C]0.0546814176729923[/C][C]140.508304361424[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 39 )[/C][C]7.6672268907563[/C][C]0.0527293687805989[/C][C]145.407143458493[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 39 )[/C][C]7.6672268907563[/C][C]0.0527293687805989[/C][C]145.407143458493[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 39 )[/C][C]7.6672268907563[/C][C]0.0527293687805989[/C][C]145.407143458493[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 39 )[/C][C]7.6672268907563[/C][C]0.0527293687805989[/C][C]145.407143458493[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 39 )[/C][C]7.6672268907563[/C][C]0.0527293687805989[/C][C]145.407143458493[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 39 )[/C][C]7.64705882352941[/C][C]0.0504335784283544[/C][C]151.626338281603[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 39 )[/C][C]7.66806722689076[/C][C]0.0478706652177604[/C][C]160.183009615790[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 39 )[/C][C]7.66806722689076[/C][C]0.0478706652177604[/C][C]160.183009615790[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 39 )[/C][C]7.66806722689076[/C][C]0.0478706652177604[/C][C]160.183009615790[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 39 )[/C][C]7.66806722689076[/C][C]0.0478706652177604[/C][C]160.183009615790[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 39 )[/C][C]7.6436974789916[/C][C]0.0452349679936483[/C][C]168.977625452612[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 39 )[/C][C]7.6436974789916[/C][C]0.0452349679936483[/C][C]168.977625452612[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 39 )[/C][C]7.66974789915966[/C][C]0.0421700665903578[/C][C]181.876589706723[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 39 )[/C][C]7.64285714285714[/C][C]0.0394119180682192[/C][C]193.922486330858[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 39 )[/C][C]7.64285714285714[/C][C]0.0394119180682192[/C][C]193.922486330858[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 39 )[/C][C]7.64285714285714[/C][C]0.0394119180682192[/C][C]193.922486330858[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 39 )[/C][C]7.67226890756303[/C][C]0.0360593516379148[/C][C]212.767799726493[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 39 )[/C][C]7.67226890756303[/C][C]0.0360593516379148[/C][C]212.767799726493[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 39 )[/C][C]7.70336134453782[/C][C]0.0327040127064016[/C][C]235.547894800993[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 39 )[/C][C]7.70336134453782[/C][C]0.0327040127064016[/C][C]235.547894800993[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 39 )[/C][C]7.70336134453781[/C][C]0.0327040127064016[/C][C]235.547894800993[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 39 )[/C][C]7.63846153846154[/C][C]0.0632740444931607[/C][C]120.720298499129[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 39 )[/C][C]7.64[/C][C]0.0621727128590694[/C][C]122.883490982902[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 39 )[/C][C]7.64424778761062[/C][C]0.0613782140998175[/C][C]124.543340006260[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 39 )[/C][C]7.64864864864865[/C][C]0.0604902827545297[/C][C]126.444253528901[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 39 )[/C][C]7.65321100917431[/C][C]0.0594968255596971[/C][C]128.632257892404[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 39 )[/C][C]7.65607476635514[/C][C]0.0587919525729941[/C][C]130.223175643803[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 39 )[/C][C]7.65904761904762[/C][C]0.0583298571140343[/C][C]131.305784001395[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 39 )[/C][C]7.6621359223301[/C][C]0.0578028530175635[/C][C]132.556362226652[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 39 )[/C][C]7.66435643564356[/C][C]0.0573953487337519[/C][C]133.536194216666[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 39 )[/C][C]7.66666666666667[/C][C]0.056925995422607[/C][C]134.677779628637[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 39 )[/C][C]7.66907216494845[/C][C]0.0563867814767394[/C][C]136.008333231647[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 39 )[/C][C]7.67052631578947[/C][C]0.0559729914914983[/C][C]137.039777782014[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 39 )[/C][C]7.67204301075269[/C][C]0.0554923054064414[/C][C]138.254176945082[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 39 )[/C][C]7.67362637362637[/C][C]0.0549355303099912[/C][C]139.684214029163[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 39 )[/C][C]7.67415730337079[/C][C]0.0545088594229086[/C][C]140.787339610807[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 39 )[/C][C]7.67471264367816[/C][C]0.0540084836664699[/C][C]142.101983293467[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 39 )[/C][C]7.67529411764706[/C][C]0.0534235725296331[/C][C]143.668679465225[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 39 )[/C][C]7.67590361445783[/C][C]0.0527412069886702[/C][C]145.539020677072[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 39 )[/C][C]7.67530864197531[/C][C]0.0521906188118869[/C][C]147.062993631859[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 39 )[/C][C]7.6759493670886[/C][C]0.0517846134087366[/C][C]148.228380243032[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 39 )[/C][C]7.67662337662338[/C][C]0.0512954566058997[/C][C]149.655035446950[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 39 )[/C][C]7.67733333333333[/C][C]0.0507093229636862[/C][C]151.398853004431[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 39 )[/C][C]7.67808219178082[/C][C]0.0500093817432104[/C][C]153.532835722834[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 39 )[/C][C]7.67887323943662[/C][C]0.0491749021129467[/C][C]156.154316724403[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 39 )[/C][C]7.68115942028986[/C][C]0.0484752757011268[/C][C]158.455198226161[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 39 )[/C][C]7.6820895522388[/C][C]0.047976954984271[/C][C]160.120406865282[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 39 )[/C][C]7.68307692307692[/C][C]0.0473616015541614[/C][C]162.221645192694[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 39 )[/C][C]7.68412698412698[/C][C]0.046605531010491[/C][C]164.875859528288[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 39 )[/C][C]7.68524590163934[/C][C]0.0456786150999819[/C][C]168.246035586188[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 39 )[/C][C]7.68813559322034[/C][C]0.0449094644658914[/C][C]171.191878697629[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 39 )[/C][C]7.69122807017544[/C][C]0.0439497820737[/C][C]175.000368768107[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 39 )[/C][C]7.69272727272727[/C][C]0.043255917284983[/C][C]177.842194908162[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 39 )[/C][C]7.69622641509434[/C][C]0.0427605361914107[/C][C]179.984329023458[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 39 )[/C][C]7.7[/C][C]0.042101651031852[/C][C]182.890689825313[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 39 )[/C][C]7.70408163265306[/C][C]0.0412350966350546[/C][C]186.833116964341[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 39 )[/C][C]7.7063829787234[/C][C]0.0407383582479655[/C][C]189.167735523762[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 39 )[/C][C]7.70888888888889[/C][C]0.0400532754082801[/C][C]192.465879764112[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 39 )[/C][C]7.7093023255814[/C][C]0.0397687046874545[/C][C]193.853493247251[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 39 )[/C][C]7.70975609756098[/C][C]0.0393243048484572[/C][C]196.055750439119[/C][/ROW]
[ROW][C]Median[/C][C]7.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.64307692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]119[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69525&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69525&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 Mean7.636134453781510.0644317252521407118.515132473933
Geometric Mean7.60324224414912
Harmonic Mean7.56958163667955
Quadratic Mean7.6681432021101
Winsorized Mean ( 1 / 39 )7.636974789915970.064267209705234118.831591179133
Winsorized Mean ( 2 / 39 )7.631932773109240.0635211932566545120.147818103365
Winsorized Mean ( 3 / 39 )7.631932773109240.0635211932566545120.147818103365
Winsorized Mean ( 4 / 39 )7.631932773109240.0635211932566545120.147818103365
Winsorized Mean ( 5 / 39 )7.640336134453780.0620051333238768123.2210258229
Winsorized Mean ( 6 / 39 )7.640336134453780.0605406883290668126.201672715133
Winsorized Mean ( 7 / 39 )7.640336134453780.0605406883290668126.201672715133
Winsorized Mean ( 8 / 39 )7.647058823529410.0595025613412543128.516464689186
Winsorized Mean ( 9 / 39 )7.647058823529410.0595025613412543128.516464689186
Winsorized Mean ( 10 / 39 )7.647058823529410.0595025613412543128.516464689186
Winsorized Mean ( 11 / 39 )7.65630252100840.0581688804417584131.621968015600
Winsorized Mean ( 12 / 39 )7.65630252100840.0581688804417584131.621968015600
Winsorized Mean ( 13 / 39 )7.65630252100840.0581688804417584131.621968015600
Winsorized Mean ( 14 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 15 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 16 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 17 / 39 )7.668067226890760.0565838082048242135.516987459268
Winsorized Mean ( 18 / 39 )7.683193277310920.0546814176729923140.508304361424
Winsorized Mean ( 19 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 20 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 21 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 22 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 23 / 39 )7.66722689075630.0527293687805989145.407143458493
Winsorized Mean ( 24 / 39 )7.647058823529410.0504335784283544151.626338281603
Winsorized Mean ( 25 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 26 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 27 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 28 / 39 )7.668067226890760.0478706652177604160.183009615790
Winsorized Mean ( 29 / 39 )7.64369747899160.0452349679936483168.977625452612
Winsorized Mean ( 30 / 39 )7.64369747899160.0452349679936483168.977625452612
Winsorized Mean ( 31 / 39 )7.669747899159660.0421700665903578181.876589706723
Winsorized Mean ( 32 / 39 )7.642857142857140.0394119180682192193.922486330858
Winsorized Mean ( 33 / 39 )7.642857142857140.0394119180682192193.922486330858
Winsorized Mean ( 34 / 39 )7.642857142857140.0394119180682192193.922486330858
Winsorized Mean ( 35 / 39 )7.672268907563030.0360593516379148212.767799726493
Winsorized Mean ( 36 / 39 )7.672268907563030.0360593516379148212.767799726493
Winsorized Mean ( 37 / 39 )7.703361344537820.0327040127064016235.547894800993
Winsorized Mean ( 38 / 39 )7.703361344537820.0327040127064016235.547894800993
Winsorized Mean ( 39 / 39 )7.703361344537810.0327040127064016235.547894800993
Trimmed Mean ( 1 / 39 )7.638461538461540.0632740444931607120.720298499129
Trimmed Mean ( 2 / 39 )7.640.0621727128590694122.883490982902
Trimmed Mean ( 3 / 39 )7.644247787610620.0613782140998175124.543340006260
Trimmed Mean ( 4 / 39 )7.648648648648650.0604902827545297126.444253528901
Trimmed Mean ( 5 / 39 )7.653211009174310.0594968255596971128.632257892404
Trimmed Mean ( 6 / 39 )7.656074766355140.0587919525729941130.223175643803
Trimmed Mean ( 7 / 39 )7.659047619047620.0583298571140343131.305784001395
Trimmed Mean ( 8 / 39 )7.66213592233010.0578028530175635132.556362226652
Trimmed Mean ( 9 / 39 )7.664356435643560.0573953487337519133.536194216666
Trimmed Mean ( 10 / 39 )7.666666666666670.056925995422607134.677779628637
Trimmed Mean ( 11 / 39 )7.669072164948450.0563867814767394136.008333231647
Trimmed Mean ( 12 / 39 )7.670526315789470.0559729914914983137.039777782014
Trimmed Mean ( 13 / 39 )7.672043010752690.0554923054064414138.254176945082
Trimmed Mean ( 14 / 39 )7.673626373626370.0549355303099912139.684214029163
Trimmed Mean ( 15 / 39 )7.674157303370790.0545088594229086140.787339610807
Trimmed Mean ( 16 / 39 )7.674712643678160.0540084836664699142.101983293467
Trimmed Mean ( 17 / 39 )7.675294117647060.0534235725296331143.668679465225
Trimmed Mean ( 18 / 39 )7.675903614457830.0527412069886702145.539020677072
Trimmed Mean ( 19 / 39 )7.675308641975310.0521906188118869147.062993631859
Trimmed Mean ( 20 / 39 )7.67594936708860.0517846134087366148.228380243032
Trimmed Mean ( 21 / 39 )7.676623376623380.0512954566058997149.655035446950
Trimmed Mean ( 22 / 39 )7.677333333333330.0507093229636862151.398853004431
Trimmed Mean ( 23 / 39 )7.678082191780820.0500093817432104153.532835722834
Trimmed Mean ( 24 / 39 )7.678873239436620.0491749021129467156.154316724403
Trimmed Mean ( 25 / 39 )7.681159420289860.0484752757011268158.455198226161
Trimmed Mean ( 26 / 39 )7.68208955223880.047976954984271160.120406865282
Trimmed Mean ( 27 / 39 )7.683076923076920.0473616015541614162.221645192694
Trimmed Mean ( 28 / 39 )7.684126984126980.046605531010491164.875859528288
Trimmed Mean ( 29 / 39 )7.685245901639340.0456786150999819168.246035586188
Trimmed Mean ( 30 / 39 )7.688135593220340.0449094644658914171.191878697629
Trimmed Mean ( 31 / 39 )7.691228070175440.0439497820737175.000368768107
Trimmed Mean ( 32 / 39 )7.692727272727270.043255917284983177.842194908162
Trimmed Mean ( 33 / 39 )7.696226415094340.0427605361914107179.984329023458
Trimmed Mean ( 34 / 39 )7.70.042101651031852182.890689825313
Trimmed Mean ( 35 / 39 )7.704081632653060.0412350966350546186.833116964341
Trimmed Mean ( 36 / 39 )7.70638297872340.0407383582479655189.167735523762
Trimmed Mean ( 37 / 39 )7.708888888888890.0400532754082801192.465879764112
Trimmed Mean ( 38 / 39 )7.70930232558140.0397687046874545193.853493247251
Trimmed Mean ( 39 / 39 )7.709756097560980.0393243048484572196.055750439119
Median7.8
Midrange7.5
Midmean - Weighted Average at Xnp7.64307692307692
Midmean - Weighted Average at X(n+1)p7.64307692307692
Midmean - Empirical Distribution Function7.64307692307692
Midmean - Empirical Distribution Function - Averaging7.64307692307692
Midmean - Empirical Distribution Function - Interpolation7.64307692307692
Midmean - Closest Observation7.64307692307692
Midmean - True Basic - Statistics Graphics Toolkit7.64307692307692
Midmean - MS Excel (old versions)7.64307692307692
Number of observations119



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')