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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 03:06:41 -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/2008/Dec/05/t1228471728vjnspc3qewciky7.htm/, Retrieved Thu, 16 May 2024 07:38:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29122, Retrieved Thu, 16 May 2024 07:38:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper 1.1 central...] [2008-12-05 10:06:41] [c577d4c76516de948d1234ed72fcf120] [Current]
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Dataseries X:
493.000
481.000
462.000
457.000
442.000
439.000
488.000
521.000
501.000
485.000
464.000
460.000
467.000
460.000
448.000
443.000
436.000
431.000
484.000
510.000
513.000
503.000
471.000
471.000
476.000
475.000
470.000
461.000
455.000
456.000
517.000
525.000
523.000
519.000
509.000
512.000
519.000
517.000
510.000
509.000
501.000
507.000
569.000
580.000
578.000
565.000
547.000
555.000
562.000
561.000
555.000
544.000
537.000
543.000
594.000
611.000
613.000
611.000
594.000
595.000




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=29122&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=29122&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29122&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 Mean510.0833333333336.4035341436733479.656533702923
Geometric Mean507.757508251467
Harmonic Mean505.481034843619
Quadratic Mean512.449330828587
Winsorized Mean ( 1 / 20 )510.1333333333336.3775943725802879.988362936124
Winsorized Mean ( 2 / 20 )510.2333333333336.3582486425411780.2474646743935
Winsorized Mean ( 3 / 20 )509.5833333333336.1277958759697483.1593192148703
Winsorized Mean ( 4 / 20 )509.5833333333336.099703228247583.5423157922621
Winsorized Mean ( 5 / 20 )5106.0248074728364484.6500078715205
Winsorized Mean ( 6 / 20 )509.35.5899577027598491.109812825337
Winsorized Mean ( 7 / 20 )509.1833333333335.5211709469310492.2237942327007
Winsorized Mean ( 8 / 20 )508.1166666666675.2544891577441996.7014397427755
Winsorized Mean ( 9 / 20 )507.9666666666675.06505512581011100.288477430030
Winsorized Mean ( 10 / 20 )507.4666666666674.97084532061767102.088605445403
Winsorized Mean ( 11 / 20 )507.4666666666674.90730267924115103.410508753281
Winsorized Mean ( 12 / 20 )506.4666666666674.65805096523502108.729309843675
Winsorized Mean ( 13 / 20 )506.94.58865587202444110.468079136290
Winsorized Mean ( 14 / 20 )505.7333333333334.15449295053956121.731662408442
Winsorized Mean ( 15 / 20 )505.7333333333333.91180067966644129.284024097173
Winsorized Mean ( 16 / 20 )505.7333333333333.82652551955283132.165153675085
Winsorized Mean ( 17 / 20 )504.0333333333333.55227043387815141.890473350887
Winsorized Mean ( 18 / 20 )501.6333333333332.82272523951195177.71242000871
Winsorized Mean ( 19 / 20 )501.3166666666672.68428063427438186.760154756391
Winsorized Mean ( 20 / 20 )502.3166666666672.33064716245443215.526689221234
Trimmed Mean ( 1 / 20 )509.6724137931036.2296923767481381.813415971456
Trimmed Mean ( 2 / 20 )509.1785714285716.0462023684108884.21460950246
Trimmed Mean ( 3 / 20 )508.5925925925935.8302039235963987.2341000859649
Trimmed Mean ( 4 / 20 )508.2115384615385.6738489133966689.5708620759337
Trimmed Mean ( 5 / 20 )507.85.4866814623584492.5513907602945
Trimmed Mean ( 6 / 20 )507.255.2732514496336996.1930233831797
Trimmed Mean ( 7 / 20 )506.8043478260875.1405952366125398.5886506326168
Trimmed Mean ( 8 / 20 )506.3409090909094.98633896783335101.545625429256
Trimmed Mean ( 9 / 20 )506.0238095238104.86024046656576104.114973941066
Trimmed Mean ( 10 / 20 )505.74.74182156927818106.646779641896
Trimmed Mean ( 11 / 20 )505.4210526315794.60496849290994109.755594074042
Trimmed Mean ( 12 / 20 )505.1111111111114.43198650823432113.969460460371
Trimmed Mean ( 13 / 20 )504.9117647058824.26409117212203118.410170966071
Trimmed Mean ( 14 / 20 )504.6254.04305208490941124.812886255782
Trimmed Mean ( 15 / 20 )504.4666666666673.86607209063174130.485581965502
Trimmed Mean ( 16 / 20 )504.2857142857143.68245415883174136.942835547938
Trimmed Mean ( 17 / 20 )504.0769230769233.42925113014627146.993295021652
Trimmed Mean ( 18 / 20 )504.0833333333333.14672400770648160.193055412171
Trimmed Mean ( 19 / 20 )504.4545454545453.00772977677097167.719370719572
Trimmed Mean ( 20 / 20 )504.952.81955110275601179.088791654256
Median509
Midrange522
Midmean - Weighted Average at Xnp503.258064516129
Midmean - Weighted Average at X(n+1)p504.466666666667
Midmean - Empirical Distribution Function503.258064516129
Midmean - Empirical Distribution Function - Averaging504.466666666667
Midmean - Empirical Distribution Function - Interpolation504.466666666667
Midmean - Closest Observation503.258064516129
Midmean - True Basic - Statistics Graphics Toolkit504.466666666667
Midmean - MS Excel (old versions)504.625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 510.083333333333 & 6.40353414367334 & 79.656533702923 \tabularnewline
Geometric Mean & 507.757508251467 &  &  \tabularnewline
Harmonic Mean & 505.481034843619 &  &  \tabularnewline
Quadratic Mean & 512.449330828587 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 510.133333333333 & 6.37759437258028 & 79.988362936124 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 510.233333333333 & 6.35824864254117 & 80.2474646743935 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 509.583333333333 & 6.12779587596974 & 83.1593192148703 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 509.583333333333 & 6.0997032282475 & 83.5423157922621 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 510 & 6.02480747283644 & 84.6500078715205 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 509.3 & 5.58995770275984 & 91.109812825337 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 509.183333333333 & 5.52117094693104 & 92.2237942327007 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 508.116666666667 & 5.25448915774419 & 96.7014397427755 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 507.966666666667 & 5.06505512581011 & 100.288477430030 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 507.466666666667 & 4.97084532061767 & 102.088605445403 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 507.466666666667 & 4.90730267924115 & 103.410508753281 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 506.466666666667 & 4.65805096523502 & 108.729309843675 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 506.9 & 4.58865587202444 & 110.468079136290 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 505.733333333333 & 4.15449295053956 & 121.731662408442 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 505.733333333333 & 3.91180067966644 & 129.284024097173 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 505.733333333333 & 3.82652551955283 & 132.165153675085 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 504.033333333333 & 3.55227043387815 & 141.890473350887 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 501.633333333333 & 2.82272523951195 & 177.71242000871 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 501.316666666667 & 2.68428063427438 & 186.760154756391 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 502.316666666667 & 2.33064716245443 & 215.526689221234 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 509.672413793103 & 6.22969237674813 & 81.813415971456 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 509.178571428571 & 6.04620236841088 & 84.21460950246 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 508.592592592593 & 5.83020392359639 & 87.2341000859649 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 508.211538461538 & 5.67384891339666 & 89.5708620759337 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 507.8 & 5.48668146235844 & 92.5513907602945 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 507.25 & 5.27325144963369 & 96.1930233831797 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 506.804347826087 & 5.14059523661253 & 98.5886506326168 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 506.340909090909 & 4.98633896783335 & 101.545625429256 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 506.023809523810 & 4.86024046656576 & 104.114973941066 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 505.7 & 4.74182156927818 & 106.646779641896 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 505.421052631579 & 4.60496849290994 & 109.755594074042 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 505.111111111111 & 4.43198650823432 & 113.969460460371 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 504.911764705882 & 4.26409117212203 & 118.410170966071 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 504.625 & 4.04305208490941 & 124.812886255782 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 504.466666666667 & 3.86607209063174 & 130.485581965502 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 504.285714285714 & 3.68245415883174 & 136.942835547938 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 504.076923076923 & 3.42925113014627 & 146.993295021652 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 504.083333333333 & 3.14672400770648 & 160.193055412171 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 504.454545454545 & 3.00772977677097 & 167.719370719572 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 504.95 & 2.81955110275601 & 179.088791654256 \tabularnewline
Median & 509 &  &  \tabularnewline
Midrange & 522 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 503.258064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 504.466666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 503.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 504.466666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 504.466666666667 &  &  \tabularnewline
Midmean - Closest Observation & 503.258064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 504.466666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 504.625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29122&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]510.083333333333[/C][C]6.40353414367334[/C][C]79.656533702923[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]507.757508251467[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]505.481034843619[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]512.449330828587[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]510.133333333333[/C][C]6.37759437258028[/C][C]79.988362936124[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]510.233333333333[/C][C]6.35824864254117[/C][C]80.2474646743935[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]509.583333333333[/C][C]6.12779587596974[/C][C]83.1593192148703[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]509.583333333333[/C][C]6.0997032282475[/C][C]83.5423157922621[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]510[/C][C]6.02480747283644[/C][C]84.6500078715205[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]509.3[/C][C]5.58995770275984[/C][C]91.109812825337[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]509.183333333333[/C][C]5.52117094693104[/C][C]92.2237942327007[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]508.116666666667[/C][C]5.25448915774419[/C][C]96.7014397427755[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]507.966666666667[/C][C]5.06505512581011[/C][C]100.288477430030[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]507.466666666667[/C][C]4.97084532061767[/C][C]102.088605445403[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]507.466666666667[/C][C]4.90730267924115[/C][C]103.410508753281[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]506.466666666667[/C][C]4.65805096523502[/C][C]108.729309843675[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]506.9[/C][C]4.58865587202444[/C][C]110.468079136290[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]505.733333333333[/C][C]4.15449295053956[/C][C]121.731662408442[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]505.733333333333[/C][C]3.91180067966644[/C][C]129.284024097173[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]505.733333333333[/C][C]3.82652551955283[/C][C]132.165153675085[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]504.033333333333[/C][C]3.55227043387815[/C][C]141.890473350887[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]501.633333333333[/C][C]2.82272523951195[/C][C]177.71242000871[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]501.316666666667[/C][C]2.68428063427438[/C][C]186.760154756391[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]502.316666666667[/C][C]2.33064716245443[/C][C]215.526689221234[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]509.672413793103[/C][C]6.22969237674813[/C][C]81.813415971456[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]509.178571428571[/C][C]6.04620236841088[/C][C]84.21460950246[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]508.592592592593[/C][C]5.83020392359639[/C][C]87.2341000859649[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]508.211538461538[/C][C]5.67384891339666[/C][C]89.5708620759337[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]507.8[/C][C]5.48668146235844[/C][C]92.5513907602945[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]507.25[/C][C]5.27325144963369[/C][C]96.1930233831797[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]506.804347826087[/C][C]5.14059523661253[/C][C]98.5886506326168[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]506.340909090909[/C][C]4.98633896783335[/C][C]101.545625429256[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]506.023809523810[/C][C]4.86024046656576[/C][C]104.114973941066[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]505.7[/C][C]4.74182156927818[/C][C]106.646779641896[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]505.421052631579[/C][C]4.60496849290994[/C][C]109.755594074042[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]505.111111111111[/C][C]4.43198650823432[/C][C]113.969460460371[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]504.911764705882[/C][C]4.26409117212203[/C][C]118.410170966071[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]504.625[/C][C]4.04305208490941[/C][C]124.812886255782[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]504.466666666667[/C][C]3.86607209063174[/C][C]130.485581965502[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]504.285714285714[/C][C]3.68245415883174[/C][C]136.942835547938[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]504.076923076923[/C][C]3.42925113014627[/C][C]146.993295021652[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]504.083333333333[/C][C]3.14672400770648[/C][C]160.193055412171[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]504.454545454545[/C][C]3.00772977677097[/C][C]167.719370719572[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]504.95[/C][C]2.81955110275601[/C][C]179.088791654256[/C][/ROW]
[ROW][C]Median[/C][C]509[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]522[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]503.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]504.466666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]503.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]504.466666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]504.466666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]503.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]504.466666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]504.625[/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=29122&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29122&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 Mean510.0833333333336.4035341436733479.656533702923
Geometric Mean507.757508251467
Harmonic Mean505.481034843619
Quadratic Mean512.449330828587
Winsorized Mean ( 1 / 20 )510.1333333333336.3775943725802879.988362936124
Winsorized Mean ( 2 / 20 )510.2333333333336.3582486425411780.2474646743935
Winsorized Mean ( 3 / 20 )509.5833333333336.1277958759697483.1593192148703
Winsorized Mean ( 4 / 20 )509.5833333333336.099703228247583.5423157922621
Winsorized Mean ( 5 / 20 )5106.0248074728364484.6500078715205
Winsorized Mean ( 6 / 20 )509.35.5899577027598491.109812825337
Winsorized Mean ( 7 / 20 )509.1833333333335.5211709469310492.2237942327007
Winsorized Mean ( 8 / 20 )508.1166666666675.2544891577441996.7014397427755
Winsorized Mean ( 9 / 20 )507.9666666666675.06505512581011100.288477430030
Winsorized Mean ( 10 / 20 )507.4666666666674.97084532061767102.088605445403
Winsorized Mean ( 11 / 20 )507.4666666666674.90730267924115103.410508753281
Winsorized Mean ( 12 / 20 )506.4666666666674.65805096523502108.729309843675
Winsorized Mean ( 13 / 20 )506.94.58865587202444110.468079136290
Winsorized Mean ( 14 / 20 )505.7333333333334.15449295053956121.731662408442
Winsorized Mean ( 15 / 20 )505.7333333333333.91180067966644129.284024097173
Winsorized Mean ( 16 / 20 )505.7333333333333.82652551955283132.165153675085
Winsorized Mean ( 17 / 20 )504.0333333333333.55227043387815141.890473350887
Winsorized Mean ( 18 / 20 )501.6333333333332.82272523951195177.71242000871
Winsorized Mean ( 19 / 20 )501.3166666666672.68428063427438186.760154756391
Winsorized Mean ( 20 / 20 )502.3166666666672.33064716245443215.526689221234
Trimmed Mean ( 1 / 20 )509.6724137931036.2296923767481381.813415971456
Trimmed Mean ( 2 / 20 )509.1785714285716.0462023684108884.21460950246
Trimmed Mean ( 3 / 20 )508.5925925925935.8302039235963987.2341000859649
Trimmed Mean ( 4 / 20 )508.2115384615385.6738489133966689.5708620759337
Trimmed Mean ( 5 / 20 )507.85.4866814623584492.5513907602945
Trimmed Mean ( 6 / 20 )507.255.2732514496336996.1930233831797
Trimmed Mean ( 7 / 20 )506.8043478260875.1405952366125398.5886506326168
Trimmed Mean ( 8 / 20 )506.3409090909094.98633896783335101.545625429256
Trimmed Mean ( 9 / 20 )506.0238095238104.86024046656576104.114973941066
Trimmed Mean ( 10 / 20 )505.74.74182156927818106.646779641896
Trimmed Mean ( 11 / 20 )505.4210526315794.60496849290994109.755594074042
Trimmed Mean ( 12 / 20 )505.1111111111114.43198650823432113.969460460371
Trimmed Mean ( 13 / 20 )504.9117647058824.26409117212203118.410170966071
Trimmed Mean ( 14 / 20 )504.6254.04305208490941124.812886255782
Trimmed Mean ( 15 / 20 )504.4666666666673.86607209063174130.485581965502
Trimmed Mean ( 16 / 20 )504.2857142857143.68245415883174136.942835547938
Trimmed Mean ( 17 / 20 )504.0769230769233.42925113014627146.993295021652
Trimmed Mean ( 18 / 20 )504.0833333333333.14672400770648160.193055412171
Trimmed Mean ( 19 / 20 )504.4545454545453.00772977677097167.719370719572
Trimmed Mean ( 20 / 20 )504.952.81955110275601179.088791654256
Median509
Midrange522
Midmean - Weighted Average at Xnp503.258064516129
Midmean - Weighted Average at X(n+1)p504.466666666667
Midmean - Empirical Distribution Function503.258064516129
Midmean - Empirical Distribution Function - Averaging504.466666666667
Midmean - Empirical Distribution Function - Interpolation504.466666666667
Midmean - Closest Observation503.258064516129
Midmean - True Basic - Statistics Graphics Toolkit504.466666666667
Midmean - MS Excel (old versions)504.625
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')