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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 computationTue, 13 Nov 2007 13:10:22 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/13/t1194984347jatqhe2xyyw091w.htm/, Retrieved Tue, 30 Apr 2024 04:04:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5382, Retrieved Tue, 30 Apr 2024 04:04:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact253
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-13 20:10:22] [bc15d8d2f79dc0888573b215bcd9118f] [Current]
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Dataseries X:
99,20
98,10
96,10
95,50
95,70
95,90
96,20
95,70
93,40
93,40
91,90
92,80
93,20
93,80
93,80
85,10
86,10
86,50
90,00
89,10
88,40
91,40
88,00
87,80
87,40
86,20
87,80
84,60
85,00
85,70
83,90
83,60
82,60
84,90
84,20
83,80
84,20
84,40
86,00
89,70
93,90
98,40
98,30
99,30
100,50
96,90
97,50
97,50
98,90
99,30
100,60
99,90
98,80
98,60
98,20
96,30
103,40
102,70
102,70
102,60
101,60
100,90
101,10
105,60
104,70
103,80
105,40
105,60
109,20
109,50
110,10
110,00
110,30
109,30
110,20
113,00
113,60
111,20
111,30
115,00




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5382&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5382&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5382&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.5850.98328611414912298.2267506986804
Geometric Mean96.1920610449796
Harmonic Mean95.8023510777396
Quadratic Mean96.9796035256899
Winsorized Mean ( 1 / 26 )96.580.9771056457916898.8429454030512
Winsorized Mean ( 2 / 26 )96.570.97301306793883699.2484101005624
Winsorized Mean ( 3 / 26 )96.510.959352036071183100.599150646759
Winsorized Mean ( 4 / 26 )96.520.955906687358504100.972198726549
Winsorized Mean ( 5 / 26 )96.463750.945226588182076102.053572345574
Winsorized Mean ( 6 / 26 )96.471250.941390356338076102.477414762633
Winsorized Mean ( 7 / 26 )96.480.93695304720046102.972075589353
Winsorized Mean ( 8 / 26 )96.50.93033953241256103.725571834786
Winsorized Mean ( 9 / 26 )96.4550.918339689227318105.03194093806
Winsorized Mean ( 10 / 26 )96.44250.911890120448814105.761097567910
Winsorized Mean ( 11 / 26 )96.511250.896639283958702107.636651356495
Winsorized Mean ( 12 / 26 )96.016250.799909891582732120.033832573340
Winsorized Mean ( 13 / 26 )96.03250.797340863452793120.440961202142
Winsorized Mean ( 14 / 26 )96.0150.789291662893967121.647046983820
Winsorized Mean ( 15 / 26 )95.940.761002836036566126.070489434273
Winsorized Mean ( 16 / 26 )95.940.707311722946623135.640336343245
Winsorized Mean ( 17 / 26 )95.940.682539005237713140.563395298685
Winsorized Mean ( 18 / 26 )95.78250.661207600157719144.859950153557
Winsorized Mean ( 19 / 26 )95.830.653978573566095146.533852749099
Winsorized Mean ( 20 / 26 )95.9050.635597247287536150.889577337351
Winsorized Mean ( 21 / 26 )95.826250.573978850418592166.950837875151
Winsorized Mean ( 22 / 26 )95.853750.532325159238437180.066165080628
Winsorized Mean ( 23 / 26 )95.88250.512600021113509187.051299357571
Winsorized Mean ( 24 / 26 )96.21250.441797160485055217.775279257945
Winsorized Mean ( 25 / 26 )96.33750.416542333770272231.279013415072
Winsorized Mean ( 26 / 26 )96.4350.353258341297418272.987184522867
Trimmed Mean ( 1 / 26 )96.52820512820510.963499520909515100.185005839012
Trimmed Mean ( 2 / 26 )96.47368421052630.947457110858309101.823800892824
Trimmed Mean ( 3 / 26 )96.42162162162160.931055919388716103.561579507413
Trimmed Mean ( 4 / 26 )96.38888888888890.91763405112403105.040662746571
Trimmed Mean ( 5 / 26 )96.35142857142860.902783234650842106.727091147958
Trimmed Mean ( 6 / 26 )96.3250.88820525898553108.449031375944
Trimmed Mean ( 7 / 26 )96.29545454545450.871657938026107110.473903058255
Trimmed Mean ( 8 / 26 )96.26250.852760166045325112.883438782580
Trimmed Mean ( 9 / 26 )96.22419354838710.831390002492627115.738935108545
Trimmed Mean ( 10 / 26 )96.190.808125053252846119.028607778980
Trimmed Mean ( 11 / 26 )96.15517241379310.781075980890293123.106041878528
Trimmed Mean ( 12 / 26 )96.10892857142860.751043761957163127.96714844016
Trimmed Mean ( 13 / 26 )96.12037037037040.73474411481357130.821558733763
Trimmed Mean ( 14 / 26 )96.13076923076920.714736809144768134.498136937702
Trimmed Mean ( 15 / 26 )96.1440.691116576598319139.114012390242
Trimmed Mean ( 16 / 26 )96.16666666666670.667105352120205144.155141854324
Trimmed Mean ( 17 / 26 )96.1913043478260.647864019899063148.474527668341
Trimmed Mean ( 18 / 26 )96.21818181818180.628105584296163153.187910160043
Trimmed Mean ( 19 / 26 )96.26428571428570.606515355170617158.716980359394
Trimmed Mean ( 20 / 26 )96.310.579376322502847166.230472767597
Trimmed Mean ( 21 / 26 )96.35263157894740.547498343263539175.987074234064
Trimmed Mean ( 22 / 26 )96.40833333333330.520384091969194185.263798069831
Trimmed Mean ( 23 / 26 )96.46764705882350.494239915693222195.183844921788
Trimmed Mean ( 24 / 26 )96.531250.462798236450065208.581715307413
Trimmed Mean ( 25 / 26 )96.56666666666670.441453537819825218.747067117354
Trimmed Mean ( 26 / 26 )96.59285714285710.418296133533168230.919794373853
Median96.6
Midrange98.8
Midmean - Weighted Average at Xnp96.1073170731707
Midmean - Weighted Average at X(n+1)p96.31
Midmean - Empirical Distribution Function96.1073170731707
Midmean - Empirical Distribution Function - Averaging96.31
Midmean - Empirical Distribution Function - Interpolation96.31
Midmean - Closest Observation96.1073170731707
Midmean - True Basic - Statistics Graphics Toolkit96.31
Midmean - MS Excel (old versions)96.413953488372
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.585 & 0.983286114149122 & 98.2267506986804 \tabularnewline
Geometric Mean & 96.1920610449796 &  &  \tabularnewline
Harmonic Mean & 95.8023510777396 &  &  \tabularnewline
Quadratic Mean & 96.9796035256899 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 96.58 & 0.97710564579168 & 98.8429454030512 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 96.57 & 0.973013067938836 & 99.2484101005624 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 96.51 & 0.959352036071183 & 100.599150646759 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 96.52 & 0.955906687358504 & 100.972198726549 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 96.46375 & 0.945226588182076 & 102.053572345574 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 96.47125 & 0.941390356338076 & 102.477414762633 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 96.48 & 0.93695304720046 & 102.972075589353 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 96.5 & 0.93033953241256 & 103.725571834786 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 96.455 & 0.918339689227318 & 105.03194093806 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 96.4425 & 0.911890120448814 & 105.761097567910 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 96.51125 & 0.896639283958702 & 107.636651356495 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 96.01625 & 0.799909891582732 & 120.033832573340 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 96.0325 & 0.797340863452793 & 120.440961202142 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 96.015 & 0.789291662893967 & 121.647046983820 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 95.94 & 0.761002836036566 & 126.070489434273 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 95.94 & 0.707311722946623 & 135.640336343245 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 95.94 & 0.682539005237713 & 140.563395298685 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 95.7825 & 0.661207600157719 & 144.859950153557 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 95.83 & 0.653978573566095 & 146.533852749099 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 95.905 & 0.635597247287536 & 150.889577337351 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 95.82625 & 0.573978850418592 & 166.950837875151 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 95.85375 & 0.532325159238437 & 180.066165080628 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 95.8825 & 0.512600021113509 & 187.051299357571 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 96.2125 & 0.441797160485055 & 217.775279257945 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 96.3375 & 0.416542333770272 & 231.279013415072 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 96.435 & 0.353258341297418 & 272.987184522867 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 96.5282051282051 & 0.963499520909515 & 100.185005839012 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 96.4736842105263 & 0.947457110858309 & 101.823800892824 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 96.4216216216216 & 0.931055919388716 & 103.561579507413 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 96.3888888888889 & 0.91763405112403 & 105.040662746571 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 96.3514285714286 & 0.902783234650842 & 106.727091147958 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 96.325 & 0.88820525898553 & 108.449031375944 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 96.2954545454545 & 0.871657938026107 & 110.473903058255 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 96.2625 & 0.852760166045325 & 112.883438782580 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 96.2241935483871 & 0.831390002492627 & 115.738935108545 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 96.19 & 0.808125053252846 & 119.028607778980 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 96.1551724137931 & 0.781075980890293 & 123.106041878528 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 96.1089285714286 & 0.751043761957163 & 127.96714844016 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 96.1203703703704 & 0.73474411481357 & 130.821558733763 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 96.1307692307692 & 0.714736809144768 & 134.498136937702 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 96.144 & 0.691116576598319 & 139.114012390242 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 96.1666666666667 & 0.667105352120205 & 144.155141854324 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 96.191304347826 & 0.647864019899063 & 148.474527668341 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 96.2181818181818 & 0.628105584296163 & 153.187910160043 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 96.2642857142857 & 0.606515355170617 & 158.716980359394 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 96.31 & 0.579376322502847 & 166.230472767597 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 96.3526315789474 & 0.547498343263539 & 175.987074234064 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 96.4083333333333 & 0.520384091969194 & 185.263798069831 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 96.4676470588235 & 0.494239915693222 & 195.183844921788 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 96.53125 & 0.462798236450065 & 208.581715307413 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 96.5666666666667 & 0.441453537819825 & 218.747067117354 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 96.5928571428571 & 0.418296133533168 & 230.919794373853 \tabularnewline
Median & 96.6 &  &  \tabularnewline
Midrange & 98.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.1073170731707 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.31 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.1073170731707 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.31 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.31 &  &  \tabularnewline
Midmean - Closest Observation & 96.1073170731707 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.31 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.413953488372 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5382&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]96.585[/C][C]0.983286114149122[/C][C]98.2267506986804[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.1920610449796[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.8023510777396[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.9796035256899[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]96.58[/C][C]0.97710564579168[/C][C]98.8429454030512[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]96.57[/C][C]0.973013067938836[/C][C]99.2484101005624[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]96.51[/C][C]0.959352036071183[/C][C]100.599150646759[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]96.52[/C][C]0.955906687358504[/C][C]100.972198726549[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]96.46375[/C][C]0.945226588182076[/C][C]102.053572345574[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]96.47125[/C][C]0.941390356338076[/C][C]102.477414762633[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]96.48[/C][C]0.93695304720046[/C][C]102.972075589353[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]96.5[/C][C]0.93033953241256[/C][C]103.725571834786[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]96.455[/C][C]0.918339689227318[/C][C]105.03194093806[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]96.4425[/C][C]0.911890120448814[/C][C]105.761097567910[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]96.51125[/C][C]0.896639283958702[/C][C]107.636651356495[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]96.01625[/C][C]0.799909891582732[/C][C]120.033832573340[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]96.0325[/C][C]0.797340863452793[/C][C]120.440961202142[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]96.015[/C][C]0.789291662893967[/C][C]121.647046983820[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]95.94[/C][C]0.761002836036566[/C][C]126.070489434273[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]95.94[/C][C]0.707311722946623[/C][C]135.640336343245[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]95.94[/C][C]0.682539005237713[/C][C]140.563395298685[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]95.7825[/C][C]0.661207600157719[/C][C]144.859950153557[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]95.83[/C][C]0.653978573566095[/C][C]146.533852749099[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]95.905[/C][C]0.635597247287536[/C][C]150.889577337351[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]95.82625[/C][C]0.573978850418592[/C][C]166.950837875151[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]95.85375[/C][C]0.532325159238437[/C][C]180.066165080628[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]95.8825[/C][C]0.512600021113509[/C][C]187.051299357571[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]96.2125[/C][C]0.441797160485055[/C][C]217.775279257945[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]96.3375[/C][C]0.416542333770272[/C][C]231.279013415072[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]96.435[/C][C]0.353258341297418[/C][C]272.987184522867[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]96.5282051282051[/C][C]0.963499520909515[/C][C]100.185005839012[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]96.4736842105263[/C][C]0.947457110858309[/C][C]101.823800892824[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]96.4216216216216[/C][C]0.931055919388716[/C][C]103.561579507413[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]96.3888888888889[/C][C]0.91763405112403[/C][C]105.040662746571[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]96.3514285714286[/C][C]0.902783234650842[/C][C]106.727091147958[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]96.325[/C][C]0.88820525898553[/C][C]108.449031375944[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]96.2954545454545[/C][C]0.871657938026107[/C][C]110.473903058255[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]96.2625[/C][C]0.852760166045325[/C][C]112.883438782580[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]96.2241935483871[/C][C]0.831390002492627[/C][C]115.738935108545[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]96.19[/C][C]0.808125053252846[/C][C]119.028607778980[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]96.1551724137931[/C][C]0.781075980890293[/C][C]123.106041878528[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]96.1089285714286[/C][C]0.751043761957163[/C][C]127.96714844016[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]96.1203703703704[/C][C]0.73474411481357[/C][C]130.821558733763[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]96.1307692307692[/C][C]0.714736809144768[/C][C]134.498136937702[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]96.144[/C][C]0.691116576598319[/C][C]139.114012390242[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]96.1666666666667[/C][C]0.667105352120205[/C][C]144.155141854324[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]96.191304347826[/C][C]0.647864019899063[/C][C]148.474527668341[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]96.2181818181818[/C][C]0.628105584296163[/C][C]153.187910160043[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]96.2642857142857[/C][C]0.606515355170617[/C][C]158.716980359394[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]96.31[/C][C]0.579376322502847[/C][C]166.230472767597[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]96.3526315789474[/C][C]0.547498343263539[/C][C]175.987074234064[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]96.4083333333333[/C][C]0.520384091969194[/C][C]185.263798069831[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]96.4676470588235[/C][C]0.494239915693222[/C][C]195.183844921788[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]96.53125[/C][C]0.462798236450065[/C][C]208.581715307413[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]96.5666666666667[/C][C]0.441453537819825[/C][C]218.747067117354[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]96.5928571428571[/C][C]0.418296133533168[/C][C]230.919794373853[/C][/ROW]
[ROW][C]Median[/C][C]96.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.1073170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.1073170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.1073170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.413953488372[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5382&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5382&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 Mean96.5850.98328611414912298.2267506986804
Geometric Mean96.1920610449796
Harmonic Mean95.8023510777396
Quadratic Mean96.9796035256899
Winsorized Mean ( 1 / 26 )96.580.9771056457916898.8429454030512
Winsorized Mean ( 2 / 26 )96.570.97301306793883699.2484101005624
Winsorized Mean ( 3 / 26 )96.510.959352036071183100.599150646759
Winsorized Mean ( 4 / 26 )96.520.955906687358504100.972198726549
Winsorized Mean ( 5 / 26 )96.463750.945226588182076102.053572345574
Winsorized Mean ( 6 / 26 )96.471250.941390356338076102.477414762633
Winsorized Mean ( 7 / 26 )96.480.93695304720046102.972075589353
Winsorized Mean ( 8 / 26 )96.50.93033953241256103.725571834786
Winsorized Mean ( 9 / 26 )96.4550.918339689227318105.03194093806
Winsorized Mean ( 10 / 26 )96.44250.911890120448814105.761097567910
Winsorized Mean ( 11 / 26 )96.511250.896639283958702107.636651356495
Winsorized Mean ( 12 / 26 )96.016250.799909891582732120.033832573340
Winsorized Mean ( 13 / 26 )96.03250.797340863452793120.440961202142
Winsorized Mean ( 14 / 26 )96.0150.789291662893967121.647046983820
Winsorized Mean ( 15 / 26 )95.940.761002836036566126.070489434273
Winsorized Mean ( 16 / 26 )95.940.707311722946623135.640336343245
Winsorized Mean ( 17 / 26 )95.940.682539005237713140.563395298685
Winsorized Mean ( 18 / 26 )95.78250.661207600157719144.859950153557
Winsorized Mean ( 19 / 26 )95.830.653978573566095146.533852749099
Winsorized Mean ( 20 / 26 )95.9050.635597247287536150.889577337351
Winsorized Mean ( 21 / 26 )95.826250.573978850418592166.950837875151
Winsorized Mean ( 22 / 26 )95.853750.532325159238437180.066165080628
Winsorized Mean ( 23 / 26 )95.88250.512600021113509187.051299357571
Winsorized Mean ( 24 / 26 )96.21250.441797160485055217.775279257945
Winsorized Mean ( 25 / 26 )96.33750.416542333770272231.279013415072
Winsorized Mean ( 26 / 26 )96.4350.353258341297418272.987184522867
Trimmed Mean ( 1 / 26 )96.52820512820510.963499520909515100.185005839012
Trimmed Mean ( 2 / 26 )96.47368421052630.947457110858309101.823800892824
Trimmed Mean ( 3 / 26 )96.42162162162160.931055919388716103.561579507413
Trimmed Mean ( 4 / 26 )96.38888888888890.91763405112403105.040662746571
Trimmed Mean ( 5 / 26 )96.35142857142860.902783234650842106.727091147958
Trimmed Mean ( 6 / 26 )96.3250.88820525898553108.449031375944
Trimmed Mean ( 7 / 26 )96.29545454545450.871657938026107110.473903058255
Trimmed Mean ( 8 / 26 )96.26250.852760166045325112.883438782580
Trimmed Mean ( 9 / 26 )96.22419354838710.831390002492627115.738935108545
Trimmed Mean ( 10 / 26 )96.190.808125053252846119.028607778980
Trimmed Mean ( 11 / 26 )96.15517241379310.781075980890293123.106041878528
Trimmed Mean ( 12 / 26 )96.10892857142860.751043761957163127.96714844016
Trimmed Mean ( 13 / 26 )96.12037037037040.73474411481357130.821558733763
Trimmed Mean ( 14 / 26 )96.13076923076920.714736809144768134.498136937702
Trimmed Mean ( 15 / 26 )96.1440.691116576598319139.114012390242
Trimmed Mean ( 16 / 26 )96.16666666666670.667105352120205144.155141854324
Trimmed Mean ( 17 / 26 )96.1913043478260.647864019899063148.474527668341
Trimmed Mean ( 18 / 26 )96.21818181818180.628105584296163153.187910160043
Trimmed Mean ( 19 / 26 )96.26428571428570.606515355170617158.716980359394
Trimmed Mean ( 20 / 26 )96.310.579376322502847166.230472767597
Trimmed Mean ( 21 / 26 )96.35263157894740.547498343263539175.987074234064
Trimmed Mean ( 22 / 26 )96.40833333333330.520384091969194185.263798069831
Trimmed Mean ( 23 / 26 )96.46764705882350.494239915693222195.183844921788
Trimmed Mean ( 24 / 26 )96.531250.462798236450065208.581715307413
Trimmed Mean ( 25 / 26 )96.56666666666670.441453537819825218.747067117354
Trimmed Mean ( 26 / 26 )96.59285714285710.418296133533168230.919794373853
Median96.6
Midrange98.8
Midmean - Weighted Average at Xnp96.1073170731707
Midmean - Weighted Average at X(n+1)p96.31
Midmean - Empirical Distribution Function96.1073170731707
Midmean - Empirical Distribution Function - Averaging96.31
Midmean - Empirical Distribution Function - Interpolation96.31
Midmean - Closest Observation96.1073170731707
Midmean - True Basic - Statistics Graphics Toolkit96.31
Midmean - MS Excel (old versions)96.413953488372
Number of observations80



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')