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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 computationTue, 20 Oct 2009 12:23:53 -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/20/t1256063120n67nsz5pisi9bw2.htm/, Retrieved Fri, 03 May 2024 00:39:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48954, Retrieved Fri, 03 May 2024 00:39:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [WS2_Rente op lang...] [2009-10-11 12:09:41] [517ac0676608e46c618c738721d88e41]
- RMPD    [Central Tendency] [WS3_2 Xt histogram] [2009-10-20 18:23:53] [5d37783481a916b2505b66314b556267] [Current]
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Dataseries X:
2.93
2.76
2.51
2.51
2.48
2.24
2.12
2.1
2.13
2.12
2.14
2.13
2.13
2.04
2.02
1.92
2.03
2.05
2.08
2.08
2.08
2.08
2.12
2.14
2.13
2.1
2.09
2.1
2.09
2.08
2.07
2.08
2.09
2.11
2.2
2.42
2.46
2.5
2.59
2.75
2.78
2.9
3.03
3.1
3.23
3.36
3.51
3.61
3.67
3.74
3.82
3.89
3.98
4.08
4.14
4.33
4.57
4.63
4.57
4.71
4.54
4.3
4.36
4.61
4.71
4.68
4.91
4.75
4.77
5.18
3.42
2.71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48954&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]3 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=48954&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48954&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.019305555555560.12083536931891524.986935303577
Geometric Mean2.86201726804434
Harmonic Mean2.72552188751582
Quadratic Mean3.1863600358054
Winsorized Mean ( 1 / 24 )3.016944444444440.11977509552889125.1884119242195
Winsorized Mean ( 2 / 24 )3.013333333333330.11890508569998525.3423418821329
Winsorized Mean ( 3 / 24 )3.012916666666670.11868417168917825.3860023942974
Winsorized Mean ( 4 / 24 )3.011250.11816624080324825.4831665925115
Winsorized Mean ( 5 / 24 )3.012638888888890.11800854605792625.5289891243139
Winsorized Mean ( 6 / 24 )3.010972222222220.1174116322258325.6445819306123
Winsorized Mean ( 7 / 24 )3.006111111111110.11644757354622125.8151459885757
Winsorized Mean ( 8 / 24 )3.003888888888890.11601268001017725.8927635205511
Winsorized Mean ( 9 / 24 )2.998888888888890.11504431267700926.0672502543293
Winsorized Mean ( 10 / 24 )2.998888888888890.11504431267700926.0672502543293
Winsorized Mean ( 11 / 24 )2.994305555555560.11416650841099526.2275302733808
Winsorized Mean ( 12 / 24 )2.965972222222220.10839663367732027.3622170874001
Winsorized Mean ( 13 / 24 )2.960555555555560.10741974638171027.5606269357162
Winsorized Mean ( 14 / 24 )2.954722222222220.10637650753125427.7760784856947
Winsorized Mean ( 15 / 24 )2.923472222222220.10031799200367229.1420528245344
Winsorized Mean ( 16 / 24 )2.910138888888890.09805891785809529.677452621905
Winsorized Mean ( 17 / 24 )2.886527777777780.094142859120618530.6611441881054
Winsorized Mean ( 18 / 24 )2.866527777777780.090209103228284431.7764801466178
Winsorized Mean ( 19 / 24 )2.850694444444440.086970919174387932.7775591140808
Winsorized Mean ( 20 / 24 )2.828472222222220.083518025314973833.8666079754056
Winsorized Mean ( 21 / 24 )2.808055555555560.080406984843453634.9230301449884
Winsorized Mean ( 22 / 24 )2.792777777777780.077288816266037236.1343065232712
Winsorized Mean ( 23 / 24 )2.760833333333330.072586559950489538.035048571202
Winsorized Mean ( 24 / 24 )2.730833333333330.068271972335452339.9993326678108
Trimmed Mean ( 1 / 24 )3.004142857142860.11930448768103425.1804681913941
Trimmed Mean ( 2 / 24 )2.990588235294120.11864650100876025.2058696199841
Trimmed Mean ( 3 / 24 )2.978181818181820.11829754061740425.1753485544878
Trimmed Mean ( 4 / 24 )2.965156250.11785660008630725.1590173806863
Trimmed Mean ( 5 / 24 )2.951774193548390.11738390288023525.1463285946458
Trimmed Mean ( 6 / 24 )2.937166666666670.11672365637936825.1634223753279
Trimmed Mean ( 7 / 24 )2.921896551724140.11594673477634725.2003349413873
Trimmed Mean ( 8 / 24 )2.906428571428570.11510143143169525.2510202112763
Trimmed Mean ( 9 / 24 )2.890185185185190.11401677354647025.348771898086
Trimmed Mean ( 10 / 24 )2.873461538461540.11274843011263925.4856013125049
Trimmed Mean ( 11 / 24 )2.85540.11100403007944125.7233903846238
Trimmed Mean ( 12 / 24 )2.836458333333330.10885505424830726.0572038011496
Trimmed Mean ( 13 / 24 )2.819565217391300.10731863997084726.2728377675793
Trimmed Mean ( 14 / 24 )2.801818181818180.10538677015753026.5860522874938
Trimmed Mean ( 15 / 24 )2.783095238095240.10293965401527727.0361821663225
Trimmed Mean ( 16 / 24 )2.766250.10104624956564227.3760779038412
Trimmed Mean ( 17 / 24 )2.749210526315790.098881642239445827.8030427494162
Trimmed Mean ( 18 / 24 )2.733055555555560.096779752772660128.2399518210759
Trimmed Mean ( 19 / 24 )2.717352941176470.094720066806815528.6882498374774
Trimmed Mean ( 20 / 24 )2.70156250.092489220573962229.2094849890059
Trimmed Mean ( 21 / 24 )2.686333333333330.090097626913692529.8158056472082
Trimmed Mean ( 22 / 24 )2.671428571428570.087345804098280630.5845094564898
Trimmed Mean ( 23 / 24 )2.656153846153850.084011129158494331.6166902261578
Trimmed Mean ( 24 / 24 )2.64250.080501710306793132.8253895467487
Median2.55
Midrange3.55
Midmean - Weighted Average at Xnp2.68435897435897
Midmean - Weighted Average at X(n+1)p2.73305555555556
Midmean - Empirical Distribution Function2.68435897435897
Midmean - Empirical Distribution Function - Averaging2.73305555555556
Midmean - Empirical Distribution Function - Interpolation2.73305555555556
Midmean - Closest Observation2.68435897435897
Midmean - True Basic - Statistics Graphics Toolkit2.73305555555556
Midmean - MS Excel (old versions)2.71675
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.01930555555556 & 0.120835369318915 & 24.986935303577 \tabularnewline
Geometric Mean & 2.86201726804434 &  &  \tabularnewline
Harmonic Mean & 2.72552188751582 &  &  \tabularnewline
Quadratic Mean & 3.1863600358054 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.01694444444444 & 0.119775095528891 & 25.1884119242195 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.01333333333333 & 0.118905085699985 & 25.3423418821329 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.01291666666667 & 0.118684171689178 & 25.3860023942974 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.01125 & 0.118166240803248 & 25.4831665925115 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.01263888888889 & 0.118008546057926 & 25.5289891243139 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.01097222222222 & 0.11741163222583 & 25.6445819306123 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.00611111111111 & 0.116447573546221 & 25.8151459885757 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.00388888888889 & 0.116012680010177 & 25.8927635205511 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.99888888888889 & 0.115044312677009 & 26.0672502543293 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.99888888888889 & 0.115044312677009 & 26.0672502543293 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.99430555555556 & 0.114166508410995 & 26.2275302733808 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.96597222222222 & 0.108396633677320 & 27.3622170874001 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.96055555555556 & 0.107419746381710 & 27.5606269357162 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.95472222222222 & 0.106376507531254 & 27.7760784856947 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.92347222222222 & 0.100317992003672 & 29.1420528245344 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.91013888888889 & 0.098058917858095 & 29.677452621905 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.88652777777778 & 0.0941428591206185 & 30.6611441881054 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.86652777777778 & 0.0902091032282844 & 31.7764801466178 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.85069444444444 & 0.0869709191743879 & 32.7775591140808 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.82847222222222 & 0.0835180253149738 & 33.8666079754056 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.80805555555556 & 0.0804069848434536 & 34.9230301449884 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.79277777777778 & 0.0772888162660372 & 36.1343065232712 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.76083333333333 & 0.0725865599504895 & 38.035048571202 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.73083333333333 & 0.0682719723354523 & 39.9993326678108 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.00414285714286 & 0.119304487681034 & 25.1804681913941 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.99058823529412 & 0.118646501008760 & 25.2058696199841 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.97818181818182 & 0.118297540617404 & 25.1753485544878 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.96515625 & 0.117856600086307 & 25.1590173806863 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.95177419354839 & 0.117383902880235 & 25.1463285946458 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.93716666666667 & 0.116723656379368 & 25.1634223753279 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.92189655172414 & 0.115946734776347 & 25.2003349413873 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.90642857142857 & 0.115101431431695 & 25.2510202112763 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.89018518518519 & 0.114016773546470 & 25.348771898086 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.87346153846154 & 0.112748430112639 & 25.4856013125049 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.8554 & 0.111004030079441 & 25.7233903846238 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.83645833333333 & 0.108855054248307 & 26.0572038011496 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.81956521739130 & 0.107318639970847 & 26.2728377675793 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.80181818181818 & 0.105386770157530 & 26.5860522874938 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.78309523809524 & 0.102939654015277 & 27.0361821663225 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.76625 & 0.101046249565642 & 27.3760779038412 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.74921052631579 & 0.0988816422394458 & 27.8030427494162 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.73305555555556 & 0.0967797527726601 & 28.2399518210759 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.71735294117647 & 0.0947200668068155 & 28.6882498374774 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.7015625 & 0.0924892205739622 & 29.2094849890059 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.68633333333333 & 0.0900976269136925 & 29.8158056472082 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.67142857142857 & 0.0873458040982806 & 30.5845094564898 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.65615384615385 & 0.0840111291584943 & 31.6166902261578 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.6425 & 0.0805017103067931 & 32.8253895467487 \tabularnewline
Median & 2.55 &  &  \tabularnewline
Midrange & 3.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.68435897435897 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.73305555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.68435897435897 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.73305555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.73305555555556 &  &  \tabularnewline
Midmean - Closest Observation & 2.68435897435897 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.73305555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.71675 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48954&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]3.01930555555556[/C][C]0.120835369318915[/C][C]24.986935303577[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.86201726804434[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.72552188751582[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.1863600358054[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.01694444444444[/C][C]0.119775095528891[/C][C]25.1884119242195[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.01333333333333[/C][C]0.118905085699985[/C][C]25.3423418821329[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.01291666666667[/C][C]0.118684171689178[/C][C]25.3860023942974[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.01125[/C][C]0.118166240803248[/C][C]25.4831665925115[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.01263888888889[/C][C]0.118008546057926[/C][C]25.5289891243139[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.01097222222222[/C][C]0.11741163222583[/C][C]25.6445819306123[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.00611111111111[/C][C]0.116447573546221[/C][C]25.8151459885757[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.00388888888889[/C][C]0.116012680010177[/C][C]25.8927635205511[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.99888888888889[/C][C]0.115044312677009[/C][C]26.0672502543293[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.99888888888889[/C][C]0.115044312677009[/C][C]26.0672502543293[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.99430555555556[/C][C]0.114166508410995[/C][C]26.2275302733808[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.96597222222222[/C][C]0.108396633677320[/C][C]27.3622170874001[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.96055555555556[/C][C]0.107419746381710[/C][C]27.5606269357162[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.95472222222222[/C][C]0.106376507531254[/C][C]27.7760784856947[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.92347222222222[/C][C]0.100317992003672[/C][C]29.1420528245344[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.91013888888889[/C][C]0.098058917858095[/C][C]29.677452621905[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.88652777777778[/C][C]0.0941428591206185[/C][C]30.6611441881054[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.86652777777778[/C][C]0.0902091032282844[/C][C]31.7764801466178[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.85069444444444[/C][C]0.0869709191743879[/C][C]32.7775591140808[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.82847222222222[/C][C]0.0835180253149738[/C][C]33.8666079754056[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.80805555555556[/C][C]0.0804069848434536[/C][C]34.9230301449884[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.79277777777778[/C][C]0.0772888162660372[/C][C]36.1343065232712[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.76083333333333[/C][C]0.0725865599504895[/C][C]38.035048571202[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.73083333333333[/C][C]0.0682719723354523[/C][C]39.9993326678108[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.00414285714286[/C][C]0.119304487681034[/C][C]25.1804681913941[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.99058823529412[/C][C]0.118646501008760[/C][C]25.2058696199841[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.97818181818182[/C][C]0.118297540617404[/C][C]25.1753485544878[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.96515625[/C][C]0.117856600086307[/C][C]25.1590173806863[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.95177419354839[/C][C]0.117383902880235[/C][C]25.1463285946458[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.93716666666667[/C][C]0.116723656379368[/C][C]25.1634223753279[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.92189655172414[/C][C]0.115946734776347[/C][C]25.2003349413873[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.90642857142857[/C][C]0.115101431431695[/C][C]25.2510202112763[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.89018518518519[/C][C]0.114016773546470[/C][C]25.348771898086[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.87346153846154[/C][C]0.112748430112639[/C][C]25.4856013125049[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.8554[/C][C]0.111004030079441[/C][C]25.7233903846238[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.83645833333333[/C][C]0.108855054248307[/C][C]26.0572038011496[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.81956521739130[/C][C]0.107318639970847[/C][C]26.2728377675793[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.80181818181818[/C][C]0.105386770157530[/C][C]26.5860522874938[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.78309523809524[/C][C]0.102939654015277[/C][C]27.0361821663225[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.76625[/C][C]0.101046249565642[/C][C]27.3760779038412[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.74921052631579[/C][C]0.0988816422394458[/C][C]27.8030427494162[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.73305555555556[/C][C]0.0967797527726601[/C][C]28.2399518210759[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.71735294117647[/C][C]0.0947200668068155[/C][C]28.6882498374774[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.7015625[/C][C]0.0924892205739622[/C][C]29.2094849890059[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.68633333333333[/C][C]0.0900976269136925[/C][C]29.8158056472082[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.67142857142857[/C][C]0.0873458040982806[/C][C]30.5845094564898[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.65615384615385[/C][C]0.0840111291584943[/C][C]31.6166902261578[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.6425[/C][C]0.0805017103067931[/C][C]32.8253895467487[/C][/ROW]
[ROW][C]Median[/C][C]2.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.68435897435897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.73305555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.68435897435897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.73305555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.73305555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.68435897435897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.73305555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.71675[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48954&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48954&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 Mean3.019305555555560.12083536931891524.986935303577
Geometric Mean2.86201726804434
Harmonic Mean2.72552188751582
Quadratic Mean3.1863600358054
Winsorized Mean ( 1 / 24 )3.016944444444440.11977509552889125.1884119242195
Winsorized Mean ( 2 / 24 )3.013333333333330.11890508569998525.3423418821329
Winsorized Mean ( 3 / 24 )3.012916666666670.11868417168917825.3860023942974
Winsorized Mean ( 4 / 24 )3.011250.11816624080324825.4831665925115
Winsorized Mean ( 5 / 24 )3.012638888888890.11800854605792625.5289891243139
Winsorized Mean ( 6 / 24 )3.010972222222220.1174116322258325.6445819306123
Winsorized Mean ( 7 / 24 )3.006111111111110.11644757354622125.8151459885757
Winsorized Mean ( 8 / 24 )3.003888888888890.11601268001017725.8927635205511
Winsorized Mean ( 9 / 24 )2.998888888888890.11504431267700926.0672502543293
Winsorized Mean ( 10 / 24 )2.998888888888890.11504431267700926.0672502543293
Winsorized Mean ( 11 / 24 )2.994305555555560.11416650841099526.2275302733808
Winsorized Mean ( 12 / 24 )2.965972222222220.10839663367732027.3622170874001
Winsorized Mean ( 13 / 24 )2.960555555555560.10741974638171027.5606269357162
Winsorized Mean ( 14 / 24 )2.954722222222220.10637650753125427.7760784856947
Winsorized Mean ( 15 / 24 )2.923472222222220.10031799200367229.1420528245344
Winsorized Mean ( 16 / 24 )2.910138888888890.09805891785809529.677452621905
Winsorized Mean ( 17 / 24 )2.886527777777780.094142859120618530.6611441881054
Winsorized Mean ( 18 / 24 )2.866527777777780.090209103228284431.7764801466178
Winsorized Mean ( 19 / 24 )2.850694444444440.086970919174387932.7775591140808
Winsorized Mean ( 20 / 24 )2.828472222222220.083518025314973833.8666079754056
Winsorized Mean ( 21 / 24 )2.808055555555560.080406984843453634.9230301449884
Winsorized Mean ( 22 / 24 )2.792777777777780.077288816266037236.1343065232712
Winsorized Mean ( 23 / 24 )2.760833333333330.072586559950489538.035048571202
Winsorized Mean ( 24 / 24 )2.730833333333330.068271972335452339.9993326678108
Trimmed Mean ( 1 / 24 )3.004142857142860.11930448768103425.1804681913941
Trimmed Mean ( 2 / 24 )2.990588235294120.11864650100876025.2058696199841
Trimmed Mean ( 3 / 24 )2.978181818181820.11829754061740425.1753485544878
Trimmed Mean ( 4 / 24 )2.965156250.11785660008630725.1590173806863
Trimmed Mean ( 5 / 24 )2.951774193548390.11738390288023525.1463285946458
Trimmed Mean ( 6 / 24 )2.937166666666670.11672365637936825.1634223753279
Trimmed Mean ( 7 / 24 )2.921896551724140.11594673477634725.2003349413873
Trimmed Mean ( 8 / 24 )2.906428571428570.11510143143169525.2510202112763
Trimmed Mean ( 9 / 24 )2.890185185185190.11401677354647025.348771898086
Trimmed Mean ( 10 / 24 )2.873461538461540.11274843011263925.4856013125049
Trimmed Mean ( 11 / 24 )2.85540.11100403007944125.7233903846238
Trimmed Mean ( 12 / 24 )2.836458333333330.10885505424830726.0572038011496
Trimmed Mean ( 13 / 24 )2.819565217391300.10731863997084726.2728377675793
Trimmed Mean ( 14 / 24 )2.801818181818180.10538677015753026.5860522874938
Trimmed Mean ( 15 / 24 )2.783095238095240.10293965401527727.0361821663225
Trimmed Mean ( 16 / 24 )2.766250.10104624956564227.3760779038412
Trimmed Mean ( 17 / 24 )2.749210526315790.098881642239445827.8030427494162
Trimmed Mean ( 18 / 24 )2.733055555555560.096779752772660128.2399518210759
Trimmed Mean ( 19 / 24 )2.717352941176470.094720066806815528.6882498374774
Trimmed Mean ( 20 / 24 )2.70156250.092489220573962229.2094849890059
Trimmed Mean ( 21 / 24 )2.686333333333330.090097626913692529.8158056472082
Trimmed Mean ( 22 / 24 )2.671428571428570.087345804098280630.5845094564898
Trimmed Mean ( 23 / 24 )2.656153846153850.084011129158494331.6166902261578
Trimmed Mean ( 24 / 24 )2.64250.080501710306793132.8253895467487
Median2.55
Midrange3.55
Midmean - Weighted Average at Xnp2.68435897435897
Midmean - Weighted Average at X(n+1)p2.73305555555556
Midmean - Empirical Distribution Function2.68435897435897
Midmean - Empirical Distribution Function - Averaging2.73305555555556
Midmean - Empirical Distribution Function - Interpolation2.73305555555556
Midmean - Closest Observation2.68435897435897
Midmean - True Basic - Statistics Graphics Toolkit2.73305555555556
Midmean - MS Excel (old versions)2.71675
Number of observations72



Parameters (Session):
par1 = Rente op langerlopende herfinancieringstransacties ; par2 = http://www.nbb.be/belgostat/PublicatieSelectieLinker?LinkID=741000054|910000082&Lang=N ; par3 = Voornaamste monetaire beleidstarieven van het ESCB (procenten per jaar) ;
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')