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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 18 Oct 2012 08:54:52 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/18/t1350564900z5dbhcb9fotv9gg.htm/, Retrieved Mon, 29 Apr 2024 06:59:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179566, Retrieved Mon, 29 Apr 2024 06:59:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-18 12:54:52] [595720b70ea55335b8ff0acbeccfc0bf] [Current]
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Dataseries X:
32,98
32,7
32,74
32,87
32,95
32,94
32,94
32,97
32,87
32,96
32,97
32,99
32,99
33,04
33,23
33,03
33,05
33,03
33,04
33,11
33,14
33,08
33,09
33,07
33,07
33,02
33
33,08
33,35
33,36
33,36
33,35
33,41
33,47
33,47
33,48
33,48
33,55
33,68
33,72
33,79
33,83
33,83
33,84
33,91
34,06
34,16
34,16
34,16
34,29
34,48
34,48
34,39
34,29
34,29
34,25
34,2
34,1
34,09
34,06
34,06
34,04
34,19
34,21
34,17
34,08
34,08
34,08
34,3
34,28
34,45
34,41




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179566&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179566&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179566&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean33.59222222222220.0653509312741356514.028209962438
Geometric Mean33.5877125417829
Harmonic Mean33.5832071039527
Quadratic Mean33.5967352084494
Winsorized Mean ( 1 / 24 )33.59277777777780.0652463797562129514.860409164372
Winsorized Mean ( 2 / 24 )33.59555555555550.0644699372167339521.10420772731
Winsorized Mean ( 3 / 24 )33.59388888888890.0641650830715983523.554046542779
Winsorized Mean ( 4 / 24 )33.59666666666670.0633747085012727530.127356183295
Winsorized Mean ( 5 / 24 )33.59041666666670.0623221844552473538.980091283345
Winsorized Mean ( 6 / 24 )33.59041666666670.0620674192667037541.19241727014
Winsorized Mean ( 7 / 24 )33.59138888888890.0619269679270157542.435549702323
Winsorized Mean ( 8 / 24 )33.59250.0617683307392722543.846654069315
Winsorized Mean ( 9 / 24 )33.591250.0615704545415816545.574175959902
Winsorized Mean ( 10 / 24 )33.58847222222220.0607258068682933553.116935853507
Winsorized Mean ( 11 / 24 )33.58388888888890.0595896096551727563.586321226617
Winsorized Mean ( 12 / 24 )33.58222222222220.0593441008792249565.889814230526
Winsorized Mean ( 13 / 24 )33.58222222222220.058827624848483570.858033257622
Winsorized Mean ( 14 / 24 )33.58222222222220.0577279865509732581.732089210654
Winsorized Mean ( 15 / 24 )33.58222222222220.057145594955155587.660733055206
Winsorized Mean ( 16 / 24 )33.58222222222220.057145594955155587.660733055206
Winsorized Mean ( 17 / 24 )33.58458333333330.056825563434289591.011884504573
Winsorized Mean ( 18 / 24 )33.56958333333330.0547313246602076613.352290333658
Winsorized Mean ( 19 / 24 )33.56958333333330.0540135747369915621.502714767423
Winsorized Mean ( 20 / 24 )33.57236111111110.0528893244046126634.766306604272
Winsorized Mean ( 21 / 24 )33.57236111111110.0528893244046126634.766306604272
Winsorized Mean ( 22 / 24 )33.57541666666670.0524818090177709639.753417327853
Winsorized Mean ( 23 / 24 )33.56902777777780.0516212733054595650.294454752001
Winsorized Mean ( 24 / 24 )33.57236111111110.0511776391163418655.996675321253
Trimmed Mean ( 1 / 24 )33.59228571428570.0647464145401122518.828508928079
Trimmed Mean ( 2 / 24 )33.59176470588240.0641233656461835523.861534206318
Trimmed Mean ( 3 / 24 )33.5896969696970.0638244860601145526.282294510915
Trimmed Mean ( 4 / 24 )33.5881250.063551814178019528.51559683118
Trimmed Mean ( 5 / 24 )33.58564516129030.0634399164721697529.408722913813
Trimmed Mean ( 6 / 24 )33.58450.0635438480222037528.524806811586
Trimmed Mean ( 7 / 24 )33.5832758620690.0636495376078345527.627962813909
Trimmed Mean ( 8 / 24 )33.58178571428570.0637197125113037527.023496980285
Trimmed Mean ( 9 / 24 )33.580.0637446644839762526.789187327845
Trimmed Mean ( 10 / 24 )33.57826923076920.0637182009852037526.980811001971
Trimmed Mean ( 11 / 24 )33.57680.0637529927268724526.670177568732
Trimmed Mean ( 12 / 24 )33.57583333333330.0639029304129821525.419305755536
Trimmed Mean ( 13 / 24 )33.5750.0640038872611739524.577512971893
Trimmed Mean ( 14 / 24 )33.57409090909090.0640876103089996523.878028018408
Trimmed Mean ( 15 / 24 )33.57309523809520.0642507863130055522.532052363372
Trimmed Mean ( 16 / 24 )33.5720.0643968067372034521.330197893256
Trimmed Mean ( 17 / 24 )33.57078947368420.0643916510086725521.353140474108
Trimmed Mean ( 18 / 24 )33.56916666666670.064245776836068522.511646988456
Trimmed Mean ( 19 / 24 )33.56911764705880.0642998319304569522.071623505413
Trimmed Mean ( 20 / 24 )33.56906250.0642737959181957522.282246138456
Trimmed Mean ( 21 / 24 )33.56866666666670.0642189740524753522.721939457281
Trimmed Mean ( 22 / 24 )33.56821428571430.0638057849532441526.099856154306
Trimmed Mean ( 23 / 24 )33.56730769230770.062971440882863533.056052421418
Trimmed Mean ( 24 / 24 )33.56708333333330.0616396704519902544.569480777448
Median33.48
Midrange33.59
Midmean - Weighted Average at Xnp33.5548648648649
Midmean - Weighted Average at X(n+1)p33.5548648648649
Midmean - Empirical Distribution Function33.5548648648649
Midmean - Empirical Distribution Function - Averaging33.5548648648649
Midmean - Empirical Distribution Function - Interpolation33.5548648648649
Midmean - Closest Observation33.5548648648649
Midmean - True Basic - Statistics Graphics Toolkit33.5548648648649
Midmean - MS Excel (old versions)33.60025
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 33.5922222222222 & 0.0653509312741356 & 514.028209962438 \tabularnewline
Geometric Mean & 33.5877125417829 &  &  \tabularnewline
Harmonic Mean & 33.5832071039527 &  &  \tabularnewline
Quadratic Mean & 33.5967352084494 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 33.5927777777778 & 0.0652463797562129 & 514.860409164372 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 33.5955555555555 & 0.0644699372167339 & 521.10420772731 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 33.5938888888889 & 0.0641650830715983 & 523.554046542779 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 33.5966666666667 & 0.0633747085012727 & 530.127356183295 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 33.5904166666667 & 0.0623221844552473 & 538.980091283345 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 33.5904166666667 & 0.0620674192667037 & 541.19241727014 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 33.5913888888889 & 0.0619269679270157 & 542.435549702323 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 33.5925 & 0.0617683307392722 & 543.846654069315 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 33.59125 & 0.0615704545415816 & 545.574175959902 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 33.5884722222222 & 0.0607258068682933 & 553.116935853507 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 33.5838888888889 & 0.0595896096551727 & 563.586321226617 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 33.5822222222222 & 0.0593441008792249 & 565.889814230526 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 33.5822222222222 & 0.058827624848483 & 570.858033257622 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 33.5822222222222 & 0.0577279865509732 & 581.732089210654 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 33.5822222222222 & 0.057145594955155 & 587.660733055206 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 33.5822222222222 & 0.057145594955155 & 587.660733055206 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 33.5845833333333 & 0.056825563434289 & 591.011884504573 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 33.5695833333333 & 0.0547313246602076 & 613.352290333658 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 33.5695833333333 & 0.0540135747369915 & 621.502714767423 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 33.5723611111111 & 0.0528893244046126 & 634.766306604272 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 33.5723611111111 & 0.0528893244046126 & 634.766306604272 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 33.5754166666667 & 0.0524818090177709 & 639.753417327853 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 33.5690277777778 & 0.0516212733054595 & 650.294454752001 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 33.5723611111111 & 0.0511776391163418 & 655.996675321253 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 33.5922857142857 & 0.0647464145401122 & 518.828508928079 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 33.5917647058824 & 0.0641233656461835 & 523.861534206318 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 33.589696969697 & 0.0638244860601145 & 526.282294510915 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 33.588125 & 0.063551814178019 & 528.51559683118 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 33.5856451612903 & 0.0634399164721697 & 529.408722913813 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 33.5845 & 0.0635438480222037 & 528.524806811586 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 33.583275862069 & 0.0636495376078345 & 527.627962813909 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 33.5817857142857 & 0.0637197125113037 & 527.023496980285 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 33.58 & 0.0637446644839762 & 526.789187327845 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 33.5782692307692 & 0.0637182009852037 & 526.980811001971 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 33.5768 & 0.0637529927268724 & 526.670177568732 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 33.5758333333333 & 0.0639029304129821 & 525.419305755536 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 33.575 & 0.0640038872611739 & 524.577512971893 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 33.5740909090909 & 0.0640876103089996 & 523.878028018408 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 33.5730952380952 & 0.0642507863130055 & 522.532052363372 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 33.572 & 0.0643968067372034 & 521.330197893256 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 33.5707894736842 & 0.0643916510086725 & 521.353140474108 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 33.5691666666667 & 0.064245776836068 & 522.511646988456 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 33.5691176470588 & 0.0642998319304569 & 522.071623505413 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 33.5690625 & 0.0642737959181957 & 522.282246138456 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 33.5686666666667 & 0.0642189740524753 & 522.721939457281 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 33.5682142857143 & 0.0638057849532441 & 526.099856154306 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 33.5673076923077 & 0.062971440882863 & 533.056052421418 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 33.5670833333333 & 0.0616396704519902 & 544.569480777448 \tabularnewline
Median & 33.48 &  &  \tabularnewline
Midrange & 33.59 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 33.5548648648649 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 33.5548648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 33.5548648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 33.5548648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 33.5548648648649 &  &  \tabularnewline
Midmean - Closest Observation & 33.5548648648649 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 33.5548648648649 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 33.60025 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179566&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]33.5922222222222[/C][C]0.0653509312741356[/C][C]514.028209962438[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]33.5877125417829[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]33.5832071039527[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]33.5967352084494[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]33.5927777777778[/C][C]0.0652463797562129[/C][C]514.860409164372[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]33.5955555555555[/C][C]0.0644699372167339[/C][C]521.10420772731[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]33.5938888888889[/C][C]0.0641650830715983[/C][C]523.554046542779[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]33.5966666666667[/C][C]0.0633747085012727[/C][C]530.127356183295[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]33.5904166666667[/C][C]0.0623221844552473[/C][C]538.980091283345[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]33.5904166666667[/C][C]0.0620674192667037[/C][C]541.19241727014[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]33.5913888888889[/C][C]0.0619269679270157[/C][C]542.435549702323[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]33.5925[/C][C]0.0617683307392722[/C][C]543.846654069315[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]33.59125[/C][C]0.0615704545415816[/C][C]545.574175959902[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]33.5884722222222[/C][C]0.0607258068682933[/C][C]553.116935853507[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]33.5838888888889[/C][C]0.0595896096551727[/C][C]563.586321226617[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]33.5822222222222[/C][C]0.0593441008792249[/C][C]565.889814230526[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]33.5822222222222[/C][C]0.058827624848483[/C][C]570.858033257622[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]33.5822222222222[/C][C]0.0577279865509732[/C][C]581.732089210654[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]33.5822222222222[/C][C]0.057145594955155[/C][C]587.660733055206[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]33.5822222222222[/C][C]0.057145594955155[/C][C]587.660733055206[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]33.5845833333333[/C][C]0.056825563434289[/C][C]591.011884504573[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]33.5695833333333[/C][C]0.0547313246602076[/C][C]613.352290333658[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]33.5695833333333[/C][C]0.0540135747369915[/C][C]621.502714767423[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]33.5723611111111[/C][C]0.0528893244046126[/C][C]634.766306604272[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]33.5723611111111[/C][C]0.0528893244046126[/C][C]634.766306604272[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]33.5754166666667[/C][C]0.0524818090177709[/C][C]639.753417327853[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]33.5690277777778[/C][C]0.0516212733054595[/C][C]650.294454752001[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]33.5723611111111[/C][C]0.0511776391163418[/C][C]655.996675321253[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]33.5922857142857[/C][C]0.0647464145401122[/C][C]518.828508928079[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]33.5917647058824[/C][C]0.0641233656461835[/C][C]523.861534206318[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]33.589696969697[/C][C]0.0638244860601145[/C][C]526.282294510915[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]33.588125[/C][C]0.063551814178019[/C][C]528.51559683118[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]33.5856451612903[/C][C]0.0634399164721697[/C][C]529.408722913813[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]33.5845[/C][C]0.0635438480222037[/C][C]528.524806811586[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]33.583275862069[/C][C]0.0636495376078345[/C][C]527.627962813909[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]33.5817857142857[/C][C]0.0637197125113037[/C][C]527.023496980285[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]33.58[/C][C]0.0637446644839762[/C][C]526.789187327845[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]33.5782692307692[/C][C]0.0637182009852037[/C][C]526.980811001971[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]33.5768[/C][C]0.0637529927268724[/C][C]526.670177568732[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]33.5758333333333[/C][C]0.0639029304129821[/C][C]525.419305755536[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]33.575[/C][C]0.0640038872611739[/C][C]524.577512971893[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]33.5740909090909[/C][C]0.0640876103089996[/C][C]523.878028018408[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]33.5730952380952[/C][C]0.0642507863130055[/C][C]522.532052363372[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]33.572[/C][C]0.0643968067372034[/C][C]521.330197893256[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]33.5707894736842[/C][C]0.0643916510086725[/C][C]521.353140474108[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]33.5691666666667[/C][C]0.064245776836068[/C][C]522.511646988456[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]33.5691176470588[/C][C]0.0642998319304569[/C][C]522.071623505413[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]33.5690625[/C][C]0.0642737959181957[/C][C]522.282246138456[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]33.5686666666667[/C][C]0.0642189740524753[/C][C]522.721939457281[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]33.5682142857143[/C][C]0.0638057849532441[/C][C]526.099856154306[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]33.5673076923077[/C][C]0.062971440882863[/C][C]533.056052421418[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]33.5670833333333[/C][C]0.0616396704519902[/C][C]544.569480777448[/C][/ROW]
[ROW][C]Median[/C][C]33.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]33.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]33.5548648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]33.5548648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]33.5548648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]33.5548648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]33.5548648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]33.5548648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]33.5548648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]33.60025[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179566&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179566&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 Mean33.59222222222220.0653509312741356514.028209962438
Geometric Mean33.5877125417829
Harmonic Mean33.5832071039527
Quadratic Mean33.5967352084494
Winsorized Mean ( 1 / 24 )33.59277777777780.0652463797562129514.860409164372
Winsorized Mean ( 2 / 24 )33.59555555555550.0644699372167339521.10420772731
Winsorized Mean ( 3 / 24 )33.59388888888890.0641650830715983523.554046542779
Winsorized Mean ( 4 / 24 )33.59666666666670.0633747085012727530.127356183295
Winsorized Mean ( 5 / 24 )33.59041666666670.0623221844552473538.980091283345
Winsorized Mean ( 6 / 24 )33.59041666666670.0620674192667037541.19241727014
Winsorized Mean ( 7 / 24 )33.59138888888890.0619269679270157542.435549702323
Winsorized Mean ( 8 / 24 )33.59250.0617683307392722543.846654069315
Winsorized Mean ( 9 / 24 )33.591250.0615704545415816545.574175959902
Winsorized Mean ( 10 / 24 )33.58847222222220.0607258068682933553.116935853507
Winsorized Mean ( 11 / 24 )33.58388888888890.0595896096551727563.586321226617
Winsorized Mean ( 12 / 24 )33.58222222222220.0593441008792249565.889814230526
Winsorized Mean ( 13 / 24 )33.58222222222220.058827624848483570.858033257622
Winsorized Mean ( 14 / 24 )33.58222222222220.0577279865509732581.732089210654
Winsorized Mean ( 15 / 24 )33.58222222222220.057145594955155587.660733055206
Winsorized Mean ( 16 / 24 )33.58222222222220.057145594955155587.660733055206
Winsorized Mean ( 17 / 24 )33.58458333333330.056825563434289591.011884504573
Winsorized Mean ( 18 / 24 )33.56958333333330.0547313246602076613.352290333658
Winsorized Mean ( 19 / 24 )33.56958333333330.0540135747369915621.502714767423
Winsorized Mean ( 20 / 24 )33.57236111111110.0528893244046126634.766306604272
Winsorized Mean ( 21 / 24 )33.57236111111110.0528893244046126634.766306604272
Winsorized Mean ( 22 / 24 )33.57541666666670.0524818090177709639.753417327853
Winsorized Mean ( 23 / 24 )33.56902777777780.0516212733054595650.294454752001
Winsorized Mean ( 24 / 24 )33.57236111111110.0511776391163418655.996675321253
Trimmed Mean ( 1 / 24 )33.59228571428570.0647464145401122518.828508928079
Trimmed Mean ( 2 / 24 )33.59176470588240.0641233656461835523.861534206318
Trimmed Mean ( 3 / 24 )33.5896969696970.0638244860601145526.282294510915
Trimmed Mean ( 4 / 24 )33.5881250.063551814178019528.51559683118
Trimmed Mean ( 5 / 24 )33.58564516129030.0634399164721697529.408722913813
Trimmed Mean ( 6 / 24 )33.58450.0635438480222037528.524806811586
Trimmed Mean ( 7 / 24 )33.5832758620690.0636495376078345527.627962813909
Trimmed Mean ( 8 / 24 )33.58178571428570.0637197125113037527.023496980285
Trimmed Mean ( 9 / 24 )33.580.0637446644839762526.789187327845
Trimmed Mean ( 10 / 24 )33.57826923076920.0637182009852037526.980811001971
Trimmed Mean ( 11 / 24 )33.57680.0637529927268724526.670177568732
Trimmed Mean ( 12 / 24 )33.57583333333330.0639029304129821525.419305755536
Trimmed Mean ( 13 / 24 )33.5750.0640038872611739524.577512971893
Trimmed Mean ( 14 / 24 )33.57409090909090.0640876103089996523.878028018408
Trimmed Mean ( 15 / 24 )33.57309523809520.0642507863130055522.532052363372
Trimmed Mean ( 16 / 24 )33.5720.0643968067372034521.330197893256
Trimmed Mean ( 17 / 24 )33.57078947368420.0643916510086725521.353140474108
Trimmed Mean ( 18 / 24 )33.56916666666670.064245776836068522.511646988456
Trimmed Mean ( 19 / 24 )33.56911764705880.0642998319304569522.071623505413
Trimmed Mean ( 20 / 24 )33.56906250.0642737959181957522.282246138456
Trimmed Mean ( 21 / 24 )33.56866666666670.0642189740524753522.721939457281
Trimmed Mean ( 22 / 24 )33.56821428571430.0638057849532441526.099856154306
Trimmed Mean ( 23 / 24 )33.56730769230770.062971440882863533.056052421418
Trimmed Mean ( 24 / 24 )33.56708333333330.0616396704519902544.569480777448
Median33.48
Midrange33.59
Midmean - Weighted Average at Xnp33.5548648648649
Midmean - Weighted Average at X(n+1)p33.5548648648649
Midmean - Empirical Distribution Function33.5548648648649
Midmean - Empirical Distribution Function - Averaging33.5548648648649
Midmean - Empirical Distribution Function - Interpolation33.5548648648649
Midmean - Closest Observation33.5548648648649
Midmean - True Basic - Statistics Graphics Toolkit33.5548648648649
Midmean - MS Excel (old versions)33.60025
Number of observations72



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')