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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, 27 Dec 2009 05:24:11 -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/27/t12619167757wah5h1pey5unn3.htm/, Retrieved Fri, 03 May 2024 01:15:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70868, Retrieved Fri, 03 May 2024 01:15:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper Central Ten...] [2009-12-27 12:24:11] [1b03feaac1d41902024770a37504c07f] [Current]
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Dataseries X:
401
394
372
334
320
334
400
427
423
395
373
377
391
398
393
375
371
364
400
406
407
397
389
394
399
401
396
392
384
370
380
376
378
376
373
374
379
376
371
375
360
338
352
344
330
334
333
343
350
341
320
302
287
304
370
385
365
333
313
330
367




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=70868&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=70868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70868&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 Mean367.8032786885253.9737402837496392.5584593921836
Geometric Mean366.464557366747
Harmonic Mean365.073226573314
Quadratic Mean369.088998108302
Winsorized Mean ( 1 / 20 )367.9836065573773.8812630896643194.81027131021
Winsorized Mean ( 2 / 20 )367.5245901639343.7545314375440597.8882708209105
Winsorized Mean ( 3 / 20 )367.9180327868853.62755808229437101.423057726531
Winsorized Mean ( 4 / 20 )368.0491803278693.4616893305999106.320684838604
Winsorized Mean ( 5 / 20 )368.0491803278693.4616893305999106.320684838604
Winsorized Mean ( 6 / 20 )368.9344262295083.23301521046074114.114658364670
Winsorized Mean ( 7 / 20 )368.9344262295083.23301521046074114.114658364670
Winsorized Mean ( 8 / 20 )369.1967213114753.13475316675254117.775372309120
Winsorized Mean ( 9 / 20 )369.0491803278693.11162339067798118.603421427379
Winsorized Mean ( 10 / 20 )369.0491803278693.0549097121614120.805265981743
Winsorized Mean ( 11 / 20 )368.8688524590163.02769325617083121.831645827137
Winsorized Mean ( 12 / 20 )368.6721311475412.99860817545028122.947750948548
Winsorized Mean ( 13 / 20 )369.3114754098362.80588189613988131.620463397945
Winsorized Mean ( 14 / 20 )3702.67971534252052138.074367127361
Winsorized Mean ( 15 / 20 )370.2459016393442.55503956507012144.908089370108
Winsorized Mean ( 16 / 20 )370.2459016393442.46977972267311149.910495353252
Winsorized Mean ( 17 / 20 )371.6393442622952.13876947243536173.763161038164
Winsorized Mean ( 18 / 20 )371.6393442622951.95118470203806190.468561932711
Winsorized Mean ( 19 / 20 )372.8852459016391.35805597972770274.572809565924
Winsorized Mean ( 20 / 20 )373.8688524590161.10697624130671337.738822666773
Trimmed Mean ( 1 / 20 )368.1694915254243.735572483318498.5577158975028
Trimmed Mean ( 2 / 20 )368.3684210526323.55608761628265103.588117279772
Trimmed Mean ( 3 / 20 )368.8363636363643.41897691161119107.879161857969
Trimmed Mean ( 4 / 20 )369.1886792452833.31093721289036111.505792924110
Trimmed Mean ( 5 / 20 )369.5294117647063.24035255176752114.039878643186
Trimmed Mean ( 6 / 20 )369.8979591836733.14910700250573117.461222781362
Trimmed Mean ( 7 / 20 )370.1063829787233.1035526243772119.252491506566
Trimmed Mean ( 8 / 20 )370.3333333333333.04179638577687121.748232414561
Trimmed Mean ( 9 / 20 )370.534883720932.98600442248241124.090534136881
Trimmed Mean ( 10 / 20 )370.7804878048782.91516476443567127.190233748814
Trimmed Mean ( 11 / 20 )371.0512820512822.83294401976002130.977272922856
Trimmed Mean ( 12 / 20 )371.3783783783782.72551930510674136.259676342243
Trimmed Mean ( 13 / 20 )371.7714285714292.58212527743705143.978850220792
Trimmed Mean ( 14 / 20 )372.1212121212122.44165150570233152.405538321970
Trimmed Mean ( 15 / 20 )372.419354838712.28260094692431163.155699790857
Trimmed Mean ( 16 / 20 )372.7241379310342.09203071008324178.163798521010
Trimmed Mean ( 17 / 20 )373.0740740740741.83113771083124203.738949761849
Trimmed Mean ( 18 / 20 )373.281.58063278467834236.158583839549
Trimmed Mean ( 19 / 20 )373.5217391304351.25561122419075297.482000745232
Trimmed Mean ( 20 / 20 )373.6190476190481.07232766508898348.418734107773
Median374
Midrange357
Midmean - Weighted Average at Xnp371.733333333333
Midmean - Weighted Average at X(n+1)p372.41935483871
Midmean - Empirical Distribution Function372.41935483871
Midmean - Empirical Distribution Function - Averaging372.41935483871
Midmean - Empirical Distribution Function - Interpolation372.41935483871
Midmean - Closest Observation371.4375
Midmean - True Basic - Statistics Graphics Toolkit372.41935483871
Midmean - MS Excel (old versions)372.41935483871
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 367.803278688525 & 3.97374028374963 & 92.5584593921836 \tabularnewline
Geometric Mean & 366.464557366747 &  &  \tabularnewline
Harmonic Mean & 365.073226573314 &  &  \tabularnewline
Quadratic Mean & 369.088998108302 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 367.983606557377 & 3.88126308966431 & 94.81027131021 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 367.524590163934 & 3.75453143754405 & 97.8882708209105 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 367.918032786885 & 3.62755808229437 & 101.423057726531 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 368.049180327869 & 3.4616893305999 & 106.320684838604 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 368.049180327869 & 3.4616893305999 & 106.320684838604 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 368.934426229508 & 3.23301521046074 & 114.114658364670 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 368.934426229508 & 3.23301521046074 & 114.114658364670 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 369.196721311475 & 3.13475316675254 & 117.775372309120 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 369.049180327869 & 3.11162339067798 & 118.603421427379 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 369.049180327869 & 3.0549097121614 & 120.805265981743 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 368.868852459016 & 3.02769325617083 & 121.831645827137 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 368.672131147541 & 2.99860817545028 & 122.947750948548 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 369.311475409836 & 2.80588189613988 & 131.620463397945 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 370 & 2.67971534252052 & 138.074367127361 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 370.245901639344 & 2.55503956507012 & 144.908089370108 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 370.245901639344 & 2.46977972267311 & 149.910495353252 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 371.639344262295 & 2.13876947243536 & 173.763161038164 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 371.639344262295 & 1.95118470203806 & 190.468561932711 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 372.885245901639 & 1.35805597972770 & 274.572809565924 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 373.868852459016 & 1.10697624130671 & 337.738822666773 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 368.169491525424 & 3.7355724833184 & 98.5577158975028 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 368.368421052632 & 3.55608761628265 & 103.588117279772 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 368.836363636364 & 3.41897691161119 & 107.879161857969 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 369.188679245283 & 3.31093721289036 & 111.505792924110 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 369.529411764706 & 3.24035255176752 & 114.039878643186 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 369.897959183673 & 3.14910700250573 & 117.461222781362 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 370.106382978723 & 3.1035526243772 & 119.252491506566 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 370.333333333333 & 3.04179638577687 & 121.748232414561 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 370.53488372093 & 2.98600442248241 & 124.090534136881 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 370.780487804878 & 2.91516476443567 & 127.190233748814 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 371.051282051282 & 2.83294401976002 & 130.977272922856 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 371.378378378378 & 2.72551930510674 & 136.259676342243 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 371.771428571429 & 2.58212527743705 & 143.978850220792 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 372.121212121212 & 2.44165150570233 & 152.405538321970 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 372.41935483871 & 2.28260094692431 & 163.155699790857 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 372.724137931034 & 2.09203071008324 & 178.163798521010 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 373.074074074074 & 1.83113771083124 & 203.738949761849 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 373.28 & 1.58063278467834 & 236.158583839549 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 373.521739130435 & 1.25561122419075 & 297.482000745232 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 373.619047619048 & 1.07232766508898 & 348.418734107773 \tabularnewline
Median & 374 &  &  \tabularnewline
Midrange & 357 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 371.733333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 372.41935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 372.41935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 372.41935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 372.41935483871 &  &  \tabularnewline
Midmean - Closest Observation & 371.4375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 372.41935483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 372.41935483871 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70868&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]367.803278688525[/C][C]3.97374028374963[/C][C]92.5584593921836[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]366.464557366747[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]365.073226573314[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]369.088998108302[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]367.983606557377[/C][C]3.88126308966431[/C][C]94.81027131021[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]367.524590163934[/C][C]3.75453143754405[/C][C]97.8882708209105[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]367.918032786885[/C][C]3.62755808229437[/C][C]101.423057726531[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]368.049180327869[/C][C]3.4616893305999[/C][C]106.320684838604[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]368.049180327869[/C][C]3.4616893305999[/C][C]106.320684838604[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]368.934426229508[/C][C]3.23301521046074[/C][C]114.114658364670[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]368.934426229508[/C][C]3.23301521046074[/C][C]114.114658364670[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]369.196721311475[/C][C]3.13475316675254[/C][C]117.775372309120[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]369.049180327869[/C][C]3.11162339067798[/C][C]118.603421427379[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]369.049180327869[/C][C]3.0549097121614[/C][C]120.805265981743[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]368.868852459016[/C][C]3.02769325617083[/C][C]121.831645827137[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]368.672131147541[/C][C]2.99860817545028[/C][C]122.947750948548[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]369.311475409836[/C][C]2.80588189613988[/C][C]131.620463397945[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]370[/C][C]2.67971534252052[/C][C]138.074367127361[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]370.245901639344[/C][C]2.55503956507012[/C][C]144.908089370108[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]370.245901639344[/C][C]2.46977972267311[/C][C]149.910495353252[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]371.639344262295[/C][C]2.13876947243536[/C][C]173.763161038164[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]371.639344262295[/C][C]1.95118470203806[/C][C]190.468561932711[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]372.885245901639[/C][C]1.35805597972770[/C][C]274.572809565924[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]373.868852459016[/C][C]1.10697624130671[/C][C]337.738822666773[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]368.169491525424[/C][C]3.7355724833184[/C][C]98.5577158975028[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]368.368421052632[/C][C]3.55608761628265[/C][C]103.588117279772[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]368.836363636364[/C][C]3.41897691161119[/C][C]107.879161857969[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]369.188679245283[/C][C]3.31093721289036[/C][C]111.505792924110[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]369.529411764706[/C][C]3.24035255176752[/C][C]114.039878643186[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]369.897959183673[/C][C]3.14910700250573[/C][C]117.461222781362[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]370.106382978723[/C][C]3.1035526243772[/C][C]119.252491506566[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]370.333333333333[/C][C]3.04179638577687[/C][C]121.748232414561[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]370.53488372093[/C][C]2.98600442248241[/C][C]124.090534136881[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]370.780487804878[/C][C]2.91516476443567[/C][C]127.190233748814[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]371.051282051282[/C][C]2.83294401976002[/C][C]130.977272922856[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]371.378378378378[/C][C]2.72551930510674[/C][C]136.259676342243[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]371.771428571429[/C][C]2.58212527743705[/C][C]143.978850220792[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]372.121212121212[/C][C]2.44165150570233[/C][C]152.405538321970[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]372.41935483871[/C][C]2.28260094692431[/C][C]163.155699790857[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]372.724137931034[/C][C]2.09203071008324[/C][C]178.163798521010[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]373.074074074074[/C][C]1.83113771083124[/C][C]203.738949761849[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]373.28[/C][C]1.58063278467834[/C][C]236.158583839549[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]373.521739130435[/C][C]1.25561122419075[/C][C]297.482000745232[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]373.619047619048[/C][C]1.07232766508898[/C][C]348.418734107773[/C][/ROW]
[ROW][C]Median[/C][C]374[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]357[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]371.733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]372.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]372.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]372.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]372.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]371.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]372.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]372.41935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70868&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 Mean367.8032786885253.9737402837496392.5584593921836
Geometric Mean366.464557366747
Harmonic Mean365.073226573314
Quadratic Mean369.088998108302
Winsorized Mean ( 1 / 20 )367.9836065573773.8812630896643194.81027131021
Winsorized Mean ( 2 / 20 )367.5245901639343.7545314375440597.8882708209105
Winsorized Mean ( 3 / 20 )367.9180327868853.62755808229437101.423057726531
Winsorized Mean ( 4 / 20 )368.0491803278693.4616893305999106.320684838604
Winsorized Mean ( 5 / 20 )368.0491803278693.4616893305999106.320684838604
Winsorized Mean ( 6 / 20 )368.9344262295083.23301521046074114.114658364670
Winsorized Mean ( 7 / 20 )368.9344262295083.23301521046074114.114658364670
Winsorized Mean ( 8 / 20 )369.1967213114753.13475316675254117.775372309120
Winsorized Mean ( 9 / 20 )369.0491803278693.11162339067798118.603421427379
Winsorized Mean ( 10 / 20 )369.0491803278693.0549097121614120.805265981743
Winsorized Mean ( 11 / 20 )368.8688524590163.02769325617083121.831645827137
Winsorized Mean ( 12 / 20 )368.6721311475412.99860817545028122.947750948548
Winsorized Mean ( 13 / 20 )369.3114754098362.80588189613988131.620463397945
Winsorized Mean ( 14 / 20 )3702.67971534252052138.074367127361
Winsorized Mean ( 15 / 20 )370.2459016393442.55503956507012144.908089370108
Winsorized Mean ( 16 / 20 )370.2459016393442.46977972267311149.910495353252
Winsorized Mean ( 17 / 20 )371.6393442622952.13876947243536173.763161038164
Winsorized Mean ( 18 / 20 )371.6393442622951.95118470203806190.468561932711
Winsorized Mean ( 19 / 20 )372.8852459016391.35805597972770274.572809565924
Winsorized Mean ( 20 / 20 )373.8688524590161.10697624130671337.738822666773
Trimmed Mean ( 1 / 20 )368.1694915254243.735572483318498.5577158975028
Trimmed Mean ( 2 / 20 )368.3684210526323.55608761628265103.588117279772
Trimmed Mean ( 3 / 20 )368.8363636363643.41897691161119107.879161857969
Trimmed Mean ( 4 / 20 )369.1886792452833.31093721289036111.505792924110
Trimmed Mean ( 5 / 20 )369.5294117647063.24035255176752114.039878643186
Trimmed Mean ( 6 / 20 )369.8979591836733.14910700250573117.461222781362
Trimmed Mean ( 7 / 20 )370.1063829787233.1035526243772119.252491506566
Trimmed Mean ( 8 / 20 )370.3333333333333.04179638577687121.748232414561
Trimmed Mean ( 9 / 20 )370.534883720932.98600442248241124.090534136881
Trimmed Mean ( 10 / 20 )370.7804878048782.91516476443567127.190233748814
Trimmed Mean ( 11 / 20 )371.0512820512822.83294401976002130.977272922856
Trimmed Mean ( 12 / 20 )371.3783783783782.72551930510674136.259676342243
Trimmed Mean ( 13 / 20 )371.7714285714292.58212527743705143.978850220792
Trimmed Mean ( 14 / 20 )372.1212121212122.44165150570233152.405538321970
Trimmed Mean ( 15 / 20 )372.419354838712.28260094692431163.155699790857
Trimmed Mean ( 16 / 20 )372.7241379310342.09203071008324178.163798521010
Trimmed Mean ( 17 / 20 )373.0740740740741.83113771083124203.738949761849
Trimmed Mean ( 18 / 20 )373.281.58063278467834236.158583839549
Trimmed Mean ( 19 / 20 )373.5217391304351.25561122419075297.482000745232
Trimmed Mean ( 20 / 20 )373.6190476190481.07232766508898348.418734107773
Median374
Midrange357
Midmean - Weighted Average at Xnp371.733333333333
Midmean - Weighted Average at X(n+1)p372.41935483871
Midmean - Empirical Distribution Function372.41935483871
Midmean - Empirical Distribution Function - Averaging372.41935483871
Midmean - Empirical Distribution Function - Interpolation372.41935483871
Midmean - Closest Observation371.4375
Midmean - True Basic - Statistics Graphics Toolkit372.41935483871
Midmean - MS Excel (old versions)372.41935483871
Number of observations61



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')