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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 computationFri, 05 Dec 2008 08:09:22 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t12284899116syty83ge0j6yp4.htm/, Retrieved Thu, 16 May 2024 21:30:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29305, Retrieved Thu, 16 May 2024 21:30:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspaper141
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper ct consumpt...] [2008-12-05 15:09:22] [d8c5724db236abb5950452133b88474d] [Current]
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Dataseries X:
103.5
103.6
103.6
103.2
103.4
101.9
103.8
102
101
103.7
101.1
99.3
115.4
111.9
109
112.8
104.6
106.1
110.7
109.9
112.3
112.5
111.3
113.8
110.2
112
115.2
113.1
110.8
117.3
117.7
115.5
115.2
112.8
115.8
119.3
119.4
113.2
115.4
115.1
115.3
113.3
110.8
113.8
114.8
111.1
112.9
112
118.5
120.1
119.6
118
120.4
118.2
117.5
118.6
119.2
119.9
118.9
118.3
120.3
120.4
119.4
119.1
119.3
119.4
131.4
118.6
116.4
118.8
118.2
116.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29305&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29305&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29305&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.4361111111110.744172208065094152.432608852800
Geometric Mean113.259512056464
Harmonic Mean113.079519077321
Quadratic Mean113.609289037277
Winsorized Mean ( 1 / 24 )113.3069444444440.700771781080265161.688794417175
Winsorized Mean ( 2 / 24 )113.3097222222220.700087071832076161.8508993827
Winsorized Mean ( 3 / 24 )113.3388888888890.691516205014711163.899107594272
Winsorized Mean ( 4 / 24 )113.3333333333330.68866862549658164.568747779982
Winsorized Mean ( 5 / 24 )113.4027777777780.668126254966234169.732557184883
Winsorized Mean ( 6 / 24 )113.3944444444440.661194942147529171.499261739881
Winsorized Mean ( 7 / 24 )113.3847222222220.65658950632865172.687380972958
Winsorized Mean ( 8 / 24 )113.3958333333330.654239925923913173.324538659417
Winsorized Mean ( 9 / 24 )113.3958333333330.654239925923913173.324538659417
Winsorized Mean ( 10 / 24 )113.3958333333330.649528652683834174.58172609443
Winsorized Mean ( 11 / 24 )113.4111111111110.646322677117249175.471347558082
Winsorized Mean ( 12 / 24 )113.5277777777780.616607097180623184.116884636704
Winsorized Mean ( 13 / 24 )113.7805555555560.560406734169931203.032099041576
Winsorized Mean ( 14 / 24 )114.3055555555560.453308515998105252.158412033965
Winsorized Mean ( 15 / 24 )114.4722222222220.420457972897054272.256038893689
Winsorized Mean ( 16 / 24 )114.4944444444440.403955834797198283.433075058627
Winsorized Mean ( 17 / 24 )114.61250.386696501499949296.388768854727
Winsorized Mean ( 18 / 24 )114.61250.379527636050159301.987231266744
Winsorized Mean ( 19 / 24 )114.5597222222220.371982695395627307.970568631911
Winsorized Mean ( 20 / 24 )114.6152777777780.356323711437561321.660540959711
Winsorized Mean ( 21 / 24 )114.6736111111110.348291116876799329.246442284874
Winsorized Mean ( 22 / 24 )114.7958333333330.315158488459696364.247949958086
Winsorized Mean ( 23 / 24 )114.7319444444440.297425220996564385.750556257534
Winsorized Mean ( 24 / 24 )114.6652777777780.288120017446096397.97747756013
Trimmed Mean ( 1 / 24 )113.3814285714290.691301448711226164.011559331754
Trimmed Mean ( 2 / 24 )113.4602941176470.679768913459746166.910095285441
Trimmed Mean ( 3 / 24 )113.5424242424240.666179521105692170.438178666874
Trimmed Mean ( 4 / 24 )113.618750.653572580556709173.84258975984
Trimmed Mean ( 5 / 24 )113.7016129032260.639124086351837177.902249862374
Trimmed Mean ( 6 / 24 )113.7733333333330.627941065043216181.184731604555
Trimmed Mean ( 7 / 24 )113.8517241379310.615868213384301184.863777125785
Trimmed Mean ( 8 / 24 )113.93750.601834654451454189.316948030932
Trimmed Mean ( 9 / 24 )114.0277777777780.584701400656085195.018820973969
Trimmed Mean ( 10 / 24 )114.1250.562918187101405202.738164470499
Trimmed Mean ( 11 / 24 )114.230.536178846190374213.044585424472
Trimmed Mean ( 12 / 24 )114.3416666666670.502324678611669227.625023287101
Trimmed Mean ( 13 / 24 )114.4478260869570.466374019321318245.399231830076
Trimmed Mean ( 14 / 24 )114.5318181818180.435353283277858263.077878543803
Trimmed Mean ( 15 / 24 )114.5595238095240.423525103899516270.490515803530
Trimmed Mean ( 16 / 24 )114.570.415396011239692275.809099991311
Trimmed Mean ( 17 / 24 )114.5789473684210.407821082690695280.953958075094
Trimmed Mean ( 18 / 24 )114.5750.401018049706589285.710331701604
Trimmed Mean ( 19 / 24 )114.5705882352940.392635625755689291.798758746828
Trimmed Mean ( 20 / 24 )114.5718750.382116199366827299.835168437893
Trimmed Mean ( 21 / 24 )114.5666666666670.370812507487021308.961171356057
Trimmed Mean ( 22 / 24 )114.5535714285710.355883361148358321.885156583135
Trimmed Mean ( 23 / 24 )114.5230769230770.343748910702954333.159097693957
Trimmed Mean ( 24 / 24 )114.4958333333330.330594499999549346.333146297018
Median114.95
Midrange115.35
Midmean - Weighted Average at Xnp114.470270270270
Midmean - Weighted Average at X(n+1)p114.575
Midmean - Empirical Distribution Function114.470270270270
Midmean - Empirical Distribution Function - Averaging114.575
Midmean - Empirical Distribution Function - Interpolation114.575
Midmean - Closest Observation114.470270270270
Midmean - True Basic - Statistics Graphics Toolkit114.575
Midmean - MS Excel (old versions)114.682051282051
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.436111111111 & 0.744172208065094 & 152.432608852800 \tabularnewline
Geometric Mean & 113.259512056464 &  &  \tabularnewline
Harmonic Mean & 113.079519077321 &  &  \tabularnewline
Quadratic Mean & 113.609289037277 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 113.306944444444 & 0.700771781080265 & 161.688794417175 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 113.309722222222 & 0.700087071832076 & 161.8508993827 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 113.338888888889 & 0.691516205014711 & 163.899107594272 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 113.333333333333 & 0.68866862549658 & 164.568747779982 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 113.402777777778 & 0.668126254966234 & 169.732557184883 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 113.394444444444 & 0.661194942147529 & 171.499261739881 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 113.384722222222 & 0.65658950632865 & 172.687380972958 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 113.395833333333 & 0.654239925923913 & 173.324538659417 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 113.395833333333 & 0.654239925923913 & 173.324538659417 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 113.395833333333 & 0.649528652683834 & 174.58172609443 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 113.411111111111 & 0.646322677117249 & 175.471347558082 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 113.527777777778 & 0.616607097180623 & 184.116884636704 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 113.780555555556 & 0.560406734169931 & 203.032099041576 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 114.305555555556 & 0.453308515998105 & 252.158412033965 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 114.472222222222 & 0.420457972897054 & 272.256038893689 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 114.494444444444 & 0.403955834797198 & 283.433075058627 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 114.6125 & 0.386696501499949 & 296.388768854727 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 114.6125 & 0.379527636050159 & 301.987231266744 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 114.559722222222 & 0.371982695395627 & 307.970568631911 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 114.615277777778 & 0.356323711437561 & 321.660540959711 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 114.673611111111 & 0.348291116876799 & 329.246442284874 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 114.795833333333 & 0.315158488459696 & 364.247949958086 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 114.731944444444 & 0.297425220996564 & 385.750556257534 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 114.665277777778 & 0.288120017446096 & 397.97747756013 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 113.381428571429 & 0.691301448711226 & 164.011559331754 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 113.460294117647 & 0.679768913459746 & 166.910095285441 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 113.542424242424 & 0.666179521105692 & 170.438178666874 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 113.61875 & 0.653572580556709 & 173.84258975984 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 113.701612903226 & 0.639124086351837 & 177.902249862374 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 113.773333333333 & 0.627941065043216 & 181.184731604555 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 113.851724137931 & 0.615868213384301 & 184.863777125785 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 113.9375 & 0.601834654451454 & 189.316948030932 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 114.027777777778 & 0.584701400656085 & 195.018820973969 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 114.125 & 0.562918187101405 & 202.738164470499 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 114.23 & 0.536178846190374 & 213.044585424472 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 114.341666666667 & 0.502324678611669 & 227.625023287101 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 114.447826086957 & 0.466374019321318 & 245.399231830076 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 114.531818181818 & 0.435353283277858 & 263.077878543803 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 114.559523809524 & 0.423525103899516 & 270.490515803530 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 114.57 & 0.415396011239692 & 275.809099991311 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 114.578947368421 & 0.407821082690695 & 280.953958075094 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 114.575 & 0.401018049706589 & 285.710331701604 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 114.570588235294 & 0.392635625755689 & 291.798758746828 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 114.571875 & 0.382116199366827 & 299.835168437893 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 114.566666666667 & 0.370812507487021 & 308.961171356057 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 114.553571428571 & 0.355883361148358 & 321.885156583135 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 114.523076923077 & 0.343748910702954 & 333.159097693957 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 114.495833333333 & 0.330594499999549 & 346.333146297018 \tabularnewline
Median & 114.95 &  &  \tabularnewline
Midrange & 115.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.470270270270 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.575 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.470270270270 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.575 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.575 &  &  \tabularnewline
Midmean - Closest Observation & 114.470270270270 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.575 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.682051282051 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29305&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]113.436111111111[/C][C]0.744172208065094[/C][C]152.432608852800[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.259512056464[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.079519077321[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.609289037277[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]113.306944444444[/C][C]0.700771781080265[/C][C]161.688794417175[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]113.309722222222[/C][C]0.700087071832076[/C][C]161.8508993827[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]113.338888888889[/C][C]0.691516205014711[/C][C]163.899107594272[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]113.333333333333[/C][C]0.68866862549658[/C][C]164.568747779982[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]113.402777777778[/C][C]0.668126254966234[/C][C]169.732557184883[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]113.394444444444[/C][C]0.661194942147529[/C][C]171.499261739881[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]113.384722222222[/C][C]0.65658950632865[/C][C]172.687380972958[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]113.395833333333[/C][C]0.654239925923913[/C][C]173.324538659417[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]113.395833333333[/C][C]0.654239925923913[/C][C]173.324538659417[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]113.395833333333[/C][C]0.649528652683834[/C][C]174.58172609443[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]113.411111111111[/C][C]0.646322677117249[/C][C]175.471347558082[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]113.527777777778[/C][C]0.616607097180623[/C][C]184.116884636704[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]113.780555555556[/C][C]0.560406734169931[/C][C]203.032099041576[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]114.305555555556[/C][C]0.453308515998105[/C][C]252.158412033965[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]114.472222222222[/C][C]0.420457972897054[/C][C]272.256038893689[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]114.494444444444[/C][C]0.403955834797198[/C][C]283.433075058627[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]114.6125[/C][C]0.386696501499949[/C][C]296.388768854727[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]114.6125[/C][C]0.379527636050159[/C][C]301.987231266744[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]114.559722222222[/C][C]0.371982695395627[/C][C]307.970568631911[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]114.615277777778[/C][C]0.356323711437561[/C][C]321.660540959711[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]114.673611111111[/C][C]0.348291116876799[/C][C]329.246442284874[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]114.795833333333[/C][C]0.315158488459696[/C][C]364.247949958086[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]114.731944444444[/C][C]0.297425220996564[/C][C]385.750556257534[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]114.665277777778[/C][C]0.288120017446096[/C][C]397.97747756013[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]113.381428571429[/C][C]0.691301448711226[/C][C]164.011559331754[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]113.460294117647[/C][C]0.679768913459746[/C][C]166.910095285441[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]113.542424242424[/C][C]0.666179521105692[/C][C]170.438178666874[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]113.61875[/C][C]0.653572580556709[/C][C]173.84258975984[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]113.701612903226[/C][C]0.639124086351837[/C][C]177.902249862374[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]113.773333333333[/C][C]0.627941065043216[/C][C]181.184731604555[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]113.851724137931[/C][C]0.615868213384301[/C][C]184.863777125785[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]113.9375[/C][C]0.601834654451454[/C][C]189.316948030932[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]114.027777777778[/C][C]0.584701400656085[/C][C]195.018820973969[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]114.125[/C][C]0.562918187101405[/C][C]202.738164470499[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]114.23[/C][C]0.536178846190374[/C][C]213.044585424472[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]114.341666666667[/C][C]0.502324678611669[/C][C]227.625023287101[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]114.447826086957[/C][C]0.466374019321318[/C][C]245.399231830076[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]114.531818181818[/C][C]0.435353283277858[/C][C]263.077878543803[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]114.559523809524[/C][C]0.423525103899516[/C][C]270.490515803530[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]114.57[/C][C]0.415396011239692[/C][C]275.809099991311[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]114.578947368421[/C][C]0.407821082690695[/C][C]280.953958075094[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]114.575[/C][C]0.401018049706589[/C][C]285.710331701604[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]114.570588235294[/C][C]0.392635625755689[/C][C]291.798758746828[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]114.571875[/C][C]0.382116199366827[/C][C]299.835168437893[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]114.566666666667[/C][C]0.370812507487021[/C][C]308.961171356057[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]114.553571428571[/C][C]0.355883361148358[/C][C]321.885156583135[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]114.523076923077[/C][C]0.343748910702954[/C][C]333.159097693957[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]114.495833333333[/C][C]0.330594499999549[/C][C]346.333146297018[/C][/ROW]
[ROW][C]Median[/C][C]114.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]115.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.470270270270[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.470270270270[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.470270270270[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.682051282051[/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=29305&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29305&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 Mean113.4361111111110.744172208065094152.432608852800
Geometric Mean113.259512056464
Harmonic Mean113.079519077321
Quadratic Mean113.609289037277
Winsorized Mean ( 1 / 24 )113.3069444444440.700771781080265161.688794417175
Winsorized Mean ( 2 / 24 )113.3097222222220.700087071832076161.8508993827
Winsorized Mean ( 3 / 24 )113.3388888888890.691516205014711163.899107594272
Winsorized Mean ( 4 / 24 )113.3333333333330.68866862549658164.568747779982
Winsorized Mean ( 5 / 24 )113.4027777777780.668126254966234169.732557184883
Winsorized Mean ( 6 / 24 )113.3944444444440.661194942147529171.499261739881
Winsorized Mean ( 7 / 24 )113.3847222222220.65658950632865172.687380972958
Winsorized Mean ( 8 / 24 )113.3958333333330.654239925923913173.324538659417
Winsorized Mean ( 9 / 24 )113.3958333333330.654239925923913173.324538659417
Winsorized Mean ( 10 / 24 )113.3958333333330.649528652683834174.58172609443
Winsorized Mean ( 11 / 24 )113.4111111111110.646322677117249175.471347558082
Winsorized Mean ( 12 / 24 )113.5277777777780.616607097180623184.116884636704
Winsorized Mean ( 13 / 24 )113.7805555555560.560406734169931203.032099041576
Winsorized Mean ( 14 / 24 )114.3055555555560.453308515998105252.158412033965
Winsorized Mean ( 15 / 24 )114.4722222222220.420457972897054272.256038893689
Winsorized Mean ( 16 / 24 )114.4944444444440.403955834797198283.433075058627
Winsorized Mean ( 17 / 24 )114.61250.386696501499949296.388768854727
Winsorized Mean ( 18 / 24 )114.61250.379527636050159301.987231266744
Winsorized Mean ( 19 / 24 )114.5597222222220.371982695395627307.970568631911
Winsorized Mean ( 20 / 24 )114.6152777777780.356323711437561321.660540959711
Winsorized Mean ( 21 / 24 )114.6736111111110.348291116876799329.246442284874
Winsorized Mean ( 22 / 24 )114.7958333333330.315158488459696364.247949958086
Winsorized Mean ( 23 / 24 )114.7319444444440.297425220996564385.750556257534
Winsorized Mean ( 24 / 24 )114.6652777777780.288120017446096397.97747756013
Trimmed Mean ( 1 / 24 )113.3814285714290.691301448711226164.011559331754
Trimmed Mean ( 2 / 24 )113.4602941176470.679768913459746166.910095285441
Trimmed Mean ( 3 / 24 )113.5424242424240.666179521105692170.438178666874
Trimmed Mean ( 4 / 24 )113.618750.653572580556709173.84258975984
Trimmed Mean ( 5 / 24 )113.7016129032260.639124086351837177.902249862374
Trimmed Mean ( 6 / 24 )113.7733333333330.627941065043216181.184731604555
Trimmed Mean ( 7 / 24 )113.8517241379310.615868213384301184.863777125785
Trimmed Mean ( 8 / 24 )113.93750.601834654451454189.316948030932
Trimmed Mean ( 9 / 24 )114.0277777777780.584701400656085195.018820973969
Trimmed Mean ( 10 / 24 )114.1250.562918187101405202.738164470499
Trimmed Mean ( 11 / 24 )114.230.536178846190374213.044585424472
Trimmed Mean ( 12 / 24 )114.3416666666670.502324678611669227.625023287101
Trimmed Mean ( 13 / 24 )114.4478260869570.466374019321318245.399231830076
Trimmed Mean ( 14 / 24 )114.5318181818180.435353283277858263.077878543803
Trimmed Mean ( 15 / 24 )114.5595238095240.423525103899516270.490515803530
Trimmed Mean ( 16 / 24 )114.570.415396011239692275.809099991311
Trimmed Mean ( 17 / 24 )114.5789473684210.407821082690695280.953958075094
Trimmed Mean ( 18 / 24 )114.5750.401018049706589285.710331701604
Trimmed Mean ( 19 / 24 )114.5705882352940.392635625755689291.798758746828
Trimmed Mean ( 20 / 24 )114.5718750.382116199366827299.835168437893
Trimmed Mean ( 21 / 24 )114.5666666666670.370812507487021308.961171356057
Trimmed Mean ( 22 / 24 )114.5535714285710.355883361148358321.885156583135
Trimmed Mean ( 23 / 24 )114.5230769230770.343748910702954333.159097693957
Trimmed Mean ( 24 / 24 )114.4958333333330.330594499999549346.333146297018
Median114.95
Midrange115.35
Midmean - Weighted Average at Xnp114.470270270270
Midmean - Weighted Average at X(n+1)p114.575
Midmean - Empirical Distribution Function114.470270270270
Midmean - Empirical Distribution Function - Averaging114.575
Midmean - Empirical Distribution Function - Interpolation114.575
Midmean - Closest Observation114.470270270270
Midmean - True Basic - Statistics Graphics Toolkit114.575
Midmean - MS Excel (old versions)114.682051282051
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')