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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 16 Apr 2008 08:03:55 -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/2008/Apr/16/t120835466827vapd6h9xw2bp6.htm/, Retrieved Fri, 10 May 2024 18:12:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10139, Retrieved Fri, 10 May 2024 18:12:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact256
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2008-04-16 14:03:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
12,23
12,25
12,33
12,37
12,38
12,41
12,41
12,41
12,43
12,44
12,46
12,46
12,46
12,47
12,55
12,58
12,6
12,62
12,62
12,66
12,7
12,76
12,79
12,81
12,86
13,03
13,09
13,15
13,17
13,18
13,18
13,19
13,19
13,19
13,25
13,24
13,3
13,35
13,35
13,35
13,36
13,37
13,38
13,39
13,4
13,4
13,44
13,44
13,44
13,47
13,52
13,58
13,65
13,66
13,68
13,68
13,77
13,78
13,79
13,79
13,82
13,86
13,94
14
14,02
14,03
14,07
14,1
14,1
14,16
14,17
14,17




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10139&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10139&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.20416666666670.0682238186898074193.5418878662
Geometric Mean13.1916185756177
Harmonic Mean13.1790443607943
Quadratic Mean13.2166745481271
Winsorized Mean ( 1 / 24 )13.20444444444440.0681684971943598193.703029814437
Winsorized Mean ( 2 / 24 )13.20638888888890.067691450385002195.096852169310
Winsorized Mean ( 3 / 24 )13.20555555555560.0669094431840695197.364600976080
Winsorized Mean ( 4 / 24 )13.20611111111110.066812210714873197.660142806370
Winsorized Mean ( 5 / 24 )13.20611111111110.0660658239701339199.893232499168
Winsorized Mean ( 6 / 24 )13.20277777777780.0654621891553218201.685552349183
Winsorized Mean ( 7 / 24 )13.20180555555560.0652898696056112202.202970159109
Winsorized Mean ( 8 / 24 )13.20180555555560.0645231474486931204.605727983949
Winsorized Mean ( 9 / 24 )13.19555555555560.0630348442059813209.337481860603
Winsorized Mean ( 10 / 24 )13.18722222222220.0607749324862627216.984563910507
Winsorized Mean ( 11 / 24 )13.18111111111110.0598389059207966220.276606135777
Winsorized Mean ( 12 / 24 )13.17611111111110.0590971308493948222.956866462596
Winsorized Mean ( 13 / 24 )13.17791666666670.0587899424704664224.152569519637
Winsorized Mean ( 14 / 24 )13.19152777777780.0559260703182782235.874391007702
Winsorized Mean ( 15 / 24 )13.19569444444440.0546162549496907241.607456545667
Winsorized Mean ( 16 / 24 )13.18013888888890.0510440652614745258.210995173940
Winsorized Mean ( 17 / 24 )13.18486111111110.0502925685495662262.163208031753
Winsorized Mean ( 18 / 24 )13.17986111111110.0496050493162389265.69595822973
Winsorized Mean ( 19 / 24 )13.18777777777780.0475808439044508277.165697276424
Winsorized Mean ( 20 / 24 )13.17944444444440.0432438082485165304.770670721318
Winsorized Mean ( 21 / 24 )13.17944444444440.0382857884824355344.23855343846
Winsorized Mean ( 22 / 24 )13.17333333333330.0350005589045472376.374942161906
Winsorized Mean ( 23 / 24 )13.17013888888890.0328887565489766400.445023492343
Winsorized Mean ( 24 / 24 )13.18680555555560.0303383543211275434.657905830189
Trimmed Mean ( 1 / 24 )13.20428571428570.0673544966316577196.041636039478
Trimmed Mean ( 2 / 24 )13.20411764705880.0663692927815623198.949199150228
Trimmed Mean ( 3 / 24 )13.20287878787880.0654743370967011201.649674870003
Trimmed Mean ( 4 / 24 )13.2018750.0647265596935439203.963798825489
Trimmed Mean ( 5 / 24 )13.20064516129030.0638322559479504206.802109141408
Trimmed Mean ( 6 / 24 )13.19933333333330.0629522582384921209.672118247580
Trimmed Mean ( 7 / 24 )13.19862068965520.062018598910004212.817137465615
Trimmed Mean ( 8 / 24 )13.19803571428570.0608897340860399216.75305225732
Trimmed Mean ( 9 / 24 )13.19740740740740.0596584649301226221.216007198063
Trimmed Mean ( 10 / 24 )13.19769230769230.0584526567040613225.784302234723
Trimmed Mean ( 11 / 24 )13.19920.0574213499368608229.86572092982
Trimmed Mean ( 12 / 24 )13.20166666666670.056281282344282234.565847059239
Trimmed Mean ( 13 / 24 )13.2050.0549455153933035240.328986005096
Trimmed Mean ( 14 / 24 )13.20840909090910.0532574654880735248.010470829991
Trimmed Mean ( 15 / 24 )13.21047619047620.0517183837460137255.430955757476
Trimmed Mean ( 16 / 24 )13.212250.0499698466770019264.404453457745
Trimmed Mean ( 17 / 24 )13.21605263157890.0484548439515936272.749875013152
Trimmed Mean ( 18 / 24 )13.21972222222220.0465482956418438284.000134482659
Trimmed Mean ( 19 / 24 )13.22441176470590.044036913652943300.302874741134
Trimmed Mean ( 20 / 24 )13.228750.041098205556934321.881450071439
Trimmed Mean ( 21 / 24 )13.23466666666670.0382301960852977346.183593647755
Trimmed Mean ( 22 / 24 )13.24142857142860.0357005264500862370.902893825438
Trimmed Mean ( 23 / 24 )13.250.0329475107032149402.154812828002
Trimmed Mean ( 24 / 24 )13.26041666666670.0292817347150524452.856253077454
Median13.275
Midrange13.2
Midmean - Weighted Average at Xnp13.2035135135135
Midmean - Weighted Average at X(n+1)p13.2035135135135
Midmean - Empirical Distribution Function13.2035135135135
Midmean - Empirical Distribution Function - Averaging13.2035135135135
Midmean - Empirical Distribution Function - Interpolation13.2035135135135
Midmean - Closest Observation13.2035135135135
Midmean - True Basic - Statistics Graphics Toolkit13.2035135135135
Midmean - MS Excel (old versions)13.2279487179487
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.2041666666667 & 0.0682238186898074 & 193.5418878662 \tabularnewline
Geometric Mean & 13.1916185756177 &  &  \tabularnewline
Harmonic Mean & 13.1790443607943 &  &  \tabularnewline
Quadratic Mean & 13.2166745481271 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 13.2044444444444 & 0.0681684971943598 & 193.703029814437 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 13.2063888888889 & 0.067691450385002 & 195.096852169310 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 13.2055555555556 & 0.0669094431840695 & 197.364600976080 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 13.2061111111111 & 0.066812210714873 & 197.660142806370 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 13.2061111111111 & 0.0660658239701339 & 199.893232499168 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 13.2027777777778 & 0.0654621891553218 & 201.685552349183 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 13.2018055555556 & 0.0652898696056112 & 202.202970159109 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13.2018055555556 & 0.0645231474486931 & 204.605727983949 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13.1955555555556 & 0.0630348442059813 & 209.337481860603 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 13.1872222222222 & 0.0607749324862627 & 216.984563910507 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 13.1811111111111 & 0.0598389059207966 & 220.276606135777 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 13.1761111111111 & 0.0590971308493948 & 222.956866462596 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 13.1779166666667 & 0.0587899424704664 & 224.152569519637 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 13.1915277777778 & 0.0559260703182782 & 235.874391007702 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 13.1956944444444 & 0.0546162549496907 & 241.607456545667 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 13.1801388888889 & 0.0510440652614745 & 258.210995173940 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 13.1848611111111 & 0.0502925685495662 & 262.163208031753 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 13.1798611111111 & 0.0496050493162389 & 265.69595822973 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 13.1877777777778 & 0.0475808439044508 & 277.165697276424 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 13.1794444444444 & 0.0432438082485165 & 304.770670721318 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 13.1794444444444 & 0.0382857884824355 & 344.23855343846 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 13.1733333333333 & 0.0350005589045472 & 376.374942161906 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 13.1701388888889 & 0.0328887565489766 & 400.445023492343 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 13.1868055555556 & 0.0303383543211275 & 434.657905830189 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 13.2042857142857 & 0.0673544966316577 & 196.041636039478 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 13.2041176470588 & 0.0663692927815623 & 198.949199150228 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 13.2028787878788 & 0.0654743370967011 & 201.649674870003 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 13.201875 & 0.0647265596935439 & 203.963798825489 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 13.2006451612903 & 0.0638322559479504 & 206.802109141408 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 13.1993333333333 & 0.0629522582384921 & 209.672118247580 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 13.1986206896552 & 0.062018598910004 & 212.817137465615 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 13.1980357142857 & 0.0608897340860399 & 216.75305225732 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 13.1974074074074 & 0.0596584649301226 & 221.216007198063 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 13.1976923076923 & 0.0584526567040613 & 225.784302234723 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 13.1992 & 0.0574213499368608 & 229.86572092982 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 13.2016666666667 & 0.056281282344282 & 234.565847059239 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 13.205 & 0.0549455153933035 & 240.328986005096 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 13.2084090909091 & 0.0532574654880735 & 248.010470829991 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 13.2104761904762 & 0.0517183837460137 & 255.430955757476 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 13.21225 & 0.0499698466770019 & 264.404453457745 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 13.2160526315789 & 0.0484548439515936 & 272.749875013152 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 13.2197222222222 & 0.0465482956418438 & 284.000134482659 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 13.2244117647059 & 0.044036913652943 & 300.302874741134 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 13.22875 & 0.041098205556934 & 321.881450071439 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 13.2346666666667 & 0.0382301960852977 & 346.183593647755 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 13.2414285714286 & 0.0357005264500862 & 370.902893825438 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 13.25 & 0.0329475107032149 & 402.154812828002 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 13.2604166666667 & 0.0292817347150524 & 452.856253077454 \tabularnewline
Median & 13.275 &  &  \tabularnewline
Midrange & 13.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.2035135135135 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.2035135135135 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.2035135135135 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.2035135135135 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.2035135135135 &  &  \tabularnewline
Midmean - Closest Observation & 13.2035135135135 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.2035135135135 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.2279487179487 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10139&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]13.2041666666667[/C][C]0.0682238186898074[/C][C]193.5418878662[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13.1916185756177[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13.1790443607943[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.2166745481271[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]13.2044444444444[/C][C]0.0681684971943598[/C][C]193.703029814437[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]13.2063888888889[/C][C]0.067691450385002[/C][C]195.096852169310[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]13.2055555555556[/C][C]0.0669094431840695[/C][C]197.364600976080[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]13.2061111111111[/C][C]0.066812210714873[/C][C]197.660142806370[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]13.2061111111111[/C][C]0.0660658239701339[/C][C]199.893232499168[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]13.2027777777778[/C][C]0.0654621891553218[/C][C]201.685552349183[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]13.2018055555556[/C][C]0.0652898696056112[/C][C]202.202970159109[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13.2018055555556[/C][C]0.0645231474486931[/C][C]204.605727983949[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13.1955555555556[/C][C]0.0630348442059813[/C][C]209.337481860603[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]13.1872222222222[/C][C]0.0607749324862627[/C][C]216.984563910507[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]13.1811111111111[/C][C]0.0598389059207966[/C][C]220.276606135777[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]13.1761111111111[/C][C]0.0590971308493948[/C][C]222.956866462596[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]13.1779166666667[/C][C]0.0587899424704664[/C][C]224.152569519637[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]13.1915277777778[/C][C]0.0559260703182782[/C][C]235.874391007702[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]13.1956944444444[/C][C]0.0546162549496907[/C][C]241.607456545667[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]13.1801388888889[/C][C]0.0510440652614745[/C][C]258.210995173940[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]13.1848611111111[/C][C]0.0502925685495662[/C][C]262.163208031753[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]13.1798611111111[/C][C]0.0496050493162389[/C][C]265.69595822973[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]13.1877777777778[/C][C]0.0475808439044508[/C][C]277.165697276424[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]13.1794444444444[/C][C]0.0432438082485165[/C][C]304.770670721318[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]13.1794444444444[/C][C]0.0382857884824355[/C][C]344.23855343846[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]13.1733333333333[/C][C]0.0350005589045472[/C][C]376.374942161906[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]13.1701388888889[/C][C]0.0328887565489766[/C][C]400.445023492343[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]13.1868055555556[/C][C]0.0303383543211275[/C][C]434.657905830189[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]13.2042857142857[/C][C]0.0673544966316577[/C][C]196.041636039478[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]13.2041176470588[/C][C]0.0663692927815623[/C][C]198.949199150228[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]13.2028787878788[/C][C]0.0654743370967011[/C][C]201.649674870003[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]13.201875[/C][C]0.0647265596935439[/C][C]203.963798825489[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]13.2006451612903[/C][C]0.0638322559479504[/C][C]206.802109141408[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]13.1993333333333[/C][C]0.0629522582384921[/C][C]209.672118247580[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]13.1986206896552[/C][C]0.062018598910004[/C][C]212.817137465615[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]13.1980357142857[/C][C]0.0608897340860399[/C][C]216.75305225732[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]13.1974074074074[/C][C]0.0596584649301226[/C][C]221.216007198063[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]13.1976923076923[/C][C]0.0584526567040613[/C][C]225.784302234723[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]13.1992[/C][C]0.0574213499368608[/C][C]229.86572092982[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]13.2016666666667[/C][C]0.056281282344282[/C][C]234.565847059239[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]13.205[/C][C]0.0549455153933035[/C][C]240.328986005096[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]13.2084090909091[/C][C]0.0532574654880735[/C][C]248.010470829991[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]13.2104761904762[/C][C]0.0517183837460137[/C][C]255.430955757476[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]13.21225[/C][C]0.0499698466770019[/C][C]264.404453457745[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]13.2160526315789[/C][C]0.0484548439515936[/C][C]272.749875013152[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]13.2197222222222[/C][C]0.0465482956418438[/C][C]284.000134482659[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]13.2244117647059[/C][C]0.044036913652943[/C][C]300.302874741134[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]13.22875[/C][C]0.041098205556934[/C][C]321.881450071439[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]13.2346666666667[/C][C]0.0382301960852977[/C][C]346.183593647755[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]13.2414285714286[/C][C]0.0357005264500862[/C][C]370.902893825438[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]13.25[/C][C]0.0329475107032149[/C][C]402.154812828002[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]13.2604166666667[/C][C]0.0292817347150524[/C][C]452.856253077454[/C][/ROW]
[ROW][C]Median[/C][C]13.275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.2035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.2035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.2035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.2035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.2035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.2035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.2035135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.2279487179487[/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=10139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10139&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 Mean13.20416666666670.0682238186898074193.5418878662
Geometric Mean13.1916185756177
Harmonic Mean13.1790443607943
Quadratic Mean13.2166745481271
Winsorized Mean ( 1 / 24 )13.20444444444440.0681684971943598193.703029814437
Winsorized Mean ( 2 / 24 )13.20638888888890.067691450385002195.096852169310
Winsorized Mean ( 3 / 24 )13.20555555555560.0669094431840695197.364600976080
Winsorized Mean ( 4 / 24 )13.20611111111110.066812210714873197.660142806370
Winsorized Mean ( 5 / 24 )13.20611111111110.0660658239701339199.893232499168
Winsorized Mean ( 6 / 24 )13.20277777777780.0654621891553218201.685552349183
Winsorized Mean ( 7 / 24 )13.20180555555560.0652898696056112202.202970159109
Winsorized Mean ( 8 / 24 )13.20180555555560.0645231474486931204.605727983949
Winsorized Mean ( 9 / 24 )13.19555555555560.0630348442059813209.337481860603
Winsorized Mean ( 10 / 24 )13.18722222222220.0607749324862627216.984563910507
Winsorized Mean ( 11 / 24 )13.18111111111110.0598389059207966220.276606135777
Winsorized Mean ( 12 / 24 )13.17611111111110.0590971308493948222.956866462596
Winsorized Mean ( 13 / 24 )13.17791666666670.0587899424704664224.152569519637
Winsorized Mean ( 14 / 24 )13.19152777777780.0559260703182782235.874391007702
Winsorized Mean ( 15 / 24 )13.19569444444440.0546162549496907241.607456545667
Winsorized Mean ( 16 / 24 )13.18013888888890.0510440652614745258.210995173940
Winsorized Mean ( 17 / 24 )13.18486111111110.0502925685495662262.163208031753
Winsorized Mean ( 18 / 24 )13.17986111111110.0496050493162389265.69595822973
Winsorized Mean ( 19 / 24 )13.18777777777780.0475808439044508277.165697276424
Winsorized Mean ( 20 / 24 )13.17944444444440.0432438082485165304.770670721318
Winsorized Mean ( 21 / 24 )13.17944444444440.0382857884824355344.23855343846
Winsorized Mean ( 22 / 24 )13.17333333333330.0350005589045472376.374942161906
Winsorized Mean ( 23 / 24 )13.17013888888890.0328887565489766400.445023492343
Winsorized Mean ( 24 / 24 )13.18680555555560.0303383543211275434.657905830189
Trimmed Mean ( 1 / 24 )13.20428571428570.0673544966316577196.041636039478
Trimmed Mean ( 2 / 24 )13.20411764705880.0663692927815623198.949199150228
Trimmed Mean ( 3 / 24 )13.20287878787880.0654743370967011201.649674870003
Trimmed Mean ( 4 / 24 )13.2018750.0647265596935439203.963798825489
Trimmed Mean ( 5 / 24 )13.20064516129030.0638322559479504206.802109141408
Trimmed Mean ( 6 / 24 )13.19933333333330.0629522582384921209.672118247580
Trimmed Mean ( 7 / 24 )13.19862068965520.062018598910004212.817137465615
Trimmed Mean ( 8 / 24 )13.19803571428570.0608897340860399216.75305225732
Trimmed Mean ( 9 / 24 )13.19740740740740.0596584649301226221.216007198063
Trimmed Mean ( 10 / 24 )13.19769230769230.0584526567040613225.784302234723
Trimmed Mean ( 11 / 24 )13.19920.0574213499368608229.86572092982
Trimmed Mean ( 12 / 24 )13.20166666666670.056281282344282234.565847059239
Trimmed Mean ( 13 / 24 )13.2050.0549455153933035240.328986005096
Trimmed Mean ( 14 / 24 )13.20840909090910.0532574654880735248.010470829991
Trimmed Mean ( 15 / 24 )13.21047619047620.0517183837460137255.430955757476
Trimmed Mean ( 16 / 24 )13.212250.0499698466770019264.404453457745
Trimmed Mean ( 17 / 24 )13.21605263157890.0484548439515936272.749875013152
Trimmed Mean ( 18 / 24 )13.21972222222220.0465482956418438284.000134482659
Trimmed Mean ( 19 / 24 )13.22441176470590.044036913652943300.302874741134
Trimmed Mean ( 20 / 24 )13.228750.041098205556934321.881450071439
Trimmed Mean ( 21 / 24 )13.23466666666670.0382301960852977346.183593647755
Trimmed Mean ( 22 / 24 )13.24142857142860.0357005264500862370.902893825438
Trimmed Mean ( 23 / 24 )13.250.0329475107032149402.154812828002
Trimmed Mean ( 24 / 24 )13.26041666666670.0292817347150524452.856253077454
Median13.275
Midrange13.2
Midmean - Weighted Average at Xnp13.2035135135135
Midmean - Weighted Average at X(n+1)p13.2035135135135
Midmean - Empirical Distribution Function13.2035135135135
Midmean - Empirical Distribution Function - Averaging13.2035135135135
Midmean - Empirical Distribution Function - Interpolation13.2035135135135
Midmean - Closest Observation13.2035135135135
Midmean - True Basic - Statistics Graphics Toolkit13.2035135135135
Midmean - MS Excel (old versions)13.2279487179487
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')