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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, 06 Dec 2009 11:25:02 -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/06/t1260123992e48pewcf7ho7idb.htm/, Retrieved Mon, 06 May 2024 02:40:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64468, Retrieved Mon, 06 May 2024 02:40:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsETP(30)
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper statistiek:...] [2009-12-06 18:25:02] [af31b947d6acaef3c71f428c4bb503e9] [Current]
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Dataseries X:
0.0239732542744507
0.0208376482783286
0.0177020422821997
0.0145664362860704
0.000881931884234765
-0.00225367411189447
0.0046107198919763
0.0309262154901407
0.0277906094940115
0.0352039019035886
0.0320682959074594
0.0289326899113301
0.0257970839152009
0.0226614779190717
0.0195258719229424
0.0163902659268132
0.0132546599306839
0.0101190539345547
0.00698344793842546
-0.00670105646341016
-0.0098366624595394
-0.0129722684556686
-0.0266567728575043
-0.0297923788536335
-0.0329279848497627
-0.036063590845892
-0.0391991968420212
-0.0423348028381505
-0.0454704088342797
-0.0486060148304089
-0.0517416208265382
-0.0548772268226674
-0.0474639344130903
-0.0505995404092195
-0.0537351464053487
-0.056870752401478
-0.0600063583976072
0.0163091372005572
0.0126246327987216
0.00948902680259236
0.00635342080646312
0.00321781481033388
0.0100822088142047
0.0169466028180754
0.0138109968219462
0.0206753908258170
0.00699088642398134
0.0038552804278521
0.0107196744317229
0.0175840684355934
0.0144484624394642
0.0318617548490413
0.0181772504472057
0.0255905428567828
0.0224549368606536
0.008770432458818
0.0261837248683951
0.0230481188722659
0.0199125128761366
0.0167769068800074




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=64468&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=64468&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64468&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 Mean1.91881196984674e-180.003665894661758565.23422560354277e-16
Geometric MeanNaN
Harmonic Mean0.0187083935328924
Quadratic Mean0.028158271193301
Winsorized Mean ( 1 / 20 )1.96601993944038e-180.003643579389585375.39584767950976e-16
Winsorized Mean ( 2 / 20 )5.95661506797519e-050.003625229716519060.0164310003331174
Winsorized Mean ( 3 / 20 )6.98932036006572e-050.003603798768620280.0193943136362788
Winsorized Mean ( 4 / 20 )6.989320360065e-050.003551751001649890.0196785201350496
Winsorized Mean ( 5 / 20 )6.98932036006581e-050.003515444073546460.0198817566539036
Winsorized Mean ( 6 / 20 )0.0001085572989200780.003446161316627550.0315009336319501
Winsorized Mean ( 7 / 20 )0.0001966919030679250.003408646436888650.0577038149041534
Winsorized Mean ( 8 / 20 )0.0004349565057869250.003342701238314240.130121262648731
Winsorized Mean ( 9 / 20 )0.000662704117856490.003204004978549960.206836169822811
Winsorized Mean ( 10 / 20 )0.001031115883513910.003067570296259820.336134394302589
Winsorized Mean ( 11 / 20 )0.001535092808051990.002932547391356040.523467348755155
Winsorized Mean ( 12 / 20 )0.002120905795594230.002792601388496970.75947315801334
Winsorized Mean ( 13 / 20 )0.002449874568585140.002606490523443930.939913092547193
Winsorized Mean ( 14 / 20 )0.003143655895429250.002449769508689681.28324558056513
Winsorized Mean ( 15 / 20 )0.006374062508468070.001746754452204553.64908902932719
Winsorized Mean ( 16 / 20 )0.007107119853250740.001578441726315714.50261782539144
Winsorized Mean ( 17 / 20 )0.007613432134028620.001368190912292015.56459779525544
Winsorized Mean ( 18 / 20 )0.008805084389981530.001118542488726777.87192661765068
Winsorized Mean ( 19 / 20 )0.009760667903997130.00095132094956435510.2601208440400
Winsorized Mean ( 20 / 20 )0.01032680700685750.00080125093491408712.8883556410013
Trimmed Mean ( 1 / 20 )0.0004276285602417020.003594822611291290.118956790496011
Trimmed Mean ( 2 / 20 )0.0008858020176435230.003532162899477940.250781756915698
Trimmed Mean ( 3 / 20 )0.001344821943734510.003464213342523450.388204134897446
Trimmed Mean ( 4 / 20 )0.001835179151478300.003387095679273110.54181497225143
Trimmed Mean ( 5 / 20 )0.002364764935841590.003307757031296590.714914944921042
Trimmed Mean ( 6 / 20 )0.002938482868901820.003216382880906400.913598591245372
Trimmed Mean ( 7 / 20 )0.003553684079767420.003117970496887161.13974268945625
Trimmed Mean ( 8 / 20 )0.004207643594708880.002998204046047331.40338800498118
Trimmed Mean ( 9 / 20 )0.004881337717730660.002857780593260851.70808694314802
Trimmed Mean ( 10 / 20 )0.005584443317709680.002709170013725892.06131150478425
Trimmed Mean ( 11 / 20 )0.006303389754687970.002546799988301682.47502347402292
Trimmed Mean ( 12 / 20 )0.007025858989026750.002363452659263972.97270984527134
Trimmed Mean ( 13 / 20 )0.007747175635119770.002149946828521413.60342662076335
Trimmed Mean ( 14 / 20 )0.008511209442793030.001901540632206084.47595454897995
Trimmed Mean ( 15 / 20 )0.009278002806702140.001584601357476805.85510214472851
Trimmed Mean ( 16 / 20 )0.009692851420735580.001441794110315356.72277085291711
Trimmed Mean ( 17 / 20 )0.01006579347373820.001294867904875747.77360643184999
Trimmed Mean ( 18 / 20 )0.01042643484722490.001157677112116139.00634100657504
Trimmed Mean ( 19 / 20 )0.01067209400741330.0010657518770201310.0136760136447
Trimmed Mean ( 20 / 20 )0.01081600339216320.0010009406630548110.8058387388853
Median0.0104193641831388
Midrange-0.0124012282470093
Midmean - Weighted Average at Xnp0.00811881649495355
Midmean - Weighted Average at X(n+1)p0.00927800280670214
Midmean - Empirical Distribution Function0.00811881649495355
Midmean - Empirical Distribution Function - Averaging0.00927800280670214
Midmean - Empirical Distribution Function - Interpolation0.00927800280670214
Midmean - Closest Observation0.00811881649495355
Midmean - True Basic - Statistics Graphics Toolkit0.00927800280670214
Midmean - MS Excel (old versions)0.00851120944279303
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.91881196984674e-18 & 0.00366589466175856 & 5.23422560354277e-16 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.0187083935328924 &  &  \tabularnewline
Quadratic Mean & 0.028158271193301 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.96601993944038e-18 & 0.00364357938958537 & 5.39584767950976e-16 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 5.95661506797519e-05 & 0.00362522971651906 & 0.0164310003331174 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6.98932036006572e-05 & 0.00360379876862028 & 0.0193943136362788 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6.989320360065e-05 & 0.00355175100164989 & 0.0196785201350496 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6.98932036006581e-05 & 0.00351544407354646 & 0.0198817566539036 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.000108557298920078 & 0.00344616131662755 & 0.0315009336319501 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.000196691903067925 & 0.00340864643688865 & 0.0577038149041534 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.000434956505786925 & 0.00334270123831424 & 0.130121262648731 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.00066270411785649 & 0.00320400497854996 & 0.206836169822811 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.00103111588351391 & 0.00306757029625982 & 0.336134394302589 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.00153509280805199 & 0.00293254739135604 & 0.523467348755155 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.00212090579559423 & 0.00279260138849697 & 0.75947315801334 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.00244987456858514 & 0.00260649052344393 & 0.939913092547193 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.00314365589542925 & 0.00244976950868968 & 1.28324558056513 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.00637406250846807 & 0.00174675445220455 & 3.64908902932719 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.00710711985325074 & 0.00157844172631571 & 4.50261782539144 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.00761343213402862 & 0.00136819091229201 & 5.56459779525544 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.00880508438998153 & 0.00111854248872677 & 7.87192661765068 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.00976066790399713 & 0.000951320949564355 & 10.2601208440400 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.0103268070068575 & 0.000801250934914087 & 12.8883556410013 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.000427628560241702 & 0.00359482261129129 & 0.118956790496011 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.000885802017643523 & 0.00353216289947794 & 0.250781756915698 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.00134482194373451 & 0.00346421334252345 & 0.388204134897446 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.00183517915147830 & 0.00338709567927311 & 0.54181497225143 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.00236476493584159 & 0.00330775703129659 & 0.714914944921042 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.00293848286890182 & 0.00321638288090640 & 0.913598591245372 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.00355368407976742 & 0.00311797049688716 & 1.13974268945625 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.00420764359470888 & 0.00299820404604733 & 1.40338800498118 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.00488133771773066 & 0.00285778059326085 & 1.70808694314802 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.00558444331770968 & 0.00270917001372589 & 2.06131150478425 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.00630338975468797 & 0.00254679998830168 & 2.47502347402292 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.00702585898902675 & 0.00236345265926397 & 2.97270984527134 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.00774717563511977 & 0.00214994682852141 & 3.60342662076335 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.00851120944279303 & 0.00190154063220608 & 4.47595454897995 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.00927800280670214 & 0.00158460135747680 & 5.85510214472851 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.00969285142073558 & 0.00144179411031535 & 6.72277085291711 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.0100657934737382 & 0.00129486790487574 & 7.77360643184999 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.0104264348472249 & 0.00115767711211613 & 9.00634100657504 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.0106720940074133 & 0.00106575187702013 & 10.0136760136447 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.0108160033921632 & 0.00100094066305481 & 10.8058387388853 \tabularnewline
Median & 0.0104193641831388 &  &  \tabularnewline
Midrange & -0.0124012282470093 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.00811881649495355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.00927800280670214 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.00811881649495355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.00927800280670214 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.00927800280670214 &  &  \tabularnewline
Midmean - Closest Observation & 0.00811881649495355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.00927800280670214 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.00851120944279303 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64468&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]1.91881196984674e-18[/C][C]0.00366589466175856[/C][C]5.23422560354277e-16[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.0187083935328924[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.028158271193301[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.96601993944038e-18[/C][C]0.00364357938958537[/C][C]5.39584767950976e-16[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]5.95661506797519e-05[/C][C]0.00362522971651906[/C][C]0.0164310003331174[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6.98932036006572e-05[/C][C]0.00360379876862028[/C][C]0.0193943136362788[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6.989320360065e-05[/C][C]0.00355175100164989[/C][C]0.0196785201350496[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6.98932036006581e-05[/C][C]0.00351544407354646[/C][C]0.0198817566539036[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.000108557298920078[/C][C]0.00344616131662755[/C][C]0.0315009336319501[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.000196691903067925[/C][C]0.00340864643688865[/C][C]0.0577038149041534[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.000434956505786925[/C][C]0.00334270123831424[/C][C]0.130121262648731[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.00066270411785649[/C][C]0.00320400497854996[/C][C]0.206836169822811[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.00103111588351391[/C][C]0.00306757029625982[/C][C]0.336134394302589[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.00153509280805199[/C][C]0.00293254739135604[/C][C]0.523467348755155[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.00212090579559423[/C][C]0.00279260138849697[/C][C]0.75947315801334[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.00244987456858514[/C][C]0.00260649052344393[/C][C]0.939913092547193[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.00314365589542925[/C][C]0.00244976950868968[/C][C]1.28324558056513[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.00637406250846807[/C][C]0.00174675445220455[/C][C]3.64908902932719[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.00710711985325074[/C][C]0.00157844172631571[/C][C]4.50261782539144[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.00761343213402862[/C][C]0.00136819091229201[/C][C]5.56459779525544[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.00880508438998153[/C][C]0.00111854248872677[/C][C]7.87192661765068[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.00976066790399713[/C][C]0.000951320949564355[/C][C]10.2601208440400[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.0103268070068575[/C][C]0.000801250934914087[/C][C]12.8883556410013[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.000427628560241702[/C][C]0.00359482261129129[/C][C]0.118956790496011[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.000885802017643523[/C][C]0.00353216289947794[/C][C]0.250781756915698[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.00134482194373451[/C][C]0.00346421334252345[/C][C]0.388204134897446[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.00183517915147830[/C][C]0.00338709567927311[/C][C]0.54181497225143[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.00236476493584159[/C][C]0.00330775703129659[/C][C]0.714914944921042[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.00293848286890182[/C][C]0.00321638288090640[/C][C]0.913598591245372[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.00355368407976742[/C][C]0.00311797049688716[/C][C]1.13974268945625[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.00420764359470888[/C][C]0.00299820404604733[/C][C]1.40338800498118[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.00488133771773066[/C][C]0.00285778059326085[/C][C]1.70808694314802[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.00558444331770968[/C][C]0.00270917001372589[/C][C]2.06131150478425[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.00630338975468797[/C][C]0.00254679998830168[/C][C]2.47502347402292[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.00702585898902675[/C][C]0.00236345265926397[/C][C]2.97270984527134[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.00774717563511977[/C][C]0.00214994682852141[/C][C]3.60342662076335[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.00851120944279303[/C][C]0.00190154063220608[/C][C]4.47595454897995[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.00927800280670214[/C][C]0.00158460135747680[/C][C]5.85510214472851[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.00969285142073558[/C][C]0.00144179411031535[/C][C]6.72277085291711[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.0100657934737382[/C][C]0.00129486790487574[/C][C]7.77360643184999[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.0104264348472249[/C][C]0.00115767711211613[/C][C]9.00634100657504[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.0106720940074133[/C][C]0.00106575187702013[/C][C]10.0136760136447[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.0108160033921632[/C][C]0.00100094066305481[/C][C]10.8058387388853[/C][/ROW]
[ROW][C]Median[/C][C]0.0104193641831388[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.0124012282470093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.00811881649495355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.00927800280670214[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.00811881649495355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.00927800280670214[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.00927800280670214[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.00811881649495355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.00927800280670214[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.00851120944279303[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64468&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64468&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 Mean1.91881196984674e-180.003665894661758565.23422560354277e-16
Geometric MeanNaN
Harmonic Mean0.0187083935328924
Quadratic Mean0.028158271193301
Winsorized Mean ( 1 / 20 )1.96601993944038e-180.003643579389585375.39584767950976e-16
Winsorized Mean ( 2 / 20 )5.95661506797519e-050.003625229716519060.0164310003331174
Winsorized Mean ( 3 / 20 )6.98932036006572e-050.003603798768620280.0193943136362788
Winsorized Mean ( 4 / 20 )6.989320360065e-050.003551751001649890.0196785201350496
Winsorized Mean ( 5 / 20 )6.98932036006581e-050.003515444073546460.0198817566539036
Winsorized Mean ( 6 / 20 )0.0001085572989200780.003446161316627550.0315009336319501
Winsorized Mean ( 7 / 20 )0.0001966919030679250.003408646436888650.0577038149041534
Winsorized Mean ( 8 / 20 )0.0004349565057869250.003342701238314240.130121262648731
Winsorized Mean ( 9 / 20 )0.000662704117856490.003204004978549960.206836169822811
Winsorized Mean ( 10 / 20 )0.001031115883513910.003067570296259820.336134394302589
Winsorized Mean ( 11 / 20 )0.001535092808051990.002932547391356040.523467348755155
Winsorized Mean ( 12 / 20 )0.002120905795594230.002792601388496970.75947315801334
Winsorized Mean ( 13 / 20 )0.002449874568585140.002606490523443930.939913092547193
Winsorized Mean ( 14 / 20 )0.003143655895429250.002449769508689681.28324558056513
Winsorized Mean ( 15 / 20 )0.006374062508468070.001746754452204553.64908902932719
Winsorized Mean ( 16 / 20 )0.007107119853250740.001578441726315714.50261782539144
Winsorized Mean ( 17 / 20 )0.007613432134028620.001368190912292015.56459779525544
Winsorized Mean ( 18 / 20 )0.008805084389981530.001118542488726777.87192661765068
Winsorized Mean ( 19 / 20 )0.009760667903997130.00095132094956435510.2601208440400
Winsorized Mean ( 20 / 20 )0.01032680700685750.00080125093491408712.8883556410013
Trimmed Mean ( 1 / 20 )0.0004276285602417020.003594822611291290.118956790496011
Trimmed Mean ( 2 / 20 )0.0008858020176435230.003532162899477940.250781756915698
Trimmed Mean ( 3 / 20 )0.001344821943734510.003464213342523450.388204134897446
Trimmed Mean ( 4 / 20 )0.001835179151478300.003387095679273110.54181497225143
Trimmed Mean ( 5 / 20 )0.002364764935841590.003307757031296590.714914944921042
Trimmed Mean ( 6 / 20 )0.002938482868901820.003216382880906400.913598591245372
Trimmed Mean ( 7 / 20 )0.003553684079767420.003117970496887161.13974268945625
Trimmed Mean ( 8 / 20 )0.004207643594708880.002998204046047331.40338800498118
Trimmed Mean ( 9 / 20 )0.004881337717730660.002857780593260851.70808694314802
Trimmed Mean ( 10 / 20 )0.005584443317709680.002709170013725892.06131150478425
Trimmed Mean ( 11 / 20 )0.006303389754687970.002546799988301682.47502347402292
Trimmed Mean ( 12 / 20 )0.007025858989026750.002363452659263972.97270984527134
Trimmed Mean ( 13 / 20 )0.007747175635119770.002149946828521413.60342662076335
Trimmed Mean ( 14 / 20 )0.008511209442793030.001901540632206084.47595454897995
Trimmed Mean ( 15 / 20 )0.009278002806702140.001584601357476805.85510214472851
Trimmed Mean ( 16 / 20 )0.009692851420735580.001441794110315356.72277085291711
Trimmed Mean ( 17 / 20 )0.01006579347373820.001294867904875747.77360643184999
Trimmed Mean ( 18 / 20 )0.01042643484722490.001157677112116139.00634100657504
Trimmed Mean ( 19 / 20 )0.01067209400741330.0010657518770201310.0136760136447
Trimmed Mean ( 20 / 20 )0.01081600339216320.0010009406630548110.8058387388853
Median0.0104193641831388
Midrange-0.0124012282470093
Midmean - Weighted Average at Xnp0.00811881649495355
Midmean - Weighted Average at X(n+1)p0.00927800280670214
Midmean - Empirical Distribution Function0.00811881649495355
Midmean - Empirical Distribution Function - Averaging0.00927800280670214
Midmean - Empirical Distribution Function - Interpolation0.00927800280670214
Midmean - Closest Observation0.00811881649495355
Midmean - True Basic - Statistics Graphics Toolkit0.00927800280670214
Midmean - MS Excel (old versions)0.00851120944279303
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')