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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 computationTue, 14 Dec 2010 09:52:46 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292320251n6g9kawbloi23y8.htm/, Retrieved Thu, 02 May 2024 22:10:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109330, Retrieved Thu, 02 May 2024 22:10:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2010-12-14 09:52:46] [e192c8164fa91adb027f71579ac0a49a] [Current]
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Dataseries X:
6
4
5
4
4
6
6
4
4
6
4
6
5
4
6
3
5
6
4
6
2
7
5
2
4
4
6
6
5
6
6
4
6
6
6
2
4
5
3
7
5
3
8
8
5
6
3
5
4
5
5
6
5
6
6
4
8
6
4
6
5
5
6
6
6
6
6
6
7
4
4
3
6
5
5
3
5
4
3
7
4
4
5
6
2
2
6
4
5
6
7
8
6
6
3
7
3
6
4
4
6
6
6
4
7
5
7
4
6
6
6
5
5
6
7
4
4
8
6
3
4
5
5
6
8
2
4
7
5
6
6
4
5
6
6
6
6
5
5
6
4
6
3
6
8
4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109330&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]3 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=109330&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109330&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.143835616438360.11541129180290944.5696043782495
Geometric Mean4.92785597675172
Harmonic Mean4.67395861122756
Quadratic Mean5.32826528608553
Winsorized Mean ( 1 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 2 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 3 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 4 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 5 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 6 / 48 )5.184931506849320.10867146566570447.7119865374708
Winsorized Mean ( 7 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 8 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 9 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 10 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 11 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 12 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 13 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 14 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 15 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 16 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 17 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 18 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 19 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 20 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 21 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 22 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 23 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 24 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 25 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 26 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 27 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 28 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 29 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 30 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 31 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 32 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 33 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 34 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 35 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 36 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 37 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 38 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 39 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 40 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 41 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 42 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 43 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 44 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 45 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 46 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 47 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 48 / 48 )5.136986301369860.073786922087636169.6191974950346
Trimmed Mean ( 1 / 48 )5.145833333333330.11321429972060845.4521500025377
Trimmed Mean ( 2 / 48 )5.147887323943660.1108206162227146.4524336662976
Trimmed Mean ( 3 / 48 )5.150.10820643739410947.5942108808435
Trimmed Mean ( 4 / 48 )5.152173913043480.10534342035507848.9083598736135
Trimmed Mean ( 5 / 48 )5.154411764705880.10219735940388750.4358605229269
Trimmed Mean ( 6 / 48 )5.156716417910450.098726305304046552.2324460743199
Trimmed Mean ( 7 / 48 )5.151515151515150.09648270031562853.3931485609625
Trimmed Mean ( 8 / 48 )5.153846153846150.095492658143320653.9711246294032
Trimmed Mean ( 9 / 48 )5.156250.094403887610961254.6190430340001
Trimmed Mean ( 10 / 48 )5.158730158730160.093205830196210855.3477196423264
Trimmed Mean ( 11 / 48 )5.161290322580650.09188635437826256.1703678147195
Trimmed Mean ( 12 / 48 )5.163934426229510.090431424478557857.1033184095638
Trimmed Mean ( 13 / 48 )5.166666666666670.088824673349835358.1670212995638
Trimmed Mean ( 14 / 48 )5.169491525423730.087046841702657259.3874679920285
Trimmed Mean ( 15 / 48 )5.172413793103450.085075028240546460.7982612533333
Trimmed Mean ( 16 / 48 )5.175438596491230.082881664374968562.4437097821395
Trimmed Mean ( 17 / 48 )5.178571428571430.080433075806942764.3836055828718
Trimmed Mean ( 18 / 48 )5.181818181818180.080843982387125664.0965230659318
Trimmed Mean ( 19 / 48 )5.185185185185190.081254600900857663.814050253128
Trimmed Mean ( 20 / 48 )5.188679245283020.081664190380525463.536774455311
Trimmed Mean ( 21 / 48 )5.192307692307690.0820718949711863.2653564795964
Trimmed Mean ( 22 / 48 )5.196078431372550.0824767260797963.0005418297731
Trimmed Mean ( 23 / 48 )5.20.082877541401074862.7431739901078
Trimmed Mean ( 24 / 48 )5.204081632653060.083273020191092762.4942102581469
Trimmed Mean ( 25 / 48 )5.208333333333330.083661634013733962.2547407151806
Trimmed Mean ( 26 / 48 )5.212765957446810.08404161200020962.026011084055
Trimmed Mean ( 27 / 48 )5.217391304347830.084410899425578361.8094504365255
Trimmed Mean ( 28 / 48 )5.222222222222220.084767108103168361.6067049953664
Trimmed Mean ( 29 / 48 )5.227272727272730.08510745670534961.4196796570963
Trimmed Mean ( 30 / 48 )5.232558139534880.085428698607272461.2505893785141
Trimmed Mean ( 31 / 48 )5.238095238095240.08572703417657361.1020232813172
Trimmed Mean ( 32 / 48 )5.243902439024390.08599800353724960.9770253184199
Trimmed Mean ( 33 / 48 )5.250.086236354635150860.8791967403043
Trimmed Mean ( 34 / 48 )5.256410256410260.086435879802979760.8128275941844
Trimmed Mean ( 35 / 48 )5.263157894736840.08658921178423260.7830673854831
Trimmed Mean ( 36 / 48 )5.270270270270270.08668756705893960.7961493103966
Trimmed Mean ( 37 / 48 )5.277777777777780.086720419909911860.8596889090311
Trimmed Mean ( 38 / 48 )5.285714285714290.086675084340827260.983087884052
Trimmed Mean ( 39 / 48 )5.294117647058820.086536171697350161.1780893841059
Trimmed Mean ( 40 / 48 )5.30303030303030.086284878005087961.4595561312331
Trimmed Mean ( 41 / 48 )5.31250.085898033867034661.8465843842649
Trimmed Mean ( 42 / 48 )5.322580645161290.085346816485954562.3641380465225
Trimmed Mean ( 43 / 48 )5.333333333333330.084594969420315463.045514052193
Trimmed Mean ( 44 / 48 )5.34482758620690.08359628497380963.9361855360133
Trimmed Mean ( 45 / 48 )5.357142857142860.082290944999692965.1000284072913
Trimmed Mean ( 46 / 48 )5.370370370370370.080600022266160666.629886932737
Trimmed Mean ( 47 / 48 )5.384615384615390.078416868365345268.6665445440692
Trimmed Mean ( 48 / 48 )5.40.075592894601845471.435285398744
Median5
Midrange5
Midmean - Weighted Average at Xnp5.17857142857143
Midmean - Weighted Average at X(n+1)p5.17857142857143
Midmean - Empirical Distribution Function5.17857142857143
Midmean - Empirical Distribution Function - Averaging5.17857142857143
Midmean - Empirical Distribution Function - Interpolation5.17857142857143
Midmean - Closest Observation5.17857142857143
Midmean - True Basic - Statistics Graphics Toolkit5.17857142857143
Midmean - MS Excel (old versions)5.17857142857143
Number of observations146

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.14383561643836 & 0.115411291802909 & 44.5696043782495 \tabularnewline
Geometric Mean & 4.92785597675172 &  &  \tabularnewline
Harmonic Mean & 4.67395861122756 &  &  \tabularnewline
Quadratic Mean & 5.32826528608553 &  &  \tabularnewline
Winsorized Mean ( 1 / 48 ) & 5.14383561643836 & 0.115411291802909 & 44.5696043782495 \tabularnewline
Winsorized Mean ( 2 / 48 ) & 5.14383561643836 & 0.115411291802909 & 44.5696043782495 \tabularnewline
Winsorized Mean ( 3 / 48 ) & 5.14383561643836 & 0.115411291802909 & 44.5696043782495 \tabularnewline
Winsorized Mean ( 4 / 48 ) & 5.14383561643836 & 0.115411291802909 & 44.5696043782495 \tabularnewline
Winsorized Mean ( 5 / 48 ) & 5.14383561643836 & 0.115411291802909 & 44.5696043782495 \tabularnewline
Winsorized Mean ( 6 / 48 ) & 5.18493150684932 & 0.108671465665704 & 47.7119865374708 \tabularnewline
Winsorized Mean ( 7 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 8 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 9 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 10 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 11 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 12 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 13 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 14 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 15 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 16 / 48 ) & 5.13698630136986 & 0.101304732105339 & 50.7082561160945 \tabularnewline
Winsorized Mean ( 17 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 18 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 19 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 20 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 21 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 22 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 23 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 24 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 25 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 26 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 27 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 28 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 29 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 30 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 31 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 32 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 33 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 34 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 35 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 36 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 37 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 38 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 39 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 40 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 41 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 42 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 43 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 44 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 45 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 46 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 47 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Winsorized Mean ( 48 / 48 ) & 5.13698630136986 & 0.0737869220876361 & 69.6191974950346 \tabularnewline
Trimmed Mean ( 1 / 48 ) & 5.14583333333333 & 0.113214299720608 & 45.4521500025377 \tabularnewline
Trimmed Mean ( 2 / 48 ) & 5.14788732394366 & 0.11082061622271 & 46.4524336662976 \tabularnewline
Trimmed Mean ( 3 / 48 ) & 5.15 & 0.108206437394109 & 47.5942108808435 \tabularnewline
Trimmed Mean ( 4 / 48 ) & 5.15217391304348 & 0.105343420355078 & 48.9083598736135 \tabularnewline
Trimmed Mean ( 5 / 48 ) & 5.15441176470588 & 0.102197359403887 & 50.4358605229269 \tabularnewline
Trimmed Mean ( 6 / 48 ) & 5.15671641791045 & 0.0987263053040465 & 52.2324460743199 \tabularnewline
Trimmed Mean ( 7 / 48 ) & 5.15151515151515 & 0.096482700315628 & 53.3931485609625 \tabularnewline
Trimmed Mean ( 8 / 48 ) & 5.15384615384615 & 0.0954926581433206 & 53.9711246294032 \tabularnewline
Trimmed Mean ( 9 / 48 ) & 5.15625 & 0.0944038876109612 & 54.6190430340001 \tabularnewline
Trimmed Mean ( 10 / 48 ) & 5.15873015873016 & 0.0932058301962108 & 55.3477196423264 \tabularnewline
Trimmed Mean ( 11 / 48 ) & 5.16129032258065 & 0.091886354378262 & 56.1703678147195 \tabularnewline
Trimmed Mean ( 12 / 48 ) & 5.16393442622951 & 0.0904314244785578 & 57.1033184095638 \tabularnewline
Trimmed Mean ( 13 / 48 ) & 5.16666666666667 & 0.0888246733498353 & 58.1670212995638 \tabularnewline
Trimmed Mean ( 14 / 48 ) & 5.16949152542373 & 0.0870468417026572 & 59.3874679920285 \tabularnewline
Trimmed Mean ( 15 / 48 ) & 5.17241379310345 & 0.0850750282405464 & 60.7982612533333 \tabularnewline
Trimmed Mean ( 16 / 48 ) & 5.17543859649123 & 0.0828816643749685 & 62.4437097821395 \tabularnewline
Trimmed Mean ( 17 / 48 ) & 5.17857142857143 & 0.0804330758069427 & 64.3836055828718 \tabularnewline
Trimmed Mean ( 18 / 48 ) & 5.18181818181818 & 0.0808439823871256 & 64.0965230659318 \tabularnewline
Trimmed Mean ( 19 / 48 ) & 5.18518518518519 & 0.0812546009008576 & 63.814050253128 \tabularnewline
Trimmed Mean ( 20 / 48 ) & 5.18867924528302 & 0.0816641903805254 & 63.536774455311 \tabularnewline
Trimmed Mean ( 21 / 48 ) & 5.19230769230769 & 0.08207189497118 & 63.2653564795964 \tabularnewline
Trimmed Mean ( 22 / 48 ) & 5.19607843137255 & 0.08247672607979 & 63.0005418297731 \tabularnewline
Trimmed Mean ( 23 / 48 ) & 5.2 & 0.0828775414010748 & 62.7431739901078 \tabularnewline
Trimmed Mean ( 24 / 48 ) & 5.20408163265306 & 0.0832730201910927 & 62.4942102581469 \tabularnewline
Trimmed Mean ( 25 / 48 ) & 5.20833333333333 & 0.0836616340137339 & 62.2547407151806 \tabularnewline
Trimmed Mean ( 26 / 48 ) & 5.21276595744681 & 0.084041612000209 & 62.026011084055 \tabularnewline
Trimmed Mean ( 27 / 48 ) & 5.21739130434783 & 0.0844108994255783 & 61.8094504365255 \tabularnewline
Trimmed Mean ( 28 / 48 ) & 5.22222222222222 & 0.0847671081031683 & 61.6067049953664 \tabularnewline
Trimmed Mean ( 29 / 48 ) & 5.22727272727273 & 0.085107456705349 & 61.4196796570963 \tabularnewline
Trimmed Mean ( 30 / 48 ) & 5.23255813953488 & 0.0854286986072724 & 61.2505893785141 \tabularnewline
Trimmed Mean ( 31 / 48 ) & 5.23809523809524 & 0.085727034176573 & 61.1020232813172 \tabularnewline
Trimmed Mean ( 32 / 48 ) & 5.24390243902439 & 0.085998003537249 & 60.9770253184199 \tabularnewline
Trimmed Mean ( 33 / 48 ) & 5.25 & 0.0862363546351508 & 60.8791967403043 \tabularnewline
Trimmed Mean ( 34 / 48 ) & 5.25641025641026 & 0.0864358798029797 & 60.8128275941844 \tabularnewline
Trimmed Mean ( 35 / 48 ) & 5.26315789473684 & 0.086589211784232 & 60.7830673854831 \tabularnewline
Trimmed Mean ( 36 / 48 ) & 5.27027027027027 & 0.086687567058939 & 60.7961493103966 \tabularnewline
Trimmed Mean ( 37 / 48 ) & 5.27777777777778 & 0.0867204199099118 & 60.8596889090311 \tabularnewline
Trimmed Mean ( 38 / 48 ) & 5.28571428571429 & 0.0866750843408272 & 60.983087884052 \tabularnewline
Trimmed Mean ( 39 / 48 ) & 5.29411764705882 & 0.0865361716973501 & 61.1780893841059 \tabularnewline
Trimmed Mean ( 40 / 48 ) & 5.3030303030303 & 0.0862848780050879 & 61.4595561312331 \tabularnewline
Trimmed Mean ( 41 / 48 ) & 5.3125 & 0.0858980338670346 & 61.8465843842649 \tabularnewline
Trimmed Mean ( 42 / 48 ) & 5.32258064516129 & 0.0853468164859545 & 62.3641380465225 \tabularnewline
Trimmed Mean ( 43 / 48 ) & 5.33333333333333 & 0.0845949694203154 & 63.045514052193 \tabularnewline
Trimmed Mean ( 44 / 48 ) & 5.3448275862069 & 0.083596284973809 & 63.9361855360133 \tabularnewline
Trimmed Mean ( 45 / 48 ) & 5.35714285714286 & 0.0822909449996929 & 65.1000284072913 \tabularnewline
Trimmed Mean ( 46 / 48 ) & 5.37037037037037 & 0.0806000222661606 & 66.629886932737 \tabularnewline
Trimmed Mean ( 47 / 48 ) & 5.38461538461539 & 0.0784168683653452 & 68.6665445440692 \tabularnewline
Trimmed Mean ( 48 / 48 ) & 5.4 & 0.0755928946018454 & 71.435285398744 \tabularnewline
Median & 5 &  &  \tabularnewline
Midrange & 5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.17857142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.17857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.17857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.17857142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.17857142857143 &  &  \tabularnewline
Midmean - Closest Observation & 5.17857142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.17857142857143 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.17857142857143 &  &  \tabularnewline
Number of observations & 146 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109330&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]5.14383561643836[/C][C]0.115411291802909[/C][C]44.5696043782495[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.92785597675172[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.67395861122756[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.32826528608553[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 48 )[/C][C]5.14383561643836[/C][C]0.115411291802909[/C][C]44.5696043782495[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 48 )[/C][C]5.14383561643836[/C][C]0.115411291802909[/C][C]44.5696043782495[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 48 )[/C][C]5.14383561643836[/C][C]0.115411291802909[/C][C]44.5696043782495[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 48 )[/C][C]5.14383561643836[/C][C]0.115411291802909[/C][C]44.5696043782495[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 48 )[/C][C]5.14383561643836[/C][C]0.115411291802909[/C][C]44.5696043782495[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 48 )[/C][C]5.18493150684932[/C][C]0.108671465665704[/C][C]47.7119865374708[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 48 )[/C][C]5.13698630136986[/C][C]0.101304732105339[/C][C]50.7082561160945[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 48 )[/C][C]5.13698630136986[/C][C]0.0737869220876361[/C][C]69.6191974950346[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 48 )[/C][C]5.14583333333333[/C][C]0.113214299720608[/C][C]45.4521500025377[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 48 )[/C][C]5.14788732394366[/C][C]0.11082061622271[/C][C]46.4524336662976[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 48 )[/C][C]5.15[/C][C]0.108206437394109[/C][C]47.5942108808435[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 48 )[/C][C]5.15217391304348[/C][C]0.105343420355078[/C][C]48.9083598736135[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 48 )[/C][C]5.15441176470588[/C][C]0.102197359403887[/C][C]50.4358605229269[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 48 )[/C][C]5.15671641791045[/C][C]0.0987263053040465[/C][C]52.2324460743199[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 48 )[/C][C]5.15151515151515[/C][C]0.096482700315628[/C][C]53.3931485609625[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 48 )[/C][C]5.15384615384615[/C][C]0.0954926581433206[/C][C]53.9711246294032[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 48 )[/C][C]5.15625[/C][C]0.0944038876109612[/C][C]54.6190430340001[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 48 )[/C][C]5.15873015873016[/C][C]0.0932058301962108[/C][C]55.3477196423264[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 48 )[/C][C]5.16129032258065[/C][C]0.091886354378262[/C][C]56.1703678147195[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 48 )[/C][C]5.16393442622951[/C][C]0.0904314244785578[/C][C]57.1033184095638[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 48 )[/C][C]5.16666666666667[/C][C]0.0888246733498353[/C][C]58.1670212995638[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 48 )[/C][C]5.16949152542373[/C][C]0.0870468417026572[/C][C]59.3874679920285[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 48 )[/C][C]5.17241379310345[/C][C]0.0850750282405464[/C][C]60.7982612533333[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 48 )[/C][C]5.17543859649123[/C][C]0.0828816643749685[/C][C]62.4437097821395[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 48 )[/C][C]5.17857142857143[/C][C]0.0804330758069427[/C][C]64.3836055828718[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 48 )[/C][C]5.18181818181818[/C][C]0.0808439823871256[/C][C]64.0965230659318[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 48 )[/C][C]5.18518518518519[/C][C]0.0812546009008576[/C][C]63.814050253128[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 48 )[/C][C]5.18867924528302[/C][C]0.0816641903805254[/C][C]63.536774455311[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 48 )[/C][C]5.19230769230769[/C][C]0.08207189497118[/C][C]63.2653564795964[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 48 )[/C][C]5.19607843137255[/C][C]0.08247672607979[/C][C]63.0005418297731[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 48 )[/C][C]5.2[/C][C]0.0828775414010748[/C][C]62.7431739901078[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 48 )[/C][C]5.20408163265306[/C][C]0.0832730201910927[/C][C]62.4942102581469[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 48 )[/C][C]5.20833333333333[/C][C]0.0836616340137339[/C][C]62.2547407151806[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 48 )[/C][C]5.21276595744681[/C][C]0.084041612000209[/C][C]62.026011084055[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 48 )[/C][C]5.21739130434783[/C][C]0.0844108994255783[/C][C]61.8094504365255[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 48 )[/C][C]5.22222222222222[/C][C]0.0847671081031683[/C][C]61.6067049953664[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 48 )[/C][C]5.22727272727273[/C][C]0.085107456705349[/C][C]61.4196796570963[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 48 )[/C][C]5.23255813953488[/C][C]0.0854286986072724[/C][C]61.2505893785141[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 48 )[/C][C]5.23809523809524[/C][C]0.085727034176573[/C][C]61.1020232813172[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 48 )[/C][C]5.24390243902439[/C][C]0.085998003537249[/C][C]60.9770253184199[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 48 )[/C][C]5.25[/C][C]0.0862363546351508[/C][C]60.8791967403043[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 48 )[/C][C]5.25641025641026[/C][C]0.0864358798029797[/C][C]60.8128275941844[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 48 )[/C][C]5.26315789473684[/C][C]0.086589211784232[/C][C]60.7830673854831[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 48 )[/C][C]5.27027027027027[/C][C]0.086687567058939[/C][C]60.7961493103966[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 48 )[/C][C]5.27777777777778[/C][C]0.0867204199099118[/C][C]60.8596889090311[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 48 )[/C][C]5.28571428571429[/C][C]0.0866750843408272[/C][C]60.983087884052[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 48 )[/C][C]5.29411764705882[/C][C]0.0865361716973501[/C][C]61.1780893841059[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 48 )[/C][C]5.3030303030303[/C][C]0.0862848780050879[/C][C]61.4595561312331[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 48 )[/C][C]5.3125[/C][C]0.0858980338670346[/C][C]61.8465843842649[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 48 )[/C][C]5.32258064516129[/C][C]0.0853468164859545[/C][C]62.3641380465225[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 48 )[/C][C]5.33333333333333[/C][C]0.0845949694203154[/C][C]63.045514052193[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 48 )[/C][C]5.3448275862069[/C][C]0.083596284973809[/C][C]63.9361855360133[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 48 )[/C][C]5.35714285714286[/C][C]0.0822909449996929[/C][C]65.1000284072913[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 48 )[/C][C]5.37037037037037[/C][C]0.0806000222661606[/C][C]66.629886932737[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 48 )[/C][C]5.38461538461539[/C][C]0.0784168683653452[/C][C]68.6665445440692[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 48 )[/C][C]5.4[/C][C]0.0755928946018454[/C][C]71.435285398744[/C][/ROW]
[ROW][C]Median[/C][C]5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.17857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]146[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109330&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109330&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 Mean5.143835616438360.11541129180290944.5696043782495
Geometric Mean4.92785597675172
Harmonic Mean4.67395861122756
Quadratic Mean5.32826528608553
Winsorized Mean ( 1 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 2 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 3 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 4 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 5 / 48 )5.143835616438360.11541129180290944.5696043782495
Winsorized Mean ( 6 / 48 )5.184931506849320.10867146566570447.7119865374708
Winsorized Mean ( 7 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 8 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 9 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 10 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 11 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 12 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 13 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 14 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 15 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 16 / 48 )5.136986301369860.10130473210533950.7082561160945
Winsorized Mean ( 17 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 18 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 19 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 20 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 21 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 22 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 23 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 24 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 25 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 26 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 27 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 28 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 29 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 30 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 31 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 32 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 33 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 34 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 35 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 36 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 37 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 38 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 39 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 40 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 41 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 42 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 43 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 44 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 45 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 46 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 47 / 48 )5.136986301369860.073786922087636169.6191974950346
Winsorized Mean ( 48 / 48 )5.136986301369860.073786922087636169.6191974950346
Trimmed Mean ( 1 / 48 )5.145833333333330.11321429972060845.4521500025377
Trimmed Mean ( 2 / 48 )5.147887323943660.1108206162227146.4524336662976
Trimmed Mean ( 3 / 48 )5.150.10820643739410947.5942108808435
Trimmed Mean ( 4 / 48 )5.152173913043480.10534342035507848.9083598736135
Trimmed Mean ( 5 / 48 )5.154411764705880.10219735940388750.4358605229269
Trimmed Mean ( 6 / 48 )5.156716417910450.098726305304046552.2324460743199
Trimmed Mean ( 7 / 48 )5.151515151515150.09648270031562853.3931485609625
Trimmed Mean ( 8 / 48 )5.153846153846150.095492658143320653.9711246294032
Trimmed Mean ( 9 / 48 )5.156250.094403887610961254.6190430340001
Trimmed Mean ( 10 / 48 )5.158730158730160.093205830196210855.3477196423264
Trimmed Mean ( 11 / 48 )5.161290322580650.09188635437826256.1703678147195
Trimmed Mean ( 12 / 48 )5.163934426229510.090431424478557857.1033184095638
Trimmed Mean ( 13 / 48 )5.166666666666670.088824673349835358.1670212995638
Trimmed Mean ( 14 / 48 )5.169491525423730.087046841702657259.3874679920285
Trimmed Mean ( 15 / 48 )5.172413793103450.085075028240546460.7982612533333
Trimmed Mean ( 16 / 48 )5.175438596491230.082881664374968562.4437097821395
Trimmed Mean ( 17 / 48 )5.178571428571430.080433075806942764.3836055828718
Trimmed Mean ( 18 / 48 )5.181818181818180.080843982387125664.0965230659318
Trimmed Mean ( 19 / 48 )5.185185185185190.081254600900857663.814050253128
Trimmed Mean ( 20 / 48 )5.188679245283020.081664190380525463.536774455311
Trimmed Mean ( 21 / 48 )5.192307692307690.0820718949711863.2653564795964
Trimmed Mean ( 22 / 48 )5.196078431372550.0824767260797963.0005418297731
Trimmed Mean ( 23 / 48 )5.20.082877541401074862.7431739901078
Trimmed Mean ( 24 / 48 )5.204081632653060.083273020191092762.4942102581469
Trimmed Mean ( 25 / 48 )5.208333333333330.083661634013733962.2547407151806
Trimmed Mean ( 26 / 48 )5.212765957446810.08404161200020962.026011084055
Trimmed Mean ( 27 / 48 )5.217391304347830.084410899425578361.8094504365255
Trimmed Mean ( 28 / 48 )5.222222222222220.084767108103168361.6067049953664
Trimmed Mean ( 29 / 48 )5.227272727272730.08510745670534961.4196796570963
Trimmed Mean ( 30 / 48 )5.232558139534880.085428698607272461.2505893785141
Trimmed Mean ( 31 / 48 )5.238095238095240.08572703417657361.1020232813172
Trimmed Mean ( 32 / 48 )5.243902439024390.08599800353724960.9770253184199
Trimmed Mean ( 33 / 48 )5.250.086236354635150860.8791967403043
Trimmed Mean ( 34 / 48 )5.256410256410260.086435879802979760.8128275941844
Trimmed Mean ( 35 / 48 )5.263157894736840.08658921178423260.7830673854831
Trimmed Mean ( 36 / 48 )5.270270270270270.08668756705893960.7961493103966
Trimmed Mean ( 37 / 48 )5.277777777777780.086720419909911860.8596889090311
Trimmed Mean ( 38 / 48 )5.285714285714290.086675084340827260.983087884052
Trimmed Mean ( 39 / 48 )5.294117647058820.086536171697350161.1780893841059
Trimmed Mean ( 40 / 48 )5.30303030303030.086284878005087961.4595561312331
Trimmed Mean ( 41 / 48 )5.31250.085898033867034661.8465843842649
Trimmed Mean ( 42 / 48 )5.322580645161290.085346816485954562.3641380465225
Trimmed Mean ( 43 / 48 )5.333333333333330.084594969420315463.045514052193
Trimmed Mean ( 44 / 48 )5.34482758620690.08359628497380963.9361855360133
Trimmed Mean ( 45 / 48 )5.357142857142860.082290944999692965.1000284072913
Trimmed Mean ( 46 / 48 )5.370370370370370.080600022266160666.629886932737
Trimmed Mean ( 47 / 48 )5.384615384615390.078416868365345268.6665445440692
Trimmed Mean ( 48 / 48 )5.40.075592894601845471.435285398744
Median5
Midrange5
Midmean - Weighted Average at Xnp5.17857142857143
Midmean - Weighted Average at X(n+1)p5.17857142857143
Midmean - Empirical Distribution Function5.17857142857143
Midmean - Empirical Distribution Function - Averaging5.17857142857143
Midmean - Empirical Distribution Function - Interpolation5.17857142857143
Midmean - Closest Observation5.17857142857143
Midmean - True Basic - Statistics Graphics Toolkit5.17857142857143
Midmean - MS Excel (old versions)5.17857142857143
Number of observations146



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')