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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 21 May 2012 12:02:51 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/21/t13376162503ta19r6mejt3hrk.htm/, Retrieved Thu, 02 May 2024 22:19:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166982, Retrieved Thu, 02 May 2024 22:19:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-05-21 16:02:51] [08f815ef91e7dd0cd9caee9b166770ec] [Current]
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Dataseries X:
104,42
104,42
104,42
104,42
104,42
104,42
104,42
104,44
104,44
104,44
105,19
105,19
105,19
106,38
106,38
106,38
106,38
106,38
106,38
106,72
106,73
106,72
108,6
108,6
109,65
109,65
109,65
109,65
109,65
109,65
109,65
109,65
112,27
112,27
112,27
112,27
112,27
114,98
114,98
114,98
114,98
114,98
114,98
116,04
116,59
116,59
116,59
116,59
118,75
118,75
118,75
118,75
118,75
118,75
118,75
119,31
119,31
119,31
119,31
119,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166982&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166982&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.2351666666670.704782031122813157.829175198258
Geometric Mean111.104084463533
Harmonic Mean110.973802149742
Quadratic Mean111.366820230863
Winsorized Mean ( 1 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 2 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 3 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 4 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 5 / 20 )111.18850.695952577488577159.764477633284
Winsorized Mean ( 6 / 20 )111.18850.695952577488577159.764477633284
Winsorized Mean ( 7 / 20 )111.1908333333330.695568348340266159.856085456809
Winsorized Mean ( 8 / 20 )111.1908333333330.695568348340266159.856085456809
Winsorized Mean ( 9 / 20 )111.1908333333330.695568348340266159.856085456809
Winsorized Mean ( 10 / 20 )111.3158333333330.675673185620444164.748040476279
Winsorized Mean ( 11 / 20 )111.3158333333330.675673185620444164.748040476279
Winsorized Mean ( 12 / 20 )110.8838333333330.600266847047864184.724233694838
Winsorized Mean ( 13 / 20 )111.1416666666670.560918141941023198.142399677193
Winsorized Mean ( 14 / 20 )111.1416666666670.560918141941023198.142399677193
Winsorized Mean ( 15 / 20 )111.1416666666670.560918141941023198.142399677193
Winsorized Mean ( 16 / 20 )110.9950.537162954370481206.63189651654
Winsorized Mean ( 17 / 20 )110.6946666666670.49096736441338225.462372226975
Winsorized Mean ( 18 / 20 )110.6946666666670.49096736441338225.462372226975
Winsorized Mean ( 19 / 20 )110.8023333333330.475105897601756233.216076442415
Winsorized Mean ( 20 / 20 )110.8023333333330.475105897601756233.216076442415
Trimmed Mean ( 1 / 20 )111.2134482758620.70575885163994157.579955274299
Trimmed Mean ( 2 / 20 )111.1901785714290.705950703324332157.504168559975
Trimmed Mean ( 3 / 20 )111.1651851851850.705169081861952157.643305761025
Trimmed Mean ( 4 / 20 )111.1382692307690.703174965254897158.052084790138
Trimmed Mean ( 5 / 20 )111.10920.699661774848157158.804159372739
Trimmed Mean ( 6 / 20 )111.0893750.697066447162501159.366980654719
Trimmed Mean ( 7 / 20 )111.0678260869570.692613541716051160.360459906357
Trimmed Mean ( 8 / 20 )111.0438636363640.685872942325068161.901507967251
Trimmed Mean ( 9 / 20 )111.0176190476190.676043247618708164.216741219836
Trimmed Mean ( 10 / 20 )110.988750.662128094693203167.624287338882
Trimmed Mean ( 11 / 20 )110.9371052631580.647767465685765171.260693288622
Trimmed Mean ( 12 / 20 )110.8797222222220.627271932386979176.764998555392
Trimmed Mean ( 13 / 20 )110.8791176470590.619637115302816178.942020916343
Trimmed Mean ( 14 / 20 )110.841250.617201303949347179.586869455312
Trimmed Mean ( 15 / 20 )110.7983333333330.611088925058786181.312946103016
Trimmed Mean ( 16 / 20 )110.7492857142860.599549418240963184.720862609152
Trimmed Mean ( 17 / 20 )110.7138461538460.58787284782264188.32957937062
Trimmed Mean ( 18 / 20 )110.7166666666670.583054695356943189.890704162645
Trimmed Mean ( 19 / 20 )110.720.571075919320457193.879651118453
Trimmed Mean ( 20 / 20 )110.7070.553743290324088199.924770077497
Median109.65
Midrange111.865
Midmean - Weighted Average at Xnp111.042285714286
Midmean - Weighted Average at X(n+1)p111.042285714286
Midmean - Empirical Distribution Function111.042285714286
Midmean - Empirical Distribution Function - Averaging111.042285714286
Midmean - Empirical Distribution Function - Interpolation111.042285714286
Midmean - Closest Observation111.042285714286
Midmean - True Basic - Statistics Graphics Toolkit111.042285714286
Midmean - MS Excel (old versions)111.042285714286
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.235166666667 & 0.704782031122813 & 157.829175198258 \tabularnewline
Geometric Mean & 111.104084463533 &  &  \tabularnewline
Harmonic Mean & 110.973802149742 &  &  \tabularnewline
Quadratic Mean & 111.366820230863 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.235166666667 & 0.704782031122813 & 157.829175198258 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 111.235166666667 & 0.704782031122813 & 157.829175198258 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 111.235166666667 & 0.704782031122813 & 157.829175198258 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 111.235166666667 & 0.704782031122813 & 157.829175198258 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.1885 & 0.695952577488577 & 159.764477633284 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.1885 & 0.695952577488577 & 159.764477633284 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.190833333333 & 0.695568348340266 & 159.856085456809 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.190833333333 & 0.695568348340266 & 159.856085456809 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.190833333333 & 0.695568348340266 & 159.856085456809 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.315833333333 & 0.675673185620444 & 164.748040476279 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.315833333333 & 0.675673185620444 & 164.748040476279 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 110.883833333333 & 0.600266847047864 & 184.724233694838 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.141666666667 & 0.560918141941023 & 198.142399677193 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.141666666667 & 0.560918141941023 & 198.142399677193 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.141666666667 & 0.560918141941023 & 198.142399677193 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 110.995 & 0.537162954370481 & 206.63189651654 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 110.694666666667 & 0.49096736441338 & 225.462372226975 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 110.694666666667 & 0.49096736441338 & 225.462372226975 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 110.802333333333 & 0.475105897601756 & 233.216076442415 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110.802333333333 & 0.475105897601756 & 233.216076442415 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 111.213448275862 & 0.70575885163994 & 157.579955274299 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 111.190178571429 & 0.705950703324332 & 157.504168559975 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 111.165185185185 & 0.705169081861952 & 157.643305761025 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.138269230769 & 0.703174965254897 & 158.052084790138 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.1092 & 0.699661774848157 & 158.804159372739 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.089375 & 0.697066447162501 & 159.366980654719 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.067826086957 & 0.692613541716051 & 160.360459906357 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.043863636364 & 0.685872942325068 & 161.901507967251 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.017619047619 & 0.676043247618708 & 164.216741219836 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 110.98875 & 0.662128094693203 & 167.624287338882 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 110.937105263158 & 0.647767465685765 & 171.260693288622 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 110.879722222222 & 0.627271932386979 & 176.764998555392 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 110.879117647059 & 0.619637115302816 & 178.942020916343 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 110.84125 & 0.617201303949347 & 179.586869455312 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 110.798333333333 & 0.611088925058786 & 181.312946103016 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 110.749285714286 & 0.599549418240963 & 184.720862609152 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 110.713846153846 & 0.58787284782264 & 188.32957937062 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 110.716666666667 & 0.583054695356943 & 189.890704162645 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 110.72 & 0.571075919320457 & 193.879651118453 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 110.707 & 0.553743290324088 & 199.924770077497 \tabularnewline
Median & 109.65 &  &  \tabularnewline
Midrange & 111.865 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.042285714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.042285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.042285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.042285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.042285714286 &  &  \tabularnewline
Midmean - Closest Observation & 111.042285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.042285714286 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.042285714286 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166982&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]111.235166666667[/C][C]0.704782031122813[/C][C]157.829175198258[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.104084463533[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.973802149742[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.366820230863[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.235166666667[/C][C]0.704782031122813[/C][C]157.829175198258[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]111.235166666667[/C][C]0.704782031122813[/C][C]157.829175198258[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]111.235166666667[/C][C]0.704782031122813[/C][C]157.829175198258[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]111.235166666667[/C][C]0.704782031122813[/C][C]157.829175198258[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.1885[/C][C]0.695952577488577[/C][C]159.764477633284[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.1885[/C][C]0.695952577488577[/C][C]159.764477633284[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.190833333333[/C][C]0.695568348340266[/C][C]159.856085456809[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.190833333333[/C][C]0.695568348340266[/C][C]159.856085456809[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.190833333333[/C][C]0.695568348340266[/C][C]159.856085456809[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.315833333333[/C][C]0.675673185620444[/C][C]164.748040476279[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.315833333333[/C][C]0.675673185620444[/C][C]164.748040476279[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]110.883833333333[/C][C]0.600266847047864[/C][C]184.724233694838[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.141666666667[/C][C]0.560918141941023[/C][C]198.142399677193[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.141666666667[/C][C]0.560918141941023[/C][C]198.142399677193[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.141666666667[/C][C]0.560918141941023[/C][C]198.142399677193[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]110.995[/C][C]0.537162954370481[/C][C]206.63189651654[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]110.694666666667[/C][C]0.49096736441338[/C][C]225.462372226975[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]110.694666666667[/C][C]0.49096736441338[/C][C]225.462372226975[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]110.802333333333[/C][C]0.475105897601756[/C][C]233.216076442415[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110.802333333333[/C][C]0.475105897601756[/C][C]233.216076442415[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]111.213448275862[/C][C]0.70575885163994[/C][C]157.579955274299[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]111.190178571429[/C][C]0.705950703324332[/C][C]157.504168559975[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]111.165185185185[/C][C]0.705169081861952[/C][C]157.643305761025[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.138269230769[/C][C]0.703174965254897[/C][C]158.052084790138[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.1092[/C][C]0.699661774848157[/C][C]158.804159372739[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.089375[/C][C]0.697066447162501[/C][C]159.366980654719[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.067826086957[/C][C]0.692613541716051[/C][C]160.360459906357[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.043863636364[/C][C]0.685872942325068[/C][C]161.901507967251[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.017619047619[/C][C]0.676043247618708[/C][C]164.216741219836[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]110.98875[/C][C]0.662128094693203[/C][C]167.624287338882[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]110.937105263158[/C][C]0.647767465685765[/C][C]171.260693288622[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]110.879722222222[/C][C]0.627271932386979[/C][C]176.764998555392[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]110.879117647059[/C][C]0.619637115302816[/C][C]178.942020916343[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]110.84125[/C][C]0.617201303949347[/C][C]179.586869455312[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]110.798333333333[/C][C]0.611088925058786[/C][C]181.312946103016[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]110.749285714286[/C][C]0.599549418240963[/C][C]184.720862609152[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]110.713846153846[/C][C]0.58787284782264[/C][C]188.32957937062[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]110.716666666667[/C][C]0.583054695356943[/C][C]189.890704162645[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]110.72[/C][C]0.571075919320457[/C][C]193.879651118453[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]110.707[/C][C]0.553743290324088[/C][C]199.924770077497[/C][/ROW]
[ROW][C]Median[/C][C]109.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.042285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166982&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 Mean111.2351666666670.704782031122813157.829175198258
Geometric Mean111.104084463533
Harmonic Mean110.973802149742
Quadratic Mean111.366820230863
Winsorized Mean ( 1 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 2 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 3 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 4 / 20 )111.2351666666670.704782031122813157.829175198258
Winsorized Mean ( 5 / 20 )111.18850.695952577488577159.764477633284
Winsorized Mean ( 6 / 20 )111.18850.695952577488577159.764477633284
Winsorized Mean ( 7 / 20 )111.1908333333330.695568348340266159.856085456809
Winsorized Mean ( 8 / 20 )111.1908333333330.695568348340266159.856085456809
Winsorized Mean ( 9 / 20 )111.1908333333330.695568348340266159.856085456809
Winsorized Mean ( 10 / 20 )111.3158333333330.675673185620444164.748040476279
Winsorized Mean ( 11 / 20 )111.3158333333330.675673185620444164.748040476279
Winsorized Mean ( 12 / 20 )110.8838333333330.600266847047864184.724233694838
Winsorized Mean ( 13 / 20 )111.1416666666670.560918141941023198.142399677193
Winsorized Mean ( 14 / 20 )111.1416666666670.560918141941023198.142399677193
Winsorized Mean ( 15 / 20 )111.1416666666670.560918141941023198.142399677193
Winsorized Mean ( 16 / 20 )110.9950.537162954370481206.63189651654
Winsorized Mean ( 17 / 20 )110.6946666666670.49096736441338225.462372226975
Winsorized Mean ( 18 / 20 )110.6946666666670.49096736441338225.462372226975
Winsorized Mean ( 19 / 20 )110.8023333333330.475105897601756233.216076442415
Winsorized Mean ( 20 / 20 )110.8023333333330.475105897601756233.216076442415
Trimmed Mean ( 1 / 20 )111.2134482758620.70575885163994157.579955274299
Trimmed Mean ( 2 / 20 )111.1901785714290.705950703324332157.504168559975
Trimmed Mean ( 3 / 20 )111.1651851851850.705169081861952157.643305761025
Trimmed Mean ( 4 / 20 )111.1382692307690.703174965254897158.052084790138
Trimmed Mean ( 5 / 20 )111.10920.699661774848157158.804159372739
Trimmed Mean ( 6 / 20 )111.0893750.697066447162501159.366980654719
Trimmed Mean ( 7 / 20 )111.0678260869570.692613541716051160.360459906357
Trimmed Mean ( 8 / 20 )111.0438636363640.685872942325068161.901507967251
Trimmed Mean ( 9 / 20 )111.0176190476190.676043247618708164.216741219836
Trimmed Mean ( 10 / 20 )110.988750.662128094693203167.624287338882
Trimmed Mean ( 11 / 20 )110.9371052631580.647767465685765171.260693288622
Trimmed Mean ( 12 / 20 )110.8797222222220.627271932386979176.764998555392
Trimmed Mean ( 13 / 20 )110.8791176470590.619637115302816178.942020916343
Trimmed Mean ( 14 / 20 )110.841250.617201303949347179.586869455312
Trimmed Mean ( 15 / 20 )110.7983333333330.611088925058786181.312946103016
Trimmed Mean ( 16 / 20 )110.7492857142860.599549418240963184.720862609152
Trimmed Mean ( 17 / 20 )110.7138461538460.58787284782264188.32957937062
Trimmed Mean ( 18 / 20 )110.7166666666670.583054695356943189.890704162645
Trimmed Mean ( 19 / 20 )110.720.571075919320457193.879651118453
Trimmed Mean ( 20 / 20 )110.7070.553743290324088199.924770077497
Median109.65
Midrange111.865
Midmean - Weighted Average at Xnp111.042285714286
Midmean - Weighted Average at X(n+1)p111.042285714286
Midmean - Empirical Distribution Function111.042285714286
Midmean - Empirical Distribution Function - Averaging111.042285714286
Midmean - Empirical Distribution Function - Interpolation111.042285714286
Midmean - Closest Observation111.042285714286
Midmean - True Basic - Statistics Graphics Toolkit111.042285714286
Midmean - MS Excel (old versions)111.042285714286
Number of observations60



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')