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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 13 Dec 2009 03:05:40 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/13/t1260699588cm92nwl5soct9uh.htm/, Retrieved Sat, 27 Apr 2024 23:57:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67195, Retrieved Sat, 27 Apr 2024 23:57:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsshwpaper1
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-12-13 10:05:40] [4407d6264e55b051ec65750e6dca2820] [Current]
-    D    [Central Tendency] [CT] [2010-12-24 10:52:02] [6e5489189f7de5cfbcc25dd35ae15009]
-    D    [Central Tendency] [CT uitvoer] [2010-12-24 10:56:09] [6e5489189f7de5cfbcc25dd35ae15009]
-    D    [Central Tendency] [CT uitvoer] [2010-12-24 10:58:09] [6e5489189f7de5cfbcc25dd35ae15009]
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Dataseries X:
15912,8
13866,5
17823,2
17872
17420,4
16704,4
15991,2
16583,6
19123,5
17838,7
17209,4
18586,5
16258,1
15141,6
19202,1
17746,5
19090,1
18040,3
17515,5
17751,8
21072,4
17170
19439,5
19795,4
17574,9
16165,4
19464,6
19932,1
19961,2
17343,4
18924,2
18574,1
21350,6
18594,6
19823,1
20844,4
19640,2
17735,4
19813,6
22160
20664,3
17877,4
20906,5
21164,1
21374,4
22952,3
21343,5
23899,3
22392,9
18274,1
22786,7
22321,5
17842,2
16373,5
15993,8
16446,1
17729
16643
16196,7
18252,1
17304




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67195&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67195&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18685.1590163934275.24315121666167.8860089117537
Geometric Mean18565.3595307222
Harmonic Mean18447.3182612394
Quadratic Mean18806.400373421
Winsorized Mean ( 1 / 20 )18690.5377049180265.31452455677370.4467187996659
Winsorized Mean ( 2 / 20 )18710.3934426229258.77154024930872.3046801228482
Winsorized Mean ( 3 / 20 )18694.8819672131253.17925554819073.8404966344281
Winsorized Mean ( 4 / 20 )18690.3704918033252.01681819306174.1631873055601
Winsorized Mean ( 5 / 20 )18691.1983606557246.41787649264975.8516331148293
Winsorized Mean ( 6 / 20 )18617.0049180328229.01845596311281.2904132103283
Winsorized Mean ( 7 / 20 )18621.3196721311227.23988890224481.9456467880154
Winsorized Mean ( 8 / 20 )18635.5229508197224.47029292652983.0199965788759
Winsorized Mean ( 9 / 20 )18619.7655737705217.43502164719785.6337007383396
Winsorized Mean ( 10 / 20 )18627.2737704918210.81630402598988.3578424190353
Winsorized Mean ( 11 / 20 )18608.068852459203.37818490647591.4949106317183
Winsorized Mean ( 12 / 20 )18607.931147541199.14958484775493.4369567567334
Winsorized Mean ( 13 / 20 )18668.7754098361176.993556559815105.477147149856
Winsorized Mean ( 14 / 20 )18516.4508196721147.144131407867125.838867255579
Winsorized Mean ( 15 / 20 )18532.5573770492142.580191020214129.979888822156
Winsorized Mean ( 16 / 20 )18514.3016393443136.474521881947135.661231005151
Winsorized Mean ( 17 / 20 )18533.1131147541133.019944752850139.325821771979
Winsorized Mean ( 18 / 20 )18555.8049180328128.303392733897144.624429039985
Winsorized Mean ( 19 / 20 )18525.9655737705118.115450789556156.84625042644
Winsorized Mean ( 20 / 20 )18518.9163934426102.511457447883180.652161763065
Trimmed Mean ( 1 / 20 )18678.4559322034257.48172832725772.542840432014
Trimmed Mean ( 2 / 20 )18665.5263157895247.84988050775675.3098055869565
Trimmed Mean ( 3 / 20 )18640.6454545455240.29130966487177.5751960424333
Trimmed Mean ( 4 / 20 )18619.8377358491233.57947026145779.7152151899607
Trimmed Mean ( 5 / 20 )18598.7470588235225.56643941642482.4535205988151
Trimmed Mean ( 6 / 20 )18575.7285714286217.35392144695185.4630477691303
Trimmed Mean ( 7 / 20 )18566.8212.49020087326487.377205742649
Trimmed Mean ( 8 / 20 )18556.2422222222206.62530701704489.8062415011514
Trimmed Mean ( 9 / 20 )18542.1837209302199.65707940597592.8701540466153
Trimmed Mean ( 10 / 20 )18529.3585365854192.41363393505496.2996132739725
Trimmed Mean ( 11 / 20 )18514.0435897436184.514439519767100.339266877594
Trimmed Mean ( 12 / 20 )18499.9513513514175.922168141391105.159864426425
Trimmed Mean ( 13 / 20 )18484.2685714286165.246175295950111.858979721158
Trimmed Mean ( 14 / 20 )18458.0333333333156.887163760385117.651647788881
Trimmed Mean ( 15 / 20 )18449.8225806452154.402273139827119.491910355082
Trimmed Mean ( 16 / 20 )18438.2206896552151.581557034449121.638945069451
Trimmed Mean ( 17 / 20 )18427.4777777778148.773041006408123.863017473603
Trimmed Mean ( 18 / 20 )18412.316144.892901790713127.075348567421
Trimmed Mean ( 19 / 20 )18391.1739130435139.655779429138131.689314887074
Trimmed Mean ( 20 / 20 )18370.5666666667134.815603225353136.264395419861
Median18252.1
Midrange18882.9
Midmean - Weighted Average at Xnp18400.4133333333
Midmean - Weighted Average at X(n+1)p18449.8225806452
Midmean - Empirical Distribution Function18449.8225806452
Midmean - Empirical Distribution Function - Averaging18449.8225806452
Midmean - Empirical Distribution Function - Interpolation18449.8225806452
Midmean - Closest Observation18411.059375
Midmean - True Basic - Statistics Graphics Toolkit18449.8225806452
Midmean - MS Excel (old versions)18449.8225806452
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18685.1590163934 & 275.243151216661 & 67.8860089117537 \tabularnewline
Geometric Mean & 18565.3595307222 &  &  \tabularnewline
Harmonic Mean & 18447.3182612394 &  &  \tabularnewline
Quadratic Mean & 18806.400373421 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18690.5377049180 & 265.314524556773 & 70.4467187996659 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18710.3934426229 & 258.771540249308 & 72.3046801228482 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18694.8819672131 & 253.179255548190 & 73.8404966344281 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18690.3704918033 & 252.016818193061 & 74.1631873055601 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18691.1983606557 & 246.417876492649 & 75.8516331148293 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18617.0049180328 & 229.018455963112 & 81.2904132103283 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18621.3196721311 & 227.239888902244 & 81.9456467880154 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18635.5229508197 & 224.470292926529 & 83.0199965788759 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18619.7655737705 & 217.435021647197 & 85.6337007383396 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18627.2737704918 & 210.816304025989 & 88.3578424190353 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18608.068852459 & 203.378184906475 & 91.4949106317183 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18607.931147541 & 199.149584847754 & 93.4369567567334 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18668.7754098361 & 176.993556559815 & 105.477147149856 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18516.4508196721 & 147.144131407867 & 125.838867255579 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18532.5573770492 & 142.580191020214 & 129.979888822156 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18514.3016393443 & 136.474521881947 & 135.661231005151 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18533.1131147541 & 133.019944752850 & 139.325821771979 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18555.8049180328 & 128.303392733897 & 144.624429039985 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18525.9655737705 & 118.115450789556 & 156.84625042644 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18518.9163934426 & 102.511457447883 & 180.652161763065 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18678.4559322034 & 257.481728327257 & 72.542840432014 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18665.5263157895 & 247.849880507756 & 75.3098055869565 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18640.6454545455 & 240.291309664871 & 77.5751960424333 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18619.8377358491 & 233.579470261457 & 79.7152151899607 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18598.7470588235 & 225.566439416424 & 82.4535205988151 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18575.7285714286 & 217.353921446951 & 85.4630477691303 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18566.8 & 212.490200873264 & 87.377205742649 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18556.2422222222 & 206.625307017044 & 89.8062415011514 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18542.1837209302 & 199.657079405975 & 92.8701540466153 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18529.3585365854 & 192.413633935054 & 96.2996132739725 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18514.0435897436 & 184.514439519767 & 100.339266877594 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18499.9513513514 & 175.922168141391 & 105.159864426425 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18484.2685714286 & 165.246175295950 & 111.858979721158 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18458.0333333333 & 156.887163760385 & 117.651647788881 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18449.8225806452 & 154.402273139827 & 119.491910355082 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18438.2206896552 & 151.581557034449 & 121.638945069451 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18427.4777777778 & 148.773041006408 & 123.863017473603 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18412.316 & 144.892901790713 & 127.075348567421 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18391.1739130435 & 139.655779429138 & 131.689314887074 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18370.5666666667 & 134.815603225353 & 136.264395419861 \tabularnewline
Median & 18252.1 &  &  \tabularnewline
Midrange & 18882.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18400.4133333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18449.8225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18449.8225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18449.8225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18449.8225806452 &  &  \tabularnewline
Midmean - Closest Observation & 18411.059375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18449.8225806452 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18449.8225806452 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67195&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]18685.1590163934[/C][C]275.243151216661[/C][C]67.8860089117537[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18565.3595307222[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18447.3182612394[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18806.400373421[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18690.5377049180[/C][C]265.314524556773[/C][C]70.4467187996659[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18710.3934426229[/C][C]258.771540249308[/C][C]72.3046801228482[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18694.8819672131[/C][C]253.179255548190[/C][C]73.8404966344281[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18690.3704918033[/C][C]252.016818193061[/C][C]74.1631873055601[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18691.1983606557[/C][C]246.417876492649[/C][C]75.8516331148293[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18617.0049180328[/C][C]229.018455963112[/C][C]81.2904132103283[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18621.3196721311[/C][C]227.239888902244[/C][C]81.9456467880154[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18635.5229508197[/C][C]224.470292926529[/C][C]83.0199965788759[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18619.7655737705[/C][C]217.435021647197[/C][C]85.6337007383396[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18627.2737704918[/C][C]210.816304025989[/C][C]88.3578424190353[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18608.068852459[/C][C]203.378184906475[/C][C]91.4949106317183[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18607.931147541[/C][C]199.149584847754[/C][C]93.4369567567334[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18668.7754098361[/C][C]176.993556559815[/C][C]105.477147149856[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18516.4508196721[/C][C]147.144131407867[/C][C]125.838867255579[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18532.5573770492[/C][C]142.580191020214[/C][C]129.979888822156[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18514.3016393443[/C][C]136.474521881947[/C][C]135.661231005151[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18533.1131147541[/C][C]133.019944752850[/C][C]139.325821771979[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18555.8049180328[/C][C]128.303392733897[/C][C]144.624429039985[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18525.9655737705[/C][C]118.115450789556[/C][C]156.84625042644[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18518.9163934426[/C][C]102.511457447883[/C][C]180.652161763065[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18678.4559322034[/C][C]257.481728327257[/C][C]72.542840432014[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18665.5263157895[/C][C]247.849880507756[/C][C]75.3098055869565[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18640.6454545455[/C][C]240.291309664871[/C][C]77.5751960424333[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18619.8377358491[/C][C]233.579470261457[/C][C]79.7152151899607[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18598.7470588235[/C][C]225.566439416424[/C][C]82.4535205988151[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18575.7285714286[/C][C]217.353921446951[/C][C]85.4630477691303[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18566.8[/C][C]212.490200873264[/C][C]87.377205742649[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18556.2422222222[/C][C]206.625307017044[/C][C]89.8062415011514[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18542.1837209302[/C][C]199.657079405975[/C][C]92.8701540466153[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18529.3585365854[/C][C]192.413633935054[/C][C]96.2996132739725[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18514.0435897436[/C][C]184.514439519767[/C][C]100.339266877594[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18499.9513513514[/C][C]175.922168141391[/C][C]105.159864426425[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18484.2685714286[/C][C]165.246175295950[/C][C]111.858979721158[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18458.0333333333[/C][C]156.887163760385[/C][C]117.651647788881[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18449.8225806452[/C][C]154.402273139827[/C][C]119.491910355082[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18438.2206896552[/C][C]151.581557034449[/C][C]121.638945069451[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18427.4777777778[/C][C]148.773041006408[/C][C]123.863017473603[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18412.316[/C][C]144.892901790713[/C][C]127.075348567421[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18391.1739130435[/C][C]139.655779429138[/C][C]131.689314887074[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18370.5666666667[/C][C]134.815603225353[/C][C]136.264395419861[/C][/ROW]
[ROW][C]Median[/C][C]18252.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18882.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18400.4133333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18449.8225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18449.8225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18449.8225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18449.8225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18411.059375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18449.8225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18449.8225806452[/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=67195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67195&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 Mean18685.1590163934275.24315121666167.8860089117537
Geometric Mean18565.3595307222
Harmonic Mean18447.3182612394
Quadratic Mean18806.400373421
Winsorized Mean ( 1 / 20 )18690.5377049180265.31452455677370.4467187996659
Winsorized Mean ( 2 / 20 )18710.3934426229258.77154024930872.3046801228482
Winsorized Mean ( 3 / 20 )18694.8819672131253.17925554819073.8404966344281
Winsorized Mean ( 4 / 20 )18690.3704918033252.01681819306174.1631873055601
Winsorized Mean ( 5 / 20 )18691.1983606557246.41787649264975.8516331148293
Winsorized Mean ( 6 / 20 )18617.0049180328229.01845596311281.2904132103283
Winsorized Mean ( 7 / 20 )18621.3196721311227.23988890224481.9456467880154
Winsorized Mean ( 8 / 20 )18635.5229508197224.47029292652983.0199965788759
Winsorized Mean ( 9 / 20 )18619.7655737705217.43502164719785.6337007383396
Winsorized Mean ( 10 / 20 )18627.2737704918210.81630402598988.3578424190353
Winsorized Mean ( 11 / 20 )18608.068852459203.37818490647591.4949106317183
Winsorized Mean ( 12 / 20 )18607.931147541199.14958484775493.4369567567334
Winsorized Mean ( 13 / 20 )18668.7754098361176.993556559815105.477147149856
Winsorized Mean ( 14 / 20 )18516.4508196721147.144131407867125.838867255579
Winsorized Mean ( 15 / 20 )18532.5573770492142.580191020214129.979888822156
Winsorized Mean ( 16 / 20 )18514.3016393443136.474521881947135.661231005151
Winsorized Mean ( 17 / 20 )18533.1131147541133.019944752850139.325821771979
Winsorized Mean ( 18 / 20 )18555.8049180328128.303392733897144.624429039985
Winsorized Mean ( 19 / 20 )18525.9655737705118.115450789556156.84625042644
Winsorized Mean ( 20 / 20 )18518.9163934426102.511457447883180.652161763065
Trimmed Mean ( 1 / 20 )18678.4559322034257.48172832725772.542840432014
Trimmed Mean ( 2 / 20 )18665.5263157895247.84988050775675.3098055869565
Trimmed Mean ( 3 / 20 )18640.6454545455240.29130966487177.5751960424333
Trimmed Mean ( 4 / 20 )18619.8377358491233.57947026145779.7152151899607
Trimmed Mean ( 5 / 20 )18598.7470588235225.56643941642482.4535205988151
Trimmed Mean ( 6 / 20 )18575.7285714286217.35392144695185.4630477691303
Trimmed Mean ( 7 / 20 )18566.8212.49020087326487.377205742649
Trimmed Mean ( 8 / 20 )18556.2422222222206.62530701704489.8062415011514
Trimmed Mean ( 9 / 20 )18542.1837209302199.65707940597592.8701540466153
Trimmed Mean ( 10 / 20 )18529.3585365854192.41363393505496.2996132739725
Trimmed Mean ( 11 / 20 )18514.0435897436184.514439519767100.339266877594
Trimmed Mean ( 12 / 20 )18499.9513513514175.922168141391105.159864426425
Trimmed Mean ( 13 / 20 )18484.2685714286165.246175295950111.858979721158
Trimmed Mean ( 14 / 20 )18458.0333333333156.887163760385117.651647788881
Trimmed Mean ( 15 / 20 )18449.8225806452154.402273139827119.491910355082
Trimmed Mean ( 16 / 20 )18438.2206896552151.581557034449121.638945069451
Trimmed Mean ( 17 / 20 )18427.4777777778148.773041006408123.863017473603
Trimmed Mean ( 18 / 20 )18412.316144.892901790713127.075348567421
Trimmed Mean ( 19 / 20 )18391.1739130435139.655779429138131.689314887074
Trimmed Mean ( 20 / 20 )18370.5666666667134.815603225353136.264395419861
Median18252.1
Midrange18882.9
Midmean - Weighted Average at Xnp18400.4133333333
Midmean - Weighted Average at X(n+1)p18449.8225806452
Midmean - Empirical Distribution Function18449.8225806452
Midmean - Empirical Distribution Function - Averaging18449.8225806452
Midmean - Empirical Distribution Function - Interpolation18449.8225806452
Midmean - Closest Observation18411.059375
Midmean - True Basic - Statistics Graphics Toolkit18449.8225806452
Midmean - MS Excel (old versions)18449.8225806452
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')