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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 11:56:11 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256061524mz0da2qp5q0c52w.htm/, Retrieved Fri, 03 May 2024 00:53:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48909, Retrieved Fri, 03 May 2024 00:53:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [WS2_vaste rentevoet] [2009-10-11 12:03:51] [517ac0676608e46c618c738721d88e41]
- RMPD    [Central Tendency] [] [2009-10-20 17:56:11] [5d37783481a916b2505b66314b556267] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.75
2.75
2.55
2.5
2.5
2.1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2.21
2.25
2.25
2.45
2.5
2.5
2.64
2.75
2.93
3
3.17
3.25
3.39
3.5
3.5
3.65
3.75
3.75
3.9
4
4
4
4
4
4
4
4
4
4
4
4
4.18
4.25
4.25
3.97
3.42
2.75

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48909&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48909&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.795972222222220.10006563959224027.9413816132652
Geometric Mean2.67603642014334
Harmonic Mean2.56837944399179
Quadratic Mean2.92034125669511
Winsorized Mean ( 1 / 24 )2.795972222222220.10006563959224027.9413816132652
Winsorized Mean ( 2 / 24 )2.794027777777780.099676248169893628.0310287463417
Winsorized Mean ( 3 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 4 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 5 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 6 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 7 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 8 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 9 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 10 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 11 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 12 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 13 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 14 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 15 / 24 )2.780277777777780.09720708019799328.6015974568402
Winsorized Mean ( 16 / 24 )2.764722222222220.094550657159310829.2406452296135
Winsorized Mean ( 17 / 24 )2.729305555555560.088681289695038330.7765658905191
Winsorized Mean ( 18 / 24 )2.729305555555560.088681289695038330.7765658905191
Winsorized Mean ( 19 / 24 )2.702916666666670.084457079852702132.0034350155216
Winsorized Mean ( 20 / 24 )2.661250.078006243856467534.1158587881341
Winsorized Mean ( 21 / 24 )2.661250.078006243856467534.1158587881341
Winsorized Mean ( 22 / 24 )2.636805555555560.074340824268566835.4691460781995
Winsorized Mean ( 23 / 24 )2.627222222222220.072923852019470836.0269260258050
Winsorized Mean ( 24 / 24 )2.580555555555560.06615528304320239.0075506724134
Trimmed Mean ( 1 / 24 )2.786571428571430.10013776963475827.8273766105952
Trimmed Mean ( 2 / 24 )2.776617647058820.10011639632754327.7338952350501
Trimmed Mean ( 3 / 24 )2.767121212121210.10021835488114127.6109223245884
Trimmed Mean ( 4 / 24 )2.759843750.10080983890678427.3767300883394
Trimmed Mean ( 5 / 24 )2.752096774193550.10136121069818927.1513802492762
Trimmed Mean ( 6 / 24 )2.743833333333330.10186068132133626.9371193844411
Trimmed Mean ( 7 / 24 )2.7350.1022934967025526.7367925446215
Trimmed Mean ( 8 / 24 )2.725535714285710.10264107163898126.5540457709972
Trimmed Mean ( 9 / 24 )2.715370370370370.10287981663604726.3936159604212
Trimmed Mean ( 10 / 24 )2.704423076923080.10297952375270226.2617555254729
Trimmed Mean ( 11 / 24 )2.69260.10290110568414926.1668714062688
Trimmed Mean ( 12 / 24 )2.679791666666670.10259336242031926.1205169949273
Trimmed Mean ( 13 / 24 )2.665869565217390.10198824223554126.1389892283916
Trimmed Mean ( 14 / 24 )2.650681818181820.10099368751717326.2460148089067
Trimmed Mean ( 15 / 24 )2.634047619047620.09948243503661426.477514528853
Trimmed Mean ( 16 / 24 )2.61650.097543908587692426.8238174775184
Trimmed Mean ( 17 / 24 )2.598947368421050.095428799039687627.2344134535339
Trimmed Mean ( 18 / 24 )2.583611111111110.09390906846162327.5118383499559
Trimmed Mean ( 19 / 24 )2.566470588235290.091534630903900128.0382469770350
Trimmed Mean ( 20 / 24 )2.55031250.089225480474623528.5827824791073
Trimmed Mean ( 21 / 24 )2.5370.08767383389258928.9367977577909
Trimmed Mean ( 22 / 24 )2.521785714285710.085024200680959829.6596227202220
Trimmed Mean ( 23 / 24 )2.507307692307690.08209480015821830.5416139326176
Trimmed Mean ( 24 / 24 )2.491666666666670.07776699373133632.0401567183464
Median2.5
Midrange3.125
Midmean - Weighted Average at Xnp2.41381818181818
Midmean - Weighted Average at X(n+1)p2.41381818181818
Midmean - Empirical Distribution Function2.41381818181818
Midmean - Empirical Distribution Function - Averaging2.41381818181818
Midmean - Empirical Distribution Function - Interpolation2.41381818181818
Midmean - Closest Observation2.41381818181818
Midmean - True Basic - Statistics Graphics Toolkit2.41381818181818
Midmean - MS Excel (old versions)2.41381818181818
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.79597222222222 & 0.100065639592240 & 27.9413816132652 \tabularnewline
Geometric Mean & 2.67603642014334 &  &  \tabularnewline
Harmonic Mean & 2.56837944399179 &  &  \tabularnewline
Quadratic Mean & 2.92034125669511 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.79597222222222 & 0.100065639592240 & 27.9413816132652 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.79402777777778 & 0.0996762481698936 & 28.0310287463417 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.78652777777778 & 0.0982891919152268 & 28.3502969500566 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.78027777777778 & 0.097207080197993 & 28.6015974568402 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.76472222222222 & 0.0945506571593108 & 29.2406452296135 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.72930555555556 & 0.0886812896950383 & 30.7765658905191 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.72930555555556 & 0.0886812896950383 & 30.7765658905191 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.70291666666667 & 0.0844570798527021 & 32.0034350155216 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.66125 & 0.0780062438564675 & 34.1158587881341 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.66125 & 0.0780062438564675 & 34.1158587881341 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.63680555555556 & 0.0743408242685668 & 35.4691460781995 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.62722222222222 & 0.0729238520194708 & 36.0269260258050 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.58055555555556 & 0.066155283043202 & 39.0075506724134 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.78657142857143 & 0.100137769634758 & 27.8273766105952 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.77661764705882 & 0.100116396327543 & 27.7338952350501 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.76712121212121 & 0.100218354881141 & 27.6109223245884 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.75984375 & 0.100809838906784 & 27.3767300883394 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.75209677419355 & 0.101361210698189 & 27.1513802492762 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.74383333333333 & 0.101860681321336 & 26.9371193844411 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.735 & 0.10229349670255 & 26.7367925446215 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.72553571428571 & 0.102641071638981 & 26.5540457709972 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.71537037037037 & 0.102879816636047 & 26.3936159604212 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.70442307692308 & 0.102979523752702 & 26.2617555254729 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.6926 & 0.102901105684149 & 26.1668714062688 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.67979166666667 & 0.102593362420319 & 26.1205169949273 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.66586956521739 & 0.101988242235541 & 26.1389892283916 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.65068181818182 & 0.100993687517173 & 26.2460148089067 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.63404761904762 & 0.099482435036614 & 26.477514528853 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.6165 & 0.0975439085876924 & 26.8238174775184 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.59894736842105 & 0.0954287990396876 & 27.2344134535339 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.58361111111111 & 0.093909068461623 & 27.5118383499559 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.56647058823529 & 0.0915346309039001 & 28.0382469770350 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.5503125 & 0.0892254804746235 & 28.5827824791073 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.537 & 0.087673833892589 & 28.9367977577909 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.52178571428571 & 0.0850242006809598 & 29.6596227202220 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.50730769230769 & 0.082094800158218 & 30.5416139326176 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.49166666666667 & 0.077766993731336 & 32.0401567183464 \tabularnewline
Median & 2.5 &  &  \tabularnewline
Midrange & 3.125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.41381818181818 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.41381818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.41381818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.41381818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.41381818181818 &  &  \tabularnewline
Midmean - Closest Observation & 2.41381818181818 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.41381818181818 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.41381818181818 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48909&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]2.79597222222222[/C][C]0.100065639592240[/C][C]27.9413816132652[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.67603642014334[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.56837944399179[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.92034125669511[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.79597222222222[/C][C]0.100065639592240[/C][C]27.9413816132652[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.79402777777778[/C][C]0.0996762481698936[/C][C]28.0310287463417[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.78652777777778[/C][C]0.0982891919152268[/C][C]28.3502969500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.78027777777778[/C][C]0.097207080197993[/C][C]28.6015974568402[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.76472222222222[/C][C]0.0945506571593108[/C][C]29.2406452296135[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.72930555555556[/C][C]0.0886812896950383[/C][C]30.7765658905191[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.72930555555556[/C][C]0.0886812896950383[/C][C]30.7765658905191[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.70291666666667[/C][C]0.0844570798527021[/C][C]32.0034350155216[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.66125[/C][C]0.0780062438564675[/C][C]34.1158587881341[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.66125[/C][C]0.0780062438564675[/C][C]34.1158587881341[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.63680555555556[/C][C]0.0743408242685668[/C][C]35.4691460781995[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.62722222222222[/C][C]0.0729238520194708[/C][C]36.0269260258050[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.58055555555556[/C][C]0.066155283043202[/C][C]39.0075506724134[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.78657142857143[/C][C]0.100137769634758[/C][C]27.8273766105952[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.77661764705882[/C][C]0.100116396327543[/C][C]27.7338952350501[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.76712121212121[/C][C]0.100218354881141[/C][C]27.6109223245884[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.75984375[/C][C]0.100809838906784[/C][C]27.3767300883394[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.75209677419355[/C][C]0.101361210698189[/C][C]27.1513802492762[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.74383333333333[/C][C]0.101860681321336[/C][C]26.9371193844411[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.735[/C][C]0.10229349670255[/C][C]26.7367925446215[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.72553571428571[/C][C]0.102641071638981[/C][C]26.5540457709972[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.71537037037037[/C][C]0.102879816636047[/C][C]26.3936159604212[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.70442307692308[/C][C]0.102979523752702[/C][C]26.2617555254729[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.6926[/C][C]0.102901105684149[/C][C]26.1668714062688[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.67979166666667[/C][C]0.102593362420319[/C][C]26.1205169949273[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.66586956521739[/C][C]0.101988242235541[/C][C]26.1389892283916[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.65068181818182[/C][C]0.100993687517173[/C][C]26.2460148089067[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.63404761904762[/C][C]0.099482435036614[/C][C]26.477514528853[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.6165[/C][C]0.0975439085876924[/C][C]26.8238174775184[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.59894736842105[/C][C]0.0954287990396876[/C][C]27.2344134535339[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.58361111111111[/C][C]0.093909068461623[/C][C]27.5118383499559[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.56647058823529[/C][C]0.0915346309039001[/C][C]28.0382469770350[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.5503125[/C][C]0.0892254804746235[/C][C]28.5827824791073[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.537[/C][C]0.087673833892589[/C][C]28.9367977577909[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.52178571428571[/C][C]0.0850242006809598[/C][C]29.6596227202220[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.50730769230769[/C][C]0.082094800158218[/C][C]30.5416139326176[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.49166666666667[/C][C]0.077766993731336[/C][C]32.0401567183464[/C][/ROW]
[ROW][C]Median[/C][C]2.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.41381818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.41381818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.41381818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.41381818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.41381818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.41381818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.41381818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.41381818181818[/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=48909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48909&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.795972222222220.10006563959224027.9413816132652
Geometric Mean2.67603642014334
Harmonic Mean2.56837944399179
Quadratic Mean2.92034125669511
Winsorized Mean ( 1 / 24 )2.795972222222220.10006563959224027.9413816132652
Winsorized Mean ( 2 / 24 )2.794027777777780.099676248169893628.0310287463417
Winsorized Mean ( 3 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 4 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 5 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 6 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 7 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 8 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 9 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 10 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 11 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 12 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 13 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 14 / 24 )2.786527777777780.098289191915226828.3502969500566
Winsorized Mean ( 15 / 24 )2.780277777777780.09720708019799328.6015974568402
Winsorized Mean ( 16 / 24 )2.764722222222220.094550657159310829.2406452296135
Winsorized Mean ( 17 / 24 )2.729305555555560.088681289695038330.7765658905191
Winsorized Mean ( 18 / 24 )2.729305555555560.088681289695038330.7765658905191
Winsorized Mean ( 19 / 24 )2.702916666666670.084457079852702132.0034350155216
Winsorized Mean ( 20 / 24 )2.661250.078006243856467534.1158587881341
Winsorized Mean ( 21 / 24 )2.661250.078006243856467534.1158587881341
Winsorized Mean ( 22 / 24 )2.636805555555560.074340824268566835.4691460781995
Winsorized Mean ( 23 / 24 )2.627222222222220.072923852019470836.0269260258050
Winsorized Mean ( 24 / 24 )2.580555555555560.06615528304320239.0075506724134
Trimmed Mean ( 1 / 24 )2.786571428571430.10013776963475827.8273766105952
Trimmed Mean ( 2 / 24 )2.776617647058820.10011639632754327.7338952350501
Trimmed Mean ( 3 / 24 )2.767121212121210.10021835488114127.6109223245884
Trimmed Mean ( 4 / 24 )2.759843750.10080983890678427.3767300883394
Trimmed Mean ( 5 / 24 )2.752096774193550.10136121069818927.1513802492762
Trimmed Mean ( 6 / 24 )2.743833333333330.10186068132133626.9371193844411
Trimmed Mean ( 7 / 24 )2.7350.1022934967025526.7367925446215
Trimmed Mean ( 8 / 24 )2.725535714285710.10264107163898126.5540457709972
Trimmed Mean ( 9 / 24 )2.715370370370370.10287981663604726.3936159604212
Trimmed Mean ( 10 / 24 )2.704423076923080.10297952375270226.2617555254729
Trimmed Mean ( 11 / 24 )2.69260.10290110568414926.1668714062688
Trimmed Mean ( 12 / 24 )2.679791666666670.10259336242031926.1205169949273
Trimmed Mean ( 13 / 24 )2.665869565217390.10198824223554126.1389892283916
Trimmed Mean ( 14 / 24 )2.650681818181820.10099368751717326.2460148089067
Trimmed Mean ( 15 / 24 )2.634047619047620.09948243503661426.477514528853
Trimmed Mean ( 16 / 24 )2.61650.097543908587692426.8238174775184
Trimmed Mean ( 17 / 24 )2.598947368421050.095428799039687627.2344134535339
Trimmed Mean ( 18 / 24 )2.583611111111110.09390906846162327.5118383499559
Trimmed Mean ( 19 / 24 )2.566470588235290.091534630903900128.0382469770350
Trimmed Mean ( 20 / 24 )2.55031250.089225480474623528.5827824791073
Trimmed Mean ( 21 / 24 )2.5370.08767383389258928.9367977577909
Trimmed Mean ( 22 / 24 )2.521785714285710.085024200680959829.6596227202220
Trimmed Mean ( 23 / 24 )2.507307692307690.08209480015821830.5416139326176
Trimmed Mean ( 24 / 24 )2.491666666666670.07776699373133632.0401567183464
Median2.5
Midrange3.125
Midmean - Weighted Average at Xnp2.41381818181818
Midmean - Weighted Average at X(n+1)p2.41381818181818
Midmean - Empirical Distribution Function2.41381818181818
Midmean - Empirical Distribution Function - Averaging2.41381818181818
Midmean - Empirical Distribution Function - Interpolation2.41381818181818
Midmean - Closest Observation2.41381818181818
Midmean - True Basic - Statistics Graphics Toolkit2.41381818181818
Midmean - MS Excel (old versions)2.41381818181818
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')