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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 26 Nov 2010 16:27:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/26/t1290788739zh3ozzlsvm6zwpr.htm/, Retrieved Sat, 04 May 2024 08:25:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102074, Retrieved Sat, 04 May 2024 08:25:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
111,36
111,9
112,11
112,34
112,72
112,74
112,86
112,94
113,29
113,46
110,96
110,75
110,64
110,46
110,66
110,48
110,5
110,96
111,17
111,07
111,75
111,45
111,24
111,09
111,29
111,15
110,88
111,22
110,62
110,2
109,29
109,32
108,71
107,85
107,44
106,93
106,19
105,71
105,67
105,7
105,28
105,34
105,58
105,23
105,46
104,92
104,68
104,58
104,32
104,36
104,38
104,25
103,93
103,95
103,6
103,23
103,31
102,82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102074&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102074&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102074&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.5567241379310.439351140384580247.084197944513
Geometric Mean108.505756338942
Harmonic Mean108.454521785266
Quadratic Mean108.607389402189
Winsorized Mean ( 1 / 19 )108.5608620689660.437220243940049248.297885501961
Winsorized Mean ( 2 / 19 )108.5515517241380.434418400561914249.877886350412
Winsorized Mean ( 3 / 19 )108.5624137931030.430585099076328252.127660771324
Winsorized Mean ( 4 / 19 )108.5768965517240.424662650845803255.677998372286
Winsorized Mean ( 5 / 19 )108.5768965517240.424036091138258256.055790582039
Winsorized Mean ( 6 / 19 )108.5686206896550.411676845428621263.722922227064
Winsorized Mean ( 7 / 19 )108.5493103448280.405758821889029267.521750579498
Winsorized Mean ( 8 / 19 )108.5258620689660.400379284371793271.057635360046
Winsorized Mean ( 9 / 19 )108.5056896551720.396420852835917273.71337526506
Winsorized Mean ( 10 / 19 )108.4884482758620.382959137838137283.28988019008
Winsorized Mean ( 11 / 19 )108.4903448275860.377284047638346287.556141073799
Winsorized Mean ( 12 / 19 )108.5255172413790.366676195147638295.970992056582
Winsorized Mean ( 13 / 19 )108.5837931034480.353415178536828307.241453389171
Winsorized Mean ( 14 / 19 )108.5910344827590.350775537770345309.574137275941
Winsorized Mean ( 15 / 19 )108.5936206896550.346519091594439313.384235742923
Winsorized Mean ( 16 / 19 )108.6212068965520.340376031124695319.121198216096
Winsorized Mean ( 17 / 19 )108.6387931034480.332387200284031326.844093306284
Winsorized Mean ( 18 / 19 )108.6605172413790.327089719123899332.204012808546
Winsorized Mean ( 19 / 19 )108.6343103448280.32089353773036338.536921351500
Trimmed Mean ( 1 / 19 )108.5716071428570.4343941726058249.937991781908
Trimmed Mean ( 2 / 19 )108.5831481481480.430488795046587252.232228567988
Trimmed Mean ( 3 / 19 )108.6007692307690.427020602234327254.322083437030
Trimmed Mean ( 4 / 19 )108.61560.423986634367699256.176943317991
Trimmed Mean ( 5 / 19 )108.6272916666670.421839178498457257.508778708813
Trimmed Mean ( 6 / 19 )108.640.418657043183037259.496410651576
Trimmed Mean ( 7 / 19 )108.6556818181820.417535606680957260.230936187454
Trimmed Mean ( 8 / 19 )108.6766666666670.416761708092028260.764519764059
Trimmed Mean ( 9 / 19 )108.7040.41605701039333261.271886507173
Trimmed Mean ( 10 / 19 )108.7376315789470.414892817948884262.086078319014
Trimmed Mean ( 11 / 19 )108.7777777777780.415304843307635261.922728642972
Trimmed Mean ( 12 / 19 )108.8223529411760.415599573072307261.844236597046
Trimmed Mean ( 13 / 19 )108.86718750.416897680834617261.136467063216
Trimmed Mean ( 14 / 19 )108.9093333333330.420044588036434259.280410783169
Trimmed Mean ( 15 / 19 )108.9564285714290.422463239778888257.907477650493
Trimmed Mean ( 16 / 19 )109.0103846153850.424033917645286257.079398791335
Trimmed Mean ( 17 / 19 )109.0691666666670.424791046957065256.759570259235
Trimmed Mean ( 18 / 19 )109.1359090909090.424495962427532257.095281817999
Trimmed Mean ( 19 / 19 )109.21250.421089986007492259.356678213803
Median110.33
Midrange108.14
Midmean - Weighted Average at Xnp108.829655172414
Midmean - Weighted Average at X(n+1)p108.909333333333
Midmean - Empirical Distribution Function108.909333333333
Midmean - Empirical Distribution Function - Averaging108.909333333333
Midmean - Empirical Distribution Function - Interpolation108.956428571429
Midmean - Closest Observation108.909333333333
Midmean - True Basic - Statistics Graphics Toolkit108.909333333333
Midmean - MS Excel (old versions)108.909333333333
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.556724137931 & 0.439351140384580 & 247.084197944513 \tabularnewline
Geometric Mean & 108.505756338942 &  &  \tabularnewline
Harmonic Mean & 108.454521785266 &  &  \tabularnewline
Quadratic Mean & 108.607389402189 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 108.560862068966 & 0.437220243940049 & 248.297885501961 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 108.551551724138 & 0.434418400561914 & 249.877886350412 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 108.562413793103 & 0.430585099076328 & 252.127660771324 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 108.576896551724 & 0.424662650845803 & 255.677998372286 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 108.576896551724 & 0.424036091138258 & 256.055790582039 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 108.568620689655 & 0.411676845428621 & 263.722922227064 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 108.549310344828 & 0.405758821889029 & 267.521750579498 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 108.525862068966 & 0.400379284371793 & 271.057635360046 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 108.505689655172 & 0.396420852835917 & 273.71337526506 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 108.488448275862 & 0.382959137838137 & 283.28988019008 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 108.490344827586 & 0.377284047638346 & 287.556141073799 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 108.525517241379 & 0.366676195147638 & 295.970992056582 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 108.583793103448 & 0.353415178536828 & 307.241453389171 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 108.591034482759 & 0.350775537770345 & 309.574137275941 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 108.593620689655 & 0.346519091594439 & 313.384235742923 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 108.621206896552 & 0.340376031124695 & 319.121198216096 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 108.638793103448 & 0.332387200284031 & 326.844093306284 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 108.660517241379 & 0.327089719123899 & 332.204012808546 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 108.634310344828 & 0.32089353773036 & 338.536921351500 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 108.571607142857 & 0.4343941726058 & 249.937991781908 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 108.583148148148 & 0.430488795046587 & 252.232228567988 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 108.600769230769 & 0.427020602234327 & 254.322083437030 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 108.6156 & 0.423986634367699 & 256.176943317991 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 108.627291666667 & 0.421839178498457 & 257.508778708813 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 108.64 & 0.418657043183037 & 259.496410651576 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 108.655681818182 & 0.417535606680957 & 260.230936187454 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 108.676666666667 & 0.416761708092028 & 260.764519764059 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 108.704 & 0.41605701039333 & 261.271886507173 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 108.737631578947 & 0.414892817948884 & 262.086078319014 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 108.777777777778 & 0.415304843307635 & 261.922728642972 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 108.822352941176 & 0.415599573072307 & 261.844236597046 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 108.8671875 & 0.416897680834617 & 261.136467063216 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 108.909333333333 & 0.420044588036434 & 259.280410783169 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 108.956428571429 & 0.422463239778888 & 257.907477650493 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 109.010384615385 & 0.424033917645286 & 257.079398791335 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 109.069166666667 & 0.424791046957065 & 256.759570259235 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 109.135909090909 & 0.424495962427532 & 257.095281817999 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 109.2125 & 0.421089986007492 & 259.356678213803 \tabularnewline
Median & 110.33 &  &  \tabularnewline
Midrange & 108.14 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.829655172414 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.909333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.909333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.909333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.956428571429 &  &  \tabularnewline
Midmean - Closest Observation & 108.909333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.909333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.909333333333 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102074&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]108.556724137931[/C][C]0.439351140384580[/C][C]247.084197944513[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.505756338942[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.454521785266[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.607389402189[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]108.560862068966[/C][C]0.437220243940049[/C][C]248.297885501961[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]108.551551724138[/C][C]0.434418400561914[/C][C]249.877886350412[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]108.562413793103[/C][C]0.430585099076328[/C][C]252.127660771324[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]108.576896551724[/C][C]0.424662650845803[/C][C]255.677998372286[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]108.576896551724[/C][C]0.424036091138258[/C][C]256.055790582039[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]108.568620689655[/C][C]0.411676845428621[/C][C]263.722922227064[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]108.549310344828[/C][C]0.405758821889029[/C][C]267.521750579498[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]108.525862068966[/C][C]0.400379284371793[/C][C]271.057635360046[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]108.505689655172[/C][C]0.396420852835917[/C][C]273.71337526506[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]108.488448275862[/C][C]0.382959137838137[/C][C]283.28988019008[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]108.490344827586[/C][C]0.377284047638346[/C][C]287.556141073799[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]108.525517241379[/C][C]0.366676195147638[/C][C]295.970992056582[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]108.583793103448[/C][C]0.353415178536828[/C][C]307.241453389171[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]108.591034482759[/C][C]0.350775537770345[/C][C]309.574137275941[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]108.593620689655[/C][C]0.346519091594439[/C][C]313.384235742923[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]108.621206896552[/C][C]0.340376031124695[/C][C]319.121198216096[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]108.638793103448[/C][C]0.332387200284031[/C][C]326.844093306284[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]108.660517241379[/C][C]0.327089719123899[/C][C]332.204012808546[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]108.634310344828[/C][C]0.32089353773036[/C][C]338.536921351500[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]108.571607142857[/C][C]0.4343941726058[/C][C]249.937991781908[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]108.583148148148[/C][C]0.430488795046587[/C][C]252.232228567988[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]108.600769230769[/C][C]0.427020602234327[/C][C]254.322083437030[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]108.6156[/C][C]0.423986634367699[/C][C]256.176943317991[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]108.627291666667[/C][C]0.421839178498457[/C][C]257.508778708813[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]108.64[/C][C]0.418657043183037[/C][C]259.496410651576[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]108.655681818182[/C][C]0.417535606680957[/C][C]260.230936187454[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]108.676666666667[/C][C]0.416761708092028[/C][C]260.764519764059[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]108.704[/C][C]0.41605701039333[/C][C]261.271886507173[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]108.737631578947[/C][C]0.414892817948884[/C][C]262.086078319014[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]108.777777777778[/C][C]0.415304843307635[/C][C]261.922728642972[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]108.822352941176[/C][C]0.415599573072307[/C][C]261.844236597046[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]108.8671875[/C][C]0.416897680834617[/C][C]261.136467063216[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]108.909333333333[/C][C]0.420044588036434[/C][C]259.280410783169[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]108.956428571429[/C][C]0.422463239778888[/C][C]257.907477650493[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]109.010384615385[/C][C]0.424033917645286[/C][C]257.079398791335[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]109.069166666667[/C][C]0.424791046957065[/C][C]256.759570259235[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]109.135909090909[/C][C]0.424495962427532[/C][C]257.095281817999[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]109.2125[/C][C]0.421089986007492[/C][C]259.356678213803[/C][/ROW]
[ROW][C]Median[/C][C]110.33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.829655172414[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.909333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.909333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.909333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.956428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.909333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.909333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.909333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102074&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102074&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.5567241379310.439351140384580247.084197944513
Geometric Mean108.505756338942
Harmonic Mean108.454521785266
Quadratic Mean108.607389402189
Winsorized Mean ( 1 / 19 )108.5608620689660.437220243940049248.297885501961
Winsorized Mean ( 2 / 19 )108.5515517241380.434418400561914249.877886350412
Winsorized Mean ( 3 / 19 )108.5624137931030.430585099076328252.127660771324
Winsorized Mean ( 4 / 19 )108.5768965517240.424662650845803255.677998372286
Winsorized Mean ( 5 / 19 )108.5768965517240.424036091138258256.055790582039
Winsorized Mean ( 6 / 19 )108.5686206896550.411676845428621263.722922227064
Winsorized Mean ( 7 / 19 )108.5493103448280.405758821889029267.521750579498
Winsorized Mean ( 8 / 19 )108.5258620689660.400379284371793271.057635360046
Winsorized Mean ( 9 / 19 )108.5056896551720.396420852835917273.71337526506
Winsorized Mean ( 10 / 19 )108.4884482758620.382959137838137283.28988019008
Winsorized Mean ( 11 / 19 )108.4903448275860.377284047638346287.556141073799
Winsorized Mean ( 12 / 19 )108.5255172413790.366676195147638295.970992056582
Winsorized Mean ( 13 / 19 )108.5837931034480.353415178536828307.241453389171
Winsorized Mean ( 14 / 19 )108.5910344827590.350775537770345309.574137275941
Winsorized Mean ( 15 / 19 )108.5936206896550.346519091594439313.384235742923
Winsorized Mean ( 16 / 19 )108.6212068965520.340376031124695319.121198216096
Winsorized Mean ( 17 / 19 )108.6387931034480.332387200284031326.844093306284
Winsorized Mean ( 18 / 19 )108.6605172413790.327089719123899332.204012808546
Winsorized Mean ( 19 / 19 )108.6343103448280.32089353773036338.536921351500
Trimmed Mean ( 1 / 19 )108.5716071428570.4343941726058249.937991781908
Trimmed Mean ( 2 / 19 )108.5831481481480.430488795046587252.232228567988
Trimmed Mean ( 3 / 19 )108.6007692307690.427020602234327254.322083437030
Trimmed Mean ( 4 / 19 )108.61560.423986634367699256.176943317991
Trimmed Mean ( 5 / 19 )108.6272916666670.421839178498457257.508778708813
Trimmed Mean ( 6 / 19 )108.640.418657043183037259.496410651576
Trimmed Mean ( 7 / 19 )108.6556818181820.417535606680957260.230936187454
Trimmed Mean ( 8 / 19 )108.6766666666670.416761708092028260.764519764059
Trimmed Mean ( 9 / 19 )108.7040.41605701039333261.271886507173
Trimmed Mean ( 10 / 19 )108.7376315789470.414892817948884262.086078319014
Trimmed Mean ( 11 / 19 )108.7777777777780.415304843307635261.922728642972
Trimmed Mean ( 12 / 19 )108.8223529411760.415599573072307261.844236597046
Trimmed Mean ( 13 / 19 )108.86718750.416897680834617261.136467063216
Trimmed Mean ( 14 / 19 )108.9093333333330.420044588036434259.280410783169
Trimmed Mean ( 15 / 19 )108.9564285714290.422463239778888257.907477650493
Trimmed Mean ( 16 / 19 )109.0103846153850.424033917645286257.079398791335
Trimmed Mean ( 17 / 19 )109.0691666666670.424791046957065256.759570259235
Trimmed Mean ( 18 / 19 )109.1359090909090.424495962427532257.095281817999
Trimmed Mean ( 19 / 19 )109.21250.421089986007492259.356678213803
Median110.33
Midrange108.14
Midmean - Weighted Average at Xnp108.829655172414
Midmean - Weighted Average at X(n+1)p108.909333333333
Midmean - Empirical Distribution Function108.909333333333
Midmean - Empirical Distribution Function - Averaging108.909333333333
Midmean - Empirical Distribution Function - Interpolation108.956428571429
Midmean - Closest Observation108.909333333333
Midmean - True Basic - Statistics Graphics Toolkit108.909333333333
Midmean - MS Excel (old versions)108.909333333333
Number of observations58



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')