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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 computationWed, 16 Nov 2011 09:25:35 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/16/t1321453556dndiuauezaofuml.htm/, Retrieved Thu, 28 Mar 2024 20:55:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143969, Retrieved Thu, 28 Mar 2024 20:55:06 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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- RMPD    [Central Tendency] [] [2011-11-16 14:25:35] [aedc5b8e4f26bdca34b1a0cf88d6dfa2] [Current]
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Dataseries X:
33.865	
	32.226	
	31.077	
	31.293	
	30.236	
	30.160	
	32.436	
	30.695	
	27.525	
	26.434	
	25.739	
	25.204	
	24.977	
	24.320	
	22.680	
	22.052	
	21.467	
	21.383	
	21.777	
	21.928	
	21.814	
	22.937	
	23.595	
	20.830	
	19.650	
	19.195	
	19.644	
	18.483	
	18.079	
	19.178	
	18.391	
	18.441	
	18.584	
	20.108	
	20.148	
	19.394	
	17.745	
	17.696	
	17.032	
	16.438	
	15.683	
	15.594	
	15.713	
	15.937	
	16.171	
	15.928	
	16.348	
	15.579	
	15.305	
	15.648	
	14.954	
	15.137	
	15.839	
	16.050	
	15.168	
	17.064	
	16.005	
	14.886	
	14.931	
	14.544	
	13.812	




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143969&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143969&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143969&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.51068852459020.69683035604396829.4342638013548
Geometric Mean19.8757774258878
Harmonic Mean19.3177347570613
Quadratic Mean21.2090239393287
Winsorized Mean ( 1 / 20 )20.4992622950820.68787149204174629.8010057579736
Winsorized Mean ( 2 / 20 )20.50359016393440.68431674686661329.9621341401002
Winsorized Mean ( 3 / 20 )20.45991803278690.67128895682055230.4785559555335
Winsorized Mean ( 4 / 20 )20.4472622950820.66729691325380430.6419254891787
Winsorized Mean ( 5 / 20 )20.43095081967210.65702722844752631.0960488927498
Winsorized Mean ( 6 / 20 )20.38885245901640.64499423932534331.6109062932762
Winsorized Mean ( 7 / 20 )20.39585245901640.6406754819208131.8349196037088
Winsorized Mean ( 8 / 20 )20.08621311475410.55284296286808436.3325835071667
Winsorized Mean ( 9 / 20 )19.92745901639340.51758758535175238.5006510595704
Winsorized Mean ( 10 / 20 )19.82237704918030.49300225127448740.2074777507332
Winsorized Mean ( 11 / 20 )19.73221311475410.47315375746662341.7035959312783
Winsorized Mean ( 12 / 20 )19.69345901639340.46376706371256542.464117349651
Winsorized Mean ( 13 / 20 )19.58029508196720.4338591656263145.1305322862121
Winsorized Mean ( 14 / 20 )19.43432786885250.40135230883102648.4221155359904
Winsorized Mean ( 15 / 20 )19.2747377049180.37381139198378151.5627348932007
Winsorized Mean ( 16 / 20 )19.22516393442620.36026304762842153.3642405486317
Winsorized Mean ( 17 / 20 )19.06268852459020.33119405810001557.5574593153889
Winsorized Mean ( 18 / 20 )19.06180327868850.32032099919363959.5084409909866
Winsorized Mean ( 19 / 20 )19.08142622950820.30679689482955762.1956302397031
Winsorized Mean ( 20 / 20 )19.09880327868850.30062843178884663.5295975335528
Trimmed Mean ( 1 / 20 )20.39788135593220.67371859238191430.2765599563106
Trimmed Mean ( 2 / 20 )20.28938596491230.65593957307843330.9317912771916
Trimmed Mean ( 3 / 20 )20.17060.63588641998754731.7204446674534
Trimmed Mean ( 4 / 20 )20.05960377358490.61697971937628732.5125820891867
Trimmed Mean ( 5 / 20 )19.94368627450980.59441004628923133.5520679689278
Trimmed Mean ( 6 / 20 )19.82236734693880.56902703964621534.835545529195
Trimmed Mean ( 7 / 20 )19.6998297872340.54013122426468736.4723032149319
Trimmed Mean ( 8 / 20 )19.56504444444440.50312078188763838.887370883467
Trimmed Mean ( 9 / 20 )19.47262790697670.4831500401180440.3034798511438
Trimmed Mean ( 10 / 20 )19.39743902439020.4671171904048141.5258513769963
Trimmed Mean ( 11 / 20 )19.33097435897440.45246328127305242.7238522087022
Trimmed Mean ( 12 / 20 )19.27083783783780.43793945156094844.0034296274309
Trimmed Mean ( 13 / 20 )19.20945714285710.42019923314329645.7151170866282
Trimmed Mean ( 14 / 20 )19.15672727272730.4042222898448847.3915658636209
Trimmed Mean ( 15 / 20 )19.11770967741940.3912698906099948.8606717159218
Trimmed Mean ( 16 / 20 )19.09568965517240.38065558597194750.1652684444771
Trimmed Mean ( 17 / 20 )19.07740740740740.36835094229965851.7913902657745
Trimmed Mean ( 18 / 20 )19.079520.35878393739593953.1783003957187
Trimmed Mean ( 19 / 20 )19.08213043478260.3462448601484855.1116641171211
Trimmed Mean ( 20 / 20 )19.08223809523810.32994762863479357.8341422673461
Median19.178
Midrange23.8385
Midmean - Weighted Average at Xnp18.9904
Midmean - Weighted Average at X(n+1)p19.1177096774194
Midmean - Empirical Distribution Function19.1177096774194
Midmean - Empirical Distribution Function - Averaging19.1177096774194
Midmean - Empirical Distribution Function - Interpolation19.1177096774194
Midmean - Closest Observation19.01803125
Midmean - True Basic - Statistics Graphics Toolkit19.1177096774194
Midmean - MS Excel (old versions)19.1177096774194
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.5106885245902 & 0.696830356043968 & 29.4342638013548 \tabularnewline
Geometric Mean & 19.8757774258878 &  &  \tabularnewline
Harmonic Mean & 19.3177347570613 &  &  \tabularnewline
Quadratic Mean & 21.2090239393287 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 20.499262295082 & 0.687871492041746 & 29.8010057579736 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 20.5035901639344 & 0.684316746866613 & 29.9621341401002 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 20.4599180327869 & 0.671288956820552 & 30.4785559555335 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 20.447262295082 & 0.667296913253804 & 30.6419254891787 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 20.4309508196721 & 0.657027228447526 & 31.0960488927498 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 20.3888524590164 & 0.644994239325343 & 31.6109062932762 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 20.3958524590164 & 0.64067548192081 & 31.8349196037088 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 20.0862131147541 & 0.552842962868084 & 36.3325835071667 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 19.9274590163934 & 0.517587585351752 & 38.5006510595704 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 19.8223770491803 & 0.493002251274487 & 40.2074777507332 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 19.7322131147541 & 0.473153757466623 & 41.7035959312783 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 19.6934590163934 & 0.463767063712565 & 42.464117349651 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 19.5802950819672 & 0.43385916562631 & 45.1305322862121 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 19.4343278688525 & 0.401352308831026 & 48.4221155359904 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 19.274737704918 & 0.373811391983781 & 51.5627348932007 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 19.2251639344262 & 0.360263047628421 & 53.3642405486317 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 19.0626885245902 & 0.331194058100015 & 57.5574593153889 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 19.0618032786885 & 0.320320999193639 & 59.5084409909866 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 19.0814262295082 & 0.306796894829557 & 62.1956302397031 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 19.0988032786885 & 0.300628431788846 & 63.5295975335528 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 20.3978813559322 & 0.673718592381914 & 30.2765599563106 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 20.2893859649123 & 0.655939573078433 & 30.9317912771916 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 20.1706 & 0.635886419987547 & 31.7204446674534 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 20.0596037735849 & 0.616979719376287 & 32.5125820891867 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 19.9436862745098 & 0.594410046289231 & 33.5520679689278 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 19.8223673469388 & 0.569027039646215 & 34.835545529195 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 19.699829787234 & 0.540131224264687 & 36.4723032149319 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 19.5650444444444 & 0.503120781887638 & 38.887370883467 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 19.4726279069767 & 0.48315004011804 & 40.3034798511438 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 19.3974390243902 & 0.46711719040481 & 41.5258513769963 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 19.3309743589744 & 0.452463281273052 & 42.7238522087022 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 19.2708378378378 & 0.437939451560948 & 44.0034296274309 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 19.2094571428571 & 0.420199233143296 & 45.7151170866282 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 19.1567272727273 & 0.40422228984488 & 47.3915658636209 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 19.1177096774194 & 0.39126989060999 & 48.8606717159218 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 19.0956896551724 & 0.380655585971947 & 50.1652684444771 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 19.0774074074074 & 0.368350942299658 & 51.7913902657745 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 19.07952 & 0.358783937395939 & 53.1783003957187 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 19.0821304347826 & 0.34624486014848 & 55.1116641171211 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 19.0822380952381 & 0.329947628634793 & 57.8341422673461 \tabularnewline
Median & 19.178 &  &  \tabularnewline
Midrange & 23.8385 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.9904 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.1177096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.1177096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.1177096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.1177096774194 &  &  \tabularnewline
Midmean - Closest Observation & 19.01803125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.1177096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.1177096774194 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143969&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]20.5106885245902[/C][C]0.696830356043968[/C][C]29.4342638013548[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19.8757774258878[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19.3177347570613[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.2090239393287[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]20.499262295082[/C][C]0.687871492041746[/C][C]29.8010057579736[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]20.5035901639344[/C][C]0.684316746866613[/C][C]29.9621341401002[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]20.4599180327869[/C][C]0.671288956820552[/C][C]30.4785559555335[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]20.447262295082[/C][C]0.667296913253804[/C][C]30.6419254891787[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]20.4309508196721[/C][C]0.657027228447526[/C][C]31.0960488927498[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]20.3888524590164[/C][C]0.644994239325343[/C][C]31.6109062932762[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]20.3958524590164[/C][C]0.64067548192081[/C][C]31.8349196037088[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]20.0862131147541[/C][C]0.552842962868084[/C][C]36.3325835071667[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]19.9274590163934[/C][C]0.517587585351752[/C][C]38.5006510595704[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]19.8223770491803[/C][C]0.493002251274487[/C][C]40.2074777507332[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]19.7322131147541[/C][C]0.473153757466623[/C][C]41.7035959312783[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]19.6934590163934[/C][C]0.463767063712565[/C][C]42.464117349651[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]19.5802950819672[/C][C]0.43385916562631[/C][C]45.1305322862121[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]19.4343278688525[/C][C]0.401352308831026[/C][C]48.4221155359904[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]19.274737704918[/C][C]0.373811391983781[/C][C]51.5627348932007[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]19.2251639344262[/C][C]0.360263047628421[/C][C]53.3642405486317[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]19.0626885245902[/C][C]0.331194058100015[/C][C]57.5574593153889[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]19.0618032786885[/C][C]0.320320999193639[/C][C]59.5084409909866[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]19.0814262295082[/C][C]0.306796894829557[/C][C]62.1956302397031[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]19.0988032786885[/C][C]0.300628431788846[/C][C]63.5295975335528[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]20.3978813559322[/C][C]0.673718592381914[/C][C]30.2765599563106[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]20.2893859649123[/C][C]0.655939573078433[/C][C]30.9317912771916[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]20.1706[/C][C]0.635886419987547[/C][C]31.7204446674534[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]20.0596037735849[/C][C]0.616979719376287[/C][C]32.5125820891867[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]19.9436862745098[/C][C]0.594410046289231[/C][C]33.5520679689278[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]19.8223673469388[/C][C]0.569027039646215[/C][C]34.835545529195[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]19.699829787234[/C][C]0.540131224264687[/C][C]36.4723032149319[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]19.5650444444444[/C][C]0.503120781887638[/C][C]38.887370883467[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]19.4726279069767[/C][C]0.48315004011804[/C][C]40.3034798511438[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]19.3974390243902[/C][C]0.46711719040481[/C][C]41.5258513769963[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]19.3309743589744[/C][C]0.452463281273052[/C][C]42.7238522087022[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]19.2708378378378[/C][C]0.437939451560948[/C][C]44.0034296274309[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]19.2094571428571[/C][C]0.420199233143296[/C][C]45.7151170866282[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]19.1567272727273[/C][C]0.40422228984488[/C][C]47.3915658636209[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]19.1177096774194[/C][C]0.39126989060999[/C][C]48.8606717159218[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]19.0956896551724[/C][C]0.380655585971947[/C][C]50.1652684444771[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]19.0774074074074[/C][C]0.368350942299658[/C][C]51.7913902657745[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]19.07952[/C][C]0.358783937395939[/C][C]53.1783003957187[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]19.0821304347826[/C][C]0.34624486014848[/C][C]55.1116641171211[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]19.0822380952381[/C][C]0.329947628634793[/C][C]57.8341422673461[/C][/ROW]
[ROW][C]Median[/C][C]19.178[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]23.8385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.9904[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.1177096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.1177096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.1177096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.1177096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.01803125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.1177096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.1177096774194[/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=143969&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143969&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 Mean20.51068852459020.69683035604396829.4342638013548
Geometric Mean19.8757774258878
Harmonic Mean19.3177347570613
Quadratic Mean21.2090239393287
Winsorized Mean ( 1 / 20 )20.4992622950820.68787149204174629.8010057579736
Winsorized Mean ( 2 / 20 )20.50359016393440.68431674686661329.9621341401002
Winsorized Mean ( 3 / 20 )20.45991803278690.67128895682055230.4785559555335
Winsorized Mean ( 4 / 20 )20.4472622950820.66729691325380430.6419254891787
Winsorized Mean ( 5 / 20 )20.43095081967210.65702722844752631.0960488927498
Winsorized Mean ( 6 / 20 )20.38885245901640.64499423932534331.6109062932762
Winsorized Mean ( 7 / 20 )20.39585245901640.6406754819208131.8349196037088
Winsorized Mean ( 8 / 20 )20.08621311475410.55284296286808436.3325835071667
Winsorized Mean ( 9 / 20 )19.92745901639340.51758758535175238.5006510595704
Winsorized Mean ( 10 / 20 )19.82237704918030.49300225127448740.2074777507332
Winsorized Mean ( 11 / 20 )19.73221311475410.47315375746662341.7035959312783
Winsorized Mean ( 12 / 20 )19.69345901639340.46376706371256542.464117349651
Winsorized Mean ( 13 / 20 )19.58029508196720.4338591656263145.1305322862121
Winsorized Mean ( 14 / 20 )19.43432786885250.40135230883102648.4221155359904
Winsorized Mean ( 15 / 20 )19.2747377049180.37381139198378151.5627348932007
Winsorized Mean ( 16 / 20 )19.22516393442620.36026304762842153.3642405486317
Winsorized Mean ( 17 / 20 )19.06268852459020.33119405810001557.5574593153889
Winsorized Mean ( 18 / 20 )19.06180327868850.32032099919363959.5084409909866
Winsorized Mean ( 19 / 20 )19.08142622950820.30679689482955762.1956302397031
Winsorized Mean ( 20 / 20 )19.09880327868850.30062843178884663.5295975335528
Trimmed Mean ( 1 / 20 )20.39788135593220.67371859238191430.2765599563106
Trimmed Mean ( 2 / 20 )20.28938596491230.65593957307843330.9317912771916
Trimmed Mean ( 3 / 20 )20.17060.63588641998754731.7204446674534
Trimmed Mean ( 4 / 20 )20.05960377358490.61697971937628732.5125820891867
Trimmed Mean ( 5 / 20 )19.94368627450980.59441004628923133.5520679689278
Trimmed Mean ( 6 / 20 )19.82236734693880.56902703964621534.835545529195
Trimmed Mean ( 7 / 20 )19.6998297872340.54013122426468736.4723032149319
Trimmed Mean ( 8 / 20 )19.56504444444440.50312078188763838.887370883467
Trimmed Mean ( 9 / 20 )19.47262790697670.4831500401180440.3034798511438
Trimmed Mean ( 10 / 20 )19.39743902439020.4671171904048141.5258513769963
Trimmed Mean ( 11 / 20 )19.33097435897440.45246328127305242.7238522087022
Trimmed Mean ( 12 / 20 )19.27083783783780.43793945156094844.0034296274309
Trimmed Mean ( 13 / 20 )19.20945714285710.42019923314329645.7151170866282
Trimmed Mean ( 14 / 20 )19.15672727272730.4042222898448847.3915658636209
Trimmed Mean ( 15 / 20 )19.11770967741940.3912698906099948.8606717159218
Trimmed Mean ( 16 / 20 )19.09568965517240.38065558597194750.1652684444771
Trimmed Mean ( 17 / 20 )19.07740740740740.36835094229965851.7913902657745
Trimmed Mean ( 18 / 20 )19.079520.35878393739593953.1783003957187
Trimmed Mean ( 19 / 20 )19.08213043478260.3462448601484855.1116641171211
Trimmed Mean ( 20 / 20 )19.08223809523810.32994762863479357.8341422673461
Median19.178
Midrange23.8385
Midmean - Weighted Average at Xnp18.9904
Midmean - Weighted Average at X(n+1)p19.1177096774194
Midmean - Empirical Distribution Function19.1177096774194
Midmean - Empirical Distribution Function - Averaging19.1177096774194
Midmean - Empirical Distribution Function - Interpolation19.1177096774194
Midmean - Closest Observation19.01803125
Midmean - True Basic - Statistics Graphics Toolkit19.1177096774194
Midmean - MS Excel (old versions)19.1177096774194
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')