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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Oct 2009 11:55:28 -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/21/t1256147847v3f62at0mmokn2o.htm/, Retrieved Thu, 02 May 2024 08:03:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49546, Retrieved Thu, 02 May 2024 08:03:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2009-10-12 18:07:51] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [cs.shw.ws3.v2.1] [2009-10-21 17:55:28] [47f146dd9fb230449e079c6cbc92f5f5] [Current]
- RMPD      [Univariate Explorative Data Analysis] [cs.shw.ws3.v2.2] [2009-10-21 19:30:37] [f03ef5b3db050a0e1a9e496be7848771]
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Dataseries X:
8,9
9
9
9
9
9
9
9
9
9
9
9,1
9
9
9,1
9
9
9
9
8,9
8,9
8,9
8,9
8,8
8,8
8,7
8,7
8,5
8,5
8,4
8,2
8,2
8,1
8,1
8
7,9
7,8
7,7
7,6
7,5
7,5
7,5
7,5
7,5
7,4
7,4
7,3
7,3
7,3
7,2
7,2
7,3
7,4
7,4
7,5
7,6
7,7
7,9
8
8,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49546&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49546&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49546&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.271666666666670.08868441052650293.2708084494151
Geometric Mean8.24322645186776
Harmonic Mean8.21450383367757
Quadratic Mean8.29966866808549
Winsorized Mean ( 1 / 20 )8.271666666666670.08868441052650293.2708084494151
Winsorized Mean ( 2 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 3 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 4 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 5 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 6 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 7 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 8 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 9 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 10 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 11 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 12 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 13 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 14 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 15 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 16 / 20 )8.3250.078640460539714105.861536705979
Winsorized Mean ( 17 / 20 )8.3250.078640460539714105.861536705979
Winsorized Mean ( 18 / 20 )8.3250.0697301092469618119.388885087151
Winsorized Mean ( 19 / 20 )8.3250.0697301092469618119.388885087151
Winsorized Mean ( 20 / 20 )8.358333333333330.064759078357827129.068132921060
Trimmed Mean ( 1 / 20 )8.275862068965520.088692537861982493.3095643496398
Trimmed Mean ( 2 / 20 )8.280357142857140.088582621307870993.4760906891497
Trimmed Mean ( 3 / 20 )8.285185185185180.08903580916585493.0545278670038
Trimmed Mean ( 4 / 20 )8.290384615384620.089419934585311892.7129353631444
Trimmed Mean ( 5 / 20 )8.2960.089714285714285792.4713375796178
Trimmed Mean ( 6 / 20 )8.302083333333330.089892054223549492.3561420978007
Trimmed Mean ( 7 / 20 )8.306521739130440.090431182574201491.8546180938715
Trimmed Mean ( 8 / 20 )8.311363636363640.090874068306649491.4602349299188
Trimmed Mean ( 9 / 20 )8.316666666666670.091186314015450591.2052072338125
Trimmed Mean ( 10 / 20 )8.32250.091321319161153991.1342507581758
Trimmed Mean ( 11 / 20 )8.326315789473680.091896736106675690.6051307394457
Trimmed Mean ( 12 / 20 )8.330555555555560.092308957109319790.246448626755
Trimmed Mean ( 13 / 20 )8.335294117647060.092488121600006790.122860897701
Trimmed Mean ( 14 / 20 )8.3406250.092333041891838590.331963824721
Trimmed Mean ( 15 / 20 )8.346666666666670.091693308563106491.0280891535527
Trimmed Mean ( 16 / 20 )8.353571428571430.090337717760573192.4704723082704
Trimmed Mean ( 17 / 20 )8.35769230769230.089300370732812593.5907907112569
Trimmed Mean ( 18 / 20 )8.36250.087188887903866895.9124517016477
Trimmed Mean ( 19 / 20 )8.368181818181820.086636615744853496.5894356126085
Trimmed Mean ( 20 / 20 )8.3750.08487607064668598.6732766513515
Median8.3
Midrange8.15
Midmean - Weighted Average at Xnp8.43541666666667
Midmean - Weighted Average at X(n+1)p8.43541666666667
Midmean - Empirical Distribution Function8.43541666666667
Midmean - Empirical Distribution Function - Averaging8.43541666666667
Midmean - Empirical Distribution Function - Interpolation8.43541666666667
Midmean - Closest Observation8.43541666666667
Midmean - True Basic - Statistics Graphics Toolkit8.43541666666667
Midmean - MS Excel (old versions)8.43541666666667
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.27166666666667 & 0.088684410526502 & 93.2708084494151 \tabularnewline
Geometric Mean & 8.24322645186776 &  &  \tabularnewline
Harmonic Mean & 8.21450383367757 &  &  \tabularnewline
Quadratic Mean & 8.29966866808549 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.27166666666667 & 0.088684410526502 & 93.2708084494151 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.27166666666667 & 0.0875301938757402 & 94.5007236978054 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.27166666666667 & 0.0875301938757402 & 94.5007236978054 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.27166666666667 & 0.0875301938757402 & 94.5007236978054 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.27166666666667 & 0.0875301938757402 & 94.5007236978054 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.28166666666667 & 0.0857170376654453 & 96.6163424707947 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.28166666666667 & 0.0857170376654453 & 96.6163424707947 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.28166666666667 & 0.0857170376654453 & 96.6163424707947 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.28166666666667 & 0.0857170376654453 & 96.6163424707947 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.29833333333333 & 0.0829025589167965 & 100.097432959359 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.29833333333333 & 0.0829025589167965 & 100.097432959359 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.29833333333333 & 0.0829025589167965 & 100.097432959359 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.29833333333333 & 0.0829025589167965 & 100.097432959359 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.29833333333333 & 0.0829025589167965 & 100.097432959359 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.29833333333333 & 0.0829025589167965 & 100.097432959359 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.325 & 0.078640460539714 & 105.861536705979 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.325 & 0.078640460539714 & 105.861536705979 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.325 & 0.0697301092469618 & 119.388885087151 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.325 & 0.0697301092469618 & 119.388885087151 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.35833333333333 & 0.064759078357827 & 129.068132921060 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.27586206896552 & 0.0886925378619824 & 93.3095643496398 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.28035714285714 & 0.0885826213078709 & 93.4760906891497 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.28518518518518 & 0.089035809165854 & 93.0545278670038 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.29038461538462 & 0.0894199345853118 & 92.7129353631444 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.296 & 0.0897142857142857 & 92.4713375796178 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.30208333333333 & 0.0898920542235494 & 92.3561420978007 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.30652173913044 & 0.0904311825742014 & 91.8546180938715 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.31136363636364 & 0.0908740683066494 & 91.4602349299188 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.31666666666667 & 0.0911863140154505 & 91.2052072338125 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.3225 & 0.0913213191611539 & 91.1342507581758 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.32631578947368 & 0.0918967361066756 & 90.6051307394457 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.33055555555556 & 0.0923089571093197 & 90.246448626755 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.33529411764706 & 0.0924881216000067 & 90.122860897701 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.340625 & 0.0923330418918385 & 90.331963824721 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.34666666666667 & 0.0916933085631064 & 91.0280891535527 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.35357142857143 & 0.0903377177605731 & 92.4704723082704 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.3576923076923 & 0.0893003707328125 & 93.5907907112569 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.3625 & 0.0871888879038668 & 95.9124517016477 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.36818181818182 & 0.0866366157448534 & 96.5894356126085 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.375 & 0.084876070646685 & 98.6732766513515 \tabularnewline
Median & 8.3 &  &  \tabularnewline
Midrange & 8.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.43541666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.43541666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.43541666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.43541666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.43541666666667 &  &  \tabularnewline
Midmean - Closest Observation & 8.43541666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.43541666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.43541666666667 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49546&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]8.27166666666667[/C][C]0.088684410526502[/C][C]93.2708084494151[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.24322645186776[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.21450383367757[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.29966866808549[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.27166666666667[/C][C]0.088684410526502[/C][C]93.2708084494151[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.27166666666667[/C][C]0.0875301938757402[/C][C]94.5007236978054[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.27166666666667[/C][C]0.0875301938757402[/C][C]94.5007236978054[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.27166666666667[/C][C]0.0875301938757402[/C][C]94.5007236978054[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.27166666666667[/C][C]0.0875301938757402[/C][C]94.5007236978054[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.28166666666667[/C][C]0.0857170376654453[/C][C]96.6163424707947[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.28166666666667[/C][C]0.0857170376654453[/C][C]96.6163424707947[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.28166666666667[/C][C]0.0857170376654453[/C][C]96.6163424707947[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.28166666666667[/C][C]0.0857170376654453[/C][C]96.6163424707947[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.29833333333333[/C][C]0.0829025589167965[/C][C]100.097432959359[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.29833333333333[/C][C]0.0829025589167965[/C][C]100.097432959359[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.29833333333333[/C][C]0.0829025589167965[/C][C]100.097432959359[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.29833333333333[/C][C]0.0829025589167965[/C][C]100.097432959359[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.29833333333333[/C][C]0.0829025589167965[/C][C]100.097432959359[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.29833333333333[/C][C]0.0829025589167965[/C][C]100.097432959359[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.325[/C][C]0.078640460539714[/C][C]105.861536705979[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.325[/C][C]0.078640460539714[/C][C]105.861536705979[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.325[/C][C]0.0697301092469618[/C][C]119.388885087151[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.325[/C][C]0.0697301092469618[/C][C]119.388885087151[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.35833333333333[/C][C]0.064759078357827[/C][C]129.068132921060[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.27586206896552[/C][C]0.0886925378619824[/C][C]93.3095643496398[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.28035714285714[/C][C]0.0885826213078709[/C][C]93.4760906891497[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.28518518518518[/C][C]0.089035809165854[/C][C]93.0545278670038[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.29038461538462[/C][C]0.0894199345853118[/C][C]92.7129353631444[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.296[/C][C]0.0897142857142857[/C][C]92.4713375796178[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.30208333333333[/C][C]0.0898920542235494[/C][C]92.3561420978007[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.30652173913044[/C][C]0.0904311825742014[/C][C]91.8546180938715[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.31136363636364[/C][C]0.0908740683066494[/C][C]91.4602349299188[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.31666666666667[/C][C]0.0911863140154505[/C][C]91.2052072338125[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.3225[/C][C]0.0913213191611539[/C][C]91.1342507581758[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.32631578947368[/C][C]0.0918967361066756[/C][C]90.6051307394457[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.33055555555556[/C][C]0.0923089571093197[/C][C]90.246448626755[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.33529411764706[/C][C]0.0924881216000067[/C][C]90.122860897701[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.340625[/C][C]0.0923330418918385[/C][C]90.331963824721[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.34666666666667[/C][C]0.0916933085631064[/C][C]91.0280891535527[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.35357142857143[/C][C]0.0903377177605731[/C][C]92.4704723082704[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.3576923076923[/C][C]0.0893003707328125[/C][C]93.5907907112569[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.3625[/C][C]0.0871888879038668[/C][C]95.9124517016477[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.36818181818182[/C][C]0.0866366157448534[/C][C]96.5894356126085[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.375[/C][C]0.084876070646685[/C][C]98.6732766513515[/C][/ROW]
[ROW][C]Median[/C][C]8.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.43541666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49546&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49546&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 Mean8.271666666666670.08868441052650293.2708084494151
Geometric Mean8.24322645186776
Harmonic Mean8.21450383367757
Quadratic Mean8.29966866808549
Winsorized Mean ( 1 / 20 )8.271666666666670.08868441052650293.2708084494151
Winsorized Mean ( 2 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 3 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 4 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 5 / 20 )8.271666666666670.087530193875740294.5007236978054
Winsorized Mean ( 6 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 7 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 8 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 9 / 20 )8.281666666666670.085717037665445396.6163424707947
Winsorized Mean ( 10 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 11 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 12 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 13 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 14 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 15 / 20 )8.298333333333330.0829025589167965100.097432959359
Winsorized Mean ( 16 / 20 )8.3250.078640460539714105.861536705979
Winsorized Mean ( 17 / 20 )8.3250.078640460539714105.861536705979
Winsorized Mean ( 18 / 20 )8.3250.0697301092469618119.388885087151
Winsorized Mean ( 19 / 20 )8.3250.0697301092469618119.388885087151
Winsorized Mean ( 20 / 20 )8.358333333333330.064759078357827129.068132921060
Trimmed Mean ( 1 / 20 )8.275862068965520.088692537861982493.3095643496398
Trimmed Mean ( 2 / 20 )8.280357142857140.088582621307870993.4760906891497
Trimmed Mean ( 3 / 20 )8.285185185185180.08903580916585493.0545278670038
Trimmed Mean ( 4 / 20 )8.290384615384620.089419934585311892.7129353631444
Trimmed Mean ( 5 / 20 )8.2960.089714285714285792.4713375796178
Trimmed Mean ( 6 / 20 )8.302083333333330.089892054223549492.3561420978007
Trimmed Mean ( 7 / 20 )8.306521739130440.090431182574201491.8546180938715
Trimmed Mean ( 8 / 20 )8.311363636363640.090874068306649491.4602349299188
Trimmed Mean ( 9 / 20 )8.316666666666670.091186314015450591.2052072338125
Trimmed Mean ( 10 / 20 )8.32250.091321319161153991.1342507581758
Trimmed Mean ( 11 / 20 )8.326315789473680.091896736106675690.6051307394457
Trimmed Mean ( 12 / 20 )8.330555555555560.092308957109319790.246448626755
Trimmed Mean ( 13 / 20 )8.335294117647060.092488121600006790.122860897701
Trimmed Mean ( 14 / 20 )8.3406250.092333041891838590.331963824721
Trimmed Mean ( 15 / 20 )8.346666666666670.091693308563106491.0280891535527
Trimmed Mean ( 16 / 20 )8.353571428571430.090337717760573192.4704723082704
Trimmed Mean ( 17 / 20 )8.35769230769230.089300370732812593.5907907112569
Trimmed Mean ( 18 / 20 )8.36250.087188887903866895.9124517016477
Trimmed Mean ( 19 / 20 )8.368181818181820.086636615744853496.5894356126085
Trimmed Mean ( 20 / 20 )8.3750.08487607064668598.6732766513515
Median8.3
Midrange8.15
Midmean - Weighted Average at Xnp8.43541666666667
Midmean - Weighted Average at X(n+1)p8.43541666666667
Midmean - Empirical Distribution Function8.43541666666667
Midmean - Empirical Distribution Function - Averaging8.43541666666667
Midmean - Empirical Distribution Function - Interpolation8.43541666666667
Midmean - Closest Observation8.43541666666667
Midmean - True Basic - Statistics Graphics Toolkit8.43541666666667
Midmean - MS Excel (old versions)8.43541666666667
Number of observations60



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')