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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 11:29:36 -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/t1321201804731t9rpehutvy6q.htm/, Retrieved Fri, 29 Mar 2024 09:23:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=141781, Retrieved Fri, 29 Mar 2024 09:23:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
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] [71981af30b475eff259f311228330cd7]
-   PD      [Central Tendency] [] [2011-11-13 16:29:36] [f04206f511735117c791d4a2bb2fa643] [Current]
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Dataseries X:
2293
2309
2299
2349
2374
2440
2485
2685
2803
2947
3066
3212
3116
3190
3193
3393
3316
3221
3246
3182
3150
3249
3192
3265
3142
3282
3326
3291
3343
3376
3307
3391
3389
3327
3258
3278
3269
3192
3413
3193
3122
3276
3122
3026
3015
3079
3035
3011
3045
3098
3018
3037
3057
3048
3014
2860
3014
3003
3015
2931




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=141781&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=141781&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141781&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 Mean3059.6333333333338.287582376254379.9118968459837
Geometric Mean3043.95172126675
Harmonic Mean3026.56036970927
Quadratic Mean3073.73494845169
Winsorized Mean ( 1 / 20 )3059.438.203005176553580.0827051657616
Winsorized Mean ( 2 / 20 )3059.6666666666738.081244302258480.3457639771822
Winsorized Mean ( 3 / 20 )3061.5666666666737.409403683999981.839493955262
Winsorized Mean ( 4 / 20 )3062.3666666666736.748772735314483.3324881003122
Winsorized Mean ( 5 / 20 )3065.1166666666734.647629700738288.4654071040642
Winsorized Mean ( 6 / 20 )3068.0166666666733.071942566508192.7679606511425
Winsorized Mean ( 7 / 20 )3091.2333333333326.4867557423551116.708643497253
Winsorized Mean ( 8 / 20 )3105.6333333333322.4155662048999138.548065435637
Winsorized Mean ( 9 / 20 )3112.8333333333320.3151604443448153.22711045582
Winsorized Mean ( 10 / 20 )312217.5292330493788178.102486926011
Winsorized Mean ( 11 / 20 )3123.2833333333316.728677155104186.702349765917
Winsorized Mean ( 12 / 20 )3133.6833333333314.7467987844124212.499226384352
Winsorized Mean ( 13 / 20 )3134.9833333333314.4184143808535217.429132671921
Winsorized Mean ( 14 / 20 )3134.0514.0483311231133223.090555919745
Winsorized Mean ( 15 / 20 )3133.0513.8863918470953225.620163574411
Winsorized Mean ( 16 / 20 )3131.4513.5494996467754231.111855170626
Winsorized Mean ( 17 / 20 )3128.913.15023361267237.934936531117
Winsorized Mean ( 18 / 20 )3128.912.879487041054242.936693831554
Winsorized Mean ( 19 / 20 )3123.5166666666711.3198613431714275.932414008844
Winsorized Mean ( 20 / 20 )3123.5166666666710.4510289728494298.871687637765
Trimmed Mean ( 1 / 20 )3066.7586206896636.786711401262883.3659357923573
Trimmed Mean ( 2 / 20 )3074.6428571428635.007034808525987.8292855695974
Trimmed Mean ( 3 / 20 )3082.9629629629632.828929596055393.9099447011337
Trimmed Mean ( 4 / 20 )3091.1923076923130.3859417966588101.731002065969
Trimmed Mean ( 5 / 20 )3099.8427.4745650092768112.825808123016
Trimmed Mean ( 6 / 20 )3108.5208333333324.4736612943046127.014948681043
Trimmed Mean ( 7 / 20 )3117.3260869565220.9805075015371148.582015317224
Trimmed Mean ( 8 / 20 )3122.4090909090918.9523246908092164.750717489728
Trimmed Mean ( 9 / 20 )3125.4047619047617.7037191550476176.539445442663
Trimmed Mean ( 10 / 20 )3127.516.7201705303535187.049527654182
Trimmed Mean ( 11 / 20 )3128.3684210526316.2385059931178192.651246511132
Trimmed Mean ( 12 / 20 )3129.1388888888915.7920088681494198.146981490112
Trimmed Mean ( 13 / 20 )3128.4705882352915.6880937002153199.416872949476
Trimmed Mean ( 14 / 20 )3127.5312515.5720868175342200.842140597264
Trimmed Mean ( 15 / 20 )3126.615.4481409066355202.39328595566
Trimmed Mean ( 16 / 20 )3125.6785714285715.2476950787789204.993512480372
Trimmed Mean ( 17 / 20 )3124.8461538461514.9865264931992208.510367980479
Trimmed Mean ( 18 / 20 )3124.2514.6516618733908213.235196593911
Trimmed Mean ( 19 / 20 )3123.5454545454514.1402571161386220.897359142111
Trimmed Mean ( 20 / 20 )3123.5513.8946174735702224.802878232632
Median3122
Midrange2853
Midmean - Weighted Average at Xnp3122.96774193548
Midmean - Weighted Average at X(n+1)p3122.96774193548
Midmean - Empirical Distribution Function3122.96774193548
Midmean - Empirical Distribution Function - Averaging3122.96774193548
Midmean - Empirical Distribution Function - Interpolation3122.96774193548
Midmean - Closest Observation3122.96774193548
Midmean - True Basic - Statistics Graphics Toolkit3122.96774193548
Midmean - MS Excel (old versions)3127.53125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3059.63333333333 & 38.2875823762543 & 79.9118968459837 \tabularnewline
Geometric Mean & 3043.95172126675 &  &  \tabularnewline
Harmonic Mean & 3026.56036970927 &  &  \tabularnewline
Quadratic Mean & 3073.73494845169 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3059.4 & 38.2030051765535 & 80.0827051657616 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3059.66666666667 & 38.0812443022584 & 80.3457639771822 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3061.56666666667 & 37.4094036839999 & 81.839493955262 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3062.36666666667 & 36.7487727353144 & 83.3324881003122 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3065.11666666667 & 34.6476297007382 & 88.4654071040642 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3068.01666666667 & 33.0719425665081 & 92.7679606511425 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3091.23333333333 & 26.4867557423551 & 116.708643497253 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3105.63333333333 & 22.4155662048999 & 138.548065435637 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3112.83333333333 & 20.3151604443448 & 153.22711045582 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3122 & 17.5292330493788 & 178.102486926011 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3123.28333333333 & 16.728677155104 & 186.702349765917 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3133.68333333333 & 14.7467987844124 & 212.499226384352 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3134.98333333333 & 14.4184143808535 & 217.429132671921 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3134.05 & 14.0483311231133 & 223.090555919745 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3133.05 & 13.8863918470953 & 225.620163574411 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3131.45 & 13.5494996467754 & 231.111855170626 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3128.9 & 13.15023361267 & 237.934936531117 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3128.9 & 12.879487041054 & 242.936693831554 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3123.51666666667 & 11.3198613431714 & 275.932414008844 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3123.51666666667 & 10.4510289728494 & 298.871687637765 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3066.75862068966 & 36.7867114012628 & 83.3659357923573 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3074.64285714286 & 35.0070348085259 & 87.8292855695974 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3082.96296296296 & 32.8289295960553 & 93.9099447011337 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3091.19230769231 & 30.3859417966588 & 101.731002065969 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3099.84 & 27.4745650092768 & 112.825808123016 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3108.52083333333 & 24.4736612943046 & 127.014948681043 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3117.32608695652 & 20.9805075015371 & 148.582015317224 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3122.40909090909 & 18.9523246908092 & 164.750717489728 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3125.40476190476 & 17.7037191550476 & 176.539445442663 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3127.5 & 16.7201705303535 & 187.049527654182 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3128.36842105263 & 16.2385059931178 & 192.651246511132 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3129.13888888889 & 15.7920088681494 & 198.146981490112 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3128.47058823529 & 15.6880937002153 & 199.416872949476 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3127.53125 & 15.5720868175342 & 200.842140597264 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3126.6 & 15.4481409066355 & 202.39328595566 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3125.67857142857 & 15.2476950787789 & 204.993512480372 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3124.84615384615 & 14.9865264931992 & 208.510367980479 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3124.25 & 14.6516618733908 & 213.235196593911 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3123.54545454545 & 14.1402571161386 & 220.897359142111 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3123.55 & 13.8946174735702 & 224.802878232632 \tabularnewline
Median & 3122 &  &  \tabularnewline
Midrange & 2853 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3122.96774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3122.96774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3122.96774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3122.96774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3122.96774193548 &  &  \tabularnewline
Midmean - Closest Observation & 3122.96774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3122.96774193548 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3127.53125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=141781&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]3059.63333333333[/C][C]38.2875823762543[/C][C]79.9118968459837[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3043.95172126675[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3026.56036970927[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3073.73494845169[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3059.4[/C][C]38.2030051765535[/C][C]80.0827051657616[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3059.66666666667[/C][C]38.0812443022584[/C][C]80.3457639771822[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3061.56666666667[/C][C]37.4094036839999[/C][C]81.839493955262[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3062.36666666667[/C][C]36.7487727353144[/C][C]83.3324881003122[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3065.11666666667[/C][C]34.6476297007382[/C][C]88.4654071040642[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3068.01666666667[/C][C]33.0719425665081[/C][C]92.7679606511425[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3091.23333333333[/C][C]26.4867557423551[/C][C]116.708643497253[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3105.63333333333[/C][C]22.4155662048999[/C][C]138.548065435637[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3112.83333333333[/C][C]20.3151604443448[/C][C]153.22711045582[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3122[/C][C]17.5292330493788[/C][C]178.102486926011[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3123.28333333333[/C][C]16.728677155104[/C][C]186.702349765917[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3133.68333333333[/C][C]14.7467987844124[/C][C]212.499226384352[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3134.98333333333[/C][C]14.4184143808535[/C][C]217.429132671921[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3134.05[/C][C]14.0483311231133[/C][C]223.090555919745[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3133.05[/C][C]13.8863918470953[/C][C]225.620163574411[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3131.45[/C][C]13.5494996467754[/C][C]231.111855170626[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3128.9[/C][C]13.15023361267[/C][C]237.934936531117[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3128.9[/C][C]12.879487041054[/C][C]242.936693831554[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3123.51666666667[/C][C]11.3198613431714[/C][C]275.932414008844[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3123.51666666667[/C][C]10.4510289728494[/C][C]298.871687637765[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3066.75862068966[/C][C]36.7867114012628[/C][C]83.3659357923573[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3074.64285714286[/C][C]35.0070348085259[/C][C]87.8292855695974[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3082.96296296296[/C][C]32.8289295960553[/C][C]93.9099447011337[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3091.19230769231[/C][C]30.3859417966588[/C][C]101.731002065969[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3099.84[/C][C]27.4745650092768[/C][C]112.825808123016[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3108.52083333333[/C][C]24.4736612943046[/C][C]127.014948681043[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3117.32608695652[/C][C]20.9805075015371[/C][C]148.582015317224[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3122.40909090909[/C][C]18.9523246908092[/C][C]164.750717489728[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3125.40476190476[/C][C]17.7037191550476[/C][C]176.539445442663[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3127.5[/C][C]16.7201705303535[/C][C]187.049527654182[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3128.36842105263[/C][C]16.2385059931178[/C][C]192.651246511132[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3129.13888888889[/C][C]15.7920088681494[/C][C]198.146981490112[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3128.47058823529[/C][C]15.6880937002153[/C][C]199.416872949476[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3127.53125[/C][C]15.5720868175342[/C][C]200.842140597264[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3126.6[/C][C]15.4481409066355[/C][C]202.39328595566[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3125.67857142857[/C][C]15.2476950787789[/C][C]204.993512480372[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3124.84615384615[/C][C]14.9865264931992[/C][C]208.510367980479[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3124.25[/C][C]14.6516618733908[/C][C]213.235196593911[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3123.54545454545[/C][C]14.1402571161386[/C][C]220.897359142111[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3123.55[/C][C]13.8946174735702[/C][C]224.802878232632[/C][/ROW]
[ROW][C]Median[/C][C]3122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2853[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3122.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3122.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3122.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3122.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3122.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3122.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3122.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3127.53125[/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=141781&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141781&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 Mean3059.6333333333338.287582376254379.9118968459837
Geometric Mean3043.95172126675
Harmonic Mean3026.56036970927
Quadratic Mean3073.73494845169
Winsorized Mean ( 1 / 20 )3059.438.203005176553580.0827051657616
Winsorized Mean ( 2 / 20 )3059.6666666666738.081244302258480.3457639771822
Winsorized Mean ( 3 / 20 )3061.5666666666737.409403683999981.839493955262
Winsorized Mean ( 4 / 20 )3062.3666666666736.748772735314483.3324881003122
Winsorized Mean ( 5 / 20 )3065.1166666666734.647629700738288.4654071040642
Winsorized Mean ( 6 / 20 )3068.0166666666733.071942566508192.7679606511425
Winsorized Mean ( 7 / 20 )3091.2333333333326.4867557423551116.708643497253
Winsorized Mean ( 8 / 20 )3105.6333333333322.4155662048999138.548065435637
Winsorized Mean ( 9 / 20 )3112.8333333333320.3151604443448153.22711045582
Winsorized Mean ( 10 / 20 )312217.5292330493788178.102486926011
Winsorized Mean ( 11 / 20 )3123.2833333333316.728677155104186.702349765917
Winsorized Mean ( 12 / 20 )3133.6833333333314.7467987844124212.499226384352
Winsorized Mean ( 13 / 20 )3134.9833333333314.4184143808535217.429132671921
Winsorized Mean ( 14 / 20 )3134.0514.0483311231133223.090555919745
Winsorized Mean ( 15 / 20 )3133.0513.8863918470953225.620163574411
Winsorized Mean ( 16 / 20 )3131.4513.5494996467754231.111855170626
Winsorized Mean ( 17 / 20 )3128.913.15023361267237.934936531117
Winsorized Mean ( 18 / 20 )3128.912.879487041054242.936693831554
Winsorized Mean ( 19 / 20 )3123.5166666666711.3198613431714275.932414008844
Winsorized Mean ( 20 / 20 )3123.5166666666710.4510289728494298.871687637765
Trimmed Mean ( 1 / 20 )3066.7586206896636.786711401262883.3659357923573
Trimmed Mean ( 2 / 20 )3074.6428571428635.007034808525987.8292855695974
Trimmed Mean ( 3 / 20 )3082.9629629629632.828929596055393.9099447011337
Trimmed Mean ( 4 / 20 )3091.1923076923130.3859417966588101.731002065969
Trimmed Mean ( 5 / 20 )3099.8427.4745650092768112.825808123016
Trimmed Mean ( 6 / 20 )3108.5208333333324.4736612943046127.014948681043
Trimmed Mean ( 7 / 20 )3117.3260869565220.9805075015371148.582015317224
Trimmed Mean ( 8 / 20 )3122.4090909090918.9523246908092164.750717489728
Trimmed Mean ( 9 / 20 )3125.4047619047617.7037191550476176.539445442663
Trimmed Mean ( 10 / 20 )3127.516.7201705303535187.049527654182
Trimmed Mean ( 11 / 20 )3128.3684210526316.2385059931178192.651246511132
Trimmed Mean ( 12 / 20 )3129.1388888888915.7920088681494198.146981490112
Trimmed Mean ( 13 / 20 )3128.4705882352915.6880937002153199.416872949476
Trimmed Mean ( 14 / 20 )3127.5312515.5720868175342200.842140597264
Trimmed Mean ( 15 / 20 )3126.615.4481409066355202.39328595566
Trimmed Mean ( 16 / 20 )3125.6785714285715.2476950787789204.993512480372
Trimmed Mean ( 17 / 20 )3124.8461538461514.9865264931992208.510367980479
Trimmed Mean ( 18 / 20 )3124.2514.6516618733908213.235196593911
Trimmed Mean ( 19 / 20 )3123.5454545454514.1402571161386220.897359142111
Trimmed Mean ( 20 / 20 )3123.5513.8946174735702224.802878232632
Median3122
Midrange2853
Midmean - Weighted Average at Xnp3122.96774193548
Midmean - Weighted Average at X(n+1)p3122.96774193548
Midmean - Empirical Distribution Function3122.96774193548
Midmean - Empirical Distribution Function - Averaging3122.96774193548
Midmean - Empirical Distribution Function - Interpolation3122.96774193548
Midmean - Closest Observation3122.96774193548
Midmean - True Basic - Statistics Graphics Toolkit3122.96774193548
Midmean - MS Excel (old versions)3127.53125
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')