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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 17:45:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t136252390391lqfxah4nwjm9y.htm/, Retrieved Sat, 04 May 2024 06:45:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207509, Retrieved Sat, 04 May 2024 06:45:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency] [2013-03-05 22:45:09] [a0dc50058fa7049d3ca1c49ed2014afb] [Current]
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Dataseries X:
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,77
109,86
110,12
110,5
113,73
119,84
119,83
113,06
112,45
110,07
110,09
110,72
109,9
109,9
110,06
110,52
116,16
118,54
118,77
113,71
106,98
106,98
106,98
106,98
106,98
106,98
107,43
107,93
111,99
115,4
115,53
115,22
102,75
102,75
102,75
102,75
102,75
102,75
102,87
103,13
108,52
111,6
111,32
108,77
100,05
100,05
100,05
100,05
100,05
100,05
100,07
100,07
109,26
110
110
109,26
99,42
99,42
99,42
99,42
99,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207509&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207509&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207509&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.0447222222220.637990351850306169.351655411198
Geometric Mean107.910606075554
Harmonic Mean107.776131766917
Quadratic Mean108.178376998363
Winsorized Mean ( 1 / 24 )108.0445833333330.637954199715822169.361034665909
Winsorized Mean ( 2 / 24 )108.0151388888890.630585340301215171.293450680748
Winsorized Mean ( 3 / 24 )108.0055555555560.628302725524692171.90050459412
Winsorized Mean ( 4 / 24 )107.8733333333330.599761657146747179.86033626511
Winsorized Mean ( 5 / 24 )107.8733333333330.582975275757021185.039293807537
Winsorized Mean ( 6 / 24 )107.86250.580983488044438185.655018119465
Winsorized Mean ( 7 / 24 )107.8450.577811558540584186.643895238771
Winsorized Mean ( 8 / 24 )107.6794444444440.550055370981766195.761099927545
Winsorized Mean ( 9 / 24 )107.6769444444440.549668474520244195.894342564263
Winsorized Mean ( 10 / 24 )107.5866666666670.536194788607838200.648475055123
Winsorized Mean ( 11 / 24 )107.4965277777780.52266116486675205.671542107368
Winsorized Mean ( 12 / 24 )107.4198611111110.512728955425221209.506133746679
Winsorized Mean ( 13 / 24 )107.8333333333330.412172618699537261.621777966627
Winsorized Mean ( 14 / 24 )107.7788888888890.40531776959419265.912074362786
Winsorized Mean ( 15 / 24 )107.6538888888890.390704569795365275.537828864591
Winsorized Mean ( 16 / 24 )107.6094444444440.385887028118115278.862559773599
Winsorized Mean ( 17 / 24 )107.6047222222220.385386366514686279.2125813774
Winsorized Mean ( 18 / 24 )107.5097222222220.37570741684985286.152781128588
Winsorized Mean ( 19 / 24 )107.5334722222220.369292727961125291.187624559837
Winsorized Mean ( 20 / 24 )107.6001388888890.35593956936059302.298896079977
Winsorized Mean ( 21 / 24 )108.7201388888890.168274811220739646.086827257065
Winsorized Mean ( 22 / 24 )108.7018055555560.16623845534991653.89085411527
Winsorized Mean ( 23 / 24 )108.7018055555560.16623845534991653.89085411527
Winsorized Mean ( 24 / 24 )108.6684722222220.162627061161407668.206579188987
Trimmed Mean ( 1 / 24 )107.9994285714290.621740024281494173.705124897238
Trimmed Mean ( 2 / 24 )107.9516176470590.602410201917061179.199517709897
Trimmed Mean ( 3 / 24 )107.916969696970.584065486704843184.768612687271
Trimmed Mean ( 4 / 24 )107.883750.563070808263976191.598904465711
Trimmed Mean ( 5 / 24 )107.8867741935480.548592872084222196.660911367046
Trimmed Mean ( 6 / 24 )107.890.536354613279723201.154231414679
Trimmed Mean ( 7 / 24 )107.8956896551720.521905631051697206.734097575745
Trimmed Mean ( 8 / 24 )107.9050.504943484043434213.697182773663
Trimmed Mean ( 9 / 24 )107.9425925925930.490864565156936219.903004320717
Trimmed Mean ( 10 / 24 )107.9834615384620.473247492212079228.17545431402
Trimmed Mean ( 11 / 24 )108.04060.454041300827516237.953243026769
Trimmed Mean ( 12 / 24 )108.1147916666670.432417846662227250.023888933331
Trimmed Mean ( 13 / 24 )108.2054347826090.40630581596755266.315249573613
Trimmed Mean ( 14 / 24 )108.2522727272730.398426724137595271.699326799897
Trimmed Mean ( 15 / 24 )108.3102380952380.388956358167933278.463729466726
Trimmed Mean ( 16 / 24 )108.3890.378547290681166286.328822496557
Trimmed Mean ( 17 / 24 )108.4813157894740.364578162100532297.552972357022
Trimmed Mean ( 18 / 24 )108.5844444444440.344544429932528315.153678338984
Trimmed Mean ( 19 / 24 )108.7108823529410.316838034402499343.111844377999
Trimmed Mean ( 20 / 24 )108.85031250.276778517331548393.27587108074
Trimmed Mean ( 21 / 24 )109.0003333333330.217373815071933501.441874667669
Trimmed Mean ( 22 / 24 )109.0346428571430.217826858420703500.556467864754
Trimmed Mean ( 23 / 24 )109.0765384615380.217227241745166502.131029171279
Trimmed Mean ( 24 / 24 )109.1254166666670.21436794452552509.056598495656
Median109.77
Midrange109.63
Midmean - Weighted Average at Xnp107.872926829268
Midmean - Weighted Average at X(n+1)p107.872926829268
Midmean - Empirical Distribution Function107.872926829268
Midmean - Empirical Distribution Function - Averaging107.872926829268
Midmean - Empirical Distribution Function - Interpolation107.872926829268
Midmean - Closest Observation107.872926829268
Midmean - True Basic - Statistics Graphics Toolkit107.872926829268
Midmean - MS Excel (old versions)107.935476190476
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.044722222222 & 0.637990351850306 & 169.351655411198 \tabularnewline
Geometric Mean & 107.910606075554 &  &  \tabularnewline
Harmonic Mean & 107.776131766917 &  &  \tabularnewline
Quadratic Mean & 108.178376998363 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 108.044583333333 & 0.637954199715822 & 169.361034665909 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 108.015138888889 & 0.630585340301215 & 171.293450680748 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 108.005555555556 & 0.628302725524692 & 171.90050459412 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 107.873333333333 & 0.599761657146747 & 179.86033626511 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 107.873333333333 & 0.582975275757021 & 185.039293807537 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 107.8625 & 0.580983488044438 & 185.655018119465 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 107.845 & 0.577811558540584 & 186.643895238771 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 107.679444444444 & 0.550055370981766 & 195.761099927545 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 107.676944444444 & 0.549668474520244 & 195.894342564263 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 107.586666666667 & 0.536194788607838 & 200.648475055123 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 107.496527777778 & 0.52266116486675 & 205.671542107368 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 107.419861111111 & 0.512728955425221 & 209.506133746679 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 107.833333333333 & 0.412172618699537 & 261.621777966627 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 107.778888888889 & 0.40531776959419 & 265.912074362786 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 107.653888888889 & 0.390704569795365 & 275.537828864591 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 107.609444444444 & 0.385887028118115 & 278.862559773599 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 107.604722222222 & 0.385386366514686 & 279.2125813774 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 107.509722222222 & 0.37570741684985 & 286.152781128588 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 107.533472222222 & 0.369292727961125 & 291.187624559837 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 107.600138888889 & 0.35593956936059 & 302.298896079977 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.720138888889 & 0.168274811220739 & 646.086827257065 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.701805555556 & 0.16623845534991 & 653.89085411527 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.701805555556 & 0.16623845534991 & 653.89085411527 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.668472222222 & 0.162627061161407 & 668.206579188987 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 107.999428571429 & 0.621740024281494 & 173.705124897238 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 107.951617647059 & 0.602410201917061 & 179.199517709897 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 107.91696969697 & 0.584065486704843 & 184.768612687271 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 107.88375 & 0.563070808263976 & 191.598904465711 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 107.886774193548 & 0.548592872084222 & 196.660911367046 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 107.89 & 0.536354613279723 & 201.154231414679 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 107.895689655172 & 0.521905631051697 & 206.734097575745 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 107.905 & 0.504943484043434 & 213.697182773663 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 107.942592592593 & 0.490864565156936 & 219.903004320717 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 107.983461538462 & 0.473247492212079 & 228.17545431402 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.0406 & 0.454041300827516 & 237.953243026769 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.114791666667 & 0.432417846662227 & 250.023888933331 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.205434782609 & 0.40630581596755 & 266.315249573613 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.252272727273 & 0.398426724137595 & 271.699326799897 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.310238095238 & 0.388956358167933 & 278.463729466726 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.389 & 0.378547290681166 & 286.328822496557 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.481315789474 & 0.364578162100532 & 297.552972357022 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.584444444444 & 0.344544429932528 & 315.153678338984 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 108.710882352941 & 0.316838034402499 & 343.111844377999 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 108.8503125 & 0.276778517331548 & 393.27587108074 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 109.000333333333 & 0.217373815071933 & 501.441874667669 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 109.034642857143 & 0.217826858420703 & 500.556467864754 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 109.076538461538 & 0.217227241745166 & 502.131029171279 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 109.125416666667 & 0.21436794452552 & 509.056598495656 \tabularnewline
Median & 109.77 &  &  \tabularnewline
Midrange & 109.63 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.872926829268 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.872926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 107.872926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.872926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.872926829268 &  &  \tabularnewline
Midmean - Closest Observation & 107.872926829268 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.872926829268 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.935476190476 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207509&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]108.044722222222[/C][C]0.637990351850306[/C][C]169.351655411198[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107.910606075554[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.776131766917[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.178376998363[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]108.044583333333[/C][C]0.637954199715822[/C][C]169.361034665909[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]108.015138888889[/C][C]0.630585340301215[/C][C]171.293450680748[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]108.005555555556[/C][C]0.628302725524692[/C][C]171.90050459412[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]107.873333333333[/C][C]0.599761657146747[/C][C]179.86033626511[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]107.873333333333[/C][C]0.582975275757021[/C][C]185.039293807537[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]107.8625[/C][C]0.580983488044438[/C][C]185.655018119465[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]107.845[/C][C]0.577811558540584[/C][C]186.643895238771[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]107.679444444444[/C][C]0.550055370981766[/C][C]195.761099927545[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]107.676944444444[/C][C]0.549668474520244[/C][C]195.894342564263[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]107.586666666667[/C][C]0.536194788607838[/C][C]200.648475055123[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]107.496527777778[/C][C]0.52266116486675[/C][C]205.671542107368[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]107.419861111111[/C][C]0.512728955425221[/C][C]209.506133746679[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]107.833333333333[/C][C]0.412172618699537[/C][C]261.621777966627[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]107.778888888889[/C][C]0.40531776959419[/C][C]265.912074362786[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]107.653888888889[/C][C]0.390704569795365[/C][C]275.537828864591[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]107.609444444444[/C][C]0.385887028118115[/C][C]278.862559773599[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]107.604722222222[/C][C]0.385386366514686[/C][C]279.2125813774[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]107.509722222222[/C][C]0.37570741684985[/C][C]286.152781128588[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]107.533472222222[/C][C]0.369292727961125[/C][C]291.187624559837[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]107.600138888889[/C][C]0.35593956936059[/C][C]302.298896079977[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.720138888889[/C][C]0.168274811220739[/C][C]646.086827257065[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.701805555556[/C][C]0.16623845534991[/C][C]653.89085411527[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.701805555556[/C][C]0.16623845534991[/C][C]653.89085411527[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.668472222222[/C][C]0.162627061161407[/C][C]668.206579188987[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]107.999428571429[/C][C]0.621740024281494[/C][C]173.705124897238[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]107.951617647059[/C][C]0.602410201917061[/C][C]179.199517709897[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]107.91696969697[/C][C]0.584065486704843[/C][C]184.768612687271[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]107.88375[/C][C]0.563070808263976[/C][C]191.598904465711[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]107.886774193548[/C][C]0.548592872084222[/C][C]196.660911367046[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]107.89[/C][C]0.536354613279723[/C][C]201.154231414679[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]107.895689655172[/C][C]0.521905631051697[/C][C]206.734097575745[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]107.905[/C][C]0.504943484043434[/C][C]213.697182773663[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]107.942592592593[/C][C]0.490864565156936[/C][C]219.903004320717[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]107.983461538462[/C][C]0.473247492212079[/C][C]228.17545431402[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.0406[/C][C]0.454041300827516[/C][C]237.953243026769[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.114791666667[/C][C]0.432417846662227[/C][C]250.023888933331[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.205434782609[/C][C]0.40630581596755[/C][C]266.315249573613[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.252272727273[/C][C]0.398426724137595[/C][C]271.699326799897[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.310238095238[/C][C]0.388956358167933[/C][C]278.463729466726[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.389[/C][C]0.378547290681166[/C][C]286.328822496557[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.481315789474[/C][C]0.364578162100532[/C][C]297.552972357022[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.584444444444[/C][C]0.344544429932528[/C][C]315.153678338984[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]108.710882352941[/C][C]0.316838034402499[/C][C]343.111844377999[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]108.8503125[/C][C]0.276778517331548[/C][C]393.27587108074[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]109.000333333333[/C][C]0.217373815071933[/C][C]501.441874667669[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]109.034642857143[/C][C]0.217826858420703[/C][C]500.556467864754[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]109.076538461538[/C][C]0.217227241745166[/C][C]502.131029171279[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]109.125416666667[/C][C]0.21436794452552[/C][C]509.056598495656[/C][/ROW]
[ROW][C]Median[/C][C]109.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.872926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.872926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]107.872926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.872926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.872926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.872926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.872926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.935476190476[/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=207509&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207509&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 Mean108.0447222222220.637990351850306169.351655411198
Geometric Mean107.910606075554
Harmonic Mean107.776131766917
Quadratic Mean108.178376998363
Winsorized Mean ( 1 / 24 )108.0445833333330.637954199715822169.361034665909
Winsorized Mean ( 2 / 24 )108.0151388888890.630585340301215171.293450680748
Winsorized Mean ( 3 / 24 )108.0055555555560.628302725524692171.90050459412
Winsorized Mean ( 4 / 24 )107.8733333333330.599761657146747179.86033626511
Winsorized Mean ( 5 / 24 )107.8733333333330.582975275757021185.039293807537
Winsorized Mean ( 6 / 24 )107.86250.580983488044438185.655018119465
Winsorized Mean ( 7 / 24 )107.8450.577811558540584186.643895238771
Winsorized Mean ( 8 / 24 )107.6794444444440.550055370981766195.761099927545
Winsorized Mean ( 9 / 24 )107.6769444444440.549668474520244195.894342564263
Winsorized Mean ( 10 / 24 )107.5866666666670.536194788607838200.648475055123
Winsorized Mean ( 11 / 24 )107.4965277777780.52266116486675205.671542107368
Winsorized Mean ( 12 / 24 )107.4198611111110.512728955425221209.506133746679
Winsorized Mean ( 13 / 24 )107.8333333333330.412172618699537261.621777966627
Winsorized Mean ( 14 / 24 )107.7788888888890.40531776959419265.912074362786
Winsorized Mean ( 15 / 24 )107.6538888888890.390704569795365275.537828864591
Winsorized Mean ( 16 / 24 )107.6094444444440.385887028118115278.862559773599
Winsorized Mean ( 17 / 24 )107.6047222222220.385386366514686279.2125813774
Winsorized Mean ( 18 / 24 )107.5097222222220.37570741684985286.152781128588
Winsorized Mean ( 19 / 24 )107.5334722222220.369292727961125291.187624559837
Winsorized Mean ( 20 / 24 )107.6001388888890.35593956936059302.298896079977
Winsorized Mean ( 21 / 24 )108.7201388888890.168274811220739646.086827257065
Winsorized Mean ( 22 / 24 )108.7018055555560.16623845534991653.89085411527
Winsorized Mean ( 23 / 24 )108.7018055555560.16623845534991653.89085411527
Winsorized Mean ( 24 / 24 )108.6684722222220.162627061161407668.206579188987
Trimmed Mean ( 1 / 24 )107.9994285714290.621740024281494173.705124897238
Trimmed Mean ( 2 / 24 )107.9516176470590.602410201917061179.199517709897
Trimmed Mean ( 3 / 24 )107.916969696970.584065486704843184.768612687271
Trimmed Mean ( 4 / 24 )107.883750.563070808263976191.598904465711
Trimmed Mean ( 5 / 24 )107.8867741935480.548592872084222196.660911367046
Trimmed Mean ( 6 / 24 )107.890.536354613279723201.154231414679
Trimmed Mean ( 7 / 24 )107.8956896551720.521905631051697206.734097575745
Trimmed Mean ( 8 / 24 )107.9050.504943484043434213.697182773663
Trimmed Mean ( 9 / 24 )107.9425925925930.490864565156936219.903004320717
Trimmed Mean ( 10 / 24 )107.9834615384620.473247492212079228.17545431402
Trimmed Mean ( 11 / 24 )108.04060.454041300827516237.953243026769
Trimmed Mean ( 12 / 24 )108.1147916666670.432417846662227250.023888933331
Trimmed Mean ( 13 / 24 )108.2054347826090.40630581596755266.315249573613
Trimmed Mean ( 14 / 24 )108.2522727272730.398426724137595271.699326799897
Trimmed Mean ( 15 / 24 )108.3102380952380.388956358167933278.463729466726
Trimmed Mean ( 16 / 24 )108.3890.378547290681166286.328822496557
Trimmed Mean ( 17 / 24 )108.4813157894740.364578162100532297.552972357022
Trimmed Mean ( 18 / 24 )108.5844444444440.344544429932528315.153678338984
Trimmed Mean ( 19 / 24 )108.7108823529410.316838034402499343.111844377999
Trimmed Mean ( 20 / 24 )108.85031250.276778517331548393.27587108074
Trimmed Mean ( 21 / 24 )109.0003333333330.217373815071933501.441874667669
Trimmed Mean ( 22 / 24 )109.0346428571430.217826858420703500.556467864754
Trimmed Mean ( 23 / 24 )109.0765384615380.217227241745166502.131029171279
Trimmed Mean ( 24 / 24 )109.1254166666670.21436794452552509.056598495656
Median109.77
Midrange109.63
Midmean - Weighted Average at Xnp107.872926829268
Midmean - Weighted Average at X(n+1)p107.872926829268
Midmean - Empirical Distribution Function107.872926829268
Midmean - Empirical Distribution Function - Averaging107.872926829268
Midmean - Empirical Distribution Function - Interpolation107.872926829268
Midmean - Closest Observation107.872926829268
Midmean - True Basic - Statistics Graphics Toolkit107.872926829268
Midmean - MS Excel (old versions)107.935476190476
Number of observations72



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')