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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 computationFri, 14 Dec 2007 07:39:30 -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/2007/Dec/14/t1197642280m4s87vx6l0hthsi.htm/, Retrieved Fri, 03 May 2024 02:03:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3906, Retrieved Fri, 03 May 2024 02:03:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-12-14 14:39:30] [ca5e0f9f346e091f4d0fe7e17f7dba21] [Current]
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Dataseries X:
-0.304471444811582 
-11.4120872000614 
-10.2549138982292 
-11.7446613606829 
5.10800759254614 
4.17272576800617 
7.92254107294948 
1.24205314101455 
0.28685320414728 
3.43270387109597 
4.31948087729212 
1.13168232030914 
3.16660400692858 
-8.64288523350335 
1.17943632464396 
-5.75210368157515 
-4.55468115271804 
-3.69007896220072 
-8.16241219005786 
-0.427820473344341 
2.39216567588355 
4.15423824899906 
-9.57567087433632 
4.93355895555405 
-2.74360794221274 
-5.49234880234087 
7.08711992606863 
2.71777817315748 
6.72299118158728 
2.40090123393581 
6.52139854928813 
-5.03682432384173 
7.19970282133266 
-4.37013677160322 
-2.08057641125454 
2.47023458380191 
-0.81759500308664 
6.64871254115303 
-1.63851859279830 
-1.69692888548841 
4.49607030023843 
2.86986725344787 
1.44296840235653 
-0.990730292016761 
-2.27584908671093 
-5.98122765735685 
4.14911398888263 
2.0029188625428 




Summary of compuational 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 compuational 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=3906&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]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=3906&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3906&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.1557146117305960.76229194736335-0.204271620957284
Geometric MeanNaN
Harmonic Mean-263.761352679518
Quadratic Mean5.22832962350422
Winsorized Mean ( 1 / 16 )-0.1638451136263320.756818833347025-0.216491855655505
Winsorized Mean ( 2 / 16 )-0.1203205133526580.741204826927123-0.162330990006476
Winsorized Mean ( 3 / 16 )-0.1006258708894380.724484771400463-0.138893010400927
Winsorized Mean ( 4 / 16 )-0.0290836208562110.702270144585813-0.0414137224548596
Winsorized Mean ( 5 / 16 )0.007703780350100330.6867228826574590.0112181791879258
Winsorized Mean ( 6 / 16 )0.1036779773449780.5878759622349950.176360293676261
Winsorized Mean ( 7 / 16 )0.1116514642517960.576007493563840.193836825908275
Winsorized Mean ( 8 / 16 )0.08202916823823950.5540039070159110.148066046465415
Winsorized Mean ( 9 / 16 )0.1343294911543950.5304102559318230.253255832918249
Winsorized Mean ( 10 / 16 )0.2042020040372570.5047860122189580.404531819611281
Winsorized Mean ( 11 / 16 )0.2422567016036080.4956471598264530.488768465229241
Winsorized Mean ( 12 / 16 )0.4109900889251250.4625344654060960.888561003911965
Winsorized Mean ( 13 / 16 )0.4732982499379830.3825926641181811.23708135133449
Winsorized Mean ( 14 / 16 )0.5321154557438550.3459061150130271.53832335610435
Winsorized Mean ( 15 / 16 )0.5004079313612550.3205956346044491.56086944845228
Winsorized Mean ( 16 / 16 )0.5775940798531690.2910427475395351.98456785037981
Trimmed Mean ( 1 / 16 )-0.07939524076815640.732643607782578-0.108368161442716
Trimmed Mean ( 2 / 16 )0.01273189325894420.700844535974370.0181665014213792
Trimmed Mean ( 3 / 16 )0.08876183989414560.6702592184015970.132429122132510
Trimmed Mean ( 4 / 16 )0.1645169242075790.6384879198040270.257666463381288
Trimmed Mean ( 5 / 16 )0.2256539384382490.6059232786372230.372413383664291
Trimmed Mean ( 6 / 16 )0.2837739805950890.5677059280623310.499860872624061
Trimmed Mean ( 7 / 16 )0.3261495107715860.5533087134892730.589453053639483
Trimmed Mean ( 8 / 16 )0.3721133778829690.5362465768464330.69392215064812
Trimmed Mean ( 9 / 16 )0.4301302198119150.5183528200545950.82980202512762
Trimmed Mean ( 10 / 16 )0.4864732157466810.4995453814468090.973831875570008
Trimmed Mean ( 11 / 16 )0.5385848240622670.4797181275962511.12271101107015
Trimmed Mean ( 12 / 16 )0.5924626645092960.4511378491857291.3132630427233
Trimmed Mean ( 13 / 16 )0.6254576782518720.4195754295041081.49069186198795
Trimmed Mean ( 14 / 16 )0.6535486496328980.4042051966072181.6168734472456
Trimmed Mean ( 15 / 16 )0.6766787818022390.3926558272149921.72333818805581
Trimmed Mean ( 16 / 16 )0.7119329518904360.3804943802131351.87107350045918
Median1.15555932247655
Midrange-1.91106014386671
Midmean - Weighted Average at Xnp0.393958687064795
Midmean - Weighted Average at X(n+1)p0.592462664509296
Midmean - Empirical Distribution Function0.393958687064795
Midmean - Empirical Distribution Function - Averaging0.592462664509296
Midmean - Empirical Distribution Function - Interpolation0.592462664509296
Midmean - Closest Observation0.393958687064795
Midmean - True Basic - Statistics Graphics Toolkit0.592462664509296
Midmean - MS Excel (old versions)0.538584824062267
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.155714611730596 & 0.76229194736335 & -0.204271620957284 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -263.761352679518 &  &  \tabularnewline
Quadratic Mean & 5.22832962350422 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -0.163845113626332 & 0.756818833347025 & -0.216491855655505 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -0.120320513352658 & 0.741204826927123 & -0.162330990006476 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -0.100625870889438 & 0.724484771400463 & -0.138893010400927 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -0.029083620856211 & 0.702270144585813 & -0.0414137224548596 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.00770378035010033 & 0.686722882657459 & 0.0112181791879258 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.103677977344978 & 0.587875962234995 & 0.176360293676261 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.111651464251796 & 0.57600749356384 & 0.193836825908275 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.0820291682382395 & 0.554003907015911 & 0.148066046465415 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.134329491154395 & 0.530410255931823 & 0.253255832918249 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.204202004037257 & 0.504786012218958 & 0.404531819611281 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.242256701603608 & 0.495647159826453 & 0.488768465229241 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.410990088925125 & 0.462534465406096 & 0.888561003911965 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.473298249937983 & 0.382592664118181 & 1.23708135133449 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.532115455743855 & 0.345906115013027 & 1.53832335610435 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.500407931361255 & 0.320595634604449 & 1.56086944845228 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.577594079853169 & 0.291042747539535 & 1.98456785037981 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -0.0793952407681564 & 0.732643607782578 & -0.108368161442716 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.0127318932589442 & 0.70084453597437 & 0.0181665014213792 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.0887618398941456 & 0.670259218401597 & 0.132429122132510 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.164516924207579 & 0.638487919804027 & 0.257666463381288 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.225653938438249 & 0.605923278637223 & 0.372413383664291 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.283773980595089 & 0.567705928062331 & 0.499860872624061 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.326149510771586 & 0.553308713489273 & 0.589453053639483 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.372113377882969 & 0.536246576846433 & 0.69392215064812 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.430130219811915 & 0.518352820054595 & 0.82980202512762 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.486473215746681 & 0.499545381446809 & 0.973831875570008 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.538584824062267 & 0.479718127596251 & 1.12271101107015 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.592462664509296 & 0.451137849185729 & 1.3132630427233 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.625457678251872 & 0.419575429504108 & 1.49069186198795 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.653548649632898 & 0.404205196607218 & 1.6168734472456 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.676678781802239 & 0.392655827214992 & 1.72333818805581 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.711932951890436 & 0.380494380213135 & 1.87107350045918 \tabularnewline
Median & 1.15555932247655 &  &  \tabularnewline
Midrange & -1.91106014386671 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.393958687064795 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.592462664509296 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.393958687064795 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.592462664509296 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.592462664509296 &  &  \tabularnewline
Midmean - Closest Observation & 0.393958687064795 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.592462664509296 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.538584824062267 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3906&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]-0.155714611730596[/C][C]0.76229194736335[/C][C]-0.204271620957284[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-263.761352679518[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.22832962350422[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-0.163845113626332[/C][C]0.756818833347025[/C][C]-0.216491855655505[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-0.120320513352658[/C][C]0.741204826927123[/C][C]-0.162330990006476[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-0.100625870889438[/C][C]0.724484771400463[/C][C]-0.138893010400927[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-0.029083620856211[/C][C]0.702270144585813[/C][C]-0.0414137224548596[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.00770378035010033[/C][C]0.686722882657459[/C][C]0.0112181791879258[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.103677977344978[/C][C]0.587875962234995[/C][C]0.176360293676261[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.111651464251796[/C][C]0.57600749356384[/C][C]0.193836825908275[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.0820291682382395[/C][C]0.554003907015911[/C][C]0.148066046465415[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.134329491154395[/C][C]0.530410255931823[/C][C]0.253255832918249[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.204202004037257[/C][C]0.504786012218958[/C][C]0.404531819611281[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.242256701603608[/C][C]0.495647159826453[/C][C]0.488768465229241[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.410990088925125[/C][C]0.462534465406096[/C][C]0.888561003911965[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.473298249937983[/C][C]0.382592664118181[/C][C]1.23708135133449[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.532115455743855[/C][C]0.345906115013027[/C][C]1.53832335610435[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.500407931361255[/C][C]0.320595634604449[/C][C]1.56086944845228[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.577594079853169[/C][C]0.291042747539535[/C][C]1.98456785037981[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-0.0793952407681564[/C][C]0.732643607782578[/C][C]-0.108368161442716[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.0127318932589442[/C][C]0.70084453597437[/C][C]0.0181665014213792[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.0887618398941456[/C][C]0.670259218401597[/C][C]0.132429122132510[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.164516924207579[/C][C]0.638487919804027[/C][C]0.257666463381288[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.225653938438249[/C][C]0.605923278637223[/C][C]0.372413383664291[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.283773980595089[/C][C]0.567705928062331[/C][C]0.499860872624061[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.326149510771586[/C][C]0.553308713489273[/C][C]0.589453053639483[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.372113377882969[/C][C]0.536246576846433[/C][C]0.69392215064812[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.430130219811915[/C][C]0.518352820054595[/C][C]0.82980202512762[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.486473215746681[/C][C]0.499545381446809[/C][C]0.973831875570008[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.538584824062267[/C][C]0.479718127596251[/C][C]1.12271101107015[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.592462664509296[/C][C]0.451137849185729[/C][C]1.3132630427233[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.625457678251872[/C][C]0.419575429504108[/C][C]1.49069186198795[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.653548649632898[/C][C]0.404205196607218[/C][C]1.6168734472456[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.676678781802239[/C][C]0.392655827214992[/C][C]1.72333818805581[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.711932951890436[/C][C]0.380494380213135[/C][C]1.87107350045918[/C][/ROW]
[ROW][C]Median[/C][C]1.15555932247655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1.91106014386671[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.393958687064795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.592462664509296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.393958687064795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.592462664509296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.592462664509296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.393958687064795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.592462664509296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.538584824062267[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3906&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3906&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 Mean-0.1557146117305960.76229194736335-0.204271620957284
Geometric MeanNaN
Harmonic Mean-263.761352679518
Quadratic Mean5.22832962350422
Winsorized Mean ( 1 / 16 )-0.1638451136263320.756818833347025-0.216491855655505
Winsorized Mean ( 2 / 16 )-0.1203205133526580.741204826927123-0.162330990006476
Winsorized Mean ( 3 / 16 )-0.1006258708894380.724484771400463-0.138893010400927
Winsorized Mean ( 4 / 16 )-0.0290836208562110.702270144585813-0.0414137224548596
Winsorized Mean ( 5 / 16 )0.007703780350100330.6867228826574590.0112181791879258
Winsorized Mean ( 6 / 16 )0.1036779773449780.5878759622349950.176360293676261
Winsorized Mean ( 7 / 16 )0.1116514642517960.576007493563840.193836825908275
Winsorized Mean ( 8 / 16 )0.08202916823823950.5540039070159110.148066046465415
Winsorized Mean ( 9 / 16 )0.1343294911543950.5304102559318230.253255832918249
Winsorized Mean ( 10 / 16 )0.2042020040372570.5047860122189580.404531819611281
Winsorized Mean ( 11 / 16 )0.2422567016036080.4956471598264530.488768465229241
Winsorized Mean ( 12 / 16 )0.4109900889251250.4625344654060960.888561003911965
Winsorized Mean ( 13 / 16 )0.4732982499379830.3825926641181811.23708135133449
Winsorized Mean ( 14 / 16 )0.5321154557438550.3459061150130271.53832335610435
Winsorized Mean ( 15 / 16 )0.5004079313612550.3205956346044491.56086944845228
Winsorized Mean ( 16 / 16 )0.5775940798531690.2910427475395351.98456785037981
Trimmed Mean ( 1 / 16 )-0.07939524076815640.732643607782578-0.108368161442716
Trimmed Mean ( 2 / 16 )0.01273189325894420.700844535974370.0181665014213792
Trimmed Mean ( 3 / 16 )0.08876183989414560.6702592184015970.132429122132510
Trimmed Mean ( 4 / 16 )0.1645169242075790.6384879198040270.257666463381288
Trimmed Mean ( 5 / 16 )0.2256539384382490.6059232786372230.372413383664291
Trimmed Mean ( 6 / 16 )0.2837739805950890.5677059280623310.499860872624061
Trimmed Mean ( 7 / 16 )0.3261495107715860.5533087134892730.589453053639483
Trimmed Mean ( 8 / 16 )0.3721133778829690.5362465768464330.69392215064812
Trimmed Mean ( 9 / 16 )0.4301302198119150.5183528200545950.82980202512762
Trimmed Mean ( 10 / 16 )0.4864732157466810.4995453814468090.973831875570008
Trimmed Mean ( 11 / 16 )0.5385848240622670.4797181275962511.12271101107015
Trimmed Mean ( 12 / 16 )0.5924626645092960.4511378491857291.3132630427233
Trimmed Mean ( 13 / 16 )0.6254576782518720.4195754295041081.49069186198795
Trimmed Mean ( 14 / 16 )0.6535486496328980.4042051966072181.6168734472456
Trimmed Mean ( 15 / 16 )0.6766787818022390.3926558272149921.72333818805581
Trimmed Mean ( 16 / 16 )0.7119329518904360.3804943802131351.87107350045918
Median1.15555932247655
Midrange-1.91106014386671
Midmean - Weighted Average at Xnp0.393958687064795
Midmean - Weighted Average at X(n+1)p0.592462664509296
Midmean - Empirical Distribution Function0.393958687064795
Midmean - Empirical Distribution Function - Averaging0.592462664509296
Midmean - Empirical Distribution Function - Interpolation0.592462664509296
Midmean - Closest Observation0.393958687064795
Midmean - True Basic - Statistics Graphics Toolkit0.592462664509296
Midmean - MS Excel (old versions)0.538584824062267
Number of observations48



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')