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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 15:39:32 +0100
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/Oct/13/t1476369707l9dhcvxdm6y5gwe.htm/, Retrieved Tue, 30 Apr 2024 18:14:26 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 18:14:26 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
99,6
96,1
109
99,5
104,6
99,9
94,1
105,3
110,4
110,5
110
108,5
101,5
99
106,2
97,6
103,7
103,4
99,9
105
103,4
117,8
110,6
102
105,1
98,5
104,4
103,9
105,8
100,3
106,3
101,4
104,3
114,6
105
103,4
102,9
96,4
102,6
104,7
100,8
102,1
101,1
98,1
109,2
114,4
104
107,2
101,3
98,1
109,6
105,9
99,5
109,9
105,3
102,5
111,9
118
112,1
113,8




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.70.689325388713794151.887630593962
Geometric Mean104.568012550809
Harmonic Mean104.437875994215
Quadratic Mean104.833797031301
Winsorized Mean ( 1 / 20 )104.730.680305265478144153.945596652691
Winsorized Mean ( 2 / 20 )104.6333333333330.646768004174685161.778771766627
Winsorized Mean ( 3 / 20 )104.6833333333330.631978181463233165.643904178714
Winsorized Mean ( 4 / 20 )104.6766666666670.615553430958961170.052933509919
Winsorized Mean ( 5 / 20 )104.5350.582095498600982179.583934682954
Winsorized Mean ( 6 / 20 )104.5550.570362284511538183.31331302795
Winsorized Mean ( 7 / 20 )104.4616666666670.528456293948644197.673237811448
Winsorized Mean ( 8 / 20 )104.5150.514478645656123203.147401515004
Winsorized Mean ( 9 / 20 )104.50.511533641774094204.287639103412
Winsorized Mean ( 10 / 20 )104.450.49592976083677210.614502795243
Winsorized Mean ( 11 / 20 )104.4866666666670.483469491828792216.118428220633
Winsorized Mean ( 12 / 20 )104.4266666666670.472204031997054221.147342230484
Winsorized Mean ( 13 / 20 )104.4266666666670.442328626629534236.083898666879
Winsorized Mean ( 14 / 20 )104.4966666666670.415749046064091251.345535620442
Winsorized Mean ( 15 / 20 )104.4466666666670.381792284363169273.56934894817
Winsorized Mean ( 16 / 20 )104.1533333333330.313756776023948331.955646195777
Winsorized Mean ( 17 / 20 )103.9266666666670.269136164334931386.14902208881
Winsorized Mean ( 18 / 20 )103.9266666666670.259909443885203399.857216087034
Winsorized Mean ( 19 / 20 )103.990.221279024716897469.949649014606
Winsorized Mean ( 20 / 20 )103.990.211354255857143492.017535101296
Trimmed Mean ( 1 / 20 )104.6534482758620.649054482472336161.239851356119
Trimmed Mean ( 2 / 20 )104.5714285714290.610076183691214171.407164165511
Trimmed Mean ( 3 / 20 )104.5370370370370.58485005751172178.741603415064
Trimmed Mean ( 4 / 20 )104.4807692307690.560576615855389186.380891167465
Trimmed Mean ( 5 / 20 )104.4220.536673731309397194.572593939389
Trimmed Mean ( 6 / 20 )104.393750.518576938576528201.308122737884
Trimmed Mean ( 7 / 20 )104.3586956521740.499057818448093209.111433173606
Trimmed Mean ( 8 / 20 )104.3386363636360.486533406777019214.453180213903
Trimmed Mean ( 9 / 20 )104.3071428571430.473727807403034220.18370301915
Trimmed Mean ( 10 / 20 )104.2750.457259815052163228.043218685431
Trimmed Mean ( 11 / 20 )104.2473684210530.439444509725742237.225329054887
Trimmed Mean ( 12 / 20 )104.2111111111110.418439614231704249.046953411552
Trimmed Mean ( 13 / 20 )104.1794117647060.392618600716528265.345074264385
Trimmed Mean ( 14 / 20 )104.143750.365689183090001284.787614224752
Trimmed Mean ( 15 / 20 )104.0933333333330.335313657702972310.435709796055
Trimmed Mean ( 16 / 20 )104.0428571428570.302914789362475343.472358552811
Trimmed Mean ( 17 / 20 )104.0269230769230.282492079796813368.247220069838
Trimmed Mean ( 18 / 20 )104.0416666666670.268511508043307387.47563344617
Trimmed Mean ( 19 / 20 )104.0590909090910.249124796254043417.698649326651
Trimmed Mean ( 20 / 20 )104.070.235316136740612442.256113165397
Median104.15
Midrange106.05
Midmean - Weighted Average at Xnp103.987096774194
Midmean - Weighted Average at X(n+1)p104.093333333333
Midmean - Empirical Distribution Function103.987096774194
Midmean - Empirical Distribution Function - Averaging104.093333333333
Midmean - Empirical Distribution Function - Interpolation104.093333333333
Midmean - Closest Observation103.987096774194
Midmean - True Basic - Statistics Graphics Toolkit104.093333333333
Midmean - MS Excel (old versions)104.14375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.7 & 0.689325388713794 & 151.887630593962 \tabularnewline
Geometric Mean & 104.568012550809 &  &  \tabularnewline
Harmonic Mean & 104.437875994215 &  &  \tabularnewline
Quadratic Mean & 104.833797031301 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 104.73 & 0.680305265478144 & 153.945596652691 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 104.633333333333 & 0.646768004174685 & 161.778771766627 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 104.683333333333 & 0.631978181463233 & 165.643904178714 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 104.676666666667 & 0.615553430958961 & 170.052933509919 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 104.535 & 0.582095498600982 & 179.583934682954 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 104.555 & 0.570362284511538 & 183.31331302795 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 104.461666666667 & 0.528456293948644 & 197.673237811448 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 104.515 & 0.514478645656123 & 203.147401515004 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 104.5 & 0.511533641774094 & 204.287639103412 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 104.45 & 0.49592976083677 & 210.614502795243 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 104.486666666667 & 0.483469491828792 & 216.118428220633 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 104.426666666667 & 0.472204031997054 & 221.147342230484 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 104.426666666667 & 0.442328626629534 & 236.083898666879 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 104.496666666667 & 0.415749046064091 & 251.345535620442 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 104.446666666667 & 0.381792284363169 & 273.56934894817 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 104.153333333333 & 0.313756776023948 & 331.955646195777 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.926666666667 & 0.269136164334931 & 386.14902208881 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.926666666667 & 0.259909443885203 & 399.857216087034 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.99 & 0.221279024716897 & 469.949649014606 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.99 & 0.211354255857143 & 492.017535101296 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 104.653448275862 & 0.649054482472336 & 161.239851356119 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 104.571428571429 & 0.610076183691214 & 171.407164165511 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 104.537037037037 & 0.58485005751172 & 178.741603415064 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 104.480769230769 & 0.560576615855389 & 186.380891167465 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 104.422 & 0.536673731309397 & 194.572593939389 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 104.39375 & 0.518576938576528 & 201.308122737884 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 104.358695652174 & 0.499057818448093 & 209.111433173606 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 104.338636363636 & 0.486533406777019 & 214.453180213903 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 104.307142857143 & 0.473727807403034 & 220.18370301915 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 104.275 & 0.457259815052163 & 228.043218685431 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 104.247368421053 & 0.439444509725742 & 237.225329054887 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 104.211111111111 & 0.418439614231704 & 249.046953411552 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 104.179411764706 & 0.392618600716528 & 265.345074264385 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 104.14375 & 0.365689183090001 & 284.787614224752 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 104.093333333333 & 0.335313657702972 & 310.435709796055 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 104.042857142857 & 0.302914789362475 & 343.472358552811 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 104.026923076923 & 0.282492079796813 & 368.247220069838 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 104.041666666667 & 0.268511508043307 & 387.47563344617 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 104.059090909091 & 0.249124796254043 & 417.698649326651 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 104.07 & 0.235316136740612 & 442.256113165397 \tabularnewline
Median & 104.15 &  &  \tabularnewline
Midrange & 106.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.987096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.093333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.987096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.093333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.093333333333 &  &  \tabularnewline
Midmean - Closest Observation & 103.987096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.093333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.14375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]104.7[/C][C]0.689325388713794[/C][C]151.887630593962[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.568012550809[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.437875994215[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.833797031301[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]104.73[/C][C]0.680305265478144[/C][C]153.945596652691[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]104.633333333333[/C][C]0.646768004174685[/C][C]161.778771766627[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]104.683333333333[/C][C]0.631978181463233[/C][C]165.643904178714[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]104.676666666667[/C][C]0.615553430958961[/C][C]170.052933509919[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]104.535[/C][C]0.582095498600982[/C][C]179.583934682954[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]104.555[/C][C]0.570362284511538[/C][C]183.31331302795[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]104.461666666667[/C][C]0.528456293948644[/C][C]197.673237811448[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]104.515[/C][C]0.514478645656123[/C][C]203.147401515004[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]104.5[/C][C]0.511533641774094[/C][C]204.287639103412[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]104.45[/C][C]0.49592976083677[/C][C]210.614502795243[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]104.486666666667[/C][C]0.483469491828792[/C][C]216.118428220633[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]104.426666666667[/C][C]0.472204031997054[/C][C]221.147342230484[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]104.426666666667[/C][C]0.442328626629534[/C][C]236.083898666879[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]104.496666666667[/C][C]0.415749046064091[/C][C]251.345535620442[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]104.446666666667[/C][C]0.381792284363169[/C][C]273.56934894817[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]104.153333333333[/C][C]0.313756776023948[/C][C]331.955646195777[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.926666666667[/C][C]0.269136164334931[/C][C]386.14902208881[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.926666666667[/C][C]0.259909443885203[/C][C]399.857216087034[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.99[/C][C]0.221279024716897[/C][C]469.949649014606[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.99[/C][C]0.211354255857143[/C][C]492.017535101296[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]104.653448275862[/C][C]0.649054482472336[/C][C]161.239851356119[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]104.571428571429[/C][C]0.610076183691214[/C][C]171.407164165511[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]104.537037037037[/C][C]0.58485005751172[/C][C]178.741603415064[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]104.480769230769[/C][C]0.560576615855389[/C][C]186.380891167465[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]104.422[/C][C]0.536673731309397[/C][C]194.572593939389[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]104.39375[/C][C]0.518576938576528[/C][C]201.308122737884[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]104.358695652174[/C][C]0.499057818448093[/C][C]209.111433173606[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]104.338636363636[/C][C]0.486533406777019[/C][C]214.453180213903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]104.307142857143[/C][C]0.473727807403034[/C][C]220.18370301915[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]104.275[/C][C]0.457259815052163[/C][C]228.043218685431[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]104.247368421053[/C][C]0.439444509725742[/C][C]237.225329054887[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]104.211111111111[/C][C]0.418439614231704[/C][C]249.046953411552[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]104.179411764706[/C][C]0.392618600716528[/C][C]265.345074264385[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]104.14375[/C][C]0.365689183090001[/C][C]284.787614224752[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]104.093333333333[/C][C]0.335313657702972[/C][C]310.435709796055[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]104.042857142857[/C][C]0.302914789362475[/C][C]343.472358552811[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]104.026923076923[/C][C]0.282492079796813[/C][C]368.247220069838[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]104.041666666667[/C][C]0.268511508043307[/C][C]387.47563344617[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]104.059090909091[/C][C]0.249124796254043[/C][C]417.698649326651[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]104.07[/C][C]0.235316136740612[/C][C]442.256113165397[/C][/ROW]
[ROW][C]Median[/C][C]104.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.987096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.987096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.987096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.093333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.14375[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean104.70.689325388713794151.887630593962
Geometric Mean104.568012550809
Harmonic Mean104.437875994215
Quadratic Mean104.833797031301
Winsorized Mean ( 1 / 20 )104.730.680305265478144153.945596652691
Winsorized Mean ( 2 / 20 )104.6333333333330.646768004174685161.778771766627
Winsorized Mean ( 3 / 20 )104.6833333333330.631978181463233165.643904178714
Winsorized Mean ( 4 / 20 )104.6766666666670.615553430958961170.052933509919
Winsorized Mean ( 5 / 20 )104.5350.582095498600982179.583934682954
Winsorized Mean ( 6 / 20 )104.5550.570362284511538183.31331302795
Winsorized Mean ( 7 / 20 )104.4616666666670.528456293948644197.673237811448
Winsorized Mean ( 8 / 20 )104.5150.514478645656123203.147401515004
Winsorized Mean ( 9 / 20 )104.50.511533641774094204.287639103412
Winsorized Mean ( 10 / 20 )104.450.49592976083677210.614502795243
Winsorized Mean ( 11 / 20 )104.4866666666670.483469491828792216.118428220633
Winsorized Mean ( 12 / 20 )104.4266666666670.472204031997054221.147342230484
Winsorized Mean ( 13 / 20 )104.4266666666670.442328626629534236.083898666879
Winsorized Mean ( 14 / 20 )104.4966666666670.415749046064091251.345535620442
Winsorized Mean ( 15 / 20 )104.4466666666670.381792284363169273.56934894817
Winsorized Mean ( 16 / 20 )104.1533333333330.313756776023948331.955646195777
Winsorized Mean ( 17 / 20 )103.9266666666670.269136164334931386.14902208881
Winsorized Mean ( 18 / 20 )103.9266666666670.259909443885203399.857216087034
Winsorized Mean ( 19 / 20 )103.990.221279024716897469.949649014606
Winsorized Mean ( 20 / 20 )103.990.211354255857143492.017535101296
Trimmed Mean ( 1 / 20 )104.6534482758620.649054482472336161.239851356119
Trimmed Mean ( 2 / 20 )104.5714285714290.610076183691214171.407164165511
Trimmed Mean ( 3 / 20 )104.5370370370370.58485005751172178.741603415064
Trimmed Mean ( 4 / 20 )104.4807692307690.560576615855389186.380891167465
Trimmed Mean ( 5 / 20 )104.4220.536673731309397194.572593939389
Trimmed Mean ( 6 / 20 )104.393750.518576938576528201.308122737884
Trimmed Mean ( 7 / 20 )104.3586956521740.499057818448093209.111433173606
Trimmed Mean ( 8 / 20 )104.3386363636360.486533406777019214.453180213903
Trimmed Mean ( 9 / 20 )104.3071428571430.473727807403034220.18370301915
Trimmed Mean ( 10 / 20 )104.2750.457259815052163228.043218685431
Trimmed Mean ( 11 / 20 )104.2473684210530.439444509725742237.225329054887
Trimmed Mean ( 12 / 20 )104.2111111111110.418439614231704249.046953411552
Trimmed Mean ( 13 / 20 )104.1794117647060.392618600716528265.345074264385
Trimmed Mean ( 14 / 20 )104.143750.365689183090001284.787614224752
Trimmed Mean ( 15 / 20 )104.0933333333330.335313657702972310.435709796055
Trimmed Mean ( 16 / 20 )104.0428571428570.302914789362475343.472358552811
Trimmed Mean ( 17 / 20 )104.0269230769230.282492079796813368.247220069838
Trimmed Mean ( 18 / 20 )104.0416666666670.268511508043307387.47563344617
Trimmed Mean ( 19 / 20 )104.0590909090910.249124796254043417.698649326651
Trimmed Mean ( 20 / 20 )104.070.235316136740612442.256113165397
Median104.15
Midrange106.05
Midmean - Weighted Average at Xnp103.987096774194
Midmean - Weighted Average at X(n+1)p104.093333333333
Midmean - Empirical Distribution Function103.987096774194
Midmean - Empirical Distribution Function - Averaging104.093333333333
Midmean - Empirical Distribution Function - Interpolation104.093333333333
Midmean - Closest Observation103.987096774194
Midmean - True Basic - Statistics Graphics Toolkit104.093333333333
Midmean - MS Excel (old versions)104.14375
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')