Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 12 Oct 2014 13:39:20 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/12/t1413117673chhnh1hkd39q2es.htm/, Retrieved Wed, 15 May 2024 12:26:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240574, Retrieved Wed, 15 May 2024 12:26:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten gemi...] [2014-10-12 12:39:20] [34904d4daa687a283c33410e9d0f3c21] [Current]
Feedback Forum

Post a new message
Dataseries X:
4,53
4,53
4,53
4,61
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,66
4,7
4,72
4,73
4,73
4,74
4,74
4,74
4,76
4,88
4,88
4,88
4,88
4,89
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,98
5
5,03
5,04
5,04
5,05
5,05
5,05
5,06
5,06
5,06
5,07
5,09
5,18
5,23
5,25
5,26
5,28
5,29
5,29
5,29
5,29
5,3
5,3
5,3
5,32
5,33
5,33
5,37
5,45
5,47
5,5
5,51




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=240574&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=240574&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240574&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 Mean4.975277777777780.0320046041669065155.455063647446
Geometric Mean4.96798548193718
Harmonic Mean4.96071531953561
Quadratic Mean4.98258104689617
Winsorized Mean ( 1 / 24 )4.975138888888890.0319722059065424155.608246219597
Winsorized Mean ( 2 / 24 )4.974305555555560.0317843294555558156.501824665238
Winsorized Mean ( 3 / 24 )4.976805555555560.0309966341683857160.559547482466
Winsorized Mean ( 4 / 24 )4.973472222222220.029920447288955166.223190923291
Winsorized Mean ( 5 / 24 )4.970694444444440.0294221382939363168.944024216923
Winsorized Mean ( 6 / 24 )4.970694444444440.0294221382939363168.944024216923
Winsorized Mean ( 7 / 24 )4.969722222222220.0292565497811134169.866995917285
Winsorized Mean ( 8 / 24 )4.96750.0288890205546536171.951139381906
Winsorized Mean ( 9 / 24 )4.96750.0288890205546536171.951139381906
Winsorized Mean ( 10 / 24 )4.96750.0288890205546536171.951139381906
Winsorized Mean ( 11 / 24 )4.965972222222220.0286434695164506173.371882179641
Winsorized Mean ( 12 / 24 )4.965972222222220.0286434695164506173.371882179641
Winsorized Mean ( 13 / 24 )4.965972222222220.0286434695164506173.371882179641
Winsorized Mean ( 14 / 24 )4.971805555555560.0276988658073653179.494914706346
Winsorized Mean ( 15 / 24 )4.978055555555560.0260729376671488190.928065686582
Winsorized Mean ( 16 / 24 )4.978055555555550.0246918717886908201.6070550729
Winsorized Mean ( 17 / 24 )4.978055555555560.0239674391872147207.700769225736
Winsorized Mean ( 18 / 24 )4.973055555555560.0231774123834437214.564744039673
Winsorized Mean ( 19 / 24 )4.96250.0207778604184376238.835948459662
Winsorized Mean ( 20 / 24 )4.93750.0173619639853108284.386029378785
Winsorized Mean ( 21 / 24 )4.931666666666670.0166596229247165296.025107468066
Winsorized Mean ( 22 / 24 )4.934722222222220.0153186960936202322.1372231725
Winsorized Mean ( 23 / 24 )4.973055555555560.0094914484385686523.95117433789
Winsorized Mean ( 24 / 24 )4.973055555555560.0094914484385686523.95117433789
Trimmed Mean ( 1 / 24 )4.9740.0313660020875553158.579342885827
Trimmed Mean ( 2 / 24 )4.972794117647060.0306426954490395162.283181840745
Trimmed Mean ( 3 / 24 )4.97196969696970.0298974312630554166.300899004444
Trimmed Mean ( 4 / 24 )4.970156250.0293569407401053169.300891874273
Trimmed Mean ( 5 / 24 )4.96919354838710.0290846595075908170.85273242034
Trimmed Mean ( 6 / 24 )4.968833333333330.0288871676656587172.008325317415
Trimmed Mean ( 7 / 24 )4.968448275862070.0286242335578056173.574892960137
Trimmed Mean ( 8 / 24 )4.968214285714290.028322249459943175.41736198394
Trimmed Mean ( 9 / 24 )4.968333333333330.0280146088474373177.347945866031
Trimmed Mean ( 10 / 24 )4.968461538461540.0276101723108811179.950399530954
Trimmed Mean ( 11 / 24 )4.96860.027084162101396183.450386295831
Trimmed Mean ( 12 / 24 )4.968958333333330.0264579144993934187.806122566737
Trimmed Mean ( 13 / 24 )4.969347826086960.0256441688975429193.780810208402
Trimmed Mean ( 14 / 24 )4.969772727272730.0245821069622253202.170332059398
Trimmed Mean ( 15 / 24 )4.969523809523810.0234234671455518212.160043542809
Trimmed Mean ( 16 / 24 )4.96850.0222991031209777222.811651798045
Trimmed Mean ( 17 / 24 )4.967368421052630.0211500236592327234.863492404851
Trimmed Mean ( 18 / 24 )4.966111111111110.0197736307405377251.148166782043
Trimmed Mean ( 19 / 24 )4.965294117647060.0180918398506946274.4493737853
Trimmed Mean ( 20 / 24 )4.9656250.0165096348946559300.771339383608
Trimmed Mean ( 21 / 24 )4.9690.0153004394798274324.761913313097
Trimmed Mean ( 22 / 24 )4.973571428571430.0136297826489159364.904676522264
Trimmed Mean ( 23 / 24 )4.978461538461540.0115517871769804430.968945513667
Trimmed Mean ( 24 / 24 )4.979166666666670.011291857183269440.951969711789
Median4.97
Midrange5.02
Midmean - Weighted Average at Xnp4.95972972972973
Midmean - Weighted Average at X(n+1)p4.95972972972973
Midmean - Empirical Distribution Function4.95972972972973
Midmean - Empirical Distribution Function - Averaging4.95972972972973
Midmean - Empirical Distribution Function - Interpolation4.95972972972973
Midmean - Closest Observation4.95972972972973
Midmean - True Basic - Statistics Graphics Toolkit4.95972972972973
Midmean - MS Excel (old versions)4.96736842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.97527777777778 & 0.0320046041669065 & 155.455063647446 \tabularnewline
Geometric Mean & 4.96798548193718 &  &  \tabularnewline
Harmonic Mean & 4.96071531953561 &  &  \tabularnewline
Quadratic Mean & 4.98258104689617 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4.97513888888889 & 0.0319722059065424 & 155.608246219597 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4.97430555555556 & 0.0317843294555558 & 156.501824665238 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4.97680555555556 & 0.0309966341683857 & 160.559547482466 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4.97347222222222 & 0.029920447288955 & 166.223190923291 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4.97069444444444 & 0.0294221382939363 & 168.944024216923 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.97069444444444 & 0.0294221382939363 & 168.944024216923 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.96972222222222 & 0.0292565497811134 & 169.866995917285 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.9675 & 0.0288890205546536 & 171.951139381906 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4.9675 & 0.0288890205546536 & 171.951139381906 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4.9675 & 0.0288890205546536 & 171.951139381906 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4.96597222222222 & 0.0286434695164506 & 173.371882179641 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4.96597222222222 & 0.0286434695164506 & 173.371882179641 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4.96597222222222 & 0.0286434695164506 & 173.371882179641 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4.97180555555556 & 0.0276988658073653 & 179.494914706346 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4.97805555555556 & 0.0260729376671488 & 190.928065686582 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4.97805555555555 & 0.0246918717886908 & 201.6070550729 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4.97805555555556 & 0.0239674391872147 & 207.700769225736 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4.97305555555556 & 0.0231774123834437 & 214.564744039673 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4.9625 & 0.0207778604184376 & 238.835948459662 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.9375 & 0.0173619639853108 & 284.386029378785 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.93166666666667 & 0.0166596229247165 & 296.025107468066 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.93472222222222 & 0.0153186960936202 & 322.1372231725 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4.97305555555556 & 0.0094914484385686 & 523.95117433789 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4.97305555555556 & 0.0094914484385686 & 523.95117433789 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4.974 & 0.0313660020875553 & 158.579342885827 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4.97279411764706 & 0.0306426954490395 & 162.283181840745 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.9719696969697 & 0.0298974312630554 & 166.300899004444 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.97015625 & 0.0293569407401053 & 169.300891874273 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.9691935483871 & 0.0290846595075908 & 170.85273242034 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.96883333333333 & 0.0288871676656587 & 172.008325317415 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.96844827586207 & 0.0286242335578056 & 173.574892960137 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.96821428571429 & 0.028322249459943 & 175.41736198394 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.96833333333333 & 0.0280146088474373 & 177.347945866031 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.96846153846154 & 0.0276101723108811 & 179.950399530954 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4.9686 & 0.027084162101396 & 183.450386295831 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.96895833333333 & 0.0264579144993934 & 187.806122566737 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.96934782608696 & 0.0256441688975429 & 193.780810208402 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.96977272727273 & 0.0245821069622253 & 202.170332059398 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4.96952380952381 & 0.0234234671455518 & 212.160043542809 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4.9685 & 0.0222991031209777 & 222.811651798045 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4.96736842105263 & 0.0211500236592327 & 234.863492404851 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4.96611111111111 & 0.0197736307405377 & 251.148166782043 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4.96529411764706 & 0.0180918398506946 & 274.4493737853 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4.965625 & 0.0165096348946559 & 300.771339383608 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4.969 & 0.0153004394798274 & 324.761913313097 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.97357142857143 & 0.0136297826489159 & 364.904676522264 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.97846153846154 & 0.0115517871769804 & 430.968945513667 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.97916666666667 & 0.011291857183269 & 440.951969711789 \tabularnewline
Median & 4.97 &  &  \tabularnewline
Midrange & 5.02 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.95972972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.95972972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.95972972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.95972972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.95972972972973 &  &  \tabularnewline
Midmean - Closest Observation & 4.95972972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.95972972972973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.96736842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240574&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]4.97527777777778[/C][C]0.0320046041669065[/C][C]155.455063647446[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.96798548193718[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.96071531953561[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.98258104689617[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4.97513888888889[/C][C]0.0319722059065424[/C][C]155.608246219597[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4.97430555555556[/C][C]0.0317843294555558[/C][C]156.501824665238[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4.97680555555556[/C][C]0.0309966341683857[/C][C]160.559547482466[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4.97347222222222[/C][C]0.029920447288955[/C][C]166.223190923291[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4.97069444444444[/C][C]0.0294221382939363[/C][C]168.944024216923[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.97069444444444[/C][C]0.0294221382939363[/C][C]168.944024216923[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.96972222222222[/C][C]0.0292565497811134[/C][C]169.866995917285[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.9675[/C][C]0.0288890205546536[/C][C]171.951139381906[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4.9675[/C][C]0.0288890205546536[/C][C]171.951139381906[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4.9675[/C][C]0.0288890205546536[/C][C]171.951139381906[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4.96597222222222[/C][C]0.0286434695164506[/C][C]173.371882179641[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4.96597222222222[/C][C]0.0286434695164506[/C][C]173.371882179641[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4.96597222222222[/C][C]0.0286434695164506[/C][C]173.371882179641[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4.97180555555556[/C][C]0.0276988658073653[/C][C]179.494914706346[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4.97805555555556[/C][C]0.0260729376671488[/C][C]190.928065686582[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4.97805555555555[/C][C]0.0246918717886908[/C][C]201.6070550729[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4.97805555555556[/C][C]0.0239674391872147[/C][C]207.700769225736[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4.97305555555556[/C][C]0.0231774123834437[/C][C]214.564744039673[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4.9625[/C][C]0.0207778604184376[/C][C]238.835948459662[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.9375[/C][C]0.0173619639853108[/C][C]284.386029378785[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.93166666666667[/C][C]0.0166596229247165[/C][C]296.025107468066[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.93472222222222[/C][C]0.0153186960936202[/C][C]322.1372231725[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4.97305555555556[/C][C]0.0094914484385686[/C][C]523.95117433789[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4.97305555555556[/C][C]0.0094914484385686[/C][C]523.95117433789[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4.974[/C][C]0.0313660020875553[/C][C]158.579342885827[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4.97279411764706[/C][C]0.0306426954490395[/C][C]162.283181840745[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.9719696969697[/C][C]0.0298974312630554[/C][C]166.300899004444[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.97015625[/C][C]0.0293569407401053[/C][C]169.300891874273[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.9691935483871[/C][C]0.0290846595075908[/C][C]170.85273242034[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.96883333333333[/C][C]0.0288871676656587[/C][C]172.008325317415[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.96844827586207[/C][C]0.0286242335578056[/C][C]173.574892960137[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.96821428571429[/C][C]0.028322249459943[/C][C]175.41736198394[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.96833333333333[/C][C]0.0280146088474373[/C][C]177.347945866031[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.96846153846154[/C][C]0.0276101723108811[/C][C]179.950399530954[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4.9686[/C][C]0.027084162101396[/C][C]183.450386295831[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.96895833333333[/C][C]0.0264579144993934[/C][C]187.806122566737[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.96934782608696[/C][C]0.0256441688975429[/C][C]193.780810208402[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.96977272727273[/C][C]0.0245821069622253[/C][C]202.170332059398[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4.96952380952381[/C][C]0.0234234671455518[/C][C]212.160043542809[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4.9685[/C][C]0.0222991031209777[/C][C]222.811651798045[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4.96736842105263[/C][C]0.0211500236592327[/C][C]234.863492404851[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4.96611111111111[/C][C]0.0197736307405377[/C][C]251.148166782043[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4.96529411764706[/C][C]0.0180918398506946[/C][C]274.4493737853[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4.965625[/C][C]0.0165096348946559[/C][C]300.771339383608[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4.969[/C][C]0.0153004394798274[/C][C]324.761913313097[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.97357142857143[/C][C]0.0136297826489159[/C][C]364.904676522264[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.97846153846154[/C][C]0.0115517871769804[/C][C]430.968945513667[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.97916666666667[/C][C]0.011291857183269[/C][C]440.951969711789[/C][/ROW]
[ROW][C]Median[/C][C]4.97[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.95972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.95972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.95972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.95972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.95972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.95972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.95972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.96736842105263[/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=240574&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240574&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 Mean4.975277777777780.0320046041669065155.455063647446
Geometric Mean4.96798548193718
Harmonic Mean4.96071531953561
Quadratic Mean4.98258104689617
Winsorized Mean ( 1 / 24 )4.975138888888890.0319722059065424155.608246219597
Winsorized Mean ( 2 / 24 )4.974305555555560.0317843294555558156.501824665238
Winsorized Mean ( 3 / 24 )4.976805555555560.0309966341683857160.559547482466
Winsorized Mean ( 4 / 24 )4.973472222222220.029920447288955166.223190923291
Winsorized Mean ( 5 / 24 )4.970694444444440.0294221382939363168.944024216923
Winsorized Mean ( 6 / 24 )4.970694444444440.0294221382939363168.944024216923
Winsorized Mean ( 7 / 24 )4.969722222222220.0292565497811134169.866995917285
Winsorized Mean ( 8 / 24 )4.96750.0288890205546536171.951139381906
Winsorized Mean ( 9 / 24 )4.96750.0288890205546536171.951139381906
Winsorized Mean ( 10 / 24 )4.96750.0288890205546536171.951139381906
Winsorized Mean ( 11 / 24 )4.965972222222220.0286434695164506173.371882179641
Winsorized Mean ( 12 / 24 )4.965972222222220.0286434695164506173.371882179641
Winsorized Mean ( 13 / 24 )4.965972222222220.0286434695164506173.371882179641
Winsorized Mean ( 14 / 24 )4.971805555555560.0276988658073653179.494914706346
Winsorized Mean ( 15 / 24 )4.978055555555560.0260729376671488190.928065686582
Winsorized Mean ( 16 / 24 )4.978055555555550.0246918717886908201.6070550729
Winsorized Mean ( 17 / 24 )4.978055555555560.0239674391872147207.700769225736
Winsorized Mean ( 18 / 24 )4.973055555555560.0231774123834437214.564744039673
Winsorized Mean ( 19 / 24 )4.96250.0207778604184376238.835948459662
Winsorized Mean ( 20 / 24 )4.93750.0173619639853108284.386029378785
Winsorized Mean ( 21 / 24 )4.931666666666670.0166596229247165296.025107468066
Winsorized Mean ( 22 / 24 )4.934722222222220.0153186960936202322.1372231725
Winsorized Mean ( 23 / 24 )4.973055555555560.0094914484385686523.95117433789
Winsorized Mean ( 24 / 24 )4.973055555555560.0094914484385686523.95117433789
Trimmed Mean ( 1 / 24 )4.9740.0313660020875553158.579342885827
Trimmed Mean ( 2 / 24 )4.972794117647060.0306426954490395162.283181840745
Trimmed Mean ( 3 / 24 )4.97196969696970.0298974312630554166.300899004444
Trimmed Mean ( 4 / 24 )4.970156250.0293569407401053169.300891874273
Trimmed Mean ( 5 / 24 )4.96919354838710.0290846595075908170.85273242034
Trimmed Mean ( 6 / 24 )4.968833333333330.0288871676656587172.008325317415
Trimmed Mean ( 7 / 24 )4.968448275862070.0286242335578056173.574892960137
Trimmed Mean ( 8 / 24 )4.968214285714290.028322249459943175.41736198394
Trimmed Mean ( 9 / 24 )4.968333333333330.0280146088474373177.347945866031
Trimmed Mean ( 10 / 24 )4.968461538461540.0276101723108811179.950399530954
Trimmed Mean ( 11 / 24 )4.96860.027084162101396183.450386295831
Trimmed Mean ( 12 / 24 )4.968958333333330.0264579144993934187.806122566737
Trimmed Mean ( 13 / 24 )4.969347826086960.0256441688975429193.780810208402
Trimmed Mean ( 14 / 24 )4.969772727272730.0245821069622253202.170332059398
Trimmed Mean ( 15 / 24 )4.969523809523810.0234234671455518212.160043542809
Trimmed Mean ( 16 / 24 )4.96850.0222991031209777222.811651798045
Trimmed Mean ( 17 / 24 )4.967368421052630.0211500236592327234.863492404851
Trimmed Mean ( 18 / 24 )4.966111111111110.0197736307405377251.148166782043
Trimmed Mean ( 19 / 24 )4.965294117647060.0180918398506946274.4493737853
Trimmed Mean ( 20 / 24 )4.9656250.0165096348946559300.771339383608
Trimmed Mean ( 21 / 24 )4.9690.0153004394798274324.761913313097
Trimmed Mean ( 22 / 24 )4.973571428571430.0136297826489159364.904676522264
Trimmed Mean ( 23 / 24 )4.978461538461540.0115517871769804430.968945513667
Trimmed Mean ( 24 / 24 )4.979166666666670.011291857183269440.951969711789
Median4.97
Midrange5.02
Midmean - Weighted Average at Xnp4.95972972972973
Midmean - Weighted Average at X(n+1)p4.95972972972973
Midmean - Empirical Distribution Function4.95972972972973
Midmean - Empirical Distribution Function - Averaging4.95972972972973
Midmean - Empirical Distribution Function - Interpolation4.95972972972973
Midmean - Closest Observation4.95972972972973
Midmean - True Basic - Statistics Graphics Toolkit4.95972972972973
Midmean - MS Excel (old versions)4.96736842105263
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')