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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 01 Jun 2009 10:42:53 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/01/t12438746465sqh2cn1bg7tjqk.htm/, Retrieved Mon, 13 May 2024 17:50:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41002, Retrieved Mon, 13 May 2024 17:50:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2009-06-01 16:42:53] [cad785efdc96cabf1c219520e59eafa5] [Current]
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Dataseries X:
9,370
9,330
9,310
9,260
9,350
9,380
9,430
9,270
9,290
9,270
9,290
9,310
9,330
9,350
9,340
9,470
9,630
9,620
9,630
9,500
9,550
9,580
9,610
9,570
9,610
9,650
9,620
9,650
9,960
10,030
10,030
9,720
9,750
9,770
9,780
9,820
9,840
9,900
9,940
10,120
10,520
10,570
10,570
10,120
10,050
10,140
10,170
10,200
10,200
10,350
10,430
10,570
10,820
10,900
10,830
10,650
10,570
10,610
10,630
10,710
10,720
10,770
10,790
10,920
10,900
11,000
10,990
10,910
10,880
10,870
11,000
10,990
11,030
11,040
10,990




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41002&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41002&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41002&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.08853333333330.07043281722139143.236260188518
Geometric Mean10.0704373397055
Harmonic Mean10.0524705089602
Quadratic Mean10.1067107738703
Winsorized Mean ( 1 / 25 )10.08853333333330.0703875227818352143.328432861639
Winsorized Mean ( 2 / 25 )10.08773333333330.0702450211972564143.607805384609
Winsorized Mean ( 3 / 25 )10.08853333333330.0701205380031404143.874157566810
Winsorized Mean ( 4 / 25 )10.0880.0700272791119277144.058146024436
Winsorized Mean ( 5 / 25 )10.08933333333330.0698240603187712144.496514342936
Winsorized Mean ( 6 / 25 )10.08933333333330.0698240603187712144.496514342936
Winsorized Mean ( 7 / 25 )10.08466666666670.0684356298680405147.359886744846
Winsorized Mean ( 8 / 25 )10.08360.0682604023026712147.722539859766
Winsorized Mean ( 9 / 25 )10.08360.0678864021995834148.536373607701
Winsorized Mean ( 10 / 25 )10.08493333333330.0676899059192976148.987255874708
Winsorized Mean ( 11 / 25 )10.0820.0672159354765072149.994193021739
Winsorized Mean ( 12 / 25 )10.08360.0664921969275512151.650877335079
Winsorized Mean ( 13 / 25 )10.07840.0651462775412185154.704157787424
Winsorized Mean ( 14 / 25 )10.08586666666670.0635275618224965158.763635457123
Winsorized Mean ( 15 / 25 )10.08786666666670.0614946839666337164.044532241848
Winsorized Mean ( 16 / 25 )10.090.059978674889009168.226457464618
Winsorized Mean ( 17 / 25 )10.090.0567780569212063177.709498125348
Winsorized Mean ( 18 / 25 )10.09240.0558065642430406180.846108999777
Winsorized Mean ( 19 / 25 )10.07973333333330.053248346701343189.296644079263
Winsorized Mean ( 20 / 25 )10.08240.0514754695361195195.868053091295
Winsorized Mean ( 21 / 25 )10.07680.0506747836077639198.852353825466
Winsorized Mean ( 22 / 25 )10.0680.0486572865204332206.916593998147
Winsorized Mean ( 23 / 25 )10.0680.0486572865204332206.916593998147
Winsorized Mean ( 24 / 25 )10.07120.0482605391561225208.6839512385
Winsorized Mean ( 25 / 25 )10.07120.0482605391561225208.6839512385
Trimmed Mean ( 1 / 25 )10.08684931506850.0702522842087159143.580375053728
Trimmed Mean ( 2 / 25 )10.08507042253520.0700436406761706143.982670306374
Trimmed Mean ( 3 / 25 )10.08362318840580.0698338580699082144.394473785358
Trimmed Mean ( 4 / 25 )10.08179104477610.069585555230591144.883388676965
Trimmed Mean ( 5 / 25 )10.080.0692681523001511145.521421681953
Trimmed Mean ( 6 / 25 )10.07777777777780.0688927290276324146.282168234846
Trimmed Mean ( 7 / 25 )10.07540983606560.068386387682385147.330633734596
Trimmed Mean ( 8 / 25 )10.07372881355930.0680520902288602148.029675204409
Trimmed Mean ( 9 / 25 )10.07210526315790.0676191683804433148.95340336766
Trimmed Mean ( 10 / 25 )10.07036363636360.0671030985432011150.073004898281
Trimmed Mean ( 11 / 25 )10.06830188679250.0664405710470915151.538461035446
Trimmed Mean ( 12 / 25 )10.06647058823530.0656519781697469153.330803867141
Trimmed Mean ( 13 / 25 )10.06428571428570.0647470220994626155.44013281144
Trimmed Mean ( 14 / 25 )10.06255319148940.0638181302954256157.675462206555
Trimmed Mean ( 15 / 25 )10.05977777777780.0628895848910339159.959360444308
Trimmed Mean ( 16 / 25 )10.05651162790700.062032645748271162.116438958873
Trimmed Mean ( 17 / 25 )10.05268292682930.0611386113981033164.424456116142
Trimmed Mean ( 18 / 25 )10.04846153846150.0605391191509758165.982949196901
Trimmed Mean ( 19 / 25 )10.04351351351350.059804757682595167.938369833684
Trimmed Mean ( 20 / 25 )10.03942857142860.0592728243555412169.376584979454
Trimmed Mean ( 21 / 25 )10.03454545454550.0587658600595613170.754677024638
Trimmed Mean ( 22 / 25 )10.02967741935480.0580572277385102172.755017937276
Trimmed Mean ( 23 / 25 )10.02517241379310.0573890462799304174.687907599869
Trimmed Mean ( 24 / 25 )10.020.0561413559851545178.478054620725
Trimmed Mean ( 25 / 25 )10.01360.0541137074439862185.047383980578
Median10.03
Midrange10.15
Midmean - Weighted Average at Xnp10.0310526315789
Midmean - Weighted Average at X(n+1)p10.0484615384615
Midmean - Empirical Distribution Function10.0484615384615
Midmean - Empirical Distribution Function - Averaging10.0484615384615
Midmean - Empirical Distribution Function - Interpolation10.0435135135135
Midmean - Closest Observation10.0310526315789
Midmean - True Basic - Statistics Graphics Toolkit10.0484615384615
Midmean - MS Excel (old versions)10.0484615384615
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.0885333333333 & 0.07043281722139 & 143.236260188518 \tabularnewline
Geometric Mean & 10.0704373397055 &  &  \tabularnewline
Harmonic Mean & 10.0524705089602 &  &  \tabularnewline
Quadratic Mean & 10.1067107738703 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 10.0885333333333 & 0.0703875227818352 & 143.328432861639 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 10.0877333333333 & 0.0702450211972564 & 143.607805384609 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 10.0885333333333 & 0.0701205380031404 & 143.874157566810 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 10.088 & 0.0700272791119277 & 144.058146024436 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 10.0893333333333 & 0.0698240603187712 & 144.496514342936 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 10.0893333333333 & 0.0698240603187712 & 144.496514342936 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 10.0846666666667 & 0.0684356298680405 & 147.359886744846 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 10.0836 & 0.0682604023026712 & 147.722539859766 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 10.0836 & 0.0678864021995834 & 148.536373607701 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 10.0849333333333 & 0.0676899059192976 & 148.987255874708 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 10.082 & 0.0672159354765072 & 149.994193021739 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 10.0836 & 0.0664921969275512 & 151.650877335079 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 10.0784 & 0.0651462775412185 & 154.704157787424 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 10.0858666666667 & 0.0635275618224965 & 158.763635457123 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 10.0878666666667 & 0.0614946839666337 & 164.044532241848 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 10.09 & 0.059978674889009 & 168.226457464618 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 10.09 & 0.0567780569212063 & 177.709498125348 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 10.0924 & 0.0558065642430406 & 180.846108999777 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 10.0797333333333 & 0.053248346701343 & 189.296644079263 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 10.0824 & 0.0514754695361195 & 195.868053091295 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 10.0768 & 0.0506747836077639 & 198.852353825466 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 10.068 & 0.0486572865204332 & 206.916593998147 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 10.068 & 0.0486572865204332 & 206.916593998147 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 10.0712 & 0.0482605391561225 & 208.6839512385 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 10.0712 & 0.0482605391561225 & 208.6839512385 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 10.0868493150685 & 0.0702522842087159 & 143.580375053728 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 10.0850704225352 & 0.0700436406761706 & 143.982670306374 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 10.0836231884058 & 0.0698338580699082 & 144.394473785358 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 10.0817910447761 & 0.069585555230591 & 144.883388676965 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 10.08 & 0.0692681523001511 & 145.521421681953 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 10.0777777777778 & 0.0688927290276324 & 146.282168234846 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 10.0754098360656 & 0.068386387682385 & 147.330633734596 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 10.0737288135593 & 0.0680520902288602 & 148.029675204409 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 10.0721052631579 & 0.0676191683804433 & 148.95340336766 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 10.0703636363636 & 0.0671030985432011 & 150.073004898281 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 10.0683018867925 & 0.0664405710470915 & 151.538461035446 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 10.0664705882353 & 0.0656519781697469 & 153.330803867141 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 10.0642857142857 & 0.0647470220994626 & 155.44013281144 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 10.0625531914894 & 0.0638181302954256 & 157.675462206555 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 10.0597777777778 & 0.0628895848910339 & 159.959360444308 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 10.0565116279070 & 0.062032645748271 & 162.116438958873 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 10.0526829268293 & 0.0611386113981033 & 164.424456116142 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 10.0484615384615 & 0.0605391191509758 & 165.982949196901 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 10.0435135135135 & 0.059804757682595 & 167.938369833684 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 10.0394285714286 & 0.0592728243555412 & 169.376584979454 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 10.0345454545455 & 0.0587658600595613 & 170.754677024638 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 10.0296774193548 & 0.0580572277385102 & 172.755017937276 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 10.0251724137931 & 0.0573890462799304 & 174.687907599869 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 10.02 & 0.0561413559851545 & 178.478054620725 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 10.0136 & 0.0541137074439862 & 185.047383980578 \tabularnewline
Median & 10.03 &  &  \tabularnewline
Midrange & 10.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10.0310526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.0484615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.0484615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.0484615384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10.0435135135135 &  &  \tabularnewline
Midmean - Closest Observation & 10.0310526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.0484615384615 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.0484615384615 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41002&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]10.0885333333333[/C][C]0.07043281722139[/C][C]143.236260188518[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.0704373397055[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10.0524705089602[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.1067107738703[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]10.0885333333333[/C][C]0.0703875227818352[/C][C]143.328432861639[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]10.0877333333333[/C][C]0.0702450211972564[/C][C]143.607805384609[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]10.0885333333333[/C][C]0.0701205380031404[/C][C]143.874157566810[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]10.088[/C][C]0.0700272791119277[/C][C]144.058146024436[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]10.0893333333333[/C][C]0.0698240603187712[/C][C]144.496514342936[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]10.0893333333333[/C][C]0.0698240603187712[/C][C]144.496514342936[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]10.0846666666667[/C][C]0.0684356298680405[/C][C]147.359886744846[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]10.0836[/C][C]0.0682604023026712[/C][C]147.722539859766[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]10.0836[/C][C]0.0678864021995834[/C][C]148.536373607701[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]10.0849333333333[/C][C]0.0676899059192976[/C][C]148.987255874708[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]10.082[/C][C]0.0672159354765072[/C][C]149.994193021739[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]10.0836[/C][C]0.0664921969275512[/C][C]151.650877335079[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]10.0784[/C][C]0.0651462775412185[/C][C]154.704157787424[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]10.0858666666667[/C][C]0.0635275618224965[/C][C]158.763635457123[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]10.0878666666667[/C][C]0.0614946839666337[/C][C]164.044532241848[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]10.09[/C][C]0.059978674889009[/C][C]168.226457464618[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]10.09[/C][C]0.0567780569212063[/C][C]177.709498125348[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]10.0924[/C][C]0.0558065642430406[/C][C]180.846108999777[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]10.0797333333333[/C][C]0.053248346701343[/C][C]189.296644079263[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]10.0824[/C][C]0.0514754695361195[/C][C]195.868053091295[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]10.0768[/C][C]0.0506747836077639[/C][C]198.852353825466[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]10.068[/C][C]0.0486572865204332[/C][C]206.916593998147[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]10.068[/C][C]0.0486572865204332[/C][C]206.916593998147[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]10.0712[/C][C]0.0482605391561225[/C][C]208.6839512385[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]10.0712[/C][C]0.0482605391561225[/C][C]208.6839512385[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]10.0868493150685[/C][C]0.0702522842087159[/C][C]143.580375053728[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]10.0850704225352[/C][C]0.0700436406761706[/C][C]143.982670306374[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]10.0836231884058[/C][C]0.0698338580699082[/C][C]144.394473785358[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]10.0817910447761[/C][C]0.069585555230591[/C][C]144.883388676965[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]10.08[/C][C]0.0692681523001511[/C][C]145.521421681953[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]10.0777777777778[/C][C]0.0688927290276324[/C][C]146.282168234846[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]10.0754098360656[/C][C]0.068386387682385[/C][C]147.330633734596[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]10.0737288135593[/C][C]0.0680520902288602[/C][C]148.029675204409[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]10.0721052631579[/C][C]0.0676191683804433[/C][C]148.95340336766[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]10.0703636363636[/C][C]0.0671030985432011[/C][C]150.073004898281[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]10.0683018867925[/C][C]0.0664405710470915[/C][C]151.538461035446[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]10.0664705882353[/C][C]0.0656519781697469[/C][C]153.330803867141[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]10.0642857142857[/C][C]0.0647470220994626[/C][C]155.44013281144[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]10.0625531914894[/C][C]0.0638181302954256[/C][C]157.675462206555[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]10.0597777777778[/C][C]0.0628895848910339[/C][C]159.959360444308[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]10.0565116279070[/C][C]0.062032645748271[/C][C]162.116438958873[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]10.0526829268293[/C][C]0.0611386113981033[/C][C]164.424456116142[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]10.0484615384615[/C][C]0.0605391191509758[/C][C]165.982949196901[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]10.0435135135135[/C][C]0.059804757682595[/C][C]167.938369833684[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]10.0394285714286[/C][C]0.0592728243555412[/C][C]169.376584979454[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]10.0345454545455[/C][C]0.0587658600595613[/C][C]170.754677024638[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]10.0296774193548[/C][C]0.0580572277385102[/C][C]172.755017937276[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]10.0251724137931[/C][C]0.0573890462799304[/C][C]174.687907599869[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]10.02[/C][C]0.0561413559851545[/C][C]178.478054620725[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]10.0136[/C][C]0.0541137074439862[/C][C]185.047383980578[/C][/ROW]
[ROW][C]Median[/C][C]10.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10.0310526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.0484615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.0484615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.0484615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10.0435135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.0310526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.0484615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.0484615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41002&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41002&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 Mean10.08853333333330.07043281722139143.236260188518
Geometric Mean10.0704373397055
Harmonic Mean10.0524705089602
Quadratic Mean10.1067107738703
Winsorized Mean ( 1 / 25 )10.08853333333330.0703875227818352143.328432861639
Winsorized Mean ( 2 / 25 )10.08773333333330.0702450211972564143.607805384609
Winsorized Mean ( 3 / 25 )10.08853333333330.0701205380031404143.874157566810
Winsorized Mean ( 4 / 25 )10.0880.0700272791119277144.058146024436
Winsorized Mean ( 5 / 25 )10.08933333333330.0698240603187712144.496514342936
Winsorized Mean ( 6 / 25 )10.08933333333330.0698240603187712144.496514342936
Winsorized Mean ( 7 / 25 )10.08466666666670.0684356298680405147.359886744846
Winsorized Mean ( 8 / 25 )10.08360.0682604023026712147.722539859766
Winsorized Mean ( 9 / 25 )10.08360.0678864021995834148.536373607701
Winsorized Mean ( 10 / 25 )10.08493333333330.0676899059192976148.987255874708
Winsorized Mean ( 11 / 25 )10.0820.0672159354765072149.994193021739
Winsorized Mean ( 12 / 25 )10.08360.0664921969275512151.650877335079
Winsorized Mean ( 13 / 25 )10.07840.0651462775412185154.704157787424
Winsorized Mean ( 14 / 25 )10.08586666666670.0635275618224965158.763635457123
Winsorized Mean ( 15 / 25 )10.08786666666670.0614946839666337164.044532241848
Winsorized Mean ( 16 / 25 )10.090.059978674889009168.226457464618
Winsorized Mean ( 17 / 25 )10.090.0567780569212063177.709498125348
Winsorized Mean ( 18 / 25 )10.09240.0558065642430406180.846108999777
Winsorized Mean ( 19 / 25 )10.07973333333330.053248346701343189.296644079263
Winsorized Mean ( 20 / 25 )10.08240.0514754695361195195.868053091295
Winsorized Mean ( 21 / 25 )10.07680.0506747836077639198.852353825466
Winsorized Mean ( 22 / 25 )10.0680.0486572865204332206.916593998147
Winsorized Mean ( 23 / 25 )10.0680.0486572865204332206.916593998147
Winsorized Mean ( 24 / 25 )10.07120.0482605391561225208.6839512385
Winsorized Mean ( 25 / 25 )10.07120.0482605391561225208.6839512385
Trimmed Mean ( 1 / 25 )10.08684931506850.0702522842087159143.580375053728
Trimmed Mean ( 2 / 25 )10.08507042253520.0700436406761706143.982670306374
Trimmed Mean ( 3 / 25 )10.08362318840580.0698338580699082144.394473785358
Trimmed Mean ( 4 / 25 )10.08179104477610.069585555230591144.883388676965
Trimmed Mean ( 5 / 25 )10.080.0692681523001511145.521421681953
Trimmed Mean ( 6 / 25 )10.07777777777780.0688927290276324146.282168234846
Trimmed Mean ( 7 / 25 )10.07540983606560.068386387682385147.330633734596
Trimmed Mean ( 8 / 25 )10.07372881355930.0680520902288602148.029675204409
Trimmed Mean ( 9 / 25 )10.07210526315790.0676191683804433148.95340336766
Trimmed Mean ( 10 / 25 )10.07036363636360.0671030985432011150.073004898281
Trimmed Mean ( 11 / 25 )10.06830188679250.0664405710470915151.538461035446
Trimmed Mean ( 12 / 25 )10.06647058823530.0656519781697469153.330803867141
Trimmed Mean ( 13 / 25 )10.06428571428570.0647470220994626155.44013281144
Trimmed Mean ( 14 / 25 )10.06255319148940.0638181302954256157.675462206555
Trimmed Mean ( 15 / 25 )10.05977777777780.0628895848910339159.959360444308
Trimmed Mean ( 16 / 25 )10.05651162790700.062032645748271162.116438958873
Trimmed Mean ( 17 / 25 )10.05268292682930.0611386113981033164.424456116142
Trimmed Mean ( 18 / 25 )10.04846153846150.0605391191509758165.982949196901
Trimmed Mean ( 19 / 25 )10.04351351351350.059804757682595167.938369833684
Trimmed Mean ( 20 / 25 )10.03942857142860.0592728243555412169.376584979454
Trimmed Mean ( 21 / 25 )10.03454545454550.0587658600595613170.754677024638
Trimmed Mean ( 22 / 25 )10.02967741935480.0580572277385102172.755017937276
Trimmed Mean ( 23 / 25 )10.02517241379310.0573890462799304174.687907599869
Trimmed Mean ( 24 / 25 )10.020.0561413559851545178.478054620725
Trimmed Mean ( 25 / 25 )10.01360.0541137074439862185.047383980578
Median10.03
Midrange10.15
Midmean - Weighted Average at Xnp10.0310526315789
Midmean - Weighted Average at X(n+1)p10.0484615384615
Midmean - Empirical Distribution Function10.0484615384615
Midmean - Empirical Distribution Function - Averaging10.0484615384615
Midmean - Empirical Distribution Function - Interpolation10.0435135135135
Midmean - Closest Observation10.0310526315789
Midmean - True Basic - Statistics Graphics Toolkit10.0484615384615
Midmean - MS Excel (old versions)10.0484615384615
Number of observations75



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')