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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 09:25:25 -0600
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/Oct/20/t1224516443z0fuvogrnthr526.htm/, Retrieved Sun, 19 May 2024 15:25:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17476, Retrieved Sun, 19 May 2024 15:25:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
F    D    [Central Tendency] [Central tendency ...] [2008-10-20 15:25:25] [284c7cdb9fcda2adcbb08e211682c8d6] [Current]
Feedback Forum
2008-10-27 20:27:50 [Olivier Uyttendaele] [reply
Berekening lijkt mij correct uitgevoerd.

Alle punten liggen in het betrouwbaarheidsinterval (rechte trekken door laagste punt van de stippellijnen) dat we kunnen zien.

Om een zeer eenvoudige voorspelling van de toekomst te maken, trek je het gemiddelde tot in het oneindige door. Dus als je zegt dat de goudprijzen gaan stijgen, is dit goed geinterpreteerd.
Toch blijft dit voor mij een zeer eenvoudige voorspelling.

Post a new message
Dataseries X:
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483




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=17476&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=17476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17476&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 Mean14155.05408.58108298115934.6444086366396
Geometric Mean13806.2145028864
Harmonic Mean13464.9649175676
Quadratic Mean14498.7865727906
Winsorized Mean ( 1 / 20 )14154.4408.41318822533734.6570590962173
Winsorized Mean ( 2 / 20 )14133.4666666667402.37795318929435.1248535230203
Winsorized Mean ( 3 / 20 )14123.8666666667399.8350044357435.3242375229221
Winsorized Mean ( 4 / 20 )14084.6666666667391.67050148381135.9604989737754
Winsorized Mean ( 5 / 20 )14077.75389.80691846918436.114674555508
Winsorized Mean ( 6 / 20 )14076.75388.4988730542336.2336958388938
Winsorized Mean ( 7 / 20 )14081.7666666667385.69532219497936.5100789569545
Winsorized Mean ( 8 / 20 )14042.0333333333377.69657654785537.1780794564712
Winsorized Mean ( 9 / 20 )13992.5333333333368.7413907578137.9467390535598
Winsorized Mean ( 10 / 20 )13992.8666666667366.00617717817338.2312308894582
Winsorized Mean ( 11 / 20 )13878.8333333333346.73843441717240.0268097093478
Winsorized Mean ( 12 / 20 )13874.6333333333345.3957036090140.1702545467662
Winsorized Mean ( 13 / 20 )13747.45326.15833857504542.1496199056609
Winsorized Mean ( 14 / 20 )13728.55322.90861244557342.5152797753698
Winsorized Mean ( 15 / 20 )13694.3315.31085576413643.4311085383112
Winsorized Mean ( 16 / 20 )13663.9310.76252373507343.9689439890395
Winsorized Mean ( 17 / 20 )13678.35304.7424992704244.8849439534924
Winsorized Mean ( 18 / 20 )13678.05298.91071397555945.7596511616456
Winsorized Mean ( 19 / 20 )13675.2298.54593359025545.8060166338383
Winsorized Mean ( 20 / 20 )13803.5333333333269.97289094569251.1293311153603
Trimmed Mean ( 1 / 20 )14118.2586206897404.18113804766534.9305232027544
Trimmed Mean ( 2 / 20 )14079.5357142857398.66379087976835.3168159145207
Trimmed Mean ( 3 / 20 )14049.5740740741395.447847031435.5282603750236
Trimmed Mean ( 4 / 20 )14021392.20590042194935.7490797178617
Trimmed Mean ( 5 / 20 )14001.9390.75451268497635.832983485691
Trimmed Mean ( 6 / 20 )13982.9375388.91979930215535.9532672933849
Trimmed Mean ( 7 / 20 )13962.5434782609386.3341970286136.1411016307906
Trimmed Mean ( 8 / 20 )13939.3181818182383.12481719743236.3832295798133
Trimmed Mean ( 9 / 20 )13920.9761904762380.42484272426736.5932363690722
Trimmed Mean ( 10 / 20 )13909.05378.40930043254236.756628296665
Trimmed Mean ( 11 / 20 )13895.8157894737375.50287165612537.0058842111841
Trimmed Mean ( 12 / 20 )13898.3888888889375.41388224278537.0215102485225
Trimmed Mean ( 13 / 20 )13901.8823529412374.28585300386937.1424200016383
Trimmed Mean ( 14 / 20 )13924.15625375.91000099697637.0411965977783
Trimmed Mean ( 15 / 20 )13952.1376.97793267529337.0103891784497
Trimmed Mean ( 16 / 20 )13988.9285714286378.16234486037236.9918601403682
Trimmed Mean ( 17 / 20 )14035.8076923077378.35681986201237.096748242642
Trimmed Mean ( 18 / 20 )14088.375377.51059977680237.3191507955792
Trimmed Mean ( 19 / 20 )14150.5454545455374.57147652638337.7779578567263
Trimmed Mean ( 20 / 20 )14225.6365.62665312266938.9074480170002
Median14942.5
Midrange15222
Midmean - Weighted Average at Xnp13845.9677419355
Midmean - Weighted Average at X(n+1)p13952.1
Midmean - Empirical Distribution Function13845.9677419355
Midmean - Empirical Distribution Function - Averaging13952.1
Midmean - Empirical Distribution Function - Interpolation13952.1
Midmean - Closest Observation13845.9677419355
Midmean - True Basic - Statistics Graphics Toolkit13952.1
Midmean - MS Excel (old versions)13924.15625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14155.05 & 408.581082981159 & 34.6444086366396 \tabularnewline
Geometric Mean & 13806.2145028864 &  &  \tabularnewline
Harmonic Mean & 13464.9649175676 &  &  \tabularnewline
Quadratic Mean & 14498.7865727906 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 14154.4 & 408.413188225337 & 34.6570590962173 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 14133.4666666667 & 402.377953189294 & 35.1248535230203 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 14123.8666666667 & 399.83500443574 & 35.3242375229221 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 14084.6666666667 & 391.670501483811 & 35.9604989737754 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 14077.75 & 389.806918469184 & 36.114674555508 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 14076.75 & 388.49887305423 & 36.2336958388938 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 14081.7666666667 & 385.695322194979 & 36.5100789569545 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 14042.0333333333 & 377.696576547855 & 37.1780794564712 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 13992.5333333333 & 368.74139075781 & 37.9467390535598 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13992.8666666667 & 366.006177178173 & 38.2312308894582 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13878.8333333333 & 346.738434417172 & 40.0268097093478 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13874.6333333333 & 345.39570360901 & 40.1702545467662 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13747.45 & 326.158338575045 & 42.1496199056609 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13728.55 & 322.908612445573 & 42.5152797753698 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13694.3 & 315.310855764136 & 43.4311085383112 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13663.9 & 310.762523735073 & 43.9689439890395 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13678.35 & 304.74249927042 & 44.8849439534924 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13678.05 & 298.910713975559 & 45.7596511616456 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13675.2 & 298.545933590255 & 45.8060166338383 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13803.5333333333 & 269.972890945692 & 51.1293311153603 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 14118.2586206897 & 404.181138047665 & 34.9305232027544 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 14079.5357142857 & 398.663790879768 & 35.3168159145207 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 14049.5740740741 & 395.4478470314 & 35.5282603750236 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 14021 & 392.205900421949 & 35.7490797178617 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 14001.9 & 390.754512684976 & 35.832983485691 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13982.9375 & 388.919799302155 & 35.9532672933849 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13962.5434782609 & 386.33419702861 & 36.1411016307906 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13939.3181818182 & 383.124817197432 & 36.3832295798133 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13920.9761904762 & 380.424842724267 & 36.5932363690722 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13909.05 & 378.409300432542 & 36.756628296665 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13895.8157894737 & 375.502871656125 & 37.0058842111841 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13898.3888888889 & 375.413882242785 & 37.0215102485225 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13901.8823529412 & 374.285853003869 & 37.1424200016383 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13924.15625 & 375.910000996976 & 37.0411965977783 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13952.1 & 376.977932675293 & 37.0103891784497 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13988.9285714286 & 378.162344860372 & 36.9918601403682 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 14035.8076923077 & 378.356819862012 & 37.096748242642 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 14088.375 & 377.510599776802 & 37.3191507955792 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 14150.5454545455 & 374.571476526383 & 37.7779578567263 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 14225.6 & 365.626653122669 & 38.9074480170002 \tabularnewline
Median & 14942.5 &  &  \tabularnewline
Midrange & 15222 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13845.9677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13952.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13845.9677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13952.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13952.1 &  &  \tabularnewline
Midmean - Closest Observation & 13845.9677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13952.1 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13924.15625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17476&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]14155.05[/C][C]408.581082981159[/C][C]34.6444086366396[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13806.2145028864[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13464.9649175676[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14498.7865727906[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]14154.4[/C][C]408.413188225337[/C][C]34.6570590962173[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]14133.4666666667[/C][C]402.377953189294[/C][C]35.1248535230203[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]14123.8666666667[/C][C]399.83500443574[/C][C]35.3242375229221[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]14084.6666666667[/C][C]391.670501483811[/C][C]35.9604989737754[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]14077.75[/C][C]389.806918469184[/C][C]36.114674555508[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]14076.75[/C][C]388.49887305423[/C][C]36.2336958388938[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]14081.7666666667[/C][C]385.695322194979[/C][C]36.5100789569545[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]14042.0333333333[/C][C]377.696576547855[/C][C]37.1780794564712[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]13992.5333333333[/C][C]368.74139075781[/C][C]37.9467390535598[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13992.8666666667[/C][C]366.006177178173[/C][C]38.2312308894582[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13878.8333333333[/C][C]346.738434417172[/C][C]40.0268097093478[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13874.6333333333[/C][C]345.39570360901[/C][C]40.1702545467662[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13747.45[/C][C]326.158338575045[/C][C]42.1496199056609[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13728.55[/C][C]322.908612445573[/C][C]42.5152797753698[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13694.3[/C][C]315.310855764136[/C][C]43.4311085383112[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13663.9[/C][C]310.762523735073[/C][C]43.9689439890395[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13678.35[/C][C]304.74249927042[/C][C]44.8849439534924[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13678.05[/C][C]298.910713975559[/C][C]45.7596511616456[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13675.2[/C][C]298.545933590255[/C][C]45.8060166338383[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13803.5333333333[/C][C]269.972890945692[/C][C]51.1293311153603[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]14118.2586206897[/C][C]404.181138047665[/C][C]34.9305232027544[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]14079.5357142857[/C][C]398.663790879768[/C][C]35.3168159145207[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]14049.5740740741[/C][C]395.4478470314[/C][C]35.5282603750236[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]14021[/C][C]392.205900421949[/C][C]35.7490797178617[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]14001.9[/C][C]390.754512684976[/C][C]35.832983485691[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13982.9375[/C][C]388.919799302155[/C][C]35.9532672933849[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13962.5434782609[/C][C]386.33419702861[/C][C]36.1411016307906[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13939.3181818182[/C][C]383.124817197432[/C][C]36.3832295798133[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13920.9761904762[/C][C]380.424842724267[/C][C]36.5932363690722[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13909.05[/C][C]378.409300432542[/C][C]36.756628296665[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13895.8157894737[/C][C]375.502871656125[/C][C]37.0058842111841[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13898.3888888889[/C][C]375.413882242785[/C][C]37.0215102485225[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13901.8823529412[/C][C]374.285853003869[/C][C]37.1424200016383[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13924.15625[/C][C]375.910000996976[/C][C]37.0411965977783[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13952.1[/C][C]376.977932675293[/C][C]37.0103891784497[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13988.9285714286[/C][C]378.162344860372[/C][C]36.9918601403682[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]14035.8076923077[/C][C]378.356819862012[/C][C]37.096748242642[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]14088.375[/C][C]377.510599776802[/C][C]37.3191507955792[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]14150.5454545455[/C][C]374.571476526383[/C][C]37.7779578567263[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]14225.6[/C][C]365.626653122669[/C][C]38.9074480170002[/C][/ROW]
[ROW][C]Median[/C][C]14942.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13845.9677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13845.9677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13845.9677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13924.15625[/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=17476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17476&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 Mean14155.05408.58108298115934.6444086366396
Geometric Mean13806.2145028864
Harmonic Mean13464.9649175676
Quadratic Mean14498.7865727906
Winsorized Mean ( 1 / 20 )14154.4408.41318822533734.6570590962173
Winsorized Mean ( 2 / 20 )14133.4666666667402.37795318929435.1248535230203
Winsorized Mean ( 3 / 20 )14123.8666666667399.8350044357435.3242375229221
Winsorized Mean ( 4 / 20 )14084.6666666667391.67050148381135.9604989737754
Winsorized Mean ( 5 / 20 )14077.75389.80691846918436.114674555508
Winsorized Mean ( 6 / 20 )14076.75388.4988730542336.2336958388938
Winsorized Mean ( 7 / 20 )14081.7666666667385.69532219497936.5100789569545
Winsorized Mean ( 8 / 20 )14042.0333333333377.69657654785537.1780794564712
Winsorized Mean ( 9 / 20 )13992.5333333333368.7413907578137.9467390535598
Winsorized Mean ( 10 / 20 )13992.8666666667366.00617717817338.2312308894582
Winsorized Mean ( 11 / 20 )13878.8333333333346.73843441717240.0268097093478
Winsorized Mean ( 12 / 20 )13874.6333333333345.3957036090140.1702545467662
Winsorized Mean ( 13 / 20 )13747.45326.15833857504542.1496199056609
Winsorized Mean ( 14 / 20 )13728.55322.90861244557342.5152797753698
Winsorized Mean ( 15 / 20 )13694.3315.31085576413643.4311085383112
Winsorized Mean ( 16 / 20 )13663.9310.76252373507343.9689439890395
Winsorized Mean ( 17 / 20 )13678.35304.7424992704244.8849439534924
Winsorized Mean ( 18 / 20 )13678.05298.91071397555945.7596511616456
Winsorized Mean ( 19 / 20 )13675.2298.54593359025545.8060166338383
Winsorized Mean ( 20 / 20 )13803.5333333333269.97289094569251.1293311153603
Trimmed Mean ( 1 / 20 )14118.2586206897404.18113804766534.9305232027544
Trimmed Mean ( 2 / 20 )14079.5357142857398.66379087976835.3168159145207
Trimmed Mean ( 3 / 20 )14049.5740740741395.447847031435.5282603750236
Trimmed Mean ( 4 / 20 )14021392.20590042194935.7490797178617
Trimmed Mean ( 5 / 20 )14001.9390.75451268497635.832983485691
Trimmed Mean ( 6 / 20 )13982.9375388.91979930215535.9532672933849
Trimmed Mean ( 7 / 20 )13962.5434782609386.3341970286136.1411016307906
Trimmed Mean ( 8 / 20 )13939.3181818182383.12481719743236.3832295798133
Trimmed Mean ( 9 / 20 )13920.9761904762380.42484272426736.5932363690722
Trimmed Mean ( 10 / 20 )13909.05378.40930043254236.756628296665
Trimmed Mean ( 11 / 20 )13895.8157894737375.50287165612537.0058842111841
Trimmed Mean ( 12 / 20 )13898.3888888889375.41388224278537.0215102485225
Trimmed Mean ( 13 / 20 )13901.8823529412374.28585300386937.1424200016383
Trimmed Mean ( 14 / 20 )13924.15625375.91000099697637.0411965977783
Trimmed Mean ( 15 / 20 )13952.1376.97793267529337.0103891784497
Trimmed Mean ( 16 / 20 )13988.9285714286378.16234486037236.9918601403682
Trimmed Mean ( 17 / 20 )14035.8076923077378.35681986201237.096748242642
Trimmed Mean ( 18 / 20 )14088.375377.51059977680237.3191507955792
Trimmed Mean ( 19 / 20 )14150.5454545455374.57147652638337.7779578567263
Trimmed Mean ( 20 / 20 )14225.6365.62665312266938.9074480170002
Median14942.5
Midrange15222
Midmean - Weighted Average at Xnp13845.9677419355
Midmean - Weighted Average at X(n+1)p13952.1
Midmean - Empirical Distribution Function13845.9677419355
Midmean - Empirical Distribution Function - Averaging13952.1
Midmean - Empirical Distribution Function - Interpolation13952.1
Midmean - Closest Observation13845.9677419355
Midmean - True Basic - Statistics Graphics Toolkit13952.1
Midmean - MS Excel (old versions)13924.15625
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')