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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 computationMon, 20 Oct 2008 11:06:38 -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/t1224522448tlhexcjie6r9ad2.htm/, Retrieved Sun, 19 May 2024 16:28:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17685, Retrieved Sun, 19 May 2024 16:28:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Investigating Ass...] [2008-10-20 17:06:38] [4f54996111e63ee83b19b6a8540c6bad] [Current]
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Dataseries X:
10846
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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17685&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17685&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17685&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14100.8032786885405.47233525304634.776240085254
Geometric Mean13751.7035508972
Harmonic Mean13411.8740634174
Quadratic Mean14446.3532416872
Winsorized Mean ( 1 / 20 )14100.1639344262405.30727477283934.7888252001618
Winsorized Mean ( 2 / 20 )14079.5737704918399.37952112016635.2536197424493
Winsorized Mean ( 3 / 20 )14070.1311475410396.8802867470535.451826702868
Winsorized Mean ( 4 / 20 )14031.5737704918388.83793487144636.0859178390884
Winsorized Mean ( 5 / 20 )14024.7704918033387.00686470623536.2390742149989
Winsorized Mean ( 6 / 20 )14023.7868852459385.73034134946036.3564526352382
Winsorized Mean ( 7 / 20 )14028.7213114754383.01081618874336.6274807878069
Winsorized Mean ( 8 / 20 )13989.6393442623375.1301515727737.2927616871354
Winsorized Mean ( 9 / 20 )13940.9508196721366.29623147755838.0592253527627
Winsorized Mean ( 10 / 20 )13941.2786885246363.63400964134338.3387645789102
Winsorized Mean ( 11 / 20 )13829.1147540984344.61223484298440.1294944168170
Winsorized Mean ( 12 / 20 )13824.9836065574343.29560339013440.2713680863723
Winsorized Mean ( 13 / 20 )13699.8852459016324.27430210327942.2478289430975
Winsorized Mean ( 14 / 20 )13681.2950819672321.06745656252942.6119022726389
Winsorized Mean ( 15 / 20 )13647.6065573770313.594500166743.5199168037777
Winsorized Mean ( 16 / 20 )13617.7049180328309.09706006018344.0564038861494
Winsorized Mean ( 17 / 20 )13631.9180327869303.28050758574244.9482168877369
Winsorized Mean ( 18 / 20 )13623.9508196721298.80050038567045.5954752488277
Winsorized Mean ( 19 / 20 )13629.2459016393297.18541217695345.8610865244088
Winsorized Mean ( 20 / 20 )13600.0655737705293.44899936595746.3455851039043
Trimmed Mean ( 1 / 20 )14062.7966101695401.12431832172835.058449382992
Trimmed Mean ( 2 / 20 )14022.8070175439395.69479789583735.4384416780613
Trimmed Mean ( 3 / 20 )13991.3272727273392.53685242039635.6433470805512
Trimmed Mean ( 4 / 20 )13961.0943396226389.37054564673535.8555481294396
Trimmed Mean ( 5 / 20 )13940.0196078431387.98255720868835.9295008212059
Trimmed Mean ( 6 / 20 )13918.9183673469386.24246116493636.0367379737754
Trimmed Mean ( 7 / 20 )13896.2340425532383.79657926807836.2072899895411
Trimmed Mean ( 8 / 20 )13870.5777777778380.77041319479436.4276669014246
Trimmed Mean ( 9 / 20 )13849.4651162791378.29299429621536.6104192387833
Trimmed Mean ( 10 / 20 )13834.3414634146376.55001062236436.7397186911485
Trimmed Mean ( 11 / 20 )13817.6153846154374.01446134436636.9440671757692
Trimmed Mean ( 12 / 20 )13815.8918918919374.33033255875736.9082884559543
Trimmed Mean ( 13 / 20 )13814.5714285714373.77528027420136.9595640954027
Trimmed Mean ( 14 / 20 )13830.8787878788376.09157481512936.7752954707307
Trimmed Mean ( 15 / 20 )13851.9032258065378.13121507865236.6325303847905
Trimmed Mean ( 16 / 20 )13880.5517241379380.64388211379136.465978770121
Trimmed Mean ( 17 / 20 )13917.6666666667382.76258141594036.3610952125507
Trimmed Mean ( 18 / 20 )13958.68384.62176970802536.2919655083391
Trimmed Mean ( 19 / 20 )14008385.25662613924036.3601792923796
Trimmed Mean ( 20 / 20 )14065.9047619048382.69272085330336.7550883396515
Median14931
Midrange15222
Midmean - Weighted Average at Xnp13774.6
Midmean - Weighted Average at X(n+1)p13851.9032258065
Midmean - Empirical Distribution Function13851.9032258065
Midmean - Empirical Distribution Function - Averaging13851.9032258065
Midmean - Empirical Distribution Function - Interpolation13851.9032258065
Midmean - Closest Observation13752.21875
Midmean - True Basic - Statistics Graphics Toolkit13851.9032258065
Midmean - MS Excel (old versions)13851.9032258065
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14100.8032786885 & 405.472335253046 & 34.776240085254 \tabularnewline
Geometric Mean & 13751.7035508972 &  &  \tabularnewline
Harmonic Mean & 13411.8740634174 &  &  \tabularnewline
Quadratic Mean & 14446.3532416872 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 14100.1639344262 & 405.307274772839 & 34.7888252001618 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 14079.5737704918 & 399.379521120166 & 35.2536197424493 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 14070.1311475410 & 396.88028674705 & 35.451826702868 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 14031.5737704918 & 388.837934871446 & 36.0859178390884 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 14024.7704918033 & 387.006864706235 & 36.2390742149989 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 14023.7868852459 & 385.730341349460 & 36.3564526352382 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 14028.7213114754 & 383.010816188743 & 36.6274807878069 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 13989.6393442623 & 375.13015157277 & 37.2927616871354 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 13940.9508196721 & 366.296231477558 & 38.0592253527627 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13941.2786885246 & 363.634009641343 & 38.3387645789102 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13829.1147540984 & 344.612234842984 & 40.1294944168170 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13824.9836065574 & 343.295603390134 & 40.2713680863723 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13699.8852459016 & 324.274302103279 & 42.2478289430975 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13681.2950819672 & 321.067456562529 & 42.6119022726389 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13647.6065573770 & 313.5945001667 & 43.5199168037777 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13617.7049180328 & 309.097060060183 & 44.0564038861494 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13631.9180327869 & 303.280507585742 & 44.9482168877369 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13623.9508196721 & 298.800500385670 & 45.5954752488277 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13629.2459016393 & 297.185412176953 & 45.8610865244088 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13600.0655737705 & 293.448999365957 & 46.3455851039043 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 14062.7966101695 & 401.124318321728 & 35.058449382992 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 14022.8070175439 & 395.694797895837 & 35.4384416780613 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 13991.3272727273 & 392.536852420396 & 35.6433470805512 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 13961.0943396226 & 389.370545646735 & 35.8555481294396 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 13940.0196078431 & 387.982557208688 & 35.9295008212059 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13918.9183673469 & 386.242461164936 & 36.0367379737754 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13896.2340425532 & 383.796579268078 & 36.2072899895411 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13870.5777777778 & 380.770413194794 & 36.4276669014246 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13849.4651162791 & 378.292994296215 & 36.6104192387833 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13834.3414634146 & 376.550010622364 & 36.7397186911485 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13817.6153846154 & 374.014461344366 & 36.9440671757692 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13815.8918918919 & 374.330332558757 & 36.9082884559543 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13814.5714285714 & 373.775280274201 & 36.9595640954027 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13830.8787878788 & 376.091574815129 & 36.7752954707307 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13851.9032258065 & 378.131215078652 & 36.6325303847905 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13880.5517241379 & 380.643882113791 & 36.465978770121 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 13917.6666666667 & 382.762581415940 & 36.3610952125507 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 13958.68 & 384.621769708025 & 36.2919655083391 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 14008 & 385.256626139240 & 36.3601792923796 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 14065.9047619048 & 382.692720853303 & 36.7550883396515 \tabularnewline
Median & 14931 &  &  \tabularnewline
Midrange & 15222 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13774.6 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13851.9032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13851.9032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13851.9032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13851.9032258065 &  &  \tabularnewline
Midmean - Closest Observation & 13752.21875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13851.9032258065 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13851.9032258065 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17685&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]14100.8032786885[/C][C]405.472335253046[/C][C]34.776240085254[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13751.7035508972[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13411.8740634174[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14446.3532416872[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]14100.1639344262[/C][C]405.307274772839[/C][C]34.7888252001618[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]14079.5737704918[/C][C]399.379521120166[/C][C]35.2536197424493[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]14070.1311475410[/C][C]396.88028674705[/C][C]35.451826702868[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]14031.5737704918[/C][C]388.837934871446[/C][C]36.0859178390884[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]14024.7704918033[/C][C]387.006864706235[/C][C]36.2390742149989[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]14023.7868852459[/C][C]385.730341349460[/C][C]36.3564526352382[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]14028.7213114754[/C][C]383.010816188743[/C][C]36.6274807878069[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]13989.6393442623[/C][C]375.13015157277[/C][C]37.2927616871354[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]13940.9508196721[/C][C]366.296231477558[/C][C]38.0592253527627[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13941.2786885246[/C][C]363.634009641343[/C][C]38.3387645789102[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13829.1147540984[/C][C]344.612234842984[/C][C]40.1294944168170[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13824.9836065574[/C][C]343.295603390134[/C][C]40.2713680863723[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13699.8852459016[/C][C]324.274302103279[/C][C]42.2478289430975[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13681.2950819672[/C][C]321.067456562529[/C][C]42.6119022726389[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13647.6065573770[/C][C]313.5945001667[/C][C]43.5199168037777[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13617.7049180328[/C][C]309.097060060183[/C][C]44.0564038861494[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13631.9180327869[/C][C]303.280507585742[/C][C]44.9482168877369[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13623.9508196721[/C][C]298.800500385670[/C][C]45.5954752488277[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13629.2459016393[/C][C]297.185412176953[/C][C]45.8610865244088[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13600.0655737705[/C][C]293.448999365957[/C][C]46.3455851039043[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]14062.7966101695[/C][C]401.124318321728[/C][C]35.058449382992[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]14022.8070175439[/C][C]395.694797895837[/C][C]35.4384416780613[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]13991.3272727273[/C][C]392.536852420396[/C][C]35.6433470805512[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]13961.0943396226[/C][C]389.370545646735[/C][C]35.8555481294396[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]13940.0196078431[/C][C]387.982557208688[/C][C]35.9295008212059[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13918.9183673469[/C][C]386.242461164936[/C][C]36.0367379737754[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13896.2340425532[/C][C]383.796579268078[/C][C]36.2072899895411[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13870.5777777778[/C][C]380.770413194794[/C][C]36.4276669014246[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13849.4651162791[/C][C]378.292994296215[/C][C]36.6104192387833[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13834.3414634146[/C][C]376.550010622364[/C][C]36.7397186911485[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13817.6153846154[/C][C]374.014461344366[/C][C]36.9440671757692[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13815.8918918919[/C][C]374.330332558757[/C][C]36.9082884559543[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13814.5714285714[/C][C]373.775280274201[/C][C]36.9595640954027[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13830.8787878788[/C][C]376.091574815129[/C][C]36.7752954707307[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13851.9032258065[/C][C]378.131215078652[/C][C]36.6325303847905[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13880.5517241379[/C][C]380.643882113791[/C][C]36.465978770121[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]13917.6666666667[/C][C]382.762581415940[/C][C]36.3610952125507[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]13958.68[/C][C]384.621769708025[/C][C]36.2919655083391[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]14008[/C][C]385.256626139240[/C][C]36.3601792923796[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]14065.9047619048[/C][C]382.692720853303[/C][C]36.7550883396515[/C][/ROW]
[ROW][C]Median[/C][C]14931[/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]13774.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13851.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13851.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13851.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13851.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13752.21875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13851.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13851.9032258065[/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=17685&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17685&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 Mean14100.8032786885405.47233525304634.776240085254
Geometric Mean13751.7035508972
Harmonic Mean13411.8740634174
Quadratic Mean14446.3532416872
Winsorized Mean ( 1 / 20 )14100.1639344262405.30727477283934.7888252001618
Winsorized Mean ( 2 / 20 )14079.5737704918399.37952112016635.2536197424493
Winsorized Mean ( 3 / 20 )14070.1311475410396.8802867470535.451826702868
Winsorized Mean ( 4 / 20 )14031.5737704918388.83793487144636.0859178390884
Winsorized Mean ( 5 / 20 )14024.7704918033387.00686470623536.2390742149989
Winsorized Mean ( 6 / 20 )14023.7868852459385.73034134946036.3564526352382
Winsorized Mean ( 7 / 20 )14028.7213114754383.01081618874336.6274807878069
Winsorized Mean ( 8 / 20 )13989.6393442623375.1301515727737.2927616871354
Winsorized Mean ( 9 / 20 )13940.9508196721366.29623147755838.0592253527627
Winsorized Mean ( 10 / 20 )13941.2786885246363.63400964134338.3387645789102
Winsorized Mean ( 11 / 20 )13829.1147540984344.61223484298440.1294944168170
Winsorized Mean ( 12 / 20 )13824.9836065574343.29560339013440.2713680863723
Winsorized Mean ( 13 / 20 )13699.8852459016324.27430210327942.2478289430975
Winsorized Mean ( 14 / 20 )13681.2950819672321.06745656252942.6119022726389
Winsorized Mean ( 15 / 20 )13647.6065573770313.594500166743.5199168037777
Winsorized Mean ( 16 / 20 )13617.7049180328309.09706006018344.0564038861494
Winsorized Mean ( 17 / 20 )13631.9180327869303.28050758574244.9482168877369
Winsorized Mean ( 18 / 20 )13623.9508196721298.80050038567045.5954752488277
Winsorized Mean ( 19 / 20 )13629.2459016393297.18541217695345.8610865244088
Winsorized Mean ( 20 / 20 )13600.0655737705293.44899936595746.3455851039043
Trimmed Mean ( 1 / 20 )14062.7966101695401.12431832172835.058449382992
Trimmed Mean ( 2 / 20 )14022.8070175439395.69479789583735.4384416780613
Trimmed Mean ( 3 / 20 )13991.3272727273392.53685242039635.6433470805512
Trimmed Mean ( 4 / 20 )13961.0943396226389.37054564673535.8555481294396
Trimmed Mean ( 5 / 20 )13940.0196078431387.98255720868835.9295008212059
Trimmed Mean ( 6 / 20 )13918.9183673469386.24246116493636.0367379737754
Trimmed Mean ( 7 / 20 )13896.2340425532383.79657926807836.2072899895411
Trimmed Mean ( 8 / 20 )13870.5777777778380.77041319479436.4276669014246
Trimmed Mean ( 9 / 20 )13849.4651162791378.29299429621536.6104192387833
Trimmed Mean ( 10 / 20 )13834.3414634146376.55001062236436.7397186911485
Trimmed Mean ( 11 / 20 )13817.6153846154374.01446134436636.9440671757692
Trimmed Mean ( 12 / 20 )13815.8918918919374.33033255875736.9082884559543
Trimmed Mean ( 13 / 20 )13814.5714285714373.77528027420136.9595640954027
Trimmed Mean ( 14 / 20 )13830.8787878788376.09157481512936.7752954707307
Trimmed Mean ( 15 / 20 )13851.9032258065378.13121507865236.6325303847905
Trimmed Mean ( 16 / 20 )13880.5517241379380.64388211379136.465978770121
Trimmed Mean ( 17 / 20 )13917.6666666667382.76258141594036.3610952125507
Trimmed Mean ( 18 / 20 )13958.68384.62176970802536.2919655083391
Trimmed Mean ( 19 / 20 )14008385.25662613924036.3601792923796
Trimmed Mean ( 20 / 20 )14065.9047619048382.69272085330336.7550883396515
Median14931
Midrange15222
Midmean - Weighted Average at Xnp13774.6
Midmean - Weighted Average at X(n+1)p13851.9032258065
Midmean - Empirical Distribution Function13851.9032258065
Midmean - Empirical Distribution Function - Averaging13851.9032258065
Midmean - Empirical Distribution Function - Interpolation13851.9032258065
Midmean - Closest Observation13752.21875
Midmean - True Basic - Statistics Graphics Toolkit13851.9032258065
Midmean - MS Excel (old versions)13851.9032258065
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')