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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Jan 2008 11:39:13 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jan/15/t1200422211kibnwz6us2phmr6.htm/, Retrieved Wed, 15 May 2024 12:07:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7966, Retrieved Wed, 15 May 2024 12:07:07 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact299
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Maximum-likelihood Fitting - Normal Distribution] [Workshop 4 questi...] [2007-11-01 14:33:21] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2008-01-15 18:39:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
281
295
294
302
314
321
313
310
319
316
319
333
356
358
340
328
355
356
351
359
378
378
389.
407
413
404
406
402
383
392
398
400
405
420
439
441
424
423
434
429
421
430
424
437
456
469
476
510
549
554
557
610
675
596
633
632
596
585
627
629




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7966&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7966&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7966&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean425.8513.354908215571131.8871528823750
Geometric Mean414.495231580933
Harmonic Mean404.164425731786
Quadratic Mean438.030915956092
Winsorized Mean ( 1 / 20 )425.36666666666713.111817386575732.4414727665573
Winsorized Mean ( 2 / 20 )425.36666666666713.097245293379632.4775673921052
Winsorized Mean ( 3 / 20 )425.56666666666712.999573366894832.7369717955845
Winsorized Mean ( 4 / 20 )425.96666666666712.880589493007833.0704325992147
Winsorized Mean ( 5 / 20 )424.812.476798807169134.0471948426316
Winsorized Mean ( 6 / 20 )423.512.116419731861634.952569271462
Winsorized Mean ( 7 / 20 )423.73333333333312.080915207096535.0746053647018
Winsorized Mean ( 8 / 20 )422.66666666666711.670370679163436.2170729864911
Winsorized Mean ( 9 / 20 )418.46666666666710.713539315764639.0596099321639
Winsorized Mean ( 10 / 20 )418.310.551977885123539.6418571526511
Winsorized Mean ( 11 / 20 )418.66666666666710.154920509100041.2279609960012
Winsorized Mean ( 12 / 20 )411.8666666666678.3692829096551449.2117032143245
Winsorized Mean ( 13 / 20 )406.0166666666676.732730226947460.3049064763662
Winsorized Mean ( 14 / 20 )406.956.0306385810223567.4804159679905
Winsorized Mean ( 15 / 20 )404.75.322975464588476.0289057675176
Winsorized Mean ( 16 / 20 )400.9666666666674.6598396390212486.0473101496871
Winsorized Mean ( 17 / 20 )400.44.5780858507128587.4601335703773
Winsorized Mean ( 18 / 20 )400.44.3944752166076191.1144062177907
Winsorized Mean ( 19 / 20 )399.7666666666674.2100476175002694.9553788904722
Winsorized Mean ( 20 / 20 )404.7666666666673.02180088732473133.948821169689
Trimmed Mean ( 1 / 20 )424.05172413793112.876241443711532.9328807627345
Trimmed Mean ( 2 / 20 )422.64285714285712.580169629362133.5959585279684
Trimmed Mean ( 3 / 20 )421.1296296296312.217400791814334.4696582199209
Trimmed Mean ( 4 / 20 )419.42307692307711.806041419220235.5261397135417
Trimmed Mean ( 5 / 20 )417.4611.327921436946536.852303604299
Trimmed Mean ( 6 / 20 )415.62510.863499666313838.2588496125973
Trimmed Mean ( 7 / 20 )413.91304347826110.384995962773339.8568323918468
Trimmed Mean ( 8 / 20 )4129.7631030834556842.1996978294908
Trimmed Mean ( 9 / 20 )410.0952380952389.0684459843573745.2222176547815
Trimmed Mean ( 10 / 20 )408.78.4601024422481648.309107695792
Trimmed Mean ( 11 / 20 )407.1842105263167.6723307397628553.0717749713305
Trimmed Mean ( 12 / 20 )405.4444444444446.6828903124089660.6690257494732
Trimmed Mean ( 13 / 20 )404.55.9754772182428967.6933381596834
Trimmed Mean ( 14 / 20 )404.281255.5710647862704572.5680395956491
Trimmed Mean ( 15 / 20 )403.95.225567119857777.2930460437753
Trimmed Mean ( 16 / 20 )403.7857142857144.9669162456886281.2950519623132
Trimmed Mean ( 17 / 20 )404.1923076923084.8003266654129484.2010004453598
Trimmed Mean ( 18 / 20 )404.754.5517356141860188.9221242856351
Trimmed Mean ( 19 / 20 )405.4090909090914.2132850551934496.2216146304579
Trimmed Mean ( 20 / 20 )406.33.70426496721933109.684378303261
Median405.5
Midrange478
Midmean - Weighted Average at Xnp402.193548387097
Midmean - Weighted Average at X(n+1)p403.9
Midmean - Empirical Distribution Function402.193548387097
Midmean - Empirical Distribution Function - Averaging403.9
Midmean - Empirical Distribution Function - Interpolation403.9
Midmean - Closest Observation402.193548387097
Midmean - True Basic - Statistics Graphics Toolkit403.9
Midmean - MS Excel (old versions)404.28125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 425.85 & 13.3549082155711 & 31.8871528823750 \tabularnewline
Geometric Mean & 414.495231580933 &  &  \tabularnewline
Harmonic Mean & 404.164425731786 &  &  \tabularnewline
Quadratic Mean & 438.030915956092 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 425.366666666667 & 13.1118173865757 & 32.4414727665573 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 425.366666666667 & 13.0972452933796 & 32.4775673921052 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 425.566666666667 & 12.9995733668948 & 32.7369717955845 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 425.966666666667 & 12.8805894930078 & 33.0704325992147 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 424.8 & 12.4767988071691 & 34.0471948426316 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 423.5 & 12.1164197318616 & 34.952569271462 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 423.733333333333 & 12.0809152070965 & 35.0746053647018 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 422.666666666667 & 11.6703706791634 & 36.2170729864911 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 418.466666666667 & 10.7135393157646 & 39.0596099321639 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 418.3 & 10.5519778851235 & 39.6418571526511 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 418.666666666667 & 10.1549205091000 & 41.2279609960012 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 411.866666666667 & 8.36928290965514 & 49.2117032143245 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 406.016666666667 & 6.7327302269474 & 60.3049064763662 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 406.95 & 6.03063858102235 & 67.4804159679905 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 404.7 & 5.3229754645884 & 76.0289057675176 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 400.966666666667 & 4.65983963902124 & 86.0473101496871 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 400.4 & 4.57808585071285 & 87.4601335703773 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 400.4 & 4.39447521660761 & 91.1144062177907 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 399.766666666667 & 4.21004761750026 & 94.9553788904722 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 404.766666666667 & 3.02180088732473 & 133.948821169689 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 424.051724137931 & 12.8762414437115 & 32.9328807627345 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 422.642857142857 & 12.5801696293621 & 33.5959585279684 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 421.12962962963 & 12.2174007918143 & 34.4696582199209 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 419.423076923077 & 11.8060414192202 & 35.5261397135417 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 417.46 & 11.3279214369465 & 36.852303604299 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 415.625 & 10.8634996663138 & 38.2588496125973 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 413.913043478261 & 10.3849959627733 & 39.8568323918468 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 412 & 9.76310308345568 & 42.1996978294908 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 410.095238095238 & 9.06844598435737 & 45.2222176547815 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 408.7 & 8.46010244224816 & 48.309107695792 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 407.184210526316 & 7.67233073976285 & 53.0717749713305 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 405.444444444444 & 6.68289031240896 & 60.6690257494732 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 404.5 & 5.97547721824289 & 67.6933381596834 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 404.28125 & 5.57106478627045 & 72.5680395956491 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 403.9 & 5.2255671198577 & 77.2930460437753 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 403.785714285714 & 4.96691624568862 & 81.2950519623132 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 404.192307692308 & 4.80032666541294 & 84.2010004453598 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 404.75 & 4.55173561418601 & 88.9221242856351 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 405.409090909091 & 4.21328505519344 & 96.2216146304579 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 406.3 & 3.70426496721933 & 109.684378303261 \tabularnewline
Median & 405.5 &  &  \tabularnewline
Midrange & 478 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 402.193548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 403.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 402.193548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 403.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 403.9 &  &  \tabularnewline
Midmean - Closest Observation & 402.193548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 403.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 404.28125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7966&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]425.85[/C][C]13.3549082155711[/C][C]31.8871528823750[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]414.495231580933[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]404.164425731786[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]438.030915956092[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]425.366666666667[/C][C]13.1118173865757[/C][C]32.4414727665573[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]425.366666666667[/C][C]13.0972452933796[/C][C]32.4775673921052[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]425.566666666667[/C][C]12.9995733668948[/C][C]32.7369717955845[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]425.966666666667[/C][C]12.8805894930078[/C][C]33.0704325992147[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]424.8[/C][C]12.4767988071691[/C][C]34.0471948426316[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]423.5[/C][C]12.1164197318616[/C][C]34.952569271462[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]423.733333333333[/C][C]12.0809152070965[/C][C]35.0746053647018[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]422.666666666667[/C][C]11.6703706791634[/C][C]36.2170729864911[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]418.466666666667[/C][C]10.7135393157646[/C][C]39.0596099321639[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]418.3[/C][C]10.5519778851235[/C][C]39.6418571526511[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]418.666666666667[/C][C]10.1549205091000[/C][C]41.2279609960012[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]411.866666666667[/C][C]8.36928290965514[/C][C]49.2117032143245[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]406.016666666667[/C][C]6.7327302269474[/C][C]60.3049064763662[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]406.95[/C][C]6.03063858102235[/C][C]67.4804159679905[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]404.7[/C][C]5.3229754645884[/C][C]76.0289057675176[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]400.966666666667[/C][C]4.65983963902124[/C][C]86.0473101496871[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]400.4[/C][C]4.57808585071285[/C][C]87.4601335703773[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]400.4[/C][C]4.39447521660761[/C][C]91.1144062177907[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]399.766666666667[/C][C]4.21004761750026[/C][C]94.9553788904722[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]404.766666666667[/C][C]3.02180088732473[/C][C]133.948821169689[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]424.051724137931[/C][C]12.8762414437115[/C][C]32.9328807627345[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]422.642857142857[/C][C]12.5801696293621[/C][C]33.5959585279684[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]421.12962962963[/C][C]12.2174007918143[/C][C]34.4696582199209[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]419.423076923077[/C][C]11.8060414192202[/C][C]35.5261397135417[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]417.46[/C][C]11.3279214369465[/C][C]36.852303604299[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]415.625[/C][C]10.8634996663138[/C][C]38.2588496125973[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]413.913043478261[/C][C]10.3849959627733[/C][C]39.8568323918468[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]412[/C][C]9.76310308345568[/C][C]42.1996978294908[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]410.095238095238[/C][C]9.06844598435737[/C][C]45.2222176547815[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]408.7[/C][C]8.46010244224816[/C][C]48.309107695792[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]407.184210526316[/C][C]7.67233073976285[/C][C]53.0717749713305[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]405.444444444444[/C][C]6.68289031240896[/C][C]60.6690257494732[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]404.5[/C][C]5.97547721824289[/C][C]67.6933381596834[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]404.28125[/C][C]5.57106478627045[/C][C]72.5680395956491[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]403.9[/C][C]5.2255671198577[/C][C]77.2930460437753[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]403.785714285714[/C][C]4.96691624568862[/C][C]81.2950519623132[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]404.192307692308[/C][C]4.80032666541294[/C][C]84.2010004453598[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]404.75[/C][C]4.55173561418601[/C][C]88.9221242856351[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]405.409090909091[/C][C]4.21328505519344[/C][C]96.2216146304579[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]406.3[/C][C]3.70426496721933[/C][C]109.684378303261[/C][/ROW]
[ROW][C]Median[/C][C]405.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]478[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]402.193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]403.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]402.193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]403.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]403.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]402.193548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]403.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]404.28125[/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=7966&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7966&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 Mean425.8513.354908215571131.8871528823750
Geometric Mean414.495231580933
Harmonic Mean404.164425731786
Quadratic Mean438.030915956092
Winsorized Mean ( 1 / 20 )425.36666666666713.111817386575732.4414727665573
Winsorized Mean ( 2 / 20 )425.36666666666713.097245293379632.4775673921052
Winsorized Mean ( 3 / 20 )425.56666666666712.999573366894832.7369717955845
Winsorized Mean ( 4 / 20 )425.96666666666712.880589493007833.0704325992147
Winsorized Mean ( 5 / 20 )424.812.476798807169134.0471948426316
Winsorized Mean ( 6 / 20 )423.512.116419731861634.952569271462
Winsorized Mean ( 7 / 20 )423.73333333333312.080915207096535.0746053647018
Winsorized Mean ( 8 / 20 )422.66666666666711.670370679163436.2170729864911
Winsorized Mean ( 9 / 20 )418.46666666666710.713539315764639.0596099321639
Winsorized Mean ( 10 / 20 )418.310.551977885123539.6418571526511
Winsorized Mean ( 11 / 20 )418.66666666666710.154920509100041.2279609960012
Winsorized Mean ( 12 / 20 )411.8666666666678.3692829096551449.2117032143245
Winsorized Mean ( 13 / 20 )406.0166666666676.732730226947460.3049064763662
Winsorized Mean ( 14 / 20 )406.956.0306385810223567.4804159679905
Winsorized Mean ( 15 / 20 )404.75.322975464588476.0289057675176
Winsorized Mean ( 16 / 20 )400.9666666666674.6598396390212486.0473101496871
Winsorized Mean ( 17 / 20 )400.44.5780858507128587.4601335703773
Winsorized Mean ( 18 / 20 )400.44.3944752166076191.1144062177907
Winsorized Mean ( 19 / 20 )399.7666666666674.2100476175002694.9553788904722
Winsorized Mean ( 20 / 20 )404.7666666666673.02180088732473133.948821169689
Trimmed Mean ( 1 / 20 )424.05172413793112.876241443711532.9328807627345
Trimmed Mean ( 2 / 20 )422.64285714285712.580169629362133.5959585279684
Trimmed Mean ( 3 / 20 )421.1296296296312.217400791814334.4696582199209
Trimmed Mean ( 4 / 20 )419.42307692307711.806041419220235.5261397135417
Trimmed Mean ( 5 / 20 )417.4611.327921436946536.852303604299
Trimmed Mean ( 6 / 20 )415.62510.863499666313838.2588496125973
Trimmed Mean ( 7 / 20 )413.91304347826110.384995962773339.8568323918468
Trimmed Mean ( 8 / 20 )4129.7631030834556842.1996978294908
Trimmed Mean ( 9 / 20 )410.0952380952389.0684459843573745.2222176547815
Trimmed Mean ( 10 / 20 )408.78.4601024422481648.309107695792
Trimmed Mean ( 11 / 20 )407.1842105263167.6723307397628553.0717749713305
Trimmed Mean ( 12 / 20 )405.4444444444446.6828903124089660.6690257494732
Trimmed Mean ( 13 / 20 )404.55.9754772182428967.6933381596834
Trimmed Mean ( 14 / 20 )404.281255.5710647862704572.5680395956491
Trimmed Mean ( 15 / 20 )403.95.225567119857777.2930460437753
Trimmed Mean ( 16 / 20 )403.7857142857144.9669162456886281.2950519623132
Trimmed Mean ( 17 / 20 )404.1923076923084.8003266654129484.2010004453598
Trimmed Mean ( 18 / 20 )404.754.5517356141860188.9221242856351
Trimmed Mean ( 19 / 20 )405.4090909090914.2132850551934496.2216146304579
Trimmed Mean ( 20 / 20 )406.33.70426496721933109.684378303261
Median405.5
Midrange478
Midmean - Weighted Average at Xnp402.193548387097
Midmean - Weighted Average at X(n+1)p403.9
Midmean - Empirical Distribution Function402.193548387097
Midmean - Empirical Distribution Function - Averaging403.9
Midmean - Empirical Distribution Function - Interpolation403.9
Midmean - Closest Observation402.193548387097
Midmean - True Basic - Statistics Graphics Toolkit403.9
Midmean - MS Excel (old versions)404.28125
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')