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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 03:54:57 -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/18/t12558597512avkqdh9l6o27kc.htm/, Retrieved Thu, 31 Oct 2024 23:07:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47236, Retrieved Thu, 31 Oct 2024 23:07:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS3 gemiddelde 1] [2009-10-18 09:54:57] [9be6fbb216efe5bb8ca600257c6e1971] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.28
3.18
2.95
2.82
2.75
2.57
2.54
2.5
2.14
2.09
2.09
2.09
2.07
2.06
2.1
2.04
2.03
2.01
2.02
2.03
2.05
2.04
2.05
2.05
2.06
2.08
2.14
2.08
2.07
2.07
2.07
2.07
2.07
2.08
2.08
2.08
2.09
2.19
2.38
2.35
2.42
2.6
2.62
2.65
2.84
2.91
3.06
3.13
3.32
3.39
3.61
3.59
3.62
3.82
3.83
3.89
4.07
4.07
4.25
4.36

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47236&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47236&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47236&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.6260.090697610206527228.9533538317090
Geometric Mean2.54466178948409
Harmonic Mean2.47482732995193
Quadratic Mean2.71683884934925
Winsorized Mean ( 1 / 20 )2.624333333333330.09010112544261829.1265322207842
Winsorized Mean ( 2 / 20 )2.618666666666670.088309441391024129.6533034907503
Winsorized Mean ( 3 / 20 )2.618666666666670.088309441391024129.6533034907503
Winsorized Mean ( 4 / 20 )2.607333333333330.08502604010120630.6651154191097
Winsorized Mean ( 5 / 20 )2.602333333333330.083765669473224831.0668242694002
Winsorized Mean ( 6 / 20 )2.602333333333330.083404726480258331.2012693183437
Winsorized Mean ( 7 / 20 )2.5790.077865848710973633.121067100583
Winsorized Mean ( 8 / 20 )2.577666666666670.077564395213889333.2326018859371
Winsorized Mean ( 9 / 20 )2.576166666666670.076718021979335833.579680500112
Winsorized Mean ( 10 / 20 )2.542833333333330.06952871685169636.5724185412075
Winsorized Mean ( 11 / 20 )2.531833333333330.066702176277469837.9572822751889
Winsorized Mean ( 12 / 20 )2.523833333333330.065113586832604738.7604716020583
Winsorized Mean ( 13 / 20 )2.502166666666670.06093577783794741.0623570494324
Winsorized Mean ( 14 / 20 )2.49050.058759504580374742.3846323719995
Winsorized Mean ( 15 / 20 )2.4730.055577756392730744.4962186405109
Winsorized Mean ( 16 / 20 )2.443666666666670.050451054014996648.4363848164656
Winsorized Mean ( 17 / 20 )2.435166666666670.04818543023967250.537406318762
Winsorized Mean ( 18 / 20 )2.414166666666670.044735438035140153.9654192001053
Winsorized Mean ( 19 / 20 )2.407833333333330.043718469940472255.0758829531747
Winsorized Mean ( 20 / 20 )2.38450.040046882835730959.5427117206857
Trimmed Mean ( 1 / 20 )2.606724137931030.088190242833870629.5579653050903
Trimmed Mean ( 2 / 20 )2.587857142857140.085750966177478530.1787520096399
Trimmed Mean ( 3 / 20 )2.570740740740740.083854076044708830.6573140150050
Trimmed Mean ( 4 / 20 )2.552307692307690.081386743792860931.3602384536187
Trimmed Mean ( 5 / 20 )2.53580.079541589686125331.8801775273336
Trimmed Mean ( 6 / 20 )2.519166666666670.077547647977587332.4854039079916
Trimmed Mean ( 7 / 20 )2.501086956521740.074986136084711933.3539916458191
Trimmed Mean ( 8 / 20 )2.485909090909090.073330119062458933.9002462111335
Trimmed Mean ( 9 / 20 )2.469523809523810.071116002127025234.7252901690512
Trimmed Mean ( 10 / 20 )2.451750.06828098761171235.9067741366333
Trimmed Mean ( 11 / 20 )2.437368421052630.066574041616418136.6113932979479
Trimmed Mean ( 12 / 20 )2.423055555555560.064918531906016337.3245587109619
Trimmed Mean ( 13 / 20 )2.408235294117650.062932596413206638.2668987356808
Trimmed Mean ( 14 / 20 )2.39468750.061301384593043239.0641665909739
Trimmed Mean ( 15 / 20 )2.3810.059461858730434640.0424751401409
Trimmed Mean ( 16 / 20 )2.367857142857140.057660191266076441.0657178005277
Trimmed Mean ( 17 / 20 )2.356923076923080.05660597747933141.6373531891341
Trimmed Mean ( 18 / 20 )2.345416666666670.055446080240262842.3008561922384
Trimmed Mean ( 19 / 20 )2.3350.054644660864891142.7306156364166
Trimmed Mean ( 20 / 20 )2.32350.053228776348690843.6512007110445
Median2.27
Midrange3.185
Midmean - Weighted Average at Xnp2.34441176470588
Midmean - Weighted Average at X(n+1)p2.34441176470588
Midmean - Empirical Distribution Function2.34441176470588
Midmean - Empirical Distribution Function - Averaging2.34441176470588
Midmean - Empirical Distribution Function - Interpolation2.34441176470588
Midmean - Closest Observation2.34441176470588
Midmean - True Basic - Statistics Graphics Toolkit2.34441176470588
Midmean - MS Excel (old versions)2.36685714285714
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.626 & 0.0906976102065272 & 28.9533538317090 \tabularnewline
Geometric Mean & 2.54466178948409 &  &  \tabularnewline
Harmonic Mean & 2.47482732995193 &  &  \tabularnewline
Quadratic Mean & 2.71683884934925 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.62433333333333 & 0.090101125442618 & 29.1265322207842 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.61866666666667 & 0.0883094413910241 & 29.6533034907503 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.61866666666667 & 0.0883094413910241 & 29.6533034907503 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.60733333333333 & 0.085026040101206 & 30.6651154191097 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.60233333333333 & 0.0837656694732248 & 31.0668242694002 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.60233333333333 & 0.0834047264802583 & 31.2012693183437 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.579 & 0.0778658487109736 & 33.121067100583 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.57766666666667 & 0.0775643952138893 & 33.2326018859371 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.57616666666667 & 0.0767180219793358 & 33.579680500112 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.54283333333333 & 0.069528716851696 & 36.5724185412075 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.53183333333333 & 0.0667021762774698 & 37.9572822751889 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.52383333333333 & 0.0651135868326047 & 38.7604716020583 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.50216666666667 & 0.060935777837947 & 41.0623570494324 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.4905 & 0.0587595045803747 & 42.3846323719995 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.473 & 0.0555777563927307 & 44.4962186405109 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.44366666666667 & 0.0504510540149966 & 48.4363848164656 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.43516666666667 & 0.048185430239672 & 50.537406318762 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.41416666666667 & 0.0447354380351401 & 53.9654192001053 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.40783333333333 & 0.0437184699404722 & 55.0758829531747 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.3845 & 0.0400468828357309 & 59.5427117206857 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.60672413793103 & 0.0881902428338706 & 29.5579653050903 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.58785714285714 & 0.0857509661774785 & 30.1787520096399 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.57074074074074 & 0.0838540760447088 & 30.6573140150050 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.55230769230769 & 0.0813867437928609 & 31.3602384536187 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.5358 & 0.0795415896861253 & 31.8801775273336 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.51916666666667 & 0.0775476479775873 & 32.4854039079916 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.50108695652174 & 0.0749861360847119 & 33.3539916458191 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.48590909090909 & 0.0733301190624589 & 33.9002462111335 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.46952380952381 & 0.0711160021270252 & 34.7252901690512 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.45175 & 0.068280987611712 & 35.9067741366333 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.43736842105263 & 0.0665740416164181 & 36.6113932979479 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.42305555555556 & 0.0649185319060163 & 37.3245587109619 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.40823529411765 & 0.0629325964132066 & 38.2668987356808 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.3946875 & 0.0613013845930432 & 39.0641665909739 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.381 & 0.0594618587304346 & 40.0424751401409 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.36785714285714 & 0.0576601912660764 & 41.0657178005277 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.35692307692308 & 0.056605977479331 & 41.6373531891341 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.34541666666667 & 0.0554460802402628 & 42.3008561922384 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.335 & 0.0546446608648911 & 42.7306156364166 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.3235 & 0.0532287763486908 & 43.6512007110445 \tabularnewline
Median & 2.27 &  &  \tabularnewline
Midrange & 3.185 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.34441176470588 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.34441176470588 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.34441176470588 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.34441176470588 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.34441176470588 &  &  \tabularnewline
Midmean - Closest Observation & 2.34441176470588 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.34441176470588 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.36685714285714 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47236&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]2.626[/C][C]0.0906976102065272[/C][C]28.9533538317090[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.54466178948409[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.47482732995193[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.71683884934925[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.62433333333333[/C][C]0.090101125442618[/C][C]29.1265322207842[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.61866666666667[/C][C]0.0883094413910241[/C][C]29.6533034907503[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.61866666666667[/C][C]0.0883094413910241[/C][C]29.6533034907503[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.60733333333333[/C][C]0.085026040101206[/C][C]30.6651154191097[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.60233333333333[/C][C]0.0837656694732248[/C][C]31.0668242694002[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.60233333333333[/C][C]0.0834047264802583[/C][C]31.2012693183437[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.579[/C][C]0.0778658487109736[/C][C]33.121067100583[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.57766666666667[/C][C]0.0775643952138893[/C][C]33.2326018859371[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.57616666666667[/C][C]0.0767180219793358[/C][C]33.579680500112[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.54283333333333[/C][C]0.069528716851696[/C][C]36.5724185412075[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.53183333333333[/C][C]0.0667021762774698[/C][C]37.9572822751889[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.52383333333333[/C][C]0.0651135868326047[/C][C]38.7604716020583[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.50216666666667[/C][C]0.060935777837947[/C][C]41.0623570494324[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.4905[/C][C]0.0587595045803747[/C][C]42.3846323719995[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.473[/C][C]0.0555777563927307[/C][C]44.4962186405109[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.44366666666667[/C][C]0.0504510540149966[/C][C]48.4363848164656[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.43516666666667[/C][C]0.048185430239672[/C][C]50.537406318762[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.41416666666667[/C][C]0.0447354380351401[/C][C]53.9654192001053[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.40783333333333[/C][C]0.0437184699404722[/C][C]55.0758829531747[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.3845[/C][C]0.0400468828357309[/C][C]59.5427117206857[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.60672413793103[/C][C]0.0881902428338706[/C][C]29.5579653050903[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.58785714285714[/C][C]0.0857509661774785[/C][C]30.1787520096399[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.57074074074074[/C][C]0.0838540760447088[/C][C]30.6573140150050[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.55230769230769[/C][C]0.0813867437928609[/C][C]31.3602384536187[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.5358[/C][C]0.0795415896861253[/C][C]31.8801775273336[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.51916666666667[/C][C]0.0775476479775873[/C][C]32.4854039079916[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.50108695652174[/C][C]0.0749861360847119[/C][C]33.3539916458191[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.48590909090909[/C][C]0.0733301190624589[/C][C]33.9002462111335[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.46952380952381[/C][C]0.0711160021270252[/C][C]34.7252901690512[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.45175[/C][C]0.068280987611712[/C][C]35.9067741366333[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.43736842105263[/C][C]0.0665740416164181[/C][C]36.6113932979479[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.42305555555556[/C][C]0.0649185319060163[/C][C]37.3245587109619[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.40823529411765[/C][C]0.0629325964132066[/C][C]38.2668987356808[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.3946875[/C][C]0.0613013845930432[/C][C]39.0641665909739[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.381[/C][C]0.0594618587304346[/C][C]40.0424751401409[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.36785714285714[/C][C]0.0576601912660764[/C][C]41.0657178005277[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.35692307692308[/C][C]0.056605977479331[/C][C]41.6373531891341[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.34541666666667[/C][C]0.0554460802402628[/C][C]42.3008561922384[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.335[/C][C]0.0546446608648911[/C][C]42.7306156364166[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.3235[/C][C]0.0532287763486908[/C][C]43.6512007110445[/C][/ROW]
[ROW][C]Median[/C][C]2.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.34441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.34441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.34441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.34441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.34441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.34441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.34441176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.36685714285714[/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=47236&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47236&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.6260.090697610206527228.9533538317090
Geometric Mean2.54466178948409
Harmonic Mean2.47482732995193
Quadratic Mean2.71683884934925
Winsorized Mean ( 1 / 20 )2.624333333333330.09010112544261829.1265322207842
Winsorized Mean ( 2 / 20 )2.618666666666670.088309441391024129.6533034907503
Winsorized Mean ( 3 / 20 )2.618666666666670.088309441391024129.6533034907503
Winsorized Mean ( 4 / 20 )2.607333333333330.08502604010120630.6651154191097
Winsorized Mean ( 5 / 20 )2.602333333333330.083765669473224831.0668242694002
Winsorized Mean ( 6 / 20 )2.602333333333330.083404726480258331.2012693183437
Winsorized Mean ( 7 / 20 )2.5790.077865848710973633.121067100583
Winsorized Mean ( 8 / 20 )2.577666666666670.077564395213889333.2326018859371
Winsorized Mean ( 9 / 20 )2.576166666666670.076718021979335833.579680500112
Winsorized Mean ( 10 / 20 )2.542833333333330.06952871685169636.5724185412075
Winsorized Mean ( 11 / 20 )2.531833333333330.066702176277469837.9572822751889
Winsorized Mean ( 12 / 20 )2.523833333333330.065113586832604738.7604716020583
Winsorized Mean ( 13 / 20 )2.502166666666670.06093577783794741.0623570494324
Winsorized Mean ( 14 / 20 )2.49050.058759504580374742.3846323719995
Winsorized Mean ( 15 / 20 )2.4730.055577756392730744.4962186405109
Winsorized Mean ( 16 / 20 )2.443666666666670.050451054014996648.4363848164656
Winsorized Mean ( 17 / 20 )2.435166666666670.04818543023967250.537406318762
Winsorized Mean ( 18 / 20 )2.414166666666670.044735438035140153.9654192001053
Winsorized Mean ( 19 / 20 )2.407833333333330.043718469940472255.0758829531747
Winsorized Mean ( 20 / 20 )2.38450.040046882835730959.5427117206857
Trimmed Mean ( 1 / 20 )2.606724137931030.088190242833870629.5579653050903
Trimmed Mean ( 2 / 20 )2.587857142857140.085750966177478530.1787520096399
Trimmed Mean ( 3 / 20 )2.570740740740740.083854076044708830.6573140150050
Trimmed Mean ( 4 / 20 )2.552307692307690.081386743792860931.3602384536187
Trimmed Mean ( 5 / 20 )2.53580.079541589686125331.8801775273336
Trimmed Mean ( 6 / 20 )2.519166666666670.077547647977587332.4854039079916
Trimmed Mean ( 7 / 20 )2.501086956521740.074986136084711933.3539916458191
Trimmed Mean ( 8 / 20 )2.485909090909090.073330119062458933.9002462111335
Trimmed Mean ( 9 / 20 )2.469523809523810.071116002127025234.7252901690512
Trimmed Mean ( 10 / 20 )2.451750.06828098761171235.9067741366333
Trimmed Mean ( 11 / 20 )2.437368421052630.066574041616418136.6113932979479
Trimmed Mean ( 12 / 20 )2.423055555555560.064918531906016337.3245587109619
Trimmed Mean ( 13 / 20 )2.408235294117650.062932596413206638.2668987356808
Trimmed Mean ( 14 / 20 )2.39468750.061301384593043239.0641665909739
Trimmed Mean ( 15 / 20 )2.3810.059461858730434640.0424751401409
Trimmed Mean ( 16 / 20 )2.367857142857140.057660191266076441.0657178005277
Trimmed Mean ( 17 / 20 )2.356923076923080.05660597747933141.6373531891341
Trimmed Mean ( 18 / 20 )2.345416666666670.055446080240262842.3008561922384
Trimmed Mean ( 19 / 20 )2.3350.054644660864891142.7306156364166
Trimmed Mean ( 20 / 20 )2.32350.053228776348690843.6512007110445
Median2.27
Midrange3.185
Midmean - Weighted Average at Xnp2.34441176470588
Midmean - Weighted Average at X(n+1)p2.34441176470588
Midmean - Empirical Distribution Function2.34441176470588
Midmean - Empirical Distribution Function - Averaging2.34441176470588
Midmean - Empirical Distribution Function - Interpolation2.34441176470588
Midmean - Closest Observation2.34441176470588
Midmean - True Basic - Statistics Graphics Toolkit2.34441176470588
Midmean - MS Excel (old versions)2.36685714285714
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')