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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 21 Oct 2008 01:26:01 -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/2008/Oct/21/t1224574023fopuzqq9sejgdkm.htm/, Retrieved Sun, 19 May 2024 19:41:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18354, Retrieved Sun, 19 May 2024 19:41:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [] [2008-10-21 07:26:01] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
F    D    [Central Tendency] [] [2008-10-21 07:30:49] [e3dae385761e8d86216d332d70171419]
F    D    [Central Tendency] [] [2008-10-21 07:32:41] [e3dae385761e8d86216d332d70171419]
F    D    [Central Tendency] [] [2008-10-21 07:34:41] [e3dae385761e8d86216d332d70171419]
Feedback Forum
2008-10-23 15:44:21 [Thomas Beyers] [reply
de reeks bevat outliers. Kijk naar plots dalend verloop naar einde toe bij winsorized mean .
2008-10-24 11:43:26 [c4ccf1f44d59ce687616256b9e80d6b0] [reply
Op basis van het verloop van de grafieken en het verschil tussen de mid-range en de mediaan kunnen we afleiden dat deze reeks duidelijk wordt beïnvloed door outliers.
2008-10-24 16:11:16 [Jan Van Riet] [reply
Het berekenen van de central tendency heeft geen nut wanneer er geen conclusies uit worden getrokken. In dit geval zou je kunnen kijken welke waarden binnen het betrouwbaarheidsinterval liggen en welke niet. Een groot aantal liggen hierbuiten, en dus wordt de datareeks duidelijk beïnvloed door outliers. Deze tijdreeks is dus niet echt bruikbaar.

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Dataseries X:
5,58
5,39
5,19
5,16
5,2
5,25
5,26
5,21
5,18
5,13
5,03
5,01
4,87
4,86
4,82
4,69
4,65
4,61
4,47
4,37
4,29
4,2
4,19
4,09
3,88
3,87
3,74
3,61
3,43
3,29
3,18
3,07
3,02
2,97
2,98
3,01
3,06
3,12
3,16
3,19
3,21
3,27
3,36
3,45
3,52
3,58
3,62
3,5
3,43
3,41
3,48
3,63
3,76
3,8
3,72
3,67
3,58
3,47




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=18354&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=18354&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18354&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 Mean4.012758620689660.10452924839064738.3888594098864
Geometric Mean3.9380120812683
Harmonic Mean3.86719662152113
Quadratic Mean4.08962522522035
Winsorized Mean ( 1 / 19 )4.009655172413790.10368555163911638.6713009578194
Winsorized Mean ( 2 / 19 )4.006206896551720.10250251279472239.0839871855123
Winsorized Mean ( 3 / 19 )4.006206896551720.1023040164006339.1598202837231
Winsorized Mean ( 4 / 19 )4.006206896551720.10126269574865539.5625147734122
Winsorized Mean ( 5 / 19 )4.006206896551720.10094257158298639.6879813316245
Winsorized Mean ( 6 / 19 )4.010344827586210.099902846186578540.1424481950844
Winsorized Mean ( 7 / 19 )4.013965517241380.09890995118055240.5820189913371
Winsorized Mean ( 8 / 19 )4.013965517241380.09792645723052240.9895918913147
Winsorized Mean ( 9 / 19 )4.010862068965520.096744743220289541.458191271775
Winsorized Mean ( 10 / 19 )3.997068965517240.092797162058912843.0731810847802
Winsorized Mean ( 11 / 19 )4.004655172413790.090398464403104144.3000353917105
Winsorized Mean ( 12 / 19 )3.97982758620690.08429254052609347.214469529186
Winsorized Mean ( 13 / 19 )3.993275862068970.081682025518859148.8880611946502
Winsorized Mean ( 14 / 19 )3.995689655172410.078277784194655251.0450020562186
Winsorized Mean ( 15 / 19 )3.967241379310350.071505203573863455.4818555996735
Winsorized Mean ( 16 / 19 )3.956206896551720.069561250341514356.8737174379203
Winsorized Mean ( 17 / 19 )3.950344827586210.066744343215850759.1862117035271
Winsorized Mean ( 18 / 19 )3.913103448275860.058521409827001366.8661855523239
Winsorized Mean ( 19 / 19 )3.883620689655170.052692592198400573.7033523617967
Trimmed Mean ( 1 / 19 )4.003392857142860.1028396421574538.9284985162975
Trimmed Mean ( 2 / 19 )3.996666666666670.10170042742881339.2984254610354
Trimmed Mean ( 3 / 19 )3.991346153846150.10095809086981639.5346833469043
Trimmed Mean ( 4 / 19 )3.98560.10000251425410739.8549979440774
Trimmed Mean ( 5 / 19 )3.9793750.099072563782833240.1662665026291
Trimmed Mean ( 6 / 19 )3.972608695652170.09786238725322140.5938257501625
Trimmed Mean ( 7 / 19 )3.964318181818180.09648275252941641.0883611618515
Trimmed Mean ( 8 / 19 )3.954523809523810.094824369947809941.7036655418889
Trimmed Mean ( 9 / 19 )3.943750.092770524372279442.5108085427447
Trimmed Mean ( 10 / 19 )3.932368421052630.090225286399695243.5838840525522
Trimmed Mean ( 11 / 19 )3.921944444444440.087809154026583144.6644144101095
Trimmed Mean ( 12 / 19 )3.909117647058820.08496971007654346.0060137140328
Trimmed Mean ( 13 / 19 )3.89843750.082735623172451447.1192135928465
Trimmed Mean ( 14 / 19 )3.884333333333330.080013911625665748.5457247922794
Trimmed Mean ( 15 / 19 )3.867857142857140.076824125989751450.3469072121059
Trimmed Mean ( 16 / 19 )3.853076923076920.074302436507869151.8566699043423
Trimmed Mean ( 17 / 19 )3.83750.070821397118773954.18560147245
Trimmed Mean ( 18 / 19 )3.820.066041440486045357.8424693932467
Trimmed Mean ( 19 / 19 )3.8050.062101360269871961.2707996002782
Median3.73
Midrange4.275
Midmean - Weighted Average at Xnp3.85206896551724
Midmean - Weighted Average at X(n+1)p3.88433333333333
Midmean - Empirical Distribution Function3.88433333333333
Midmean - Empirical Distribution Function - Averaging3.88433333333333
Midmean - Empirical Distribution Function - Interpolation3.86785714285714
Midmean - Closest Observation3.88433333333333
Midmean - True Basic - Statistics Graphics Toolkit3.88433333333333
Midmean - MS Excel (old versions)3.88433333333333
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.01275862068966 & 0.104529248390647 & 38.3888594098864 \tabularnewline
Geometric Mean & 3.9380120812683 &  &  \tabularnewline
Harmonic Mean & 3.86719662152113 &  &  \tabularnewline
Quadratic Mean & 4.08962522522035 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 4.00965517241379 & 0.103685551639116 & 38.6713009578194 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 4.00620689655172 & 0.102502512794722 & 39.0839871855123 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 4.00620689655172 & 0.10230401640063 & 39.1598202837231 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 4.00620689655172 & 0.101262695748655 & 39.5625147734122 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 4.00620689655172 & 0.100942571582986 & 39.6879813316245 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 4.01034482758621 & 0.0999028461865785 & 40.1424481950844 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 4.01396551724138 & 0.098909951180552 & 40.5820189913371 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 4.01396551724138 & 0.097926457230522 & 40.9895918913147 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 4.01086206896552 & 0.0967447432202895 & 41.458191271775 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 3.99706896551724 & 0.0927971620589128 & 43.0731810847802 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 4.00465517241379 & 0.0903984644031041 & 44.3000353917105 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 3.9798275862069 & 0.084292540526093 & 47.214469529186 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 3.99327586206897 & 0.0816820255188591 & 48.8880611946502 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 3.99568965517241 & 0.0782777841946552 & 51.0450020562186 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 3.96724137931035 & 0.0715052035738634 & 55.4818555996735 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 3.95620689655172 & 0.0695612503415143 & 56.8737174379203 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 3.95034482758621 & 0.0667443432158507 & 59.1862117035271 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 3.91310344827586 & 0.0585214098270013 & 66.8661855523239 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 3.88362068965517 & 0.0526925921984005 & 73.7033523617967 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 4.00339285714286 & 0.10283964215745 & 38.9284985162975 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 3.99666666666667 & 0.101700427428813 & 39.2984254610354 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 3.99134615384615 & 0.100958090869816 & 39.5346833469043 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 3.9856 & 0.100002514254107 & 39.8549979440774 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 3.979375 & 0.0990725637828332 & 40.1662665026291 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 3.97260869565217 & 0.097862387253221 & 40.5938257501625 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 3.96431818181818 & 0.096482752529416 & 41.0883611618515 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 3.95452380952381 & 0.0948243699478099 & 41.7036655418889 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 3.94375 & 0.0927705243722794 & 42.5108085427447 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 3.93236842105263 & 0.0902252863996952 & 43.5838840525522 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 3.92194444444444 & 0.0878091540265831 & 44.6644144101095 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 3.90911764705882 & 0.084969710076543 & 46.0060137140328 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 3.8984375 & 0.0827356231724514 & 47.1192135928465 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 3.88433333333333 & 0.0800139116256657 & 48.5457247922794 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 3.86785714285714 & 0.0768241259897514 & 50.3469072121059 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 3.85307692307692 & 0.0743024365078691 & 51.8566699043423 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 3.8375 & 0.0708213971187739 & 54.18560147245 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 3.82 & 0.0660414404860453 & 57.8424693932467 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 3.805 & 0.0621013602698719 & 61.2707996002782 \tabularnewline
Median & 3.73 &  &  \tabularnewline
Midrange & 4.275 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.85206896551724 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.88433333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.88433333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.88433333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.86785714285714 &  &  \tabularnewline
Midmean - Closest Observation & 3.88433333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.88433333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.88433333333333 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18354&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]4.01275862068966[/C][C]0.104529248390647[/C][C]38.3888594098864[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.9380120812683[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.86719662152113[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.08962522522035[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]4.00965517241379[/C][C]0.103685551639116[/C][C]38.6713009578194[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]4.00620689655172[/C][C]0.102502512794722[/C][C]39.0839871855123[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]4.00620689655172[/C][C]0.10230401640063[/C][C]39.1598202837231[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]4.00620689655172[/C][C]0.101262695748655[/C][C]39.5625147734122[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]4.00620689655172[/C][C]0.100942571582986[/C][C]39.6879813316245[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]4.01034482758621[/C][C]0.0999028461865785[/C][C]40.1424481950844[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]4.01396551724138[/C][C]0.098909951180552[/C][C]40.5820189913371[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]4.01396551724138[/C][C]0.097926457230522[/C][C]40.9895918913147[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]4.01086206896552[/C][C]0.0967447432202895[/C][C]41.458191271775[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]3.99706896551724[/C][C]0.0927971620589128[/C][C]43.0731810847802[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]4.00465517241379[/C][C]0.0903984644031041[/C][C]44.3000353917105[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]3.9798275862069[/C][C]0.084292540526093[/C][C]47.214469529186[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]3.99327586206897[/C][C]0.0816820255188591[/C][C]48.8880611946502[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]3.99568965517241[/C][C]0.0782777841946552[/C][C]51.0450020562186[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]3.96724137931035[/C][C]0.0715052035738634[/C][C]55.4818555996735[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]3.95620689655172[/C][C]0.0695612503415143[/C][C]56.8737174379203[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]3.95034482758621[/C][C]0.0667443432158507[/C][C]59.1862117035271[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]3.91310344827586[/C][C]0.0585214098270013[/C][C]66.8661855523239[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]3.88362068965517[/C][C]0.0526925921984005[/C][C]73.7033523617967[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]4.00339285714286[/C][C]0.10283964215745[/C][C]38.9284985162975[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]3.99666666666667[/C][C]0.101700427428813[/C][C]39.2984254610354[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]3.99134615384615[/C][C]0.100958090869816[/C][C]39.5346833469043[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]3.9856[/C][C]0.100002514254107[/C][C]39.8549979440774[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]3.979375[/C][C]0.0990725637828332[/C][C]40.1662665026291[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]3.97260869565217[/C][C]0.097862387253221[/C][C]40.5938257501625[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]3.96431818181818[/C][C]0.096482752529416[/C][C]41.0883611618515[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]3.95452380952381[/C][C]0.0948243699478099[/C][C]41.7036655418889[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]3.94375[/C][C]0.0927705243722794[/C][C]42.5108085427447[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]3.93236842105263[/C][C]0.0902252863996952[/C][C]43.5838840525522[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]3.92194444444444[/C][C]0.0878091540265831[/C][C]44.6644144101095[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]3.90911764705882[/C][C]0.084969710076543[/C][C]46.0060137140328[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]3.8984375[/C][C]0.0827356231724514[/C][C]47.1192135928465[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]3.88433333333333[/C][C]0.0800139116256657[/C][C]48.5457247922794[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]3.86785714285714[/C][C]0.0768241259897514[/C][C]50.3469072121059[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]3.85307692307692[/C][C]0.0743024365078691[/C][C]51.8566699043423[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]3.8375[/C][C]0.0708213971187739[/C][C]54.18560147245[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]3.82[/C][C]0.0660414404860453[/C][C]57.8424693932467[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]3.805[/C][C]0.0621013602698719[/C][C]61.2707996002782[/C][/ROW]
[ROW][C]Median[/C][C]3.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.85206896551724[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.88433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.88433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.88433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.86785714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.88433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.88433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.88433333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18354&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18354&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.012758620689660.10452924839064738.3888594098864
Geometric Mean3.9380120812683
Harmonic Mean3.86719662152113
Quadratic Mean4.08962522522035
Winsorized Mean ( 1 / 19 )4.009655172413790.10368555163911638.6713009578194
Winsorized Mean ( 2 / 19 )4.006206896551720.10250251279472239.0839871855123
Winsorized Mean ( 3 / 19 )4.006206896551720.1023040164006339.1598202837231
Winsorized Mean ( 4 / 19 )4.006206896551720.10126269574865539.5625147734122
Winsorized Mean ( 5 / 19 )4.006206896551720.10094257158298639.6879813316245
Winsorized Mean ( 6 / 19 )4.010344827586210.099902846186578540.1424481950844
Winsorized Mean ( 7 / 19 )4.013965517241380.09890995118055240.5820189913371
Winsorized Mean ( 8 / 19 )4.013965517241380.09792645723052240.9895918913147
Winsorized Mean ( 9 / 19 )4.010862068965520.096744743220289541.458191271775
Winsorized Mean ( 10 / 19 )3.997068965517240.092797162058912843.0731810847802
Winsorized Mean ( 11 / 19 )4.004655172413790.090398464403104144.3000353917105
Winsorized Mean ( 12 / 19 )3.97982758620690.08429254052609347.214469529186
Winsorized Mean ( 13 / 19 )3.993275862068970.081682025518859148.8880611946502
Winsorized Mean ( 14 / 19 )3.995689655172410.078277784194655251.0450020562186
Winsorized Mean ( 15 / 19 )3.967241379310350.071505203573863455.4818555996735
Winsorized Mean ( 16 / 19 )3.956206896551720.069561250341514356.8737174379203
Winsorized Mean ( 17 / 19 )3.950344827586210.066744343215850759.1862117035271
Winsorized Mean ( 18 / 19 )3.913103448275860.058521409827001366.8661855523239
Winsorized Mean ( 19 / 19 )3.883620689655170.052692592198400573.7033523617967
Trimmed Mean ( 1 / 19 )4.003392857142860.1028396421574538.9284985162975
Trimmed Mean ( 2 / 19 )3.996666666666670.10170042742881339.2984254610354
Trimmed Mean ( 3 / 19 )3.991346153846150.10095809086981639.5346833469043
Trimmed Mean ( 4 / 19 )3.98560.10000251425410739.8549979440774
Trimmed Mean ( 5 / 19 )3.9793750.099072563782833240.1662665026291
Trimmed Mean ( 6 / 19 )3.972608695652170.09786238725322140.5938257501625
Trimmed Mean ( 7 / 19 )3.964318181818180.09648275252941641.0883611618515
Trimmed Mean ( 8 / 19 )3.954523809523810.094824369947809941.7036655418889
Trimmed Mean ( 9 / 19 )3.943750.092770524372279442.5108085427447
Trimmed Mean ( 10 / 19 )3.932368421052630.090225286399695243.5838840525522
Trimmed Mean ( 11 / 19 )3.921944444444440.087809154026583144.6644144101095
Trimmed Mean ( 12 / 19 )3.909117647058820.08496971007654346.0060137140328
Trimmed Mean ( 13 / 19 )3.89843750.082735623172451447.1192135928465
Trimmed Mean ( 14 / 19 )3.884333333333330.080013911625665748.5457247922794
Trimmed Mean ( 15 / 19 )3.867857142857140.076824125989751450.3469072121059
Trimmed Mean ( 16 / 19 )3.853076923076920.074302436507869151.8566699043423
Trimmed Mean ( 17 / 19 )3.83750.070821397118773954.18560147245
Trimmed Mean ( 18 / 19 )3.820.066041440486045357.8424693932467
Trimmed Mean ( 19 / 19 )3.8050.062101360269871961.2707996002782
Median3.73
Midrange4.275
Midmean - Weighted Average at Xnp3.85206896551724
Midmean - Weighted Average at X(n+1)p3.88433333333333
Midmean - Empirical Distribution Function3.88433333333333
Midmean - Empirical Distribution Function - Averaging3.88433333333333
Midmean - Empirical Distribution Function - Interpolation3.86785714285714
Midmean - Closest Observation3.88433333333333
Midmean - True Basic - Statistics Graphics Toolkit3.88433333333333
Midmean - MS Excel (old versions)3.88433333333333
Number of observations58



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')