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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Mar 2012 09:35:01 -0500
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/Mar/06/t1331044588ezjbxp7pkngijcd.htm/, Retrieved Wed, 01 May 2024 22:28:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163533, Retrieved Wed, 01 May 2024 22:28:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [rekenkundig gemid...] [2012-03-06 14:35:01] [6aa41422895d0082cb99bdd8f056be10] [Current]
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Dataseries X:
86,9
85,8
84,4
80,4
84,4
90,7
91,6
91,9
92,5
92,5
92
92
94,5
95,5
96,3
100
103,1
109,2
108,7
107,5
104,5
103,8
102,5
100,8
100,7
102,7
106,5
105,5
110,1
110,1
109
106,9
108
106,1
101,7
100,6
102,6
100,5
105,2
104,3
104,1
104,8
105,2
102,7
101
93,9
90,2
92,4
94,4
93,3
93,9
95,1
97,6
99,3
101,1
100,6
99,3
97
96,4
98,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163533&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163533&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.88333333333330.915954525635424107.956596715034
Geometric Mean98.6259931639483
Harmonic Mean98.3614195913027
Quadratic Mean99.1333092355945
Winsorized Mean ( 1 / 20 )98.950.895347358657726110.515766917928
Winsorized Mean ( 2 / 20 )98.920.889241408440855111.240883590251
Winsorized Mean ( 3 / 20 )98.980.868588048352102113.955056355871
Winsorized Mean ( 4 / 20 )99.03333333333330.846350312355413117.012225183354
Winsorized Mean ( 5 / 20 )99.250.774186286871358128.199119104898
Winsorized Mean ( 6 / 20 )99.250.75501150513178131.45495045493
Winsorized Mean ( 7 / 20 )99.2850.722721727164235137.37652580277
Winsorized Mean ( 8 / 20 )99.27166666666670.706187710784125140.574050143749
Winsorized Mean ( 9 / 20 )99.22666666666670.693288514414061143.124636574326
Winsorized Mean ( 10 / 20 )99.12666666666670.676902494320508146.441573931815
Winsorized Mean ( 11 / 20 )99.1450.655263025638072151.305653029112
Winsorized Mean ( 12 / 20 )99.1650.651785141021562152.143695458561
Winsorized Mean ( 13 / 20 )99.07833333333330.638399710375213155.197960968844
Winsorized Mean ( 14 / 20 )99.1950.59582552047345166.483301892102
Winsorized Mean ( 15 / 20 )99.2950.563531164072898176.201435395958
Winsorized Mean ( 16 / 20 )99.24166666666670.55556400652706178.632282690605
Winsorized Mean ( 17 / 20 )99.29833333333330.520172133975108190.895141911014
Winsorized Mean ( 18 / 20 )99.11833333333330.485329939998691204.228763083523
Winsorized Mean ( 19 / 20 )99.18166666666670.437523149777629226.688957411912
Winsorized Mean ( 20 / 20 )99.3150.41663045040346238.376719473636
Trimmed Mean ( 1 / 20 )99.00862068965520.869877311174293113.819063237778
Trimmed Mean ( 2 / 20 )99.07142857142860.838395631919395118.167873017918
Trimmed Mean ( 3 / 20 )99.15555555555560.803280601741346123.438254752582
Trimmed Mean ( 4 / 20 )99.22307692307690.769716287199319128.908636303006
Trimmed Mean ( 5 / 20 )99.280.736616644960357134.778382594576
Trimmed Mean ( 6 / 20 )99.28750.720425313949144137.8178946208
Trimmed Mean ( 7 / 20 )99.2956521739130.705293693043369140.786247138335
Trimmed Mean ( 8 / 20 )99.29772727272730.694530798440719142.970948870315
Trimmed Mean ( 9 / 20 )99.3023809523810.68417051429276145.14273690241
Trimmed Mean ( 10 / 20 )99.3150.672972262925201147.576661730914
Trimmed Mean ( 11 / 20 )99.34473684210530.661216790419013150.245332970372
Trimmed Mean ( 12 / 20 )99.3750.649888574088019152.910828043795
Trimmed Mean ( 13 / 20 )99.40588235294120.633960771523077156.801314557872
Trimmed Mean ( 14 / 20 )99.4531250.614081801695333161.954196860147
Trimmed Mean ( 15 / 20 )99.490.597607298113586166.480563932287
Trimmed Mean ( 16 / 20 )99.51785714285710.582256456602006170.917567361355
Trimmed Mean ( 17 / 20 )99.55769230769230.559812415750492177.841165194995
Trimmed Mean ( 18 / 20 )99.59583333333330.536814246293962185.531278316325
Trimmed Mean ( 19 / 20 )99.66818181818180.511147862124019194.988943911497
Trimmed Mean ( 20 / 20 )99.7450.488093767954262204.35622527626
Median100.55
Midrange95.25
Midmean - Weighted Average at Xnp99.2903225806451
Midmean - Weighted Average at X(n+1)p99.49
Midmean - Empirical Distribution Function99.2903225806451
Midmean - Empirical Distribution Function - Averaging99.49
Midmean - Empirical Distribution Function - Interpolation99.49
Midmean - Closest Observation99.2903225806451
Midmean - True Basic - Statistics Graphics Toolkit99.49
Midmean - MS Excel (old versions)99.453125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.8833333333333 & 0.915954525635424 & 107.956596715034 \tabularnewline
Geometric Mean & 98.6259931639483 &  &  \tabularnewline
Harmonic Mean & 98.3614195913027 &  &  \tabularnewline
Quadratic Mean & 99.1333092355945 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 98.95 & 0.895347358657726 & 110.515766917928 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 98.92 & 0.889241408440855 & 111.240883590251 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 98.98 & 0.868588048352102 & 113.955056355871 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.0333333333333 & 0.846350312355413 & 117.012225183354 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.25 & 0.774186286871358 & 128.199119104898 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.25 & 0.75501150513178 & 131.45495045493 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.285 & 0.722721727164235 & 137.37652580277 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.2716666666667 & 0.706187710784125 & 140.574050143749 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.2266666666667 & 0.693288514414061 & 143.124636574326 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.1266666666667 & 0.676902494320508 & 146.441573931815 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.145 & 0.655263025638072 & 151.305653029112 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 99.165 & 0.651785141021562 & 152.143695458561 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 99.0783333333333 & 0.638399710375213 & 155.197960968844 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 99.195 & 0.59582552047345 & 166.483301892102 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.295 & 0.563531164072898 & 176.201435395958 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.2416666666667 & 0.55556400652706 & 178.632282690605 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.2983333333333 & 0.520172133975108 & 190.895141911014 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.1183333333333 & 0.485329939998691 & 204.228763083523 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.1816666666667 & 0.437523149777629 & 226.688957411912 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 99.315 & 0.41663045040346 & 238.376719473636 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.0086206896552 & 0.869877311174293 & 113.819063237778 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.0714285714286 & 0.838395631919395 & 118.167873017918 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.1555555555556 & 0.803280601741346 & 123.438254752582 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.2230769230769 & 0.769716287199319 & 128.908636303006 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.28 & 0.736616644960357 & 134.778382594576 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.2875 & 0.720425313949144 & 137.8178946208 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.295652173913 & 0.705293693043369 & 140.786247138335 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.2977272727273 & 0.694530798440719 & 142.970948870315 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.302380952381 & 0.68417051429276 & 145.14273690241 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.315 & 0.672972262925201 & 147.576661730914 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.3447368421053 & 0.661216790419013 & 150.245332970372 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.375 & 0.649888574088019 & 152.910828043795 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.4058823529412 & 0.633960771523077 & 156.801314557872 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.453125 & 0.614081801695333 & 161.954196860147 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.49 & 0.597607298113586 & 166.480563932287 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.5178571428571 & 0.582256456602006 & 170.917567361355 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.5576923076923 & 0.559812415750492 & 177.841165194995 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.5958333333333 & 0.536814246293962 & 185.531278316325 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.6681818181818 & 0.511147862124019 & 194.988943911497 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.745 & 0.488093767954262 & 204.35622527626 \tabularnewline
Median & 100.55 &  &  \tabularnewline
Midrange & 95.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.2903225806451 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.49 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.2903225806451 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.49 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.49 &  &  \tabularnewline
Midmean - Closest Observation & 99.2903225806451 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.49 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.453125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163533&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]98.8833333333333[/C][C]0.915954525635424[/C][C]107.956596715034[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.6259931639483[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.3614195913027[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.1333092355945[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]98.95[/C][C]0.895347358657726[/C][C]110.515766917928[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]98.92[/C][C]0.889241408440855[/C][C]111.240883590251[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]98.98[/C][C]0.868588048352102[/C][C]113.955056355871[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.0333333333333[/C][C]0.846350312355413[/C][C]117.012225183354[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.25[/C][C]0.774186286871358[/C][C]128.199119104898[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.25[/C][C]0.75501150513178[/C][C]131.45495045493[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.285[/C][C]0.722721727164235[/C][C]137.37652580277[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.2716666666667[/C][C]0.706187710784125[/C][C]140.574050143749[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.2266666666667[/C][C]0.693288514414061[/C][C]143.124636574326[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.1266666666667[/C][C]0.676902494320508[/C][C]146.441573931815[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.145[/C][C]0.655263025638072[/C][C]151.305653029112[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]99.165[/C][C]0.651785141021562[/C][C]152.143695458561[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]99.0783333333333[/C][C]0.638399710375213[/C][C]155.197960968844[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]99.195[/C][C]0.59582552047345[/C][C]166.483301892102[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.295[/C][C]0.563531164072898[/C][C]176.201435395958[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.2416666666667[/C][C]0.55556400652706[/C][C]178.632282690605[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.2983333333333[/C][C]0.520172133975108[/C][C]190.895141911014[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.1183333333333[/C][C]0.485329939998691[/C][C]204.228763083523[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.1816666666667[/C][C]0.437523149777629[/C][C]226.688957411912[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]99.315[/C][C]0.41663045040346[/C][C]238.376719473636[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.0086206896552[/C][C]0.869877311174293[/C][C]113.819063237778[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.0714285714286[/C][C]0.838395631919395[/C][C]118.167873017918[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.1555555555556[/C][C]0.803280601741346[/C][C]123.438254752582[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.2230769230769[/C][C]0.769716287199319[/C][C]128.908636303006[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.28[/C][C]0.736616644960357[/C][C]134.778382594576[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.2875[/C][C]0.720425313949144[/C][C]137.8178946208[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.295652173913[/C][C]0.705293693043369[/C][C]140.786247138335[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.2977272727273[/C][C]0.694530798440719[/C][C]142.970948870315[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.302380952381[/C][C]0.68417051429276[/C][C]145.14273690241[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.315[/C][C]0.672972262925201[/C][C]147.576661730914[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.3447368421053[/C][C]0.661216790419013[/C][C]150.245332970372[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.375[/C][C]0.649888574088019[/C][C]152.910828043795[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.4058823529412[/C][C]0.633960771523077[/C][C]156.801314557872[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.453125[/C][C]0.614081801695333[/C][C]161.954196860147[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.49[/C][C]0.597607298113586[/C][C]166.480563932287[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.5178571428571[/C][C]0.582256456602006[/C][C]170.917567361355[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.5576923076923[/C][C]0.559812415750492[/C][C]177.841165194995[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.5958333333333[/C][C]0.536814246293962[/C][C]185.531278316325[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.6681818181818[/C][C]0.511147862124019[/C][C]194.988943911497[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.745[/C][C]0.488093767954262[/C][C]204.35622527626[/C][/ROW]
[ROW][C]Median[/C][C]100.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.2903225806451[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.2903225806451[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.2903225806451[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.453125[/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=163533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163533&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 Mean98.88333333333330.915954525635424107.956596715034
Geometric Mean98.6259931639483
Harmonic Mean98.3614195913027
Quadratic Mean99.1333092355945
Winsorized Mean ( 1 / 20 )98.950.895347358657726110.515766917928
Winsorized Mean ( 2 / 20 )98.920.889241408440855111.240883590251
Winsorized Mean ( 3 / 20 )98.980.868588048352102113.955056355871
Winsorized Mean ( 4 / 20 )99.03333333333330.846350312355413117.012225183354
Winsorized Mean ( 5 / 20 )99.250.774186286871358128.199119104898
Winsorized Mean ( 6 / 20 )99.250.75501150513178131.45495045493
Winsorized Mean ( 7 / 20 )99.2850.722721727164235137.37652580277
Winsorized Mean ( 8 / 20 )99.27166666666670.706187710784125140.574050143749
Winsorized Mean ( 9 / 20 )99.22666666666670.693288514414061143.124636574326
Winsorized Mean ( 10 / 20 )99.12666666666670.676902494320508146.441573931815
Winsorized Mean ( 11 / 20 )99.1450.655263025638072151.305653029112
Winsorized Mean ( 12 / 20 )99.1650.651785141021562152.143695458561
Winsorized Mean ( 13 / 20 )99.07833333333330.638399710375213155.197960968844
Winsorized Mean ( 14 / 20 )99.1950.59582552047345166.483301892102
Winsorized Mean ( 15 / 20 )99.2950.563531164072898176.201435395958
Winsorized Mean ( 16 / 20 )99.24166666666670.55556400652706178.632282690605
Winsorized Mean ( 17 / 20 )99.29833333333330.520172133975108190.895141911014
Winsorized Mean ( 18 / 20 )99.11833333333330.485329939998691204.228763083523
Winsorized Mean ( 19 / 20 )99.18166666666670.437523149777629226.688957411912
Winsorized Mean ( 20 / 20 )99.3150.41663045040346238.376719473636
Trimmed Mean ( 1 / 20 )99.00862068965520.869877311174293113.819063237778
Trimmed Mean ( 2 / 20 )99.07142857142860.838395631919395118.167873017918
Trimmed Mean ( 3 / 20 )99.15555555555560.803280601741346123.438254752582
Trimmed Mean ( 4 / 20 )99.22307692307690.769716287199319128.908636303006
Trimmed Mean ( 5 / 20 )99.280.736616644960357134.778382594576
Trimmed Mean ( 6 / 20 )99.28750.720425313949144137.8178946208
Trimmed Mean ( 7 / 20 )99.2956521739130.705293693043369140.786247138335
Trimmed Mean ( 8 / 20 )99.29772727272730.694530798440719142.970948870315
Trimmed Mean ( 9 / 20 )99.3023809523810.68417051429276145.14273690241
Trimmed Mean ( 10 / 20 )99.3150.672972262925201147.576661730914
Trimmed Mean ( 11 / 20 )99.34473684210530.661216790419013150.245332970372
Trimmed Mean ( 12 / 20 )99.3750.649888574088019152.910828043795
Trimmed Mean ( 13 / 20 )99.40588235294120.633960771523077156.801314557872
Trimmed Mean ( 14 / 20 )99.4531250.614081801695333161.954196860147
Trimmed Mean ( 15 / 20 )99.490.597607298113586166.480563932287
Trimmed Mean ( 16 / 20 )99.51785714285710.582256456602006170.917567361355
Trimmed Mean ( 17 / 20 )99.55769230769230.559812415750492177.841165194995
Trimmed Mean ( 18 / 20 )99.59583333333330.536814246293962185.531278316325
Trimmed Mean ( 19 / 20 )99.66818181818180.511147862124019194.988943911497
Trimmed Mean ( 20 / 20 )99.7450.488093767954262204.35622527626
Median100.55
Midrange95.25
Midmean - Weighted Average at Xnp99.2903225806451
Midmean - Weighted Average at X(n+1)p99.49
Midmean - Empirical Distribution Function99.2903225806451
Midmean - Empirical Distribution Function - Averaging99.49
Midmean - Empirical Distribution Function - Interpolation99.49
Midmean - Closest Observation99.2903225806451
Midmean - True Basic - Statistics Graphics Toolkit99.49
Midmean - MS Excel (old versions)99.453125
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')