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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 computationFri, 26 Nov 2010 14:11:41 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/26/t1290780599tjwlf6mxc26e1bc.htm/, Retrieved Sat, 04 May 2024 00:54:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101901, Retrieved Sat, 04 May 2024 00:54:45 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [minitutorial - ce...] [2010-11-26 14:11:41] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,4
1,0
0,4
0,2
0,3
-0,3
-2,5
-1,9
-0,5
-0,3
0,6
0,5
0,6
0,4
0,9
0,9
0,6
1,0
1,0
0,6
0,6
0,8
0,3
0,5
0,4
0,6
0,7
0,8
0,6
0,2
0,2
0,2
0,4
0,5
0,3
0,2
0,2
0,1
0,8
0,7
0,5
0,9
1,2
1,2
1,2
0,6
0,9
0,4
0,6
0,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101901&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]2 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=101901&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101901&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.4180.09234761303170244.52637579118047
Geometric MeanNaN
Harmonic Mean0.513038331292467
Quadratic Mean0.769805170156709
Winsorized Mean ( 1 / 16 )0.430.0851049771920375.05258345854106
Winsorized Mean ( 2 / 16 )0.4860.05876344830881578.27044725908452
Winsorized Mean ( 3 / 16 )0.4860.05213874739185669.32128262206596
Winsorized Mean ( 4 / 16 )0.4860.05213874739185669.32128262206596
Winsorized Mean ( 5 / 16 )0.5260.041581981969235112.6497096840927
Winsorized Mean ( 6 / 16 )0.5260.036568080203859714.3841294666730
Winsorized Mean ( 7 / 16 )0.5260.036568080203859714.384129466673
Winsorized Mean ( 8 / 16 )0.5260.036568080203859714.384129466673
Winsorized Mean ( 9 / 16 )0.5260.036568080203859714.3841294666730
Winsorized Mean ( 10 / 16 )0.5060.032627770818298815.5082614383272
Winsorized Mean ( 11 / 16 )0.5060.032627770818298815.5082614383272
Winsorized Mean ( 12 / 16 )0.530.028320325145141418.7144744025273
Winsorized Mean ( 13 / 16 )0.5040.023553672966314221.3979365647475
Winsorized Mean ( 14 / 16 )0.5040.023553672966314221.3979365647475
Winsorized Mean ( 15 / 16 )0.5040.013690455486526836.813968716819
Winsorized Mean ( 16 / 16 )0.5040.013690455486526836.813968716819
Trimmed Mean ( 1 / 16 )0.46250.07193038646117446.42982782039746
Trimmed Mean ( 2 / 16 )0.4978260869565220.0514982416504659.66685601297664
Trimmed Mean ( 3 / 16 )0.5045454545454550.045974823684694510.9743858509548
Trimmed Mean ( 4 / 16 )0.5119047619047620.042456834806030812.0570637034876
Trimmed Mean ( 5 / 16 )0.520.037587504743205713.8343846858841
Trimmed Mean ( 6 / 16 )0.5184210526315790.035751485989646914.5006854479197
Trimmed Mean ( 7 / 16 )0.5166666666666670.035073618720610114.7309198626562
Trimmed Mean ( 8 / 16 )0.5147058823529410.034073516237033315.1057460219948
Trimmed Mean ( 9 / 16 )0.51250.032611471363864115.7153289491834
Trimmed Mean ( 10 / 16 )0.510.030456299954140116.7453039524807
Trimmed Mean ( 11 / 16 )0.5107142857142860.028793777672494817.7369670462568
Trimmed Mean ( 12 / 16 )0.5115384615384610.026210346211385919.5166617568847
Trimmed Mean ( 13 / 16 )0.5083333333333330.024014387796819621.1678655993327
Trimmed Mean ( 14 / 16 )0.5090909090909090.022705617388646522.4213638579795
Trimmed Mean ( 15 / 16 )0.510.020390916450326925.0111367599579
Trimmed Mean ( 16 / 16 )0.5111111111111110.021219193569605124.0872071520776
Median0.5
Midrange-0.65
Midmean - Weighted Average at Xnp0.5
Midmean - Weighted Average at X(n+1)p0.532142857142857
Midmean - Empirical Distribution Function0.532142857142857
Midmean - Empirical Distribution Function - Averaging0.532142857142857
Midmean - Empirical Distribution Function - Interpolation0.5
Midmean - Closest Observation0.532142857142857
Midmean - True Basic - Statistics Graphics Toolkit0.532142857142857
Midmean - MS Excel (old versions)0.532142857142857
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.418 & 0.0923476130317024 & 4.52637579118047 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.513038331292467 &  &  \tabularnewline
Quadratic Mean & 0.769805170156709 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.43 & 0.085104977192037 & 5.05258345854106 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.486 & 0.0587634483088157 & 8.27044725908452 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.486 & 0.0521387473918566 & 9.32128262206596 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.486 & 0.0521387473918566 & 9.32128262206596 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.526 & 0.0415819819692351 & 12.6497096840927 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.526 & 0.0365680802038597 & 14.3841294666730 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.526 & 0.0365680802038597 & 14.384129466673 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.526 & 0.0365680802038597 & 14.384129466673 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.526 & 0.0365680802038597 & 14.3841294666730 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.506 & 0.0326277708182988 & 15.5082614383272 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.506 & 0.0326277708182988 & 15.5082614383272 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.53 & 0.0283203251451414 & 18.7144744025273 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.504 & 0.0235536729663142 & 21.3979365647475 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.504 & 0.0235536729663142 & 21.3979365647475 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.504 & 0.0136904554865268 & 36.813968716819 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.504 & 0.0136904554865268 & 36.813968716819 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.4625 & 0.0719303864611744 & 6.42982782039746 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.497826086956522 & 0.051498241650465 & 9.66685601297664 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.504545454545455 & 0.0459748236846945 & 10.9743858509548 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.511904761904762 & 0.0424568348060308 & 12.0570637034876 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.52 & 0.0375875047432057 & 13.8343846858841 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.518421052631579 & 0.0357514859896469 & 14.5006854479197 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.516666666666667 & 0.0350736187206101 & 14.7309198626562 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.514705882352941 & 0.0340735162370333 & 15.1057460219948 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.5125 & 0.0326114713638641 & 15.7153289491834 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.51 & 0.0304562999541401 & 16.7453039524807 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.510714285714286 & 0.0287937776724948 & 17.7369670462568 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.511538461538461 & 0.0262103462113859 & 19.5166617568847 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.508333333333333 & 0.0240143877968196 & 21.1678655993327 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.509090909090909 & 0.0227056173886465 & 22.4213638579795 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.51 & 0.0203909164503269 & 25.0111367599579 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.511111111111111 & 0.0212191935696051 & 24.0872071520776 \tabularnewline
Median & 0.5 &  &  \tabularnewline
Midrange & -0.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.5 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.532142857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.532142857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.532142857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.5 &  &  \tabularnewline
Midmean - Closest Observation & 0.532142857142857 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.532142857142857 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.532142857142857 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101901&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]0.418[/C][C]0.0923476130317024[/C][C]4.52637579118047[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.513038331292467[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.769805170156709[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.43[/C][C]0.085104977192037[/C][C]5.05258345854106[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.486[/C][C]0.0587634483088157[/C][C]8.27044725908452[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.486[/C][C]0.0521387473918566[/C][C]9.32128262206596[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.486[/C][C]0.0521387473918566[/C][C]9.32128262206596[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.526[/C][C]0.0415819819692351[/C][C]12.6497096840927[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.526[/C][C]0.0365680802038597[/C][C]14.3841294666730[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.526[/C][C]0.0365680802038597[/C][C]14.384129466673[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.526[/C][C]0.0365680802038597[/C][C]14.384129466673[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.526[/C][C]0.0365680802038597[/C][C]14.3841294666730[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.506[/C][C]0.0326277708182988[/C][C]15.5082614383272[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.506[/C][C]0.0326277708182988[/C][C]15.5082614383272[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.53[/C][C]0.0283203251451414[/C][C]18.7144744025273[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.504[/C][C]0.0235536729663142[/C][C]21.3979365647475[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.504[/C][C]0.0235536729663142[/C][C]21.3979365647475[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.504[/C][C]0.0136904554865268[/C][C]36.813968716819[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.504[/C][C]0.0136904554865268[/C][C]36.813968716819[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.4625[/C][C]0.0719303864611744[/C][C]6.42982782039746[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.497826086956522[/C][C]0.051498241650465[/C][C]9.66685601297664[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.504545454545455[/C][C]0.0459748236846945[/C][C]10.9743858509548[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.511904761904762[/C][C]0.0424568348060308[/C][C]12.0570637034876[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.52[/C][C]0.0375875047432057[/C][C]13.8343846858841[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.518421052631579[/C][C]0.0357514859896469[/C][C]14.5006854479197[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.516666666666667[/C][C]0.0350736187206101[/C][C]14.7309198626562[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.514705882352941[/C][C]0.0340735162370333[/C][C]15.1057460219948[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.5125[/C][C]0.0326114713638641[/C][C]15.7153289491834[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.51[/C][C]0.0304562999541401[/C][C]16.7453039524807[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.510714285714286[/C][C]0.0287937776724948[/C][C]17.7369670462568[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.511538461538461[/C][C]0.0262103462113859[/C][C]19.5166617568847[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.508333333333333[/C][C]0.0240143877968196[/C][C]21.1678655993327[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.509090909090909[/C][C]0.0227056173886465[/C][C]22.4213638579795[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.51[/C][C]0.0203909164503269[/C][C]25.0111367599579[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.511111111111111[/C][C]0.0212191935696051[/C][C]24.0872071520776[/C][/ROW]
[ROW][C]Median[/C][C]0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.532142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.532142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.532142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.532142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.532142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.532142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101901&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101901&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 Mean0.4180.09234761303170244.52637579118047
Geometric MeanNaN
Harmonic Mean0.513038331292467
Quadratic Mean0.769805170156709
Winsorized Mean ( 1 / 16 )0.430.0851049771920375.05258345854106
Winsorized Mean ( 2 / 16 )0.4860.05876344830881578.27044725908452
Winsorized Mean ( 3 / 16 )0.4860.05213874739185669.32128262206596
Winsorized Mean ( 4 / 16 )0.4860.05213874739185669.32128262206596
Winsorized Mean ( 5 / 16 )0.5260.041581981969235112.6497096840927
Winsorized Mean ( 6 / 16 )0.5260.036568080203859714.3841294666730
Winsorized Mean ( 7 / 16 )0.5260.036568080203859714.384129466673
Winsorized Mean ( 8 / 16 )0.5260.036568080203859714.384129466673
Winsorized Mean ( 9 / 16 )0.5260.036568080203859714.3841294666730
Winsorized Mean ( 10 / 16 )0.5060.032627770818298815.5082614383272
Winsorized Mean ( 11 / 16 )0.5060.032627770818298815.5082614383272
Winsorized Mean ( 12 / 16 )0.530.028320325145141418.7144744025273
Winsorized Mean ( 13 / 16 )0.5040.023553672966314221.3979365647475
Winsorized Mean ( 14 / 16 )0.5040.023553672966314221.3979365647475
Winsorized Mean ( 15 / 16 )0.5040.013690455486526836.813968716819
Winsorized Mean ( 16 / 16 )0.5040.013690455486526836.813968716819
Trimmed Mean ( 1 / 16 )0.46250.07193038646117446.42982782039746
Trimmed Mean ( 2 / 16 )0.4978260869565220.0514982416504659.66685601297664
Trimmed Mean ( 3 / 16 )0.5045454545454550.045974823684694510.9743858509548
Trimmed Mean ( 4 / 16 )0.5119047619047620.042456834806030812.0570637034876
Trimmed Mean ( 5 / 16 )0.520.037587504743205713.8343846858841
Trimmed Mean ( 6 / 16 )0.5184210526315790.035751485989646914.5006854479197
Trimmed Mean ( 7 / 16 )0.5166666666666670.035073618720610114.7309198626562
Trimmed Mean ( 8 / 16 )0.5147058823529410.034073516237033315.1057460219948
Trimmed Mean ( 9 / 16 )0.51250.032611471363864115.7153289491834
Trimmed Mean ( 10 / 16 )0.510.030456299954140116.7453039524807
Trimmed Mean ( 11 / 16 )0.5107142857142860.028793777672494817.7369670462568
Trimmed Mean ( 12 / 16 )0.5115384615384610.026210346211385919.5166617568847
Trimmed Mean ( 13 / 16 )0.5083333333333330.024014387796819621.1678655993327
Trimmed Mean ( 14 / 16 )0.5090909090909090.022705617388646522.4213638579795
Trimmed Mean ( 15 / 16 )0.510.020390916450326925.0111367599579
Trimmed Mean ( 16 / 16 )0.5111111111111110.021219193569605124.0872071520776
Median0.5
Midrange-0.65
Midmean - Weighted Average at Xnp0.5
Midmean - Weighted Average at X(n+1)p0.532142857142857
Midmean - Empirical Distribution Function0.532142857142857
Midmean - Empirical Distribution Function - Averaging0.532142857142857
Midmean - Empirical Distribution Function - Interpolation0.5
Midmean - Closest Observation0.532142857142857
Midmean - True Basic - Statistics Graphics Toolkit0.532142857142857
Midmean - MS Excel (old versions)0.532142857142857
Number of observations50


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')