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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 computationSun, 13 Nov 2011 11:00:52 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/13/t1321200066lufq0mefy2655k6.htm/, Retrieved Thu, 25 Apr 2024 21:37:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=141760, Retrieved Thu, 25 Apr 2024 21:37:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2011-11-13 16:00:52] [f04206f511735117c791d4a2bb2fa643] [Current]
-   PD      [Central Tendency] [] [2011-11-13 16:29:36] [71981af30b475eff259f311228330cd7]
- RMPD      [Histogram] [] [2011-11-13 16:34:19] [71981af30b475eff259f311228330cd7]
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Dataseries X:
2591
2664
2723
2811
2809
2914
2952
3182
3152
3491
3683
3735
3808
3801
3815
3933
3827
3903
3870
3853
3849
3917
4050
4130
4111
4074
3993
4276
4322
4506
4402
4340
4279
4192
4200
3905
3878
3804
3912
3796
3875
3822
3739
3772
3740
3733
3714
3652
3591
3641
3487
3357
3312
3311
3240
3322
3431
3301
3318
3284




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=141760&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=141760&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141760&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3668.2558.758995584905162.4287390123864
Geometric Mean3638.67314506983
Harmonic Mean3607.16125896601
Quadratic Mean3695.91160834058
Winsorized Mean ( 1 / 20 )3667.7333333333357.995888548346663.2412645988833
Winsorized Mean ( 2 / 20 )3667.6333333333357.002680909630264.3414182422026
Winsorized Mean ( 3 / 20 )3671.0333333333355.654711155687265.9608729809785
Winsorized Mean ( 4 / 20 )3668.355.065960960444366.6164711560207
Winsorized Mean ( 5 / 20 )3676.6333333333352.834310707600569.587987126033
Winsorized Mean ( 6 / 20 )3672.8333333333350.505507708082972.7214416804196
Winsorized Mean ( 7 / 20 )3695.2333333333345.107594952630281.9204246471995
Winsorized Mean ( 8 / 20 )3690.9666666666742.804693540279186.2280829833176
Winsorized Mean ( 9 / 20 )3696.8166666666740.603139866804891.0475563908053
Winsorized Mean ( 10 / 20 )3697.9833333333338.180995447617696.8540314357905
Winsorized Mean ( 11 / 20 )3696.736.8866817176009100.217743311838
Winsorized Mean ( 12 / 20 )3687.334.7437130027914106.128553378959
Winsorized Mean ( 13 / 20 )3674.5166666666732.8648876880711111.806761719146
Winsorized Mean ( 14 / 20 )3672.1833333333332.1130373903364114.351790791312
Winsorized Mean ( 15 / 20 )3671.9333333333331.765390563706115.595409600559
Winsorized Mean ( 16 / 20 )3679.429.7984775707875123.476106833292
Winsorized Mean ( 17 / 20 )3699.825.9564585433567142.538705494819
Winsorized Mean ( 18 / 20 )3709.122.0602628665234168.134895873275
Winsorized Mean ( 19 / 20 )3709.4166666666721.7212345227017170.77374965911
Winsorized Mean ( 20 / 20 )3741.0833333333315.9781328619829234.137703425571
Trimmed Mean ( 1 / 20 )3672.3793103448355.976703236746765.6054947504311
Trimmed Mean ( 2 / 20 )3677.3571428571453.477841196820568.7641284793631
Trimmed Mean ( 3 / 20 )3682.7592592592651.044163167014672.1484892838659
Trimmed Mean ( 4 / 20 )3687.2692307692348.677139274222375.7495055327107
Trimmed Mean ( 5 / 20 )3692.9645.911209426679380.4370010312557
Trimmed Mean ( 6 / 20 )3697.0416666666743.233101055687185.5141448656351
Trimmed Mean ( 7 / 20 )3702.3043478260940.571781316494491.2531870105717
Trimmed Mean ( 8 / 20 )3703.6818181818238.911209338509195.1829018204379
Trimmed Mean ( 9 / 20 )3705.9523809523837.414462295054599.0513334583521
Trimmed Mean ( 10 / 20 )3707.47536.0667114703025102.794927756381
Trimmed Mean ( 11 / 20 )3708.9736842105334.9303612600197106.181944601177
Trimmed Mean ( 12 / 20 )3710.8333333333333.719630663213110.049643496888
Trimmed Mean ( 13 / 20 )3714.2941176470632.604487990116113.919719235372
Trimmed Mean ( 14 / 20 )3720.0312531.4632877583145118.234028133851
Trimmed Mean ( 15 / 20 )3726.8666666666729.9461483460943124.452287606221
Trimmed Mean ( 16 / 20 )3734.7142857142927.7048816751109134.803473608386
Trimmed Mean ( 17 / 20 )3742.6923076923125.0216994584097149.577861963904
Trimmed Mean ( 18 / 20 )374922.6484634920501165.529992854303
Trimmed Mean ( 19 / 20 )3755.0454545454520.6528173054549181.817589291009
Trimmed Mean ( 20 / 20 )3762.2517.1612898239338219.22885975348
Median3784
Midrange3548.5
Midmean - Weighted Average at Xnp3713.67741935484
Midmean - Weighted Average at X(n+1)p3726.86666666667
Midmean - Empirical Distribution Function3713.67741935484
Midmean - Empirical Distribution Function - Averaging3726.86666666667
Midmean - Empirical Distribution Function - Interpolation3726.86666666667
Midmean - Closest Observation3713.67741935484
Midmean - True Basic - Statistics Graphics Toolkit3726.86666666667
Midmean - MS Excel (old versions)3720.03125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3668.25 & 58.7589955849051 & 62.4287390123864 \tabularnewline
Geometric Mean & 3638.67314506983 &  &  \tabularnewline
Harmonic Mean & 3607.16125896601 &  &  \tabularnewline
Quadratic Mean & 3695.91160834058 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3667.73333333333 & 57.9958885483466 & 63.2412645988833 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3667.63333333333 & 57.0026809096302 & 64.3414182422026 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3671.03333333333 & 55.6547111556872 & 65.9608729809785 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3668.3 & 55.0659609604443 & 66.6164711560207 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3676.63333333333 & 52.8343107076005 & 69.587987126033 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3672.83333333333 & 50.5055077080829 & 72.7214416804196 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3695.23333333333 & 45.1075949526302 & 81.9204246471995 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3690.96666666667 & 42.8046935402791 & 86.2280829833176 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3696.81666666667 & 40.6031398668048 & 91.0475563908053 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3697.98333333333 & 38.1809954476176 & 96.8540314357905 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3696.7 & 36.8866817176009 & 100.217743311838 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3687.3 & 34.7437130027914 & 106.128553378959 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3674.51666666667 & 32.8648876880711 & 111.806761719146 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3672.18333333333 & 32.1130373903364 & 114.351790791312 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3671.93333333333 & 31.765390563706 & 115.595409600559 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3679.4 & 29.7984775707875 & 123.476106833292 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3699.8 & 25.9564585433567 & 142.538705494819 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3709.1 & 22.0602628665234 & 168.134895873275 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3709.41666666667 & 21.7212345227017 & 170.77374965911 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3741.08333333333 & 15.9781328619829 & 234.137703425571 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3672.37931034483 & 55.9767032367467 & 65.6054947504311 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3677.35714285714 & 53.4778411968205 & 68.7641284793631 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3682.75925925926 & 51.0441631670146 & 72.1484892838659 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3687.26923076923 & 48.6771392742223 & 75.7495055327107 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3692.96 & 45.9112094266793 & 80.4370010312557 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3697.04166666667 & 43.2331010556871 & 85.5141448656351 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3702.30434782609 & 40.5717813164944 & 91.2531870105717 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3703.68181818182 & 38.9112093385091 & 95.1829018204379 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3705.95238095238 & 37.4144622950545 & 99.0513334583521 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3707.475 & 36.0667114703025 & 102.794927756381 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3708.97368421053 & 34.9303612600197 & 106.181944601177 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3710.83333333333 & 33.719630663213 & 110.049643496888 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3714.29411764706 & 32.604487990116 & 113.919719235372 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3720.03125 & 31.4632877583145 & 118.234028133851 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3726.86666666667 & 29.9461483460943 & 124.452287606221 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3734.71428571429 & 27.7048816751109 & 134.803473608386 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3742.69230769231 & 25.0216994584097 & 149.577861963904 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3749 & 22.6484634920501 & 165.529992854303 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3755.04545454545 & 20.6528173054549 & 181.817589291009 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3762.25 & 17.1612898239338 & 219.22885975348 \tabularnewline
Median & 3784 &  &  \tabularnewline
Midrange & 3548.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3713.67741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3726.86666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3713.67741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3726.86666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3726.86666666667 &  &  \tabularnewline
Midmean - Closest Observation & 3713.67741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3726.86666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3720.03125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=141760&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]3668.25[/C][C]58.7589955849051[/C][C]62.4287390123864[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3638.67314506983[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3607.16125896601[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3695.91160834058[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3667.73333333333[/C][C]57.9958885483466[/C][C]63.2412645988833[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3667.63333333333[/C][C]57.0026809096302[/C][C]64.3414182422026[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3671.03333333333[/C][C]55.6547111556872[/C][C]65.9608729809785[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3668.3[/C][C]55.0659609604443[/C][C]66.6164711560207[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3676.63333333333[/C][C]52.8343107076005[/C][C]69.587987126033[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3672.83333333333[/C][C]50.5055077080829[/C][C]72.7214416804196[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3695.23333333333[/C][C]45.1075949526302[/C][C]81.9204246471995[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3690.96666666667[/C][C]42.8046935402791[/C][C]86.2280829833176[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3696.81666666667[/C][C]40.6031398668048[/C][C]91.0475563908053[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3697.98333333333[/C][C]38.1809954476176[/C][C]96.8540314357905[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3696.7[/C][C]36.8866817176009[/C][C]100.217743311838[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3687.3[/C][C]34.7437130027914[/C][C]106.128553378959[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3674.51666666667[/C][C]32.8648876880711[/C][C]111.806761719146[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3672.18333333333[/C][C]32.1130373903364[/C][C]114.351790791312[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3671.93333333333[/C][C]31.765390563706[/C][C]115.595409600559[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3679.4[/C][C]29.7984775707875[/C][C]123.476106833292[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3699.8[/C][C]25.9564585433567[/C][C]142.538705494819[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3709.1[/C][C]22.0602628665234[/C][C]168.134895873275[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3709.41666666667[/C][C]21.7212345227017[/C][C]170.77374965911[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3741.08333333333[/C][C]15.9781328619829[/C][C]234.137703425571[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3672.37931034483[/C][C]55.9767032367467[/C][C]65.6054947504311[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3677.35714285714[/C][C]53.4778411968205[/C][C]68.7641284793631[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3682.75925925926[/C][C]51.0441631670146[/C][C]72.1484892838659[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3687.26923076923[/C][C]48.6771392742223[/C][C]75.7495055327107[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3692.96[/C][C]45.9112094266793[/C][C]80.4370010312557[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3697.04166666667[/C][C]43.2331010556871[/C][C]85.5141448656351[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3702.30434782609[/C][C]40.5717813164944[/C][C]91.2531870105717[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3703.68181818182[/C][C]38.9112093385091[/C][C]95.1829018204379[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3705.95238095238[/C][C]37.4144622950545[/C][C]99.0513334583521[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3707.475[/C][C]36.0667114703025[/C][C]102.794927756381[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3708.97368421053[/C][C]34.9303612600197[/C][C]106.181944601177[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3710.83333333333[/C][C]33.719630663213[/C][C]110.049643496888[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3714.29411764706[/C][C]32.604487990116[/C][C]113.919719235372[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3720.03125[/C][C]31.4632877583145[/C][C]118.234028133851[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3726.86666666667[/C][C]29.9461483460943[/C][C]124.452287606221[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3734.71428571429[/C][C]27.7048816751109[/C][C]134.803473608386[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3742.69230769231[/C][C]25.0216994584097[/C][C]149.577861963904[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3749[/C][C]22.6484634920501[/C][C]165.529992854303[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3755.04545454545[/C][C]20.6528173054549[/C][C]181.817589291009[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3762.25[/C][C]17.1612898239338[/C][C]219.22885975348[/C][/ROW]
[ROW][C]Median[/C][C]3784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3548.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3713.67741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3726.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3713.67741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3726.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3726.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3713.67741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3726.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3720.03125[/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=141760&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141760&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 Mean3668.2558.758995584905162.4287390123864
Geometric Mean3638.67314506983
Harmonic Mean3607.16125896601
Quadratic Mean3695.91160834058
Winsorized Mean ( 1 / 20 )3667.7333333333357.995888548346663.2412645988833
Winsorized Mean ( 2 / 20 )3667.6333333333357.002680909630264.3414182422026
Winsorized Mean ( 3 / 20 )3671.0333333333355.654711155687265.9608729809785
Winsorized Mean ( 4 / 20 )3668.355.065960960444366.6164711560207
Winsorized Mean ( 5 / 20 )3676.6333333333352.834310707600569.587987126033
Winsorized Mean ( 6 / 20 )3672.8333333333350.505507708082972.7214416804196
Winsorized Mean ( 7 / 20 )3695.2333333333345.107594952630281.9204246471995
Winsorized Mean ( 8 / 20 )3690.9666666666742.804693540279186.2280829833176
Winsorized Mean ( 9 / 20 )3696.8166666666740.603139866804891.0475563908053
Winsorized Mean ( 10 / 20 )3697.9833333333338.180995447617696.8540314357905
Winsorized Mean ( 11 / 20 )3696.736.8866817176009100.217743311838
Winsorized Mean ( 12 / 20 )3687.334.7437130027914106.128553378959
Winsorized Mean ( 13 / 20 )3674.5166666666732.8648876880711111.806761719146
Winsorized Mean ( 14 / 20 )3672.1833333333332.1130373903364114.351790791312
Winsorized Mean ( 15 / 20 )3671.9333333333331.765390563706115.595409600559
Winsorized Mean ( 16 / 20 )3679.429.7984775707875123.476106833292
Winsorized Mean ( 17 / 20 )3699.825.9564585433567142.538705494819
Winsorized Mean ( 18 / 20 )3709.122.0602628665234168.134895873275
Winsorized Mean ( 19 / 20 )3709.4166666666721.7212345227017170.77374965911
Winsorized Mean ( 20 / 20 )3741.0833333333315.9781328619829234.137703425571
Trimmed Mean ( 1 / 20 )3672.3793103448355.976703236746765.6054947504311
Trimmed Mean ( 2 / 20 )3677.3571428571453.477841196820568.7641284793631
Trimmed Mean ( 3 / 20 )3682.7592592592651.044163167014672.1484892838659
Trimmed Mean ( 4 / 20 )3687.2692307692348.677139274222375.7495055327107
Trimmed Mean ( 5 / 20 )3692.9645.911209426679380.4370010312557
Trimmed Mean ( 6 / 20 )3697.0416666666743.233101055687185.5141448656351
Trimmed Mean ( 7 / 20 )3702.3043478260940.571781316494491.2531870105717
Trimmed Mean ( 8 / 20 )3703.6818181818238.911209338509195.1829018204379
Trimmed Mean ( 9 / 20 )3705.9523809523837.414462295054599.0513334583521
Trimmed Mean ( 10 / 20 )3707.47536.0667114703025102.794927756381
Trimmed Mean ( 11 / 20 )3708.9736842105334.9303612600197106.181944601177
Trimmed Mean ( 12 / 20 )3710.8333333333333.719630663213110.049643496888
Trimmed Mean ( 13 / 20 )3714.2941176470632.604487990116113.919719235372
Trimmed Mean ( 14 / 20 )3720.0312531.4632877583145118.234028133851
Trimmed Mean ( 15 / 20 )3726.8666666666729.9461483460943124.452287606221
Trimmed Mean ( 16 / 20 )3734.7142857142927.7048816751109134.803473608386
Trimmed Mean ( 17 / 20 )3742.6923076923125.0216994584097149.577861963904
Trimmed Mean ( 18 / 20 )374922.6484634920501165.529992854303
Trimmed Mean ( 19 / 20 )3755.0454545454520.6528173054549181.817589291009
Trimmed Mean ( 20 / 20 )3762.2517.1612898239338219.22885975348
Median3784
Midrange3548.5
Midmean - Weighted Average at Xnp3713.67741935484
Midmean - Weighted Average at X(n+1)p3726.86666666667
Midmean - Empirical Distribution Function3713.67741935484
Midmean - Empirical Distribution Function - Averaging3726.86666666667
Midmean - Empirical Distribution Function - Interpolation3726.86666666667
Midmean - Closest Observation3713.67741935484
Midmean - True Basic - Statistics Graphics Toolkit3726.86666666667
Midmean - MS Excel (old versions)3720.03125
Number of observations60



Parameters (Session):
par1 = usa price ; par2 = www.ico.org ; par3 = Retail prices in importing Member countries in US cents per lb (Arabica, 1977/1 - 2006/12) ; par4 = 12 ;
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')