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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 17:26:12 +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/10/t14129588266trcy5cn4ikhb6h.htm/, Retrieved Mon, 13 May 2024 07:55:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240356, Retrieved Mon, 13 May 2024 07:55:02 +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] [Ziekteverzuimperc...] [2014-10-10 16:26:12] [7e6d0f152da1c8c00143095b938e0e97] [Current]
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Dataseries X:
4,8
4
3,5
4,1
4,1
3,8
3,5
4,1
4,5
4,1
3,8
4,6
5,2
4,4
4,3
4,7
5,1
4,6
4,7
4,9
5,1
4,6
4,6
4,8
5,1
4,8
4,4
4,8
4,7
4
3,5
4
3,7
3,1
2,9
3,3
3,5
3
2,7
3,2
3,8
3,3
3,1
3,5
3,9
3,4
3,2
3,6
3,9
3,2
3
3,4
3,6
3
3
3,6
3,6
3,3
3,3
3,6
3,8
3,3
3,1
3,4
3,5
3,1
3
3,3
3,7
3,1
2,9
3,1
3,2




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=240356&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=240356&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240356&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 Mean3.80.078440856933932648.4441418481771
Geometric Mean3.74379092227458
Harmonic Mean3.69010504134852
Quadratic Mean3.85785091710788
Winsorized Mean ( 1 / 24 )3.80136986301370.077623892004409448.9716473221642
Winsorized Mean ( 2 / 24 )3.80136986301370.077623892004409448.9716473221642
Winsorized Mean ( 3 / 24 )3.805479452054790.07699380302206849.425788864645
Winsorized Mean ( 4 / 24 )3.794520547945210.074583838062599350.8759088632635
Winsorized Mean ( 5 / 24 )3.787671232876710.073220783428430451.7294551563897
Winsorized Mean ( 6 / 24 )3.787671232876710.073220783428430451.7294551563897
Winsorized Mean ( 7 / 24 )3.787671232876710.073220783428430451.7294551563897
Winsorized Mean ( 8 / 24 )3.79863013698630.071659316568106553.009578082928
Winsorized Mean ( 9 / 24 )3.786301369863010.069333505347881954.6099804252675
Winsorized Mean ( 10 / 24 )3.786301369863010.069333505347881954.6099804252675
Winsorized Mean ( 11 / 24 )3.786301369863010.069333505347881954.6099804252675
Winsorized Mean ( 12 / 24 )3.769863013698630.066400293510921856.7747944228371
Winsorized Mean ( 13 / 24 )3.769863013698630.066400293510921856.7747944228371
Winsorized Mean ( 14 / 24 )3.789041095890410.063825343272237459.3657770037966
Winsorized Mean ( 15 / 24 )3.789041095890410.063825343272237459.3657770037966
Winsorized Mean ( 16 / 24 )3.767123287671230.060030902573398162.7530676065594
Winsorized Mean ( 17 / 24 )3.743835616438360.056164383561643966.6585365853658
Winsorized Mean ( 18 / 24 )3.768493150684930.052988206677647871.1194695380134
Winsorized Mean ( 19 / 24 )3.742465753424660.048763937952852376.7465859103316
Winsorized Mean ( 20 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 21 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 22 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 23 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 24 / 24 )3.687671232876710.0316315116974482116.582200311793
Trimmed Mean ( 1 / 24 )3.795774647887320.07660913940461149.5472821831341
Trimmed Mean ( 2 / 24 )3.789855072463770.075383218952515850.2745189861289
Trimmed Mean ( 3 / 24 )3.783582089552240.073903778645475851.1960573450849
Trimmed Mean ( 4 / 24 )3.775384615384620.072391522600223752.1523029185872
Trimmed Mean ( 5 / 24 )3.769841269841270.071435967074603852.7723137828351
Trimmed Mean ( 6 / 24 )3.76557377049180.070667591210893453.285724134196
Trimmed Mean ( 7 / 24 )3.761016949152540.069691519883089753.9666369087917
Trimmed Mean ( 8 / 24 )3.756140350877190.068460402539808354.8658817583358
Trimmed Mean ( 9 / 24 )3.749090909090910.06726362664806355.7372698428367
Trimmed Mean ( 10 / 24 )3.743396226415090.066288142289131556.4715814494752
Trimmed Mean ( 11 / 24 )3.737254901960780.065016485650811457.4816504545128
Trimmed Mean ( 12 / 24 )3.730612244897960.063366717054062658.8733710429579
Trimmed Mean ( 13 / 24 )3.725531914893620.061920249886729360.1666162799526
Trimmed Mean ( 14 / 24 )3.720.060016832655682561.9826111341412
Trimmed Mean ( 15 / 24 )3.711627906976740.058042000137028163.9472778025252
Trimmed Mean ( 16 / 24 )3.702439024390240.055379819878113666.855382204908
Trimmed Mean ( 17 / 24 )3.694871794871790.05284723457038369.9160859581194
Trimmed Mean ( 18 / 24 )3.689189189189190.050490653222349773.0667748136038
Trimmed Mean ( 19 / 24 )3.680.047949553322899176.7473259910964
Trimmed Mean ( 20 / 24 )3.672727272727270.045700094338956680.3658575732194
Trimmed Mean ( 21 / 24 )3.670967741935480.045007418357970681.5636149742717
Trimmed Mean ( 22 / 24 )3.668965517241380.04386034944115383.6510781147331
Trimmed Mean ( 23 / 24 )3.666666666666670.042028344797074387.2427092803785
Trimmed Mean ( 24 / 24 )3.6640.039106691669499993.6924051506414
Median3.6
Midrange3.95
Midmean - Weighted Average at Xnp3.66944444444444
Midmean - Weighted Average at X(n+1)p3.70789473684211
Midmean - Empirical Distribution Function3.70789473684211
Midmean - Empirical Distribution Function - Averaging3.70789473684211
Midmean - Empirical Distribution Function - Interpolation3.70789473684211
Midmean - Closest Observation3.65952380952381
Midmean - True Basic - Statistics Graphics Toolkit3.70789473684211
Midmean - MS Excel (old versions)3.70789473684211
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.8 & 0.0784408569339326 & 48.4441418481771 \tabularnewline
Geometric Mean & 3.74379092227458 &  &  \tabularnewline
Harmonic Mean & 3.69010504134852 &  &  \tabularnewline
Quadratic Mean & 3.85785091710788 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.8013698630137 & 0.0776238920044094 & 48.9716473221642 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.8013698630137 & 0.0776238920044094 & 48.9716473221642 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.80547945205479 & 0.076993803022068 & 49.425788864645 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.79452054794521 & 0.0745838380625993 & 50.8759088632635 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.78767123287671 & 0.0732207834284304 & 51.7294551563897 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.78767123287671 & 0.0732207834284304 & 51.7294551563897 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.78767123287671 & 0.0732207834284304 & 51.7294551563897 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.7986301369863 & 0.0716593165681065 & 53.009578082928 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.78630136986301 & 0.0693335053478819 & 54.6099804252675 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.78630136986301 & 0.0693335053478819 & 54.6099804252675 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.78630136986301 & 0.0693335053478819 & 54.6099804252675 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.76986301369863 & 0.0664002935109218 & 56.7747944228371 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.76986301369863 & 0.0664002935109218 & 56.7747944228371 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.78904109589041 & 0.0638253432722374 & 59.3657770037966 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.78904109589041 & 0.0638253432722374 & 59.3657770037966 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.76712328767123 & 0.0600309025733981 & 62.7530676065594 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.74383561643836 & 0.0561643835616439 & 66.6585365853658 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.76849315068493 & 0.0529882066776478 & 71.1194695380134 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.74246575342466 & 0.0487639379528523 & 76.7465859103316 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.68767123287671 & 0.0404947149472433 & 91.0654942918112 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.68767123287671 & 0.0404947149472433 & 91.0654942918112 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.68767123287671 & 0.0404947149472433 & 91.0654942918112 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.68767123287671 & 0.0404947149472433 & 91.0654942918112 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.68767123287671 & 0.0316315116974482 & 116.582200311793 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.79577464788732 & 0.076609139404611 & 49.5472821831341 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.78985507246377 & 0.0753832189525158 & 50.2745189861289 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.78358208955224 & 0.0739037786454758 & 51.1960573450849 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.77538461538462 & 0.0723915226002237 & 52.1523029185872 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.76984126984127 & 0.0714359670746038 & 52.7723137828351 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.7655737704918 & 0.0706675912108934 & 53.285724134196 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.76101694915254 & 0.0696915198830897 & 53.9666369087917 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.75614035087719 & 0.0684604025398083 & 54.8658817583358 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.74909090909091 & 0.067263626648063 & 55.7372698428367 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.74339622641509 & 0.0662881422891315 & 56.4715814494752 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.73725490196078 & 0.0650164856508114 & 57.4816504545128 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.73061224489796 & 0.0633667170540626 & 58.8733710429579 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.72553191489362 & 0.0619202498867293 & 60.1666162799526 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.72 & 0.0600168326556825 & 61.9826111341412 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.71162790697674 & 0.0580420001370281 & 63.9472778025252 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.70243902439024 & 0.0553798198781136 & 66.855382204908 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.69487179487179 & 0.052847234570383 & 69.9160859581194 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.68918918918919 & 0.0504906532223497 & 73.0667748136038 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.68 & 0.0479495533228991 & 76.7473259910964 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.67272727272727 & 0.0457000943389566 & 80.3658575732194 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.67096774193548 & 0.0450074183579706 & 81.5636149742717 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.66896551724138 & 0.043860349441153 & 83.6510781147331 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.66666666666667 & 0.0420283447970743 & 87.2427092803785 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.664 & 0.0391066916694999 & 93.6924051506414 \tabularnewline
Median & 3.6 &  &  \tabularnewline
Midrange & 3.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.66944444444444 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.70789473684211 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.70789473684211 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.70789473684211 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.70789473684211 &  &  \tabularnewline
Midmean - Closest Observation & 3.65952380952381 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.70789473684211 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.70789473684211 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240356&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]3.8[/C][C]0.0784408569339326[/C][C]48.4441418481771[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.74379092227458[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.69010504134852[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.85785091710788[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.8013698630137[/C][C]0.0776238920044094[/C][C]48.9716473221642[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.8013698630137[/C][C]0.0776238920044094[/C][C]48.9716473221642[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.80547945205479[/C][C]0.076993803022068[/C][C]49.425788864645[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.79452054794521[/C][C]0.0745838380625993[/C][C]50.8759088632635[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.78767123287671[/C][C]0.0732207834284304[/C][C]51.7294551563897[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.78767123287671[/C][C]0.0732207834284304[/C][C]51.7294551563897[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.78767123287671[/C][C]0.0732207834284304[/C][C]51.7294551563897[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.7986301369863[/C][C]0.0716593165681065[/C][C]53.009578082928[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.78630136986301[/C][C]0.0693335053478819[/C][C]54.6099804252675[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.78630136986301[/C][C]0.0693335053478819[/C][C]54.6099804252675[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.78630136986301[/C][C]0.0693335053478819[/C][C]54.6099804252675[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.76986301369863[/C][C]0.0664002935109218[/C][C]56.7747944228371[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.76986301369863[/C][C]0.0664002935109218[/C][C]56.7747944228371[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.78904109589041[/C][C]0.0638253432722374[/C][C]59.3657770037966[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.78904109589041[/C][C]0.0638253432722374[/C][C]59.3657770037966[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.76712328767123[/C][C]0.0600309025733981[/C][C]62.7530676065594[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.74383561643836[/C][C]0.0561643835616439[/C][C]66.6585365853658[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.76849315068493[/C][C]0.0529882066776478[/C][C]71.1194695380134[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.74246575342466[/C][C]0.0487639379528523[/C][C]76.7465859103316[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.68767123287671[/C][C]0.0404947149472433[/C][C]91.0654942918112[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.68767123287671[/C][C]0.0404947149472433[/C][C]91.0654942918112[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.68767123287671[/C][C]0.0404947149472433[/C][C]91.0654942918112[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.68767123287671[/C][C]0.0404947149472433[/C][C]91.0654942918112[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.68767123287671[/C][C]0.0316315116974482[/C][C]116.582200311793[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.79577464788732[/C][C]0.076609139404611[/C][C]49.5472821831341[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.78985507246377[/C][C]0.0753832189525158[/C][C]50.2745189861289[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.78358208955224[/C][C]0.0739037786454758[/C][C]51.1960573450849[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.77538461538462[/C][C]0.0723915226002237[/C][C]52.1523029185872[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.76984126984127[/C][C]0.0714359670746038[/C][C]52.7723137828351[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.7655737704918[/C][C]0.0706675912108934[/C][C]53.285724134196[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.76101694915254[/C][C]0.0696915198830897[/C][C]53.9666369087917[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.75614035087719[/C][C]0.0684604025398083[/C][C]54.8658817583358[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.74909090909091[/C][C]0.067263626648063[/C][C]55.7372698428367[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.74339622641509[/C][C]0.0662881422891315[/C][C]56.4715814494752[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.73725490196078[/C][C]0.0650164856508114[/C][C]57.4816504545128[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.73061224489796[/C][C]0.0633667170540626[/C][C]58.8733710429579[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.72553191489362[/C][C]0.0619202498867293[/C][C]60.1666162799526[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.72[/C][C]0.0600168326556825[/C][C]61.9826111341412[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.71162790697674[/C][C]0.0580420001370281[/C][C]63.9472778025252[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.70243902439024[/C][C]0.0553798198781136[/C][C]66.855382204908[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.69487179487179[/C][C]0.052847234570383[/C][C]69.9160859581194[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.68918918918919[/C][C]0.0504906532223497[/C][C]73.0667748136038[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.68[/C][C]0.0479495533228991[/C][C]76.7473259910964[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.67272727272727[/C][C]0.0457000943389566[/C][C]80.3658575732194[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.67096774193548[/C][C]0.0450074183579706[/C][C]81.5636149742717[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.66896551724138[/C][C]0.043860349441153[/C][C]83.6510781147331[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.66666666666667[/C][C]0.0420283447970743[/C][C]87.2427092803785[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.664[/C][C]0.0391066916694999[/C][C]93.6924051506414[/C][/ROW]
[ROW][C]Median[/C][C]3.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.66944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.70789473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.70789473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.70789473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.70789473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.65952380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.70789473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.70789473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240356&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240356&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 Mean3.80.078440856933932648.4441418481771
Geometric Mean3.74379092227458
Harmonic Mean3.69010504134852
Quadratic Mean3.85785091710788
Winsorized Mean ( 1 / 24 )3.80136986301370.077623892004409448.9716473221642
Winsorized Mean ( 2 / 24 )3.80136986301370.077623892004409448.9716473221642
Winsorized Mean ( 3 / 24 )3.805479452054790.07699380302206849.425788864645
Winsorized Mean ( 4 / 24 )3.794520547945210.074583838062599350.8759088632635
Winsorized Mean ( 5 / 24 )3.787671232876710.073220783428430451.7294551563897
Winsorized Mean ( 6 / 24 )3.787671232876710.073220783428430451.7294551563897
Winsorized Mean ( 7 / 24 )3.787671232876710.073220783428430451.7294551563897
Winsorized Mean ( 8 / 24 )3.79863013698630.071659316568106553.009578082928
Winsorized Mean ( 9 / 24 )3.786301369863010.069333505347881954.6099804252675
Winsorized Mean ( 10 / 24 )3.786301369863010.069333505347881954.6099804252675
Winsorized Mean ( 11 / 24 )3.786301369863010.069333505347881954.6099804252675
Winsorized Mean ( 12 / 24 )3.769863013698630.066400293510921856.7747944228371
Winsorized Mean ( 13 / 24 )3.769863013698630.066400293510921856.7747944228371
Winsorized Mean ( 14 / 24 )3.789041095890410.063825343272237459.3657770037966
Winsorized Mean ( 15 / 24 )3.789041095890410.063825343272237459.3657770037966
Winsorized Mean ( 16 / 24 )3.767123287671230.060030902573398162.7530676065594
Winsorized Mean ( 17 / 24 )3.743835616438360.056164383561643966.6585365853658
Winsorized Mean ( 18 / 24 )3.768493150684930.052988206677647871.1194695380134
Winsorized Mean ( 19 / 24 )3.742465753424660.048763937952852376.7465859103316
Winsorized Mean ( 20 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 21 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 22 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 23 / 24 )3.687671232876710.040494714947243391.0654942918112
Winsorized Mean ( 24 / 24 )3.687671232876710.0316315116974482116.582200311793
Trimmed Mean ( 1 / 24 )3.795774647887320.07660913940461149.5472821831341
Trimmed Mean ( 2 / 24 )3.789855072463770.075383218952515850.2745189861289
Trimmed Mean ( 3 / 24 )3.783582089552240.073903778645475851.1960573450849
Trimmed Mean ( 4 / 24 )3.775384615384620.072391522600223752.1523029185872
Trimmed Mean ( 5 / 24 )3.769841269841270.071435967074603852.7723137828351
Trimmed Mean ( 6 / 24 )3.76557377049180.070667591210893453.285724134196
Trimmed Mean ( 7 / 24 )3.761016949152540.069691519883089753.9666369087917
Trimmed Mean ( 8 / 24 )3.756140350877190.068460402539808354.8658817583358
Trimmed Mean ( 9 / 24 )3.749090909090910.06726362664806355.7372698428367
Trimmed Mean ( 10 / 24 )3.743396226415090.066288142289131556.4715814494752
Trimmed Mean ( 11 / 24 )3.737254901960780.065016485650811457.4816504545128
Trimmed Mean ( 12 / 24 )3.730612244897960.063366717054062658.8733710429579
Trimmed Mean ( 13 / 24 )3.725531914893620.061920249886729360.1666162799526
Trimmed Mean ( 14 / 24 )3.720.060016832655682561.9826111341412
Trimmed Mean ( 15 / 24 )3.711627906976740.058042000137028163.9472778025252
Trimmed Mean ( 16 / 24 )3.702439024390240.055379819878113666.855382204908
Trimmed Mean ( 17 / 24 )3.694871794871790.05284723457038369.9160859581194
Trimmed Mean ( 18 / 24 )3.689189189189190.050490653222349773.0667748136038
Trimmed Mean ( 19 / 24 )3.680.047949553322899176.7473259910964
Trimmed Mean ( 20 / 24 )3.672727272727270.045700094338956680.3658575732194
Trimmed Mean ( 21 / 24 )3.670967741935480.045007418357970681.5636149742717
Trimmed Mean ( 22 / 24 )3.668965517241380.04386034944115383.6510781147331
Trimmed Mean ( 23 / 24 )3.666666666666670.042028344797074387.2427092803785
Trimmed Mean ( 24 / 24 )3.6640.039106691669499993.6924051506414
Median3.6
Midrange3.95
Midmean - Weighted Average at Xnp3.66944444444444
Midmean - Weighted Average at X(n+1)p3.70789473684211
Midmean - Empirical Distribution Function3.70789473684211
Midmean - Empirical Distribution Function - Averaging3.70789473684211
Midmean - Empirical Distribution Function - Interpolation3.70789473684211
Midmean - Closest Observation3.65952380952381
Midmean - True Basic - Statistics Graphics Toolkit3.70789473684211
Midmean - MS Excel (old versions)3.70789473684211
Number of observations73



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')