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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 Dec 2009 09:40:32 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/13/t1260722493p8g8icr9ea7lxcn.htm/, Retrieved Sun, 28 Apr 2024 03:50:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67363, Retrieved Sun, 28 Apr 2024 03:50:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Central Tendency] [WS 3: Part 1: Cen...] [2009-10-18 15:24:12] [8cf9233b7464ea02e32be3b30fdac052]
-  M D        [Central Tendency] [Paper: Central Te...] [2009-12-13 16:14:14] [8cf9233b7464ea02e32be3b30fdac052]
-    D            [Central Tendency] [Paper: Central Te...] [2009-12-13 16:40:32] [b9056af0304697100f456398102f1287] [Current]
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Dataseries X:
423
427
441
449
452
462
455
461
461
463
462
456
455
456
472
472
471
465
459
465
468
467
463
460
462
461
476
476
471
453
443
442
444
438
427
424
416
406
431
434
418
412
404
409
412
406
398
397
385
390
413
413
401
397
397
409
419
424
428
430




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67363&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67363&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean437.5166666666673.39711506607122128.790652703047
Geometric Mean436.728905855514
Harmonic Mean435.932551867853
Quadratic Mean438.294098370793
Winsorized Mean ( 1 / 20 )437.63.37623800269582129.611715658253
Winsorized Mean ( 2 / 20 )437.73.29931511468497132.663896834781
Winsorized Mean ( 3 / 20 )437.73.29931511468497132.663896834781
Winsorized Mean ( 4 / 20 )437.6333333333333.28770751674033133.112003152651
Winsorized Mean ( 5 / 20 )437.7166666666673.27040242402459133.841836543164
Winsorized Mean ( 6 / 20 )437.7166666666673.1596942270236138.531337280377
Winsorized Mean ( 7 / 20 )437.953.07361883914736142.486763297394
Winsorized Mean ( 8 / 20 )437.952.98256941897134146.836481730925
Winsorized Mean ( 9 / 20 )437.952.98256941897134146.836481730925
Winsorized Mean ( 10 / 20 )438.1166666666672.84337784189669154.083168339815
Winsorized Mean ( 11 / 20 )438.1166666666672.84337784189669154.083168339815
Winsorized Mean ( 12 / 20 )438.5166666666672.71202508057444161.693440745682
Winsorized Mean ( 13 / 20 )438.5166666666672.71202508057444161.693440745682
Winsorized Mean ( 14 / 20 )438.752.67364464845549164.101837637046
Winsorized Mean ( 15 / 20 )438.52.63714234997114166.278471848438
Winsorized Mean ( 16 / 20 )439.32.5085503500542175.121061449099
Winsorized Mean ( 17 / 20 )439.8666666666672.42054140960879181.722429916107
Winsorized Mean ( 18 / 20 )439.8666666666672.33064413232975188.731801893311
Winsorized Mean ( 19 / 20 )440.8166666666672.09660630633566210.252475791272
Winsorized Mean ( 20 / 20 )440.151.90447362124323231.113728796450
Trimmed Mean ( 1 / 20 )437.7586206896553.32776095131231131.547496077513
Trimmed Mean ( 2 / 20 )437.9285714285713.26660166785005134.062434284128
Trimmed Mean ( 3 / 20 )438.0555555555563.23917502359008135.236766264654
Trimmed Mean ( 4 / 20 )438.1923076923083.20197884487554136.850469325740
Trimmed Mean ( 5 / 20 )438.363.15682092734874138.861218323257
Trimmed Mean ( 6 / 20 )438.5208333333333.10284552303761141.328606299431
Trimmed Mean ( 7 / 20 )438.6956521739133.06466058601216143.146570349821
Trimmed Mean ( 8 / 20 )438.8409090909093.03571816194999144.559173704393
Trimmed Mean ( 9 / 20 )4393.01679387697722145.518725475494
Trimmed Mean ( 10 / 20 )439.1752.98562528347637147.096490115678
Trimmed Mean ( 11 / 20 )439.3421052631582.97291622656441147.781528903314
Trimmed Mean ( 12 / 20 )439.5277777777782.94728449435282149.129742520595
Trimmed Mean ( 13 / 20 )439.6764705882352.93747092775398149.678577729590
Trimmed Mean ( 14 / 20 )439.843752.91274638131349151.006538990756
Trimmed Mean ( 15 / 20 )4402.87757880345872152.906325092171
Trimmed Mean ( 16 / 20 )440.2142857142862.8248505803333155.836308220715
Trimmed Mean ( 17 / 20 )440.3461538461542.77734921085795158.549076984859
Trimmed Mean ( 18 / 20 )440.4166666666672.72130394647164161.840307194533
Trimmed Mean ( 19 / 20 )440.52.65045123986309166.198115013334
Trimmed Mean ( 20 / 20 )440.452.61420713551326168.483206252715
Median441.5
Midrange430.5
Midmean - Weighted Average at Xnp439.129032258065
Midmean - Weighted Average at X(n+1)p439.129032258065
Midmean - Empirical Distribution Function439.129032258065
Midmean - Empirical Distribution Function - Averaging439.129032258065
Midmean - Empirical Distribution Function - Interpolation439.129032258065
Midmean - Closest Observation439.129032258065
Midmean - True Basic - Statistics Graphics Toolkit439.129032258065
Midmean - MS Excel (old versions)441.147058823529
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 437.516666666667 & 3.39711506607122 & 128.790652703047 \tabularnewline
Geometric Mean & 436.728905855514 &  &  \tabularnewline
Harmonic Mean & 435.932551867853 &  &  \tabularnewline
Quadratic Mean & 438.294098370793 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 437.6 & 3.37623800269582 & 129.611715658253 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 437.7 & 3.29931511468497 & 132.663896834781 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 437.7 & 3.29931511468497 & 132.663896834781 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 437.633333333333 & 3.28770751674033 & 133.112003152651 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 437.716666666667 & 3.27040242402459 & 133.841836543164 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 437.716666666667 & 3.1596942270236 & 138.531337280377 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 437.95 & 3.07361883914736 & 142.486763297394 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 437.95 & 2.98256941897134 & 146.836481730925 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 437.95 & 2.98256941897134 & 146.836481730925 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 438.116666666667 & 2.84337784189669 & 154.083168339815 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 438.116666666667 & 2.84337784189669 & 154.083168339815 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 438.516666666667 & 2.71202508057444 & 161.693440745682 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 438.516666666667 & 2.71202508057444 & 161.693440745682 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 438.75 & 2.67364464845549 & 164.101837637046 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 438.5 & 2.63714234997114 & 166.278471848438 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 439.3 & 2.5085503500542 & 175.121061449099 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 439.866666666667 & 2.42054140960879 & 181.722429916107 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 439.866666666667 & 2.33064413232975 & 188.731801893311 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 440.816666666667 & 2.09660630633566 & 210.252475791272 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 440.15 & 1.90447362124323 & 231.113728796450 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 437.758620689655 & 3.32776095131231 & 131.547496077513 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 437.928571428571 & 3.26660166785005 & 134.062434284128 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 438.055555555556 & 3.23917502359008 & 135.236766264654 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 438.192307692308 & 3.20197884487554 & 136.850469325740 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 438.36 & 3.15682092734874 & 138.861218323257 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 438.520833333333 & 3.10284552303761 & 141.328606299431 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 438.695652173913 & 3.06466058601216 & 143.146570349821 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 438.840909090909 & 3.03571816194999 & 144.559173704393 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 439 & 3.01679387697722 & 145.518725475494 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 439.175 & 2.98562528347637 & 147.096490115678 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 439.342105263158 & 2.97291622656441 & 147.781528903314 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 439.527777777778 & 2.94728449435282 & 149.129742520595 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 439.676470588235 & 2.93747092775398 & 149.678577729590 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 439.84375 & 2.91274638131349 & 151.006538990756 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 440 & 2.87757880345872 & 152.906325092171 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 440.214285714286 & 2.8248505803333 & 155.836308220715 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 440.346153846154 & 2.77734921085795 & 158.549076984859 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 440.416666666667 & 2.72130394647164 & 161.840307194533 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 440.5 & 2.65045123986309 & 166.198115013334 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 440.45 & 2.61420713551326 & 168.483206252715 \tabularnewline
Median & 441.5 &  &  \tabularnewline
Midrange & 430.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 439.129032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 439.129032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 439.129032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 439.129032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 439.129032258065 &  &  \tabularnewline
Midmean - Closest Observation & 439.129032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 439.129032258065 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 441.147058823529 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67363&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]437.516666666667[/C][C]3.39711506607122[/C][C]128.790652703047[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]436.728905855514[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]435.932551867853[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]438.294098370793[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]437.6[/C][C]3.37623800269582[/C][C]129.611715658253[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]437.7[/C][C]3.29931511468497[/C][C]132.663896834781[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]437.7[/C][C]3.29931511468497[/C][C]132.663896834781[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]437.633333333333[/C][C]3.28770751674033[/C][C]133.112003152651[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]437.716666666667[/C][C]3.27040242402459[/C][C]133.841836543164[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]437.716666666667[/C][C]3.1596942270236[/C][C]138.531337280377[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]437.95[/C][C]3.07361883914736[/C][C]142.486763297394[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]437.95[/C][C]2.98256941897134[/C][C]146.836481730925[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]437.95[/C][C]2.98256941897134[/C][C]146.836481730925[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]438.116666666667[/C][C]2.84337784189669[/C][C]154.083168339815[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]438.116666666667[/C][C]2.84337784189669[/C][C]154.083168339815[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]438.516666666667[/C][C]2.71202508057444[/C][C]161.693440745682[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]438.516666666667[/C][C]2.71202508057444[/C][C]161.693440745682[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]438.75[/C][C]2.67364464845549[/C][C]164.101837637046[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]438.5[/C][C]2.63714234997114[/C][C]166.278471848438[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]439.3[/C][C]2.5085503500542[/C][C]175.121061449099[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]439.866666666667[/C][C]2.42054140960879[/C][C]181.722429916107[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]439.866666666667[/C][C]2.33064413232975[/C][C]188.731801893311[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]440.816666666667[/C][C]2.09660630633566[/C][C]210.252475791272[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]440.15[/C][C]1.90447362124323[/C][C]231.113728796450[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]437.758620689655[/C][C]3.32776095131231[/C][C]131.547496077513[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]437.928571428571[/C][C]3.26660166785005[/C][C]134.062434284128[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]438.055555555556[/C][C]3.23917502359008[/C][C]135.236766264654[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]438.192307692308[/C][C]3.20197884487554[/C][C]136.850469325740[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]438.36[/C][C]3.15682092734874[/C][C]138.861218323257[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]438.520833333333[/C][C]3.10284552303761[/C][C]141.328606299431[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]438.695652173913[/C][C]3.06466058601216[/C][C]143.146570349821[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]438.840909090909[/C][C]3.03571816194999[/C][C]144.559173704393[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]439[/C][C]3.01679387697722[/C][C]145.518725475494[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]439.175[/C][C]2.98562528347637[/C][C]147.096490115678[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]439.342105263158[/C][C]2.97291622656441[/C][C]147.781528903314[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]439.527777777778[/C][C]2.94728449435282[/C][C]149.129742520595[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]439.676470588235[/C][C]2.93747092775398[/C][C]149.678577729590[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]439.84375[/C][C]2.91274638131349[/C][C]151.006538990756[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]440[/C][C]2.87757880345872[/C][C]152.906325092171[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]440.214285714286[/C][C]2.8248505803333[/C][C]155.836308220715[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]440.346153846154[/C][C]2.77734921085795[/C][C]158.549076984859[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]440.416666666667[/C][C]2.72130394647164[/C][C]161.840307194533[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]440.5[/C][C]2.65045123986309[/C][C]166.198115013334[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]440.45[/C][C]2.61420713551326[/C][C]168.483206252715[/C][/ROW]
[ROW][C]Median[/C][C]441.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]430.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]439.129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]439.129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]439.129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]439.129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]439.129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]439.129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]439.129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]441.147058823529[/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=67363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67363&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 Mean437.5166666666673.39711506607122128.790652703047
Geometric Mean436.728905855514
Harmonic Mean435.932551867853
Quadratic Mean438.294098370793
Winsorized Mean ( 1 / 20 )437.63.37623800269582129.611715658253
Winsorized Mean ( 2 / 20 )437.73.29931511468497132.663896834781
Winsorized Mean ( 3 / 20 )437.73.29931511468497132.663896834781
Winsorized Mean ( 4 / 20 )437.6333333333333.28770751674033133.112003152651
Winsorized Mean ( 5 / 20 )437.7166666666673.27040242402459133.841836543164
Winsorized Mean ( 6 / 20 )437.7166666666673.1596942270236138.531337280377
Winsorized Mean ( 7 / 20 )437.953.07361883914736142.486763297394
Winsorized Mean ( 8 / 20 )437.952.98256941897134146.836481730925
Winsorized Mean ( 9 / 20 )437.952.98256941897134146.836481730925
Winsorized Mean ( 10 / 20 )438.1166666666672.84337784189669154.083168339815
Winsorized Mean ( 11 / 20 )438.1166666666672.84337784189669154.083168339815
Winsorized Mean ( 12 / 20 )438.5166666666672.71202508057444161.693440745682
Winsorized Mean ( 13 / 20 )438.5166666666672.71202508057444161.693440745682
Winsorized Mean ( 14 / 20 )438.752.67364464845549164.101837637046
Winsorized Mean ( 15 / 20 )438.52.63714234997114166.278471848438
Winsorized Mean ( 16 / 20 )439.32.5085503500542175.121061449099
Winsorized Mean ( 17 / 20 )439.8666666666672.42054140960879181.722429916107
Winsorized Mean ( 18 / 20 )439.8666666666672.33064413232975188.731801893311
Winsorized Mean ( 19 / 20 )440.8166666666672.09660630633566210.252475791272
Winsorized Mean ( 20 / 20 )440.151.90447362124323231.113728796450
Trimmed Mean ( 1 / 20 )437.7586206896553.32776095131231131.547496077513
Trimmed Mean ( 2 / 20 )437.9285714285713.26660166785005134.062434284128
Trimmed Mean ( 3 / 20 )438.0555555555563.23917502359008135.236766264654
Trimmed Mean ( 4 / 20 )438.1923076923083.20197884487554136.850469325740
Trimmed Mean ( 5 / 20 )438.363.15682092734874138.861218323257
Trimmed Mean ( 6 / 20 )438.5208333333333.10284552303761141.328606299431
Trimmed Mean ( 7 / 20 )438.6956521739133.06466058601216143.146570349821
Trimmed Mean ( 8 / 20 )438.8409090909093.03571816194999144.559173704393
Trimmed Mean ( 9 / 20 )4393.01679387697722145.518725475494
Trimmed Mean ( 10 / 20 )439.1752.98562528347637147.096490115678
Trimmed Mean ( 11 / 20 )439.3421052631582.97291622656441147.781528903314
Trimmed Mean ( 12 / 20 )439.5277777777782.94728449435282149.129742520595
Trimmed Mean ( 13 / 20 )439.6764705882352.93747092775398149.678577729590
Trimmed Mean ( 14 / 20 )439.843752.91274638131349151.006538990756
Trimmed Mean ( 15 / 20 )4402.87757880345872152.906325092171
Trimmed Mean ( 16 / 20 )440.2142857142862.8248505803333155.836308220715
Trimmed Mean ( 17 / 20 )440.3461538461542.77734921085795158.549076984859
Trimmed Mean ( 18 / 20 )440.4166666666672.72130394647164161.840307194533
Trimmed Mean ( 19 / 20 )440.52.65045123986309166.198115013334
Trimmed Mean ( 20 / 20 )440.452.61420713551326168.483206252715
Median441.5
Midrange430.5
Midmean - Weighted Average at Xnp439.129032258065
Midmean - Weighted Average at X(n+1)p439.129032258065
Midmean - Empirical Distribution Function439.129032258065
Midmean - Empirical Distribution Function - Averaging439.129032258065
Midmean - Empirical Distribution Function - Interpolation439.129032258065
Midmean - Closest Observation439.129032258065
Midmean - True Basic - Statistics Graphics Toolkit439.129032258065
Midmean - MS Excel (old versions)441.147058823529
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')