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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 computationSat, 12 Dec 2009 08:59:50 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/12/t126063406127frd1c9di4336w.htm/, Retrieved Mon, 29 Apr 2024 10:44:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67032, Retrieved Mon, 29 Apr 2024 10:44:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper CT Y] [2009-12-12 15:59:50] [b653746fe14da1ddc21bd75262e8c46b] [Current]
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Dataseries X:
3.66
3.59
3.57
3.76
3.6
3.43
3.26
3.3
3.31
3.14
3.3
3.49
3.39
3.37
3.54
3.7
3.96
4.03
4.02
4.04
3.92
3.79
3.83
3.76
3.82
4.06
4.11
4.01
4.22
4.34
4.64
4.62
4.44
4.39
4.42
4.28
4.41
4.25
4.23
4.23
4.37
4.51
4.84
4.85
4.58
4.56
4.46
4.26
3.87
4.13
4.24
4.03
3.93
4.03
4.12
3.92
3.77
3.72
3.68
3.64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67032&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67032&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67032&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.9790.054149145362626273.4822308524616
Geometric Mean3.9570719101992
Harmonic Mean3.93498490568152
Quadratic Mean4.00067952561395
Winsorized Mean ( 1 / 20 )3.980833333333330.053613121162907774.251102099377
Winsorized Mean ( 2 / 20 )3.97550.051678288286532876.9278575551429
Winsorized Mean ( 3 / 20 )3.97450.051463016724590577.2302179887731
Winsorized Mean ( 4 / 20 )3.97250.050761225136920578.2585524538622
Winsorized Mean ( 5 / 20 )3.975833333333330.049351324212290380.5618369272289
Winsorized Mean ( 6 / 20 )3.972833333333330.047960725261491782.8351387864265
Winsorized Mean ( 7 / 20 )3.971666666666670.045933608848484586.4653739654446
Winsorized Mean ( 8 / 20 )3.9770.043902369857401290.5873649399259
Winsorized Mean ( 9 / 20 )3.98150.04199463578873294.8097280812308
Winsorized Mean ( 10 / 20 )3.984833333333330.040823785347443797.6105792106035
Winsorized Mean ( 11 / 20 )3.984833333333330.0395557902985057100.739570699056
Winsorized Mean ( 12 / 20 )3.982833333333330.038530266675617103.368953214481
Winsorized Mean ( 13 / 20 )3.9850.0359986660142047110.698546396901
Winsorized Mean ( 14 / 20 )3.975666666666670.0329726531670386120.574666725363
Winsorized Mean ( 15 / 20 )3.975666666666670.0313926893021223126.643073755325
Winsorized Mean ( 16 / 20 )3.978333333333330.0301410682038153131.990455893324
Winsorized Mean ( 17 / 20 )3.981166666666670.0288303940241143138.08922151174
Winsorized Mean ( 18 / 20 )3.990166666666670.0265688442351652150.182169436843
Winsorized Mean ( 19 / 20 )3.990166666666670.0265688442351652150.182169436843
Winsorized Mean ( 20 / 20 )3.990166666666670.025571978469851156.036681767546
Trimmed Mean ( 1 / 20 )3.978448275862070.051935206575511176.604071461189
Trimmed Mean ( 2 / 20 )3.975892857142860.049864606807427779.7337653237169
Trimmed Mean ( 3 / 20 )3.976111111111110.048601990758681581.8096347298465
Trimmed Mean ( 4 / 20 )3.976730769230770.047122094514050584.3920630065587
Trimmed Mean ( 5 / 20 )3.9780.045536260500925787.3589521018999
Trimmed Mean ( 6 / 20 )3.978541666666670.044021059579089290.3781441134721
Trimmed Mean ( 7 / 20 )3.979782608695650.042522502290060493.5923897786684
Trimmed Mean ( 8 / 20 )3.981363636363640.041189490065671896.659697170706
Trimmed Mean ( 9 / 20 )3.982142857142860.040021097389628499.5010910963887
Trimmed Mean ( 10 / 20 )3.982250.0389846904533509102.149073230815
Trimmed Mean ( 11 / 20 )3.981842105263160.0378847831482551105.103996231969
Trimmed Mean ( 12 / 20 )3.981388888888890.03670809948637108.460774177841
Trimmed Mean ( 13 / 20 )3.981176470588240.0353408781149066112.650751281389
Trimmed Mean ( 14 / 20 )3.9806250.0341395898150803116.598501082214
Trimmed Mean ( 15 / 20 )3.981333333333330.0332829504291917119.620805307014
Trimmed Mean ( 16 / 20 )3.982142857142860.0324337221744466122.777855582676
Trimmed Mean ( 17 / 20 )3.982692307692310.0314743250300094126.537814675771
Trimmed Mean ( 18 / 20 )3.982916666666670.0303570489788668131.202366522497
Trimmed Mean ( 19 / 20 )3.981818181818180.0293481591097743135.675228109693
Trimmed Mean ( 20 / 20 )3.98050.0274865996058941144.816021518589
Median4.015
Midrange3.995
Midmean - Weighted Average at Xnp3.97096774193548
Midmean - Weighted Average at X(n+1)p3.98133333333333
Midmean - Empirical Distribution Function3.97096774193548
Midmean - Empirical Distribution Function - Averaging3.98133333333333
Midmean - Empirical Distribution Function - Interpolation3.98133333333333
Midmean - Closest Observation3.97096774193548
Midmean - True Basic - Statistics Graphics Toolkit3.98133333333333
Midmean - MS Excel (old versions)3.980625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.979 & 0.0541491453626262 & 73.4822308524616 \tabularnewline
Geometric Mean & 3.9570719101992 &  &  \tabularnewline
Harmonic Mean & 3.93498490568152 &  &  \tabularnewline
Quadratic Mean & 4.00067952561395 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3.98083333333333 & 0.0536131211629077 & 74.251102099377 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3.9755 & 0.0516782882865328 & 76.9278575551429 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3.9745 & 0.0514630167245905 & 77.2302179887731 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3.9725 & 0.0507612251369205 & 78.2585524538622 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3.97583333333333 & 0.0493513242122903 & 80.5618369272289 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3.97283333333333 & 0.0479607252614917 & 82.8351387864265 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3.97166666666667 & 0.0459336088484845 & 86.4653739654446 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3.977 & 0.0439023698574012 & 90.5873649399259 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3.9815 & 0.041994635788732 & 94.8097280812308 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3.98483333333333 & 0.0408237853474437 & 97.6105792106035 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3.98483333333333 & 0.0395557902985057 & 100.739570699056 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3.98283333333333 & 0.038530266675617 & 103.368953214481 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3.985 & 0.0359986660142047 & 110.698546396901 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3.97566666666667 & 0.0329726531670386 & 120.574666725363 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3.97566666666667 & 0.0313926893021223 & 126.643073755325 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3.97833333333333 & 0.0301410682038153 & 131.990455893324 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3.98116666666667 & 0.0288303940241143 & 138.08922151174 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3.99016666666667 & 0.0265688442351652 & 150.182169436843 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3.99016666666667 & 0.0265688442351652 & 150.182169436843 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3.99016666666667 & 0.025571978469851 & 156.036681767546 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3.97844827586207 & 0.0519352065755111 & 76.604071461189 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3.97589285714286 & 0.0498646068074277 & 79.7337653237169 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3.97611111111111 & 0.0486019907586815 & 81.8096347298465 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3.97673076923077 & 0.0471220945140505 & 84.3920630065587 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3.978 & 0.0455362605009257 & 87.3589521018999 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3.97854166666667 & 0.0440210595790892 & 90.3781441134721 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3.97978260869565 & 0.0425225022900604 & 93.5923897786684 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3.98136363636364 & 0.0411894900656718 & 96.659697170706 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3.98214285714286 & 0.0400210973896284 & 99.5010910963887 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3.98225 & 0.0389846904533509 & 102.149073230815 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3.98184210526316 & 0.0378847831482551 & 105.103996231969 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3.98138888888889 & 0.03670809948637 & 108.460774177841 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3.98117647058824 & 0.0353408781149066 & 112.650751281389 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3.980625 & 0.0341395898150803 & 116.598501082214 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3.98133333333333 & 0.0332829504291917 & 119.620805307014 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3.98214285714286 & 0.0324337221744466 & 122.777855582676 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3.98269230769231 & 0.0314743250300094 & 126.537814675771 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3.98291666666667 & 0.0303570489788668 & 131.202366522497 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3.98181818181818 & 0.0293481591097743 & 135.675228109693 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3.9805 & 0.0274865996058941 & 144.816021518589 \tabularnewline
Median & 4.015 &  &  \tabularnewline
Midrange & 3.995 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.97096774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.98133333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.97096774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.98133333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.98133333333333 &  &  \tabularnewline
Midmean - Closest Observation & 3.97096774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.98133333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.980625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67032&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]3.979[/C][C]0.0541491453626262[/C][C]73.4822308524616[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.9570719101992[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.93498490568152[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.00067952561395[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3.98083333333333[/C][C]0.0536131211629077[/C][C]74.251102099377[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3.9755[/C][C]0.0516782882865328[/C][C]76.9278575551429[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3.9745[/C][C]0.0514630167245905[/C][C]77.2302179887731[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3.9725[/C][C]0.0507612251369205[/C][C]78.2585524538622[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3.97583333333333[/C][C]0.0493513242122903[/C][C]80.5618369272289[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3.97283333333333[/C][C]0.0479607252614917[/C][C]82.8351387864265[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3.97166666666667[/C][C]0.0459336088484845[/C][C]86.4653739654446[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3.977[/C][C]0.0439023698574012[/C][C]90.5873649399259[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3.9815[/C][C]0.041994635788732[/C][C]94.8097280812308[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3.98483333333333[/C][C]0.0408237853474437[/C][C]97.6105792106035[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3.98483333333333[/C][C]0.0395557902985057[/C][C]100.739570699056[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3.98283333333333[/C][C]0.038530266675617[/C][C]103.368953214481[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3.985[/C][C]0.0359986660142047[/C][C]110.698546396901[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3.97566666666667[/C][C]0.0329726531670386[/C][C]120.574666725363[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3.97566666666667[/C][C]0.0313926893021223[/C][C]126.643073755325[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3.97833333333333[/C][C]0.0301410682038153[/C][C]131.990455893324[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3.98116666666667[/C][C]0.0288303940241143[/C][C]138.08922151174[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3.99016666666667[/C][C]0.0265688442351652[/C][C]150.182169436843[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3.99016666666667[/C][C]0.0265688442351652[/C][C]150.182169436843[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3.99016666666667[/C][C]0.025571978469851[/C][C]156.036681767546[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3.97844827586207[/C][C]0.0519352065755111[/C][C]76.604071461189[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3.97589285714286[/C][C]0.0498646068074277[/C][C]79.7337653237169[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3.97611111111111[/C][C]0.0486019907586815[/C][C]81.8096347298465[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3.97673076923077[/C][C]0.0471220945140505[/C][C]84.3920630065587[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3.978[/C][C]0.0455362605009257[/C][C]87.3589521018999[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3.97854166666667[/C][C]0.0440210595790892[/C][C]90.3781441134721[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3.97978260869565[/C][C]0.0425225022900604[/C][C]93.5923897786684[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3.98136363636364[/C][C]0.0411894900656718[/C][C]96.659697170706[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3.98214285714286[/C][C]0.0400210973896284[/C][C]99.5010910963887[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3.98225[/C][C]0.0389846904533509[/C][C]102.149073230815[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3.98184210526316[/C][C]0.0378847831482551[/C][C]105.103996231969[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3.98138888888889[/C][C]0.03670809948637[/C][C]108.460774177841[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3.98117647058824[/C][C]0.0353408781149066[/C][C]112.650751281389[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3.980625[/C][C]0.0341395898150803[/C][C]116.598501082214[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3.98133333333333[/C][C]0.0332829504291917[/C][C]119.620805307014[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3.98214285714286[/C][C]0.0324337221744466[/C][C]122.777855582676[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3.98269230769231[/C][C]0.0314743250300094[/C][C]126.537814675771[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3.98291666666667[/C][C]0.0303570489788668[/C][C]131.202366522497[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3.98181818181818[/C][C]0.0293481591097743[/C][C]135.675228109693[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3.9805[/C][C]0.0274865996058941[/C][C]144.816021518589[/C][/ROW]
[ROW][C]Median[/C][C]4.015[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.995[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.97096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.98133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.97096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.98133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.98133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.97096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.98133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.980625[/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=67032&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67032&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 Mean3.9790.054149145362626273.4822308524616
Geometric Mean3.9570719101992
Harmonic Mean3.93498490568152
Quadratic Mean4.00067952561395
Winsorized Mean ( 1 / 20 )3.980833333333330.053613121162907774.251102099377
Winsorized Mean ( 2 / 20 )3.97550.051678288286532876.9278575551429
Winsorized Mean ( 3 / 20 )3.97450.051463016724590577.2302179887731
Winsorized Mean ( 4 / 20 )3.97250.050761225136920578.2585524538622
Winsorized Mean ( 5 / 20 )3.975833333333330.049351324212290380.5618369272289
Winsorized Mean ( 6 / 20 )3.972833333333330.047960725261491782.8351387864265
Winsorized Mean ( 7 / 20 )3.971666666666670.045933608848484586.4653739654446
Winsorized Mean ( 8 / 20 )3.9770.043902369857401290.5873649399259
Winsorized Mean ( 9 / 20 )3.98150.04199463578873294.8097280812308
Winsorized Mean ( 10 / 20 )3.984833333333330.040823785347443797.6105792106035
Winsorized Mean ( 11 / 20 )3.984833333333330.0395557902985057100.739570699056
Winsorized Mean ( 12 / 20 )3.982833333333330.038530266675617103.368953214481
Winsorized Mean ( 13 / 20 )3.9850.0359986660142047110.698546396901
Winsorized Mean ( 14 / 20 )3.975666666666670.0329726531670386120.574666725363
Winsorized Mean ( 15 / 20 )3.975666666666670.0313926893021223126.643073755325
Winsorized Mean ( 16 / 20 )3.978333333333330.0301410682038153131.990455893324
Winsorized Mean ( 17 / 20 )3.981166666666670.0288303940241143138.08922151174
Winsorized Mean ( 18 / 20 )3.990166666666670.0265688442351652150.182169436843
Winsorized Mean ( 19 / 20 )3.990166666666670.0265688442351652150.182169436843
Winsorized Mean ( 20 / 20 )3.990166666666670.025571978469851156.036681767546
Trimmed Mean ( 1 / 20 )3.978448275862070.051935206575511176.604071461189
Trimmed Mean ( 2 / 20 )3.975892857142860.049864606807427779.7337653237169
Trimmed Mean ( 3 / 20 )3.976111111111110.048601990758681581.8096347298465
Trimmed Mean ( 4 / 20 )3.976730769230770.047122094514050584.3920630065587
Trimmed Mean ( 5 / 20 )3.9780.045536260500925787.3589521018999
Trimmed Mean ( 6 / 20 )3.978541666666670.044021059579089290.3781441134721
Trimmed Mean ( 7 / 20 )3.979782608695650.042522502290060493.5923897786684
Trimmed Mean ( 8 / 20 )3.981363636363640.041189490065671896.659697170706
Trimmed Mean ( 9 / 20 )3.982142857142860.040021097389628499.5010910963887
Trimmed Mean ( 10 / 20 )3.982250.0389846904533509102.149073230815
Trimmed Mean ( 11 / 20 )3.981842105263160.0378847831482551105.103996231969
Trimmed Mean ( 12 / 20 )3.981388888888890.03670809948637108.460774177841
Trimmed Mean ( 13 / 20 )3.981176470588240.0353408781149066112.650751281389
Trimmed Mean ( 14 / 20 )3.9806250.0341395898150803116.598501082214
Trimmed Mean ( 15 / 20 )3.981333333333330.0332829504291917119.620805307014
Trimmed Mean ( 16 / 20 )3.982142857142860.0324337221744466122.777855582676
Trimmed Mean ( 17 / 20 )3.982692307692310.0314743250300094126.537814675771
Trimmed Mean ( 18 / 20 )3.982916666666670.0303570489788668131.202366522497
Trimmed Mean ( 19 / 20 )3.981818181818180.0293481591097743135.675228109693
Trimmed Mean ( 20 / 20 )3.98050.0274865996058941144.816021518589
Median4.015
Midrange3.995
Midmean - Weighted Average at Xnp3.97096774193548
Midmean - Weighted Average at X(n+1)p3.98133333333333
Midmean - Empirical Distribution Function3.97096774193548
Midmean - Empirical Distribution Function - Averaging3.98133333333333
Midmean - Empirical Distribution Function - Interpolation3.98133333333333
Midmean - Closest Observation3.97096774193548
Midmean - True Basic - Statistics Graphics Toolkit3.98133333333333
Midmean - MS Excel (old versions)3.980625
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')