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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 15:06:35 +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/2016/Mar/05/t1457190428rfxsrmgiawkxy1z.htm/, Retrieved Sat, 27 Apr 2024 08:18:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293477, Retrieved Sat, 27 Apr 2024 08:18:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid Index...] [2016-03-05 15:06:35] [b2b9e3f51b35fbbda207a2f484be6b24] [Current]
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Dataseries X:
90,75
92,82
97,78
99,32
98,33
98,66
98,13
97,8
99,36
100,37
103,22
101,68
104,39
103,99
106,71
106,06
103,5
100,17
101,1
105,93
108,09
107,27
104,9
102,7
102,06
103,05
102,08
100,13
97,56
97,38
99,66
99,58
102,7
98,92
97,85
99,01
97,71
97,95
97,24
96,69
96,41
96,99
98,36
97,8
96,79
94,73
92,67
87,15
79,54
82,35
86,38
84,75
87,54
86,73
84,74
80,75
79,28
78,52
78,54
77,33




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293477&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293477&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293477&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.16583333333331.0509531399420591.5034454710666
Geometric Mean95.8063326322916
Harmonic Mean95.4254703795614
Quadratic Mean96.5040576780756
Winsorized Mean ( 1 / 20 )96.1721.0425468814398792.2471705705704
Winsorized Mean ( 2 / 20 )96.1541.0390642574323592.5390314527877
Winsorized Mean ( 3 / 20 )96.15851.0231102967806293.9864453545018
Winsorized Mean ( 4 / 20 )96.16716666666671.016869047884894.5718299388746
Winsorized Mean ( 5 / 20 )96.18216666666670.97588230661558298.5591869169472
Winsorized Mean ( 6 / 20 )96.29116666666670.926365661341266103.945094993319
Winsorized Mean ( 7 / 20 )96.52333333333330.851039333561794113.418181189536
Winsorized Mean ( 8 / 20 )96.45933333333330.841232679967662114.66427259702
Winsorized Mean ( 9 / 20 )96.66183333333330.77901156013799124.082668704186
Winsorized Mean ( 10 / 20 )96.69183333333330.76199824620061126.892461781175
Winsorized Mean ( 11 / 20 )96.70466666666670.736026723088103131.387439658344
Winsorized Mean ( 12 / 20 )96.78266666666670.718946886240844134.617269396233
Winsorized Mean ( 13 / 20 )97.34383333333330.553123441830186175.989346991406
Winsorized Mean ( 14 / 20 )97.78716666666670.465090058204919210.254261387763
Winsorized Mean ( 15 / 20 )97.72966666666670.443503193745574220.358428180185
Winsorized Mean ( 16 / 20 )98.08433333333330.327250259862444299.722705719353
Winsorized Mean ( 17 / 20 )98.35350.216124679568633455.077597784323
Winsorized Mean ( 18 / 20 )98.37750.194079258228633506.893425386589
Winsorized Mean ( 19 / 20 )98.39650.187461457432184524.889229753245
Winsorized Mean ( 20 / 20 )98.30650.153759079471015639.354113839706
Trimmed Mean ( 1 / 20 )96.2851.015925942313894.7756091164561
Trimmed Mean ( 2 / 20 )96.40607142857140.98281574942093498.0917038472094
Trimmed Mean ( 3 / 20 )96.54611111111110.943666238147436102.309595499195
Trimmed Mean ( 4 / 20 )96.69519230769230.902242826754645107.172026687653
Trimmed Mean ( 5 / 20 )96.85360.851889317329189113.692704004849
Trimmed Mean ( 6 / 20 )97.02145833333330.802417611907436120.91142678524
Trimmed Mean ( 7 / 20 )97.18021739130440.755614507519512128.610841142161
Trimmed Mean ( 8 / 20 )97.30818181818180.719709190208179135.204862105533
Trimmed Mean ( 9 / 20 )97.45976190476190.674321226065732144.53017069236
Trimmed Mean ( 10 / 20 )97.592750.633650492870782154.016687587272
Trimmed Mean ( 11 / 20 )97.7350.582955113448604167.65441754482
Trimmed Mean ( 12 / 20 )97.89111111111110.519645449607769188.380579845354
Trimmed Mean ( 13 / 20 )98.05411764705880.431662647552242227.154511058759
Trimmed Mean ( 14 / 20 )98.15656250.37455823693768262.059548609878
Trimmed Mean ( 15 / 20 )98.20933333333330.328263957896142299.177935837858
Trimmed Mean ( 16 / 20 )98.27785714285710.263590570131277372.842841433635
Trimmed Mean ( 17 / 20 )98.30576923076920.221723440401931443.371116073991
Trimmed Mean ( 18 / 20 )98.298750.208942569340498470.458223569607
Trimmed Mean ( 19 / 20 )98.28681818181820.197417730537504497.862162198985
Trimmed Mean ( 20 / 20 )98.26950.180365819786811544.834382235795
Median98.04
Midrange92.71
Midmean - Weighted Average at Xnp98.0306451612903
Midmean - Weighted Average at X(n+1)p98.2093333333333
Midmean - Empirical Distribution Function98.0306451612903
Midmean - Empirical Distribution Function - Averaging98.2093333333333
Midmean - Empirical Distribution Function - Interpolation98.2093333333333
Midmean - Closest Observation98.0306451612903
Midmean - True Basic - Statistics Graphics Toolkit98.2093333333333
Midmean - MS Excel (old versions)98.1565625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.1658333333333 & 1.05095313994205 & 91.5034454710666 \tabularnewline
Geometric Mean & 95.8063326322916 &  &  \tabularnewline
Harmonic Mean & 95.4254703795614 &  &  \tabularnewline
Quadratic Mean & 96.5040576780756 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 96.172 & 1.04254688143987 & 92.2471705705704 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 96.154 & 1.03906425743235 & 92.5390314527877 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96.1585 & 1.02311029678062 & 93.9864453545018 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96.1671666666667 & 1.0168690478848 & 94.5718299388746 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96.1821666666667 & 0.975882306615582 & 98.5591869169472 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 96.2911666666667 & 0.926365661341266 & 103.945094993319 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 96.5233333333333 & 0.851039333561794 & 113.418181189536 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 96.4593333333333 & 0.841232679967662 & 114.66427259702 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 96.6618333333333 & 0.77901156013799 & 124.082668704186 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 96.6918333333333 & 0.76199824620061 & 126.892461781175 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 96.7046666666667 & 0.736026723088103 & 131.387439658344 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 96.7826666666667 & 0.718946886240844 & 134.617269396233 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.3438333333333 & 0.553123441830186 & 175.989346991406 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.7871666666667 & 0.465090058204919 & 210.254261387763 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.7296666666667 & 0.443503193745574 & 220.358428180185 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 98.0843333333333 & 0.327250259862444 & 299.722705719353 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 98.3535 & 0.216124679568633 & 455.077597784323 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 98.3775 & 0.194079258228633 & 506.893425386589 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 98.3965 & 0.187461457432184 & 524.889229753245 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 98.3065 & 0.153759079471015 & 639.354113839706 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96.285 & 1.0159259423138 & 94.7756091164561 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96.4060714285714 & 0.982815749420934 & 98.0917038472094 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 96.5461111111111 & 0.943666238147436 & 102.309595499195 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 96.6951923076923 & 0.902242826754645 & 107.172026687653 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 96.8536 & 0.851889317329189 & 113.692704004849 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.0214583333333 & 0.802417611907436 & 120.91142678524 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.1802173913044 & 0.755614507519512 & 128.610841142161 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.3081818181818 & 0.719709190208179 & 135.204862105533 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.4597619047619 & 0.674321226065732 & 144.53017069236 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.59275 & 0.633650492870782 & 154.016687587272 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.735 & 0.582955113448604 & 167.65441754482 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.8911111111111 & 0.519645449607769 & 188.380579845354 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 98.0541176470588 & 0.431662647552242 & 227.154511058759 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 98.1565625 & 0.37455823693768 & 262.059548609878 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 98.2093333333333 & 0.328263957896142 & 299.177935837858 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 98.2778571428571 & 0.263590570131277 & 372.842841433635 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 98.3057692307692 & 0.221723440401931 & 443.371116073991 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 98.29875 & 0.208942569340498 & 470.458223569607 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 98.2868181818182 & 0.197417730537504 & 497.862162198985 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 98.2695 & 0.180365819786811 & 544.834382235795 \tabularnewline
Median & 98.04 &  &  \tabularnewline
Midrange & 92.71 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.0306451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.2093333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.0306451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.2093333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.2093333333333 &  &  \tabularnewline
Midmean - Closest Observation & 98.0306451612903 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.2093333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.1565625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293477&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]96.1658333333333[/C][C]1.05095313994205[/C][C]91.5034454710666[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.8063326322916[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.4254703795614[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.5040576780756[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]96.172[/C][C]1.04254688143987[/C][C]92.2471705705704[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]96.154[/C][C]1.03906425743235[/C][C]92.5390314527877[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96.1585[/C][C]1.02311029678062[/C][C]93.9864453545018[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96.1671666666667[/C][C]1.0168690478848[/C][C]94.5718299388746[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96.1821666666667[/C][C]0.975882306615582[/C][C]98.5591869169472[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]96.2911666666667[/C][C]0.926365661341266[/C][C]103.945094993319[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]96.5233333333333[/C][C]0.851039333561794[/C][C]113.418181189536[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]96.4593333333333[/C][C]0.841232679967662[/C][C]114.66427259702[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]96.6618333333333[/C][C]0.77901156013799[/C][C]124.082668704186[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]96.6918333333333[/C][C]0.76199824620061[/C][C]126.892461781175[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]96.7046666666667[/C][C]0.736026723088103[/C][C]131.387439658344[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]96.7826666666667[/C][C]0.718946886240844[/C][C]134.617269396233[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.3438333333333[/C][C]0.553123441830186[/C][C]175.989346991406[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.7871666666667[/C][C]0.465090058204919[/C][C]210.254261387763[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.7296666666667[/C][C]0.443503193745574[/C][C]220.358428180185[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]98.0843333333333[/C][C]0.327250259862444[/C][C]299.722705719353[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]98.3535[/C][C]0.216124679568633[/C][C]455.077597784323[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]98.3775[/C][C]0.194079258228633[/C][C]506.893425386589[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]98.3965[/C][C]0.187461457432184[/C][C]524.889229753245[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]98.3065[/C][C]0.153759079471015[/C][C]639.354113839706[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96.285[/C][C]1.0159259423138[/C][C]94.7756091164561[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96.4060714285714[/C][C]0.982815749420934[/C][C]98.0917038472094[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]96.5461111111111[/C][C]0.943666238147436[/C][C]102.309595499195[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]96.6951923076923[/C][C]0.902242826754645[/C][C]107.172026687653[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]96.8536[/C][C]0.851889317329189[/C][C]113.692704004849[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.0214583333333[/C][C]0.802417611907436[/C][C]120.91142678524[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.1802173913044[/C][C]0.755614507519512[/C][C]128.610841142161[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.3081818181818[/C][C]0.719709190208179[/C][C]135.204862105533[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.4597619047619[/C][C]0.674321226065732[/C][C]144.53017069236[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.59275[/C][C]0.633650492870782[/C][C]154.016687587272[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.735[/C][C]0.582955113448604[/C][C]167.65441754482[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.8911111111111[/C][C]0.519645449607769[/C][C]188.380579845354[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]98.0541176470588[/C][C]0.431662647552242[/C][C]227.154511058759[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]98.1565625[/C][C]0.37455823693768[/C][C]262.059548609878[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]98.2093333333333[/C][C]0.328263957896142[/C][C]299.177935837858[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]98.2778571428571[/C][C]0.263590570131277[/C][C]372.842841433635[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]98.3057692307692[/C][C]0.221723440401931[/C][C]443.371116073991[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]98.29875[/C][C]0.208942569340498[/C][C]470.458223569607[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]98.2868181818182[/C][C]0.197417730537504[/C][C]497.862162198985[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]98.2695[/C][C]0.180365819786811[/C][C]544.834382235795[/C][/ROW]
[ROW][C]Median[/C][C]98.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92.71[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.0306451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.2093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.0306451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.2093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.2093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.0306451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.2093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.1565625[/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=293477&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293477&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 Mean96.16583333333331.0509531399420591.5034454710666
Geometric Mean95.8063326322916
Harmonic Mean95.4254703795614
Quadratic Mean96.5040576780756
Winsorized Mean ( 1 / 20 )96.1721.0425468814398792.2471705705704
Winsorized Mean ( 2 / 20 )96.1541.0390642574323592.5390314527877
Winsorized Mean ( 3 / 20 )96.15851.0231102967806293.9864453545018
Winsorized Mean ( 4 / 20 )96.16716666666671.016869047884894.5718299388746
Winsorized Mean ( 5 / 20 )96.18216666666670.97588230661558298.5591869169472
Winsorized Mean ( 6 / 20 )96.29116666666670.926365661341266103.945094993319
Winsorized Mean ( 7 / 20 )96.52333333333330.851039333561794113.418181189536
Winsorized Mean ( 8 / 20 )96.45933333333330.841232679967662114.66427259702
Winsorized Mean ( 9 / 20 )96.66183333333330.77901156013799124.082668704186
Winsorized Mean ( 10 / 20 )96.69183333333330.76199824620061126.892461781175
Winsorized Mean ( 11 / 20 )96.70466666666670.736026723088103131.387439658344
Winsorized Mean ( 12 / 20 )96.78266666666670.718946886240844134.617269396233
Winsorized Mean ( 13 / 20 )97.34383333333330.553123441830186175.989346991406
Winsorized Mean ( 14 / 20 )97.78716666666670.465090058204919210.254261387763
Winsorized Mean ( 15 / 20 )97.72966666666670.443503193745574220.358428180185
Winsorized Mean ( 16 / 20 )98.08433333333330.327250259862444299.722705719353
Winsorized Mean ( 17 / 20 )98.35350.216124679568633455.077597784323
Winsorized Mean ( 18 / 20 )98.37750.194079258228633506.893425386589
Winsorized Mean ( 19 / 20 )98.39650.187461457432184524.889229753245
Winsorized Mean ( 20 / 20 )98.30650.153759079471015639.354113839706
Trimmed Mean ( 1 / 20 )96.2851.015925942313894.7756091164561
Trimmed Mean ( 2 / 20 )96.40607142857140.98281574942093498.0917038472094
Trimmed Mean ( 3 / 20 )96.54611111111110.943666238147436102.309595499195
Trimmed Mean ( 4 / 20 )96.69519230769230.902242826754645107.172026687653
Trimmed Mean ( 5 / 20 )96.85360.851889317329189113.692704004849
Trimmed Mean ( 6 / 20 )97.02145833333330.802417611907436120.91142678524
Trimmed Mean ( 7 / 20 )97.18021739130440.755614507519512128.610841142161
Trimmed Mean ( 8 / 20 )97.30818181818180.719709190208179135.204862105533
Trimmed Mean ( 9 / 20 )97.45976190476190.674321226065732144.53017069236
Trimmed Mean ( 10 / 20 )97.592750.633650492870782154.016687587272
Trimmed Mean ( 11 / 20 )97.7350.582955113448604167.65441754482
Trimmed Mean ( 12 / 20 )97.89111111111110.519645449607769188.380579845354
Trimmed Mean ( 13 / 20 )98.05411764705880.431662647552242227.154511058759
Trimmed Mean ( 14 / 20 )98.15656250.37455823693768262.059548609878
Trimmed Mean ( 15 / 20 )98.20933333333330.328263957896142299.177935837858
Trimmed Mean ( 16 / 20 )98.27785714285710.263590570131277372.842841433635
Trimmed Mean ( 17 / 20 )98.30576923076920.221723440401931443.371116073991
Trimmed Mean ( 18 / 20 )98.298750.208942569340498470.458223569607
Trimmed Mean ( 19 / 20 )98.28681818181820.197417730537504497.862162198985
Trimmed Mean ( 20 / 20 )98.26950.180365819786811544.834382235795
Median98.04
Midrange92.71
Midmean - Weighted Average at Xnp98.0306451612903
Midmean - Weighted Average at X(n+1)p98.2093333333333
Midmean - Empirical Distribution Function98.0306451612903
Midmean - Empirical Distribution Function - Averaging98.2093333333333
Midmean - Empirical Distribution Function - Interpolation98.2093333333333
Midmean - Closest Observation98.0306451612903
Midmean - True Basic - Statistics Graphics Toolkit98.2093333333333
Midmean - MS Excel (old versions)98.1565625
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')