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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 13:05:07 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t14762739474emancrs1wdog5m.htm/, Retrieved Sun, 05 May 2024 21:29:16 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 21:29:16 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99,78
99,8
99,88
99,74
100,15
100,27
100,26
100,36
100,37
100,54
99,8
99,82
99,82
99,82
99,67
99,78
99,44
99,61
99,71
99,71
99,77
99,77
99,89
99,96
100,02
100
100,04
99,99
99,77
99,77
99,93
99,9
100,01
100,08
100,21
100,28
100,48
100,72
100,74
100,88
101,03
101,47
101,46
101,46
101,45
101,74
102,41
102,54
102,67
102,87
102,9
102,88
102,82
102,94
102,97
103,01
103,11
103,21
104,66
104,79

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.8821666666670.179159066978489563.087140204739
Geometric Mean100.872873991578
Harmonic Mean100.863674239622
Quadratic Mean100.891552330543
Winsorized Mean ( 1 / 20 )100.8828333333330.178003855044058566.74521632334
Winsorized Mean ( 2 / 20 )100.83650.162984666188048618.687035770943
Winsorized Mean ( 3 / 20 )100.83350.161531131665618624.235705899301
Winsorized Mean ( 4 / 20 )100.8268333333330.159963712634143630.310660292918
Winsorized Mean ( 5 / 20 )100.8260.158904299095986634.507691570361
Winsorized Mean ( 6 / 20 )100.8260.157877017144272638.636337471859
Winsorized Mean ( 7 / 20 )100.8213333333330.156823241868695642.897902963574
Winsorized Mean ( 8 / 20 )100.8186666666670.1562255118287645.340607219219
Winsorized Mean ( 9 / 20 )100.8171666666670.15589038805684646.718299462484
Winsorized Mean ( 10 / 20 )100.81050.153848451552811655.258463653728
Winsorized Mean ( 11 / 20 )100.7830.147828213785327681.757544242229
Winsorized Mean ( 12 / 20 )100.7610.141790348137166710.633701967675
Winsorized Mean ( 13 / 20 )100.7328333333330.135847432632785741.514442938563
Winsorized Mean ( 14 / 20 )100.5811666666670.103951610772982967.576797692188
Winsorized Mean ( 15 / 20 )100.5136666666670.09157534228437791097.60623503357
Winsorized Mean ( 16 / 20 )100.5110.09110393270146081103.25643492653
Winsorized Mean ( 17 / 20 )100.5280.08896130054327131130.01945099827
Winsorized Mean ( 18 / 20 )100.5280.08805936621053521141.59349909077
Winsorized Mean ( 19 / 20 )100.3981666666670.06473609689388591550.8838419968
Winsorized Mean ( 20 / 20 )100.3581666666670.05528175988079461815.39384569289
Trimmed Mean ( 1 / 20 )100.8396551724140.170557423100098591.235803986276
Trimmed Mean ( 2 / 20 )100.7933928571430.161108231102394625.62534618782
Trimmed Mean ( 3 / 20 )100.7694444444440.159501191517507631.778631154515
Trimmed Mean ( 4 / 20 )100.7448076923080.157969413573585637.748823732758
Trimmed Mean ( 5 / 20 )100.72020.156422632633516643.897870175718
Trimmed Mean ( 6 / 20 )100.693750.154556568002677651.500944290224
Trimmed Mean ( 7 / 20 )100.6650.152204017036123661.382018426682
Trimmed Mean ( 8 / 20 )100.6345454545450.149199220699159674.497795517728
Trimmed Mean ( 9 / 20 )100.6016666666670.145153575872119693.070536238784
Trimmed Mean ( 10 / 20 )100.565750.139580822786454720.484003406802
Trimmed Mean ( 11 / 20 )100.5271052631580.132374585910529759.413935625859
Trimmed Mean ( 12 / 20 )100.4883333333330.12418975496431809.151554910567
Trimmed Mean ( 13 / 20 )100.4482352941180.114443916775989877.707073681635
Trimmed Mean ( 14 / 20 )100.40718750.102256037733838981.919402757902
Trimmed Mean ( 15 / 20 )100.3823333333330.09727870061770831031.90454535183
Trimmed Mean ( 16 / 20 )100.3635714285710.09430785774927621064.21218574803
Trimmed Mean ( 17 / 20 )100.3423076923080.08956700575943151120.30436701008
Trimmed Mean ( 18 / 20 )100.3150.08224213102748511219.75195373373
Trimmed Mean ( 19 / 20 )100.2827272727270.06965959848829561439.61104354595
Trimmed Mean ( 20 / 20 )100.26450.06345937365955591579.97935085043
Median100.235
Midrange102.115
Midmean - Weighted Average at Xnp100.364193548387
Midmean - Weighted Average at X(n+1)p100.364193548387
Midmean - Empirical Distribution Function100.364193548387
Midmean - Empirical Distribution Function - Averaging100.364193548387
Midmean - Empirical Distribution Function - Interpolation100.364193548387
Midmean - Closest Observation100.364193548387
Midmean - True Basic - Statistics Graphics Toolkit100.364193548387
Midmean - MS Excel (old versions)100.4071875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.882166666667 & 0.179159066978489 & 563.087140204739 \tabularnewline
Geometric Mean & 100.872873991578 &  &  \tabularnewline
Harmonic Mean & 100.863674239622 &  &  \tabularnewline
Quadratic Mean & 100.891552330543 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 100.882833333333 & 0.178003855044058 & 566.74521632334 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 100.8365 & 0.162984666188048 & 618.687035770943 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 100.8335 & 0.161531131665618 & 624.235705899301 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 100.826833333333 & 0.159963712634143 & 630.310660292918 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 100.826 & 0.158904299095986 & 634.507691570361 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 100.826 & 0.157877017144272 & 638.636337471859 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 100.821333333333 & 0.156823241868695 & 642.897902963574 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 100.818666666667 & 0.1562255118287 & 645.340607219219 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 100.817166666667 & 0.15589038805684 & 646.718299462484 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 100.8105 & 0.153848451552811 & 655.258463653728 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 100.783 & 0.147828213785327 & 681.757544242229 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 100.761 & 0.141790348137166 & 710.633701967675 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 100.732833333333 & 0.135847432632785 & 741.514442938563 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 100.581166666667 & 0.103951610772982 & 967.576797692188 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 100.513666666667 & 0.0915753422843779 & 1097.60623503357 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 100.511 & 0.0911039327014608 & 1103.25643492653 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 100.528 & 0.0889613005432713 & 1130.01945099827 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 100.528 & 0.0880593662105352 & 1141.59349909077 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 100.398166666667 & 0.0647360968938859 & 1550.8838419968 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 100.358166666667 & 0.0552817598807946 & 1815.39384569289 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 100.839655172414 & 0.170557423100098 & 591.235803986276 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 100.793392857143 & 0.161108231102394 & 625.62534618782 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 100.769444444444 & 0.159501191517507 & 631.778631154515 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 100.744807692308 & 0.157969413573585 & 637.748823732758 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 100.7202 & 0.156422632633516 & 643.897870175718 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 100.69375 & 0.154556568002677 & 651.500944290224 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 100.665 & 0.152204017036123 & 661.382018426682 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 100.634545454545 & 0.149199220699159 & 674.497795517728 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 100.601666666667 & 0.145153575872119 & 693.070536238784 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 100.56575 & 0.139580822786454 & 720.484003406802 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 100.527105263158 & 0.132374585910529 & 759.413935625859 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 100.488333333333 & 0.12418975496431 & 809.151554910567 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 100.448235294118 & 0.114443916775989 & 877.707073681635 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 100.4071875 & 0.102256037733838 & 981.919402757902 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 100.382333333333 & 0.0972787006177083 & 1031.90454535183 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 100.363571428571 & 0.0943078577492762 & 1064.21218574803 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 100.342307692308 & 0.0895670057594315 & 1120.30436701008 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 100.315 & 0.0822421310274851 & 1219.75195373373 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.282727272727 & 0.0696595984882956 & 1439.61104354595 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.2645 & 0.0634593736595559 & 1579.97935085043 \tabularnewline
Median & 100.235 &  &  \tabularnewline
Midrange & 102.115 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.364193548387 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.364193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.364193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.364193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.364193548387 &  &  \tabularnewline
Midmean - Closest Observation & 100.364193548387 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.364193548387 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.4071875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.882166666667[/C][C]0.179159066978489[/C][C]563.087140204739[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.872873991578[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.863674239622[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.891552330543[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]100.882833333333[/C][C]0.178003855044058[/C][C]566.74521632334[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]100.8365[/C][C]0.162984666188048[/C][C]618.687035770943[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]100.8335[/C][C]0.161531131665618[/C][C]624.235705899301[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]100.826833333333[/C][C]0.159963712634143[/C][C]630.310660292918[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]100.826[/C][C]0.158904299095986[/C][C]634.507691570361[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]100.826[/C][C]0.157877017144272[/C][C]638.636337471859[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]100.821333333333[/C][C]0.156823241868695[/C][C]642.897902963574[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]100.818666666667[/C][C]0.1562255118287[/C][C]645.340607219219[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]100.817166666667[/C][C]0.15589038805684[/C][C]646.718299462484[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]100.8105[/C][C]0.153848451552811[/C][C]655.258463653728[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]100.783[/C][C]0.147828213785327[/C][C]681.757544242229[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]100.761[/C][C]0.141790348137166[/C][C]710.633701967675[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]100.732833333333[/C][C]0.135847432632785[/C][C]741.514442938563[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]100.581166666667[/C][C]0.103951610772982[/C][C]967.576797692188[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]100.513666666667[/C][C]0.0915753422843779[/C][C]1097.60623503357[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]100.511[/C][C]0.0911039327014608[/C][C]1103.25643492653[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]100.528[/C][C]0.0889613005432713[/C][C]1130.01945099827[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]100.528[/C][C]0.0880593662105352[/C][C]1141.59349909077[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]100.398166666667[/C][C]0.0647360968938859[/C][C]1550.8838419968[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]100.358166666667[/C][C]0.0552817598807946[/C][C]1815.39384569289[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]100.839655172414[/C][C]0.170557423100098[/C][C]591.235803986276[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]100.793392857143[/C][C]0.161108231102394[/C][C]625.62534618782[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]100.769444444444[/C][C]0.159501191517507[/C][C]631.778631154515[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]100.744807692308[/C][C]0.157969413573585[/C][C]637.748823732758[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]100.7202[/C][C]0.156422632633516[/C][C]643.897870175718[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]100.69375[/C][C]0.154556568002677[/C][C]651.500944290224[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]100.665[/C][C]0.152204017036123[/C][C]661.382018426682[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]100.634545454545[/C][C]0.149199220699159[/C][C]674.497795517728[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]100.601666666667[/C][C]0.145153575872119[/C][C]693.070536238784[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]100.56575[/C][C]0.139580822786454[/C][C]720.484003406802[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]100.527105263158[/C][C]0.132374585910529[/C][C]759.413935625859[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]100.488333333333[/C][C]0.12418975496431[/C][C]809.151554910567[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]100.448235294118[/C][C]0.114443916775989[/C][C]877.707073681635[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]100.4071875[/C][C]0.102256037733838[/C][C]981.919402757902[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]100.382333333333[/C][C]0.0972787006177083[/C][C]1031.90454535183[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]100.363571428571[/C][C]0.0943078577492762[/C][C]1064.21218574803[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]100.342307692308[/C][C]0.0895670057594315[/C][C]1120.30436701008[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]100.315[/C][C]0.0822421310274851[/C][C]1219.75195373373[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.282727272727[/C][C]0.0696595984882956[/C][C]1439.61104354595[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.2645[/C][C]0.0634593736595559[/C][C]1579.97935085043[/C][/ROW]
[ROW][C]Median[/C][C]100.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.364193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.364193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.364193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.364193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.364193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.364193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.364193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.4071875[/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=&T=1

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

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


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.8821666666670.179159066978489563.087140204739
Geometric Mean100.872873991578
Harmonic Mean100.863674239622
Quadratic Mean100.891552330543
Winsorized Mean ( 1 / 20 )100.8828333333330.178003855044058566.74521632334
Winsorized Mean ( 2 / 20 )100.83650.162984666188048618.687035770943
Winsorized Mean ( 3 / 20 )100.83350.161531131665618624.235705899301
Winsorized Mean ( 4 / 20 )100.8268333333330.159963712634143630.310660292918
Winsorized Mean ( 5 / 20 )100.8260.158904299095986634.507691570361
Winsorized Mean ( 6 / 20 )100.8260.157877017144272638.636337471859
Winsorized Mean ( 7 / 20 )100.8213333333330.156823241868695642.897902963574
Winsorized Mean ( 8 / 20 )100.8186666666670.1562255118287645.340607219219
Winsorized Mean ( 9 / 20 )100.8171666666670.15589038805684646.718299462484
Winsorized Mean ( 10 / 20 )100.81050.153848451552811655.258463653728
Winsorized Mean ( 11 / 20 )100.7830.147828213785327681.757544242229
Winsorized Mean ( 12 / 20 )100.7610.141790348137166710.633701967675
Winsorized Mean ( 13 / 20 )100.7328333333330.135847432632785741.514442938563
Winsorized Mean ( 14 / 20 )100.5811666666670.103951610772982967.576797692188
Winsorized Mean ( 15 / 20 )100.5136666666670.09157534228437791097.60623503357
Winsorized Mean ( 16 / 20 )100.5110.09110393270146081103.25643492653
Winsorized Mean ( 17 / 20 )100.5280.08896130054327131130.01945099827
Winsorized Mean ( 18 / 20 )100.5280.08805936621053521141.59349909077
Winsorized Mean ( 19 / 20 )100.3981666666670.06473609689388591550.8838419968
Winsorized Mean ( 20 / 20 )100.3581666666670.05528175988079461815.39384569289
Trimmed Mean ( 1 / 20 )100.8396551724140.170557423100098591.235803986276
Trimmed Mean ( 2 / 20 )100.7933928571430.161108231102394625.62534618782
Trimmed Mean ( 3 / 20 )100.7694444444440.159501191517507631.778631154515
Trimmed Mean ( 4 / 20 )100.7448076923080.157969413573585637.748823732758
Trimmed Mean ( 5 / 20 )100.72020.156422632633516643.897870175718
Trimmed Mean ( 6 / 20 )100.693750.154556568002677651.500944290224
Trimmed Mean ( 7 / 20 )100.6650.152204017036123661.382018426682
Trimmed Mean ( 8 / 20 )100.6345454545450.149199220699159674.497795517728
Trimmed Mean ( 9 / 20 )100.6016666666670.145153575872119693.070536238784
Trimmed Mean ( 10 / 20 )100.565750.139580822786454720.484003406802
Trimmed Mean ( 11 / 20 )100.5271052631580.132374585910529759.413935625859
Trimmed Mean ( 12 / 20 )100.4883333333330.12418975496431809.151554910567
Trimmed Mean ( 13 / 20 )100.4482352941180.114443916775989877.707073681635
Trimmed Mean ( 14 / 20 )100.40718750.102256037733838981.919402757902
Trimmed Mean ( 15 / 20 )100.3823333333330.09727870061770831031.90454535183
Trimmed Mean ( 16 / 20 )100.3635714285710.09430785774927621064.21218574803
Trimmed Mean ( 17 / 20 )100.3423076923080.08956700575943151120.30436701008
Trimmed Mean ( 18 / 20 )100.3150.08224213102748511219.75195373373
Trimmed Mean ( 19 / 20 )100.2827272727270.06965959848829561439.61104354595
Trimmed Mean ( 20 / 20 )100.26450.06345937365955591579.97935085043
Median100.235
Midrange102.115
Midmean - Weighted Average at Xnp100.364193548387
Midmean - Weighted Average at X(n+1)p100.364193548387
Midmean - Empirical Distribution Function100.364193548387
Midmean - Empirical Distribution Function - Averaging100.364193548387
Midmean - Empirical Distribution Function - Interpolation100.364193548387
Midmean - Closest Observation100.364193548387
Midmean - True Basic - Statistics Graphics Toolkit100.364193548387
Midmean - MS Excel (old versions)100.4071875
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')