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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 05:18:06 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318843126l4twsxowy8pkieu.htm/, Retrieved Wed, 15 May 2024 14:32:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130289, Retrieved Wed, 15 May 2024 14:32:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten prij...] [2011-10-17 09:18:06] [659094c92b72720b61457cd096818e91] [Current]
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Dataseries X:
31,5
31,29
31,3
31,06
31,09
31,11
31,13
31,1
31,03
30,74
30,83
30,82
30,8
30,74
30,71
30,58
30,71
30,7
30,7
30,72
30,68
30,78
30,84
30,8
30,8
30,88
30,87
30,92
30,82
30,75
30,75
30,75
30,63
30,52
30,58
30,6
30,6
30,63
30,56
30,61
30,53
30,6
30,6
30,63
30,66
30,34
30,32
30,3
30,3
30,08
29,96
29,91
29,83
29,89
29,85
30,06
29,83
29,95
30,02
30,03




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130289&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130289&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean30.6120.0507295922063615603.434773839189
Geometric Mean30.6095113356511
Harmonic Mean30.6070139629929
Quadratic Mean30.6144799073902
Winsorized Mean ( 1 / 20 )30.60866666666670.0498423881197921614.109151293097
Winsorized Mean ( 2 / 20 )30.6090.049589672243526617.245458886775
Winsorized Mean ( 3 / 20 )30.6030.0473860810572693645.822556269512
Winsorized Mean ( 4 / 20 )30.6030.0468006349853103653.901384235612
Winsorized Mean ( 5 / 20 )30.60550.0458254024982247667.871929792339
Winsorized Mean ( 6 / 20 )30.60550.045401800034004674.103228882507
Winsorized Mean ( 7 / 20 )30.6090.0431203151880979709.851026516818
Winsorized Mean ( 8 / 20 )30.60633333333330.0421156375984046726.72135763873
Winsorized Mean ( 9 / 20 )30.59433333333330.0384636938408089795.408092107722
Winsorized Mean ( 10 / 20 )30.5910.0367551833463644832.290774112704
Winsorized Mean ( 11 / 20 )30.62950.0275664835796871111.11378828782
Winsorized Mean ( 12 / 20 )30.62350.02671023101131781146.50824199252
Winsorized Mean ( 13 / 20 )30.62566666666670.02552982820271731199.6033198299
Winsorized Mean ( 14 / 20 )30.6280.02427223193152731261.85346639742
Winsorized Mean ( 15 / 20 )30.6730.01589922358904561929.21370205356
Winsorized Mean ( 16 / 20 )30.67033333333330.01464642928403122094.04850414788
Winsorized Mean ( 17 / 20 )30.67883333333330.01331090981678792304.7886099146
Winsorized Mean ( 18 / 20 )30.68483333333330.01242717012995312469.17303074286
Winsorized Mean ( 19 / 20 )30.67850.01145323332829292678.58858024091
Winsorized Mean ( 20 / 20 )30.67516666666670.009036935091991773394.42148852546
Trimmed Mean ( 1 / 20 )30.61017241379310.0482917450753907633.859314174835
Trimmed Mean ( 2 / 20 )30.61178571428570.0463793695339571660.030225117075
Trimmed Mean ( 3 / 20 )30.61333333333330.0441742309886449693.013384685804
Trimmed Mean ( 4 / 20 )30.61730769230770.0425161803860195720.133074380678
Trimmed Mean ( 5 / 20 )30.62160.040657213131151753.165247731605
Trimmed Mean ( 6 / 20 )30.6256250.0386449402269151792.487317102126
Trimmed Mean ( 7 / 20 )30.630.0361799047434674846.602560652968
Trimmed Mean ( 8 / 20 )30.63409090909090.0337245999978131908.360393038833
Trimmed Mean ( 9 / 20 )30.63904761904760.0307585281297279996.115532246004
Trimmed Mean ( 10 / 20 )30.64650.02788150292090091099.16958518855
Trimmed Mean ( 11 / 20 )30.65526315789470.02436019665260951258.41607910874
Trimmed Mean ( 12 / 20 )30.65916666666670.02291244549868391338.10101887325
Trimmed Mean ( 13 / 20 )30.66441176470590.02108547741123361454.29060801673
Trimmed Mean ( 14 / 20 )30.670.01883181076726811628.6272403134
Trimmed Mean ( 15 / 20 )30.6760.01587740388171161932.05389423483
Trimmed Mean ( 16 / 20 )30.67642857142860.01518156677572132020.6365406558
Trimmed Mean ( 17 / 20 )30.67730769230770.01454497208721122109.13486174931
Trimmed Mean ( 18 / 20 )30.67708333333330.01403256004960942186.13590284883
Trimmed Mean ( 19 / 20 )30.67590909090910.01349457307802092273.20337690949
Trimmed Mean ( 20 / 20 )30.67550.01298734201565422361.95365941896
Median30.69
Midrange30.665
Midmean - Weighted Average at Xnp30.67
Midmean - Weighted Average at X(n+1)p30.6806451612903
Midmean - Empirical Distribution Function30.67
Midmean - Empirical Distribution Function - Averaging30.6806451612903
Midmean - Empirical Distribution Function - Interpolation30.6806451612903
Midmean - Closest Observation30.67
Midmean - True Basic - Statistics Graphics Toolkit30.6806451612903
Midmean - MS Excel (old versions)30.67
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 30.612 & 0.0507295922063615 & 603.434773839189 \tabularnewline
Geometric Mean & 30.6095113356511 &  &  \tabularnewline
Harmonic Mean & 30.6070139629929 &  &  \tabularnewline
Quadratic Mean & 30.6144799073902 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 30.6086666666667 & 0.0498423881197921 & 614.109151293097 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 30.609 & 0.049589672243526 & 617.245458886775 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 30.603 & 0.0473860810572693 & 645.822556269512 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 30.603 & 0.0468006349853103 & 653.901384235612 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 30.6055 & 0.0458254024982247 & 667.871929792339 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 30.6055 & 0.045401800034004 & 674.103228882507 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 30.609 & 0.0431203151880979 & 709.851026516818 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 30.6063333333333 & 0.0421156375984046 & 726.72135763873 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 30.5943333333333 & 0.0384636938408089 & 795.408092107722 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 30.591 & 0.0367551833463644 & 832.290774112704 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 30.6295 & 0.027566483579687 & 1111.11378828782 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 30.6235 & 0.0267102310113178 & 1146.50824199252 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 30.6256666666667 & 0.0255298282027173 & 1199.6033198299 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 30.628 & 0.0242722319315273 & 1261.85346639742 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 30.673 & 0.0158992235890456 & 1929.21370205356 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 30.6703333333333 & 0.0146464292840312 & 2094.04850414788 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 30.6788333333333 & 0.0133109098167879 & 2304.7886099146 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 30.6848333333333 & 0.0124271701299531 & 2469.17303074286 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 30.6785 & 0.0114532333282929 & 2678.58858024091 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 30.6751666666667 & 0.00903693509199177 & 3394.42148852546 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 30.6101724137931 & 0.0482917450753907 & 633.859314174835 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 30.6117857142857 & 0.0463793695339571 & 660.030225117075 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 30.6133333333333 & 0.0441742309886449 & 693.013384685804 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 30.6173076923077 & 0.0425161803860195 & 720.133074380678 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 30.6216 & 0.040657213131151 & 753.165247731605 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 30.625625 & 0.0386449402269151 & 792.487317102126 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 30.63 & 0.0361799047434674 & 846.602560652968 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 30.6340909090909 & 0.0337245999978131 & 908.360393038833 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 30.6390476190476 & 0.0307585281297279 & 996.115532246004 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 30.6465 & 0.0278815029209009 & 1099.16958518855 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 30.6552631578947 & 0.0243601966526095 & 1258.41607910874 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 30.6591666666667 & 0.0229124454986839 & 1338.10101887325 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 30.6644117647059 & 0.0210854774112336 & 1454.29060801673 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 30.67 & 0.0188318107672681 & 1628.6272403134 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 30.676 & 0.0158774038817116 & 1932.05389423483 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 30.6764285714286 & 0.0151815667757213 & 2020.6365406558 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 30.6773076923077 & 0.0145449720872112 & 2109.13486174931 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 30.6770833333333 & 0.0140325600496094 & 2186.13590284883 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 30.6759090909091 & 0.0134945730780209 & 2273.20337690949 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 30.6755 & 0.0129873420156542 & 2361.95365941896 \tabularnewline
Median & 30.69 &  &  \tabularnewline
Midrange & 30.665 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 30.67 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 30.6806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 30.67 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 30.6806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 30.6806451612903 &  &  \tabularnewline
Midmean - Closest Observation & 30.67 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 30.6806451612903 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 30.67 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130289&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]30.612[/C][C]0.0507295922063615[/C][C]603.434773839189[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]30.6095113356511[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]30.6070139629929[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]30.6144799073902[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]30.6086666666667[/C][C]0.0498423881197921[/C][C]614.109151293097[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]30.609[/C][C]0.049589672243526[/C][C]617.245458886775[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]30.603[/C][C]0.0473860810572693[/C][C]645.822556269512[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]30.603[/C][C]0.0468006349853103[/C][C]653.901384235612[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]30.6055[/C][C]0.0458254024982247[/C][C]667.871929792339[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]30.6055[/C][C]0.045401800034004[/C][C]674.103228882507[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]30.609[/C][C]0.0431203151880979[/C][C]709.851026516818[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]30.6063333333333[/C][C]0.0421156375984046[/C][C]726.72135763873[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]30.5943333333333[/C][C]0.0384636938408089[/C][C]795.408092107722[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]30.591[/C][C]0.0367551833463644[/C][C]832.290774112704[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]30.6295[/C][C]0.027566483579687[/C][C]1111.11378828782[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]30.6235[/C][C]0.0267102310113178[/C][C]1146.50824199252[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]30.6256666666667[/C][C]0.0255298282027173[/C][C]1199.6033198299[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]30.628[/C][C]0.0242722319315273[/C][C]1261.85346639742[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]30.673[/C][C]0.0158992235890456[/C][C]1929.21370205356[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]30.6703333333333[/C][C]0.0146464292840312[/C][C]2094.04850414788[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]30.6788333333333[/C][C]0.0133109098167879[/C][C]2304.7886099146[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]30.6848333333333[/C][C]0.0124271701299531[/C][C]2469.17303074286[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]30.6785[/C][C]0.0114532333282929[/C][C]2678.58858024091[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]30.6751666666667[/C][C]0.00903693509199177[/C][C]3394.42148852546[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]30.6101724137931[/C][C]0.0482917450753907[/C][C]633.859314174835[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]30.6117857142857[/C][C]0.0463793695339571[/C][C]660.030225117075[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]30.6133333333333[/C][C]0.0441742309886449[/C][C]693.013384685804[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]30.6173076923077[/C][C]0.0425161803860195[/C][C]720.133074380678[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]30.6216[/C][C]0.040657213131151[/C][C]753.165247731605[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]30.625625[/C][C]0.0386449402269151[/C][C]792.487317102126[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]30.63[/C][C]0.0361799047434674[/C][C]846.602560652968[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]30.6340909090909[/C][C]0.0337245999978131[/C][C]908.360393038833[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]30.6390476190476[/C][C]0.0307585281297279[/C][C]996.115532246004[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]30.6465[/C][C]0.0278815029209009[/C][C]1099.16958518855[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]30.6552631578947[/C][C]0.0243601966526095[/C][C]1258.41607910874[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]30.6591666666667[/C][C]0.0229124454986839[/C][C]1338.10101887325[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]30.6644117647059[/C][C]0.0210854774112336[/C][C]1454.29060801673[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]30.67[/C][C]0.0188318107672681[/C][C]1628.6272403134[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]30.676[/C][C]0.0158774038817116[/C][C]1932.05389423483[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]30.6764285714286[/C][C]0.0151815667757213[/C][C]2020.6365406558[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]30.6773076923077[/C][C]0.0145449720872112[/C][C]2109.13486174931[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]30.6770833333333[/C][C]0.0140325600496094[/C][C]2186.13590284883[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]30.6759090909091[/C][C]0.0134945730780209[/C][C]2273.20337690949[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]30.6755[/C][C]0.0129873420156542[/C][C]2361.95365941896[/C][/ROW]
[ROW][C]Median[/C][C]30.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]30.665[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]30.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]30.6806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]30.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]30.6806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]30.6806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]30.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]30.6806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]30.67[/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=130289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130289&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 Mean30.6120.0507295922063615603.434773839189
Geometric Mean30.6095113356511
Harmonic Mean30.6070139629929
Quadratic Mean30.6144799073902
Winsorized Mean ( 1 / 20 )30.60866666666670.0498423881197921614.109151293097
Winsorized Mean ( 2 / 20 )30.6090.049589672243526617.245458886775
Winsorized Mean ( 3 / 20 )30.6030.0473860810572693645.822556269512
Winsorized Mean ( 4 / 20 )30.6030.0468006349853103653.901384235612
Winsorized Mean ( 5 / 20 )30.60550.0458254024982247667.871929792339
Winsorized Mean ( 6 / 20 )30.60550.045401800034004674.103228882507
Winsorized Mean ( 7 / 20 )30.6090.0431203151880979709.851026516818
Winsorized Mean ( 8 / 20 )30.60633333333330.0421156375984046726.72135763873
Winsorized Mean ( 9 / 20 )30.59433333333330.0384636938408089795.408092107722
Winsorized Mean ( 10 / 20 )30.5910.0367551833463644832.290774112704
Winsorized Mean ( 11 / 20 )30.62950.0275664835796871111.11378828782
Winsorized Mean ( 12 / 20 )30.62350.02671023101131781146.50824199252
Winsorized Mean ( 13 / 20 )30.62566666666670.02552982820271731199.6033198299
Winsorized Mean ( 14 / 20 )30.6280.02427223193152731261.85346639742
Winsorized Mean ( 15 / 20 )30.6730.01589922358904561929.21370205356
Winsorized Mean ( 16 / 20 )30.67033333333330.01464642928403122094.04850414788
Winsorized Mean ( 17 / 20 )30.67883333333330.01331090981678792304.7886099146
Winsorized Mean ( 18 / 20 )30.68483333333330.01242717012995312469.17303074286
Winsorized Mean ( 19 / 20 )30.67850.01145323332829292678.58858024091
Winsorized Mean ( 20 / 20 )30.67516666666670.009036935091991773394.42148852546
Trimmed Mean ( 1 / 20 )30.61017241379310.0482917450753907633.859314174835
Trimmed Mean ( 2 / 20 )30.61178571428570.0463793695339571660.030225117075
Trimmed Mean ( 3 / 20 )30.61333333333330.0441742309886449693.013384685804
Trimmed Mean ( 4 / 20 )30.61730769230770.0425161803860195720.133074380678
Trimmed Mean ( 5 / 20 )30.62160.040657213131151753.165247731605
Trimmed Mean ( 6 / 20 )30.6256250.0386449402269151792.487317102126
Trimmed Mean ( 7 / 20 )30.630.0361799047434674846.602560652968
Trimmed Mean ( 8 / 20 )30.63409090909090.0337245999978131908.360393038833
Trimmed Mean ( 9 / 20 )30.63904761904760.0307585281297279996.115532246004
Trimmed Mean ( 10 / 20 )30.64650.02788150292090091099.16958518855
Trimmed Mean ( 11 / 20 )30.65526315789470.02436019665260951258.41607910874
Trimmed Mean ( 12 / 20 )30.65916666666670.02291244549868391338.10101887325
Trimmed Mean ( 13 / 20 )30.66441176470590.02108547741123361454.29060801673
Trimmed Mean ( 14 / 20 )30.670.01883181076726811628.6272403134
Trimmed Mean ( 15 / 20 )30.6760.01587740388171161932.05389423483
Trimmed Mean ( 16 / 20 )30.67642857142860.01518156677572132020.6365406558
Trimmed Mean ( 17 / 20 )30.67730769230770.01454497208721122109.13486174931
Trimmed Mean ( 18 / 20 )30.67708333333330.01403256004960942186.13590284883
Trimmed Mean ( 19 / 20 )30.67590909090910.01349457307802092273.20337690949
Trimmed Mean ( 20 / 20 )30.67550.01298734201565422361.95365941896
Median30.69
Midrange30.665
Midmean - Weighted Average at Xnp30.67
Midmean - Weighted Average at X(n+1)p30.6806451612903
Midmean - Empirical Distribution Function30.67
Midmean - Empirical Distribution Function - Averaging30.6806451612903
Midmean - Empirical Distribution Function - Interpolation30.6806451612903
Midmean - Closest Observation30.67
Midmean - True Basic - Statistics Graphics Toolkit30.6806451612903
Midmean - MS Excel (old versions)30.67
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')