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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, 20 Dec 2009 16:15:18 -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/21/t1261350958rxkapp2facltpf8.htm/, Retrieved Sun, 05 May 2024 12:05:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70046, Retrieved Sun, 05 May 2024 12:05:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-12-20 23:15:18] [71596e6a53ccce532e52aaf6113616ef] [Current]
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Dataseries X:
2.15418755068342
-1.20867705435185
2.23402074997159
-0.315227856696888
-2.05471111867122
-0.188755235805451
-1.70607988548339
1.31473818526770
4.24600077923484
3.01614099882724
-1.88865472594506
-1.17988420280436
2.93517243273008
3.81666419198670
2.37339834074884
-2.64727172073952
-1.57580042750357
2.23831035286297
-2.32836444385928
-5.05451947276176
-7.29938271711795
1.24786578858060
-1.85142811909361
2.43220645318740
-5.62593007807252
-0.664726380986282
0.641476856006124
-5.6313219882853
0.835799675983572
2.51019230081246
2.49476121131850
-3.52573557314125
2.47478456766280
-2.15782857688021
4.64089426989528
0.0911415552623357
-2.34057414315528
-2.02314875239176
0.60616742530706
1.98646775057574
2.10970012609582
-0.0166472188729180
2.84625223680116
-0.223047331629558
4.86646710195109
-2.40167652490070
1.41841309876503
-0.183355621630165
1.19504251622018
1.41569212113938
-4.87374431587117
2.20007052398130
1.74739380116604
-2.97258774402668
2.17595443105776
6.77636982753436
-3.65312845700514
1.89751054733407
0.115711132888437
0.449658449051261
-2.98751012889258
-3.61366762024811
-1.31123991406762
4.40728329116467
-1.06238205707065
-1.57051245497038
-3.48252354983475
0.712194364730514
-0.634741274725637
-1.60201223296099
-2.43493565651008
-1.60976663306648
4.66961185048669
2.27786349485193
0.329920857905177




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=70046&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=70046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70046&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 Mean-2.75712612463064e-180.323411487124367-8.52513356636089e-18
Geometric MeanNaN
Harmonic Mean-1.45747101473654
Quadratic Mean2.78209080734178
Winsorized Mean ( 1 / 25 )-0.003224559956674920.310969286159803-0.0103693840523461
Winsorized Mean ( 2 / 25 )-0.008330249056718150.309843102614015-0.0268853783945467
Winsorized Mean ( 3 / 25 )0.01337747193205580.3042332389342590.0439711057835681
Winsorized Mean ( 4 / 25 )0.01055956143392140.2995693768476310.0352491350919767
Winsorized Mean ( 5 / 25 )0.08118178456300150.2811055500897260.288794669963254
Winsorized Mean ( 6 / 25 )0.04999172452371270.2739039010272180.182515562342228
Winsorized Mean ( 7 / 25 )-0.01651678244119660.259543377234315-0.0636378497390256
Winsorized Mean ( 8 / 25 )-0.02054414700553380.257351187327505-0.0798292295399021
Winsorized Mean ( 9 / 25 )0.02818703999605630.2453513688414500.114884380426144
Winsorized Mean ( 10 / 25 )-0.01463130015365040.238330629044551-0.0613907671553007
Winsorized Mean ( 11 / 25 )0.03081849013601900.2302497665709860.133848084169578
Winsorized Mean ( 12 / 25 )0.06159599742781740.2245631393099930.27429255583566
Winsorized Mean ( 13 / 25 )0.05998070706437390.2226321585240760.269416186152134
Winsorized Mean ( 14 / 25 )0.06040897066832120.2193639934704450.275382343805024
Winsorized Mean ( 15 / 25 )0.04374394134813910.2163076040533100.202230252327875
Winsorized Mean ( 16 / 25 )0.07168692267936260.2098210110348960.341657502867719
Winsorized Mean ( 17 / 25 )0.09408790321802080.2063622002330270.455935743618624
Winsorized Mean ( 18 / 25 )0.09351481688742160.2041596191708130.458047567228175
Winsorized Mean ( 19 / 25 )0.1214772267132890.1985888124594050.611702266652714
Winsorized Mean ( 20 / 25 )0.1255998204405180.1964239466391700.639432322736312
Winsorized Mean ( 21 / 25 )0.1538408469668520.1892127618691320.813057456839274
Winsorized Mean ( 22 / 25 )0.1459445708565890.1804621711041140.80872667087879
Winsorized Mean ( 23 / 25 )0.1210423778948270.1764125694162770.686132390086137
Winsorized Mean ( 24 / 25 )0.08139279686743140.1688299684241700.482099224605310
Winsorized Mean ( 25 / 25 )-0.02650477975517510.154328387841984-0.171742737196952
Trimmed Mean ( 1 / 25 )0.007164560131282060.3026073501842600.023676094208946
Trimmed Mean ( 2 / 25 )0.01813898275940560.2927302850831590.0619648313950594
Trimmed Mean ( 3 / 25 )0.03252443483338590.2817171096252820.115450690505264
Trimmed Mean ( 4 / 25 )0.03966882397567330.2712101071233160.146266023771881
Trimmed Mean ( 5 / 25 )0.04806572663194790.2603795298357240.184598715045968
Trimmed Mean ( 6 / 25 )0.04018095093407800.2533504038522080.158598329914317
Trimmed Mean ( 7 / 25 )0.03817054650997250.2468929895743580.154603606103917
Trimmed Mean ( 8 / 25 )0.04810165951563270.2426740453133450.198215097348062
Trimmed Mean ( 9 / 25 )0.0593920882197720.2379397991772100.249609726599536
Trimmed Mean ( 10 / 25 )0.06412012582942590.2347466280941240.273146099477587
Trimmed Mean ( 11 / 25 )0.07526419554401210.2320894184859600.324289646787861
Trimmed Mean ( 12 / 25 )0.08120613476967970.2302473901422670.352690793669815
Trimmed Mean ( 13 / 25 )0.08370742779797840.2287990411601120.365855675677419
Trimmed Mean ( 14 / 25 )0.08661987305987750.2270266636323970.381540527768724
Trimmed Mean ( 15 / 25 )0.08974021858268180.2250822593452220.398699652490346
Trimmed Mean ( 16 / 25 )0.09508862291227980.2228309536235270.426729865694206
Trimmed Mean ( 17 / 25 )0.0977641221767140.2208701390169220.442631686709011
Trimmed Mean ( 18 / 25 )0.09817998404986930.2185839367592270.449163765213067
Trimmed Mean ( 19 / 25 )0.09870534071230710.2155557026497070.457911061962069
Trimmed Mean ( 20 / 25 )0.09613708289264750.2122817235894180.452874987385112
Trimmed Mean ( 21 / 25 )0.0927890445349350.2077947182516410.446541881890216
Trimmed Mean ( 22 / 25 )0.08575542674323940.2029122795959770.422623149835923
Trimmed Mean ( 23 / 25 )0.07867990039762630.1979024908666940.397569025296526
Trimmed Mean ( 24 / 25 )0.0735636591540030.1912201180288650.384706692540051
Trimmed Mean ( 25 / 25 )0.07258501693982450.1832420556085170.396115491603615
Median0.0911415552623357
Midrange-0.261506444791795
Midmean - Weighted Average at Xnp0.0428670751043052
Midmean - Weighted Average at X(n+1)p0.0981799840498692
Midmean - Empirical Distribution Function0.0981799840498692
Midmean - Empirical Distribution Function - Averaging0.0981799840498692
Midmean - Empirical Distribution Function - Interpolation0.098705340712307
Midmean - Closest Observation0.0428670751043052
Midmean - True Basic - Statistics Graphics Toolkit0.0981799840498692
Midmean - MS Excel (old versions)0.0981799840498692
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -2.75712612463064e-18 & 0.323411487124367 & -8.52513356636089e-18 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -1.45747101473654 &  &  \tabularnewline
Quadratic Mean & 2.78209080734178 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & -0.00322455995667492 & 0.310969286159803 & -0.0103693840523461 \tabularnewline
Winsorized Mean ( 2 / 25 ) & -0.00833024905671815 & 0.309843102614015 & -0.0268853783945467 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 0.0133774719320558 & 0.304233238934259 & 0.0439711057835681 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 0.0105595614339214 & 0.299569376847631 & 0.0352491350919767 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 0.0811817845630015 & 0.281105550089726 & 0.288794669963254 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 0.0499917245237127 & 0.273903901027218 & 0.182515562342228 \tabularnewline
Winsorized Mean ( 7 / 25 ) & -0.0165167824411966 & 0.259543377234315 & -0.0636378497390256 \tabularnewline
Winsorized Mean ( 8 / 25 ) & -0.0205441470055338 & 0.257351187327505 & -0.0798292295399021 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 0.0281870399960563 & 0.245351368841450 & 0.114884380426144 \tabularnewline
Winsorized Mean ( 10 / 25 ) & -0.0146313001536504 & 0.238330629044551 & -0.0613907671553007 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 0.0308184901360190 & 0.230249766570986 & 0.133848084169578 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 0.0615959974278174 & 0.224563139309993 & 0.27429255583566 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 0.0599807070643739 & 0.222632158524076 & 0.269416186152134 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 0.0604089706683212 & 0.219363993470445 & 0.275382343805024 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 0.0437439413481391 & 0.216307604053310 & 0.202230252327875 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 0.0716869226793626 & 0.209821011034896 & 0.341657502867719 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 0.0940879032180208 & 0.206362200233027 & 0.455935743618624 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 0.0935148168874216 & 0.204159619170813 & 0.458047567228175 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 0.121477226713289 & 0.198588812459405 & 0.611702266652714 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 0.125599820440518 & 0.196423946639170 & 0.639432322736312 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 0.153840846966852 & 0.189212761869132 & 0.813057456839274 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 0.145944570856589 & 0.180462171104114 & 0.80872667087879 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 0.121042377894827 & 0.176412569416277 & 0.686132390086137 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 0.0813927968674314 & 0.168829968424170 & 0.482099224605310 \tabularnewline
Winsorized Mean ( 25 / 25 ) & -0.0265047797551751 & 0.154328387841984 & -0.171742737196952 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 0.00716456013128206 & 0.302607350184260 & 0.023676094208946 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 0.0181389827594056 & 0.292730285083159 & 0.0619648313950594 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 0.0325244348333859 & 0.281717109625282 & 0.115450690505264 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 0.0396688239756733 & 0.271210107123316 & 0.146266023771881 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 0.0480657266319479 & 0.260379529835724 & 0.184598715045968 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 0.0401809509340780 & 0.253350403852208 & 0.158598329914317 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 0.0381705465099725 & 0.246892989574358 & 0.154603606103917 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 0.0481016595156327 & 0.242674045313345 & 0.198215097348062 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 0.059392088219772 & 0.237939799177210 & 0.249609726599536 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 0.0641201258294259 & 0.234746628094124 & 0.273146099477587 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 0.0752641955440121 & 0.232089418485960 & 0.324289646787861 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 0.0812061347696797 & 0.230247390142267 & 0.352690793669815 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 0.0837074277979784 & 0.228799041160112 & 0.365855675677419 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 0.0866198730598775 & 0.227026663632397 & 0.381540527768724 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 0.0897402185826818 & 0.225082259345222 & 0.398699652490346 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 0.0950886229122798 & 0.222830953623527 & 0.426729865694206 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 0.097764122176714 & 0.220870139016922 & 0.442631686709011 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 0.0981799840498693 & 0.218583936759227 & 0.449163765213067 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 0.0987053407123071 & 0.215555702649707 & 0.457911061962069 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 0.0961370828926475 & 0.212281723589418 & 0.452874987385112 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 0.092789044534935 & 0.207794718251641 & 0.446541881890216 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 0.0857554267432394 & 0.202912279595977 & 0.422623149835923 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 0.0786799003976263 & 0.197902490866694 & 0.397569025296526 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 0.073563659154003 & 0.191220118028865 & 0.384706692540051 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 0.0725850169398245 & 0.183242055608517 & 0.396115491603615 \tabularnewline
Median & 0.0911415552623357 &  &  \tabularnewline
Midrange & -0.261506444791795 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.0428670751043052 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0981799840498692 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.0981799840498692 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0981799840498692 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.098705340712307 &  &  \tabularnewline
Midmean - Closest Observation & 0.0428670751043052 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0981799840498692 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0981799840498692 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70046&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]-2.75712612463064e-18[/C][C]0.323411487124367[/C][C]-8.52513356636089e-18[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-1.45747101473654[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.78209080734178[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]-0.00322455995667492[/C][C]0.310969286159803[/C][C]-0.0103693840523461[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]-0.00833024905671815[/C][C]0.309843102614015[/C][C]-0.0268853783945467[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]0.0133774719320558[/C][C]0.304233238934259[/C][C]0.0439711057835681[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]0.0105595614339214[/C][C]0.299569376847631[/C][C]0.0352491350919767[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]0.0811817845630015[/C][C]0.281105550089726[/C][C]0.288794669963254[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]0.0499917245237127[/C][C]0.273903901027218[/C][C]0.182515562342228[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]-0.0165167824411966[/C][C]0.259543377234315[/C][C]-0.0636378497390256[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]-0.0205441470055338[/C][C]0.257351187327505[/C][C]-0.0798292295399021[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]0.0281870399960563[/C][C]0.245351368841450[/C][C]0.114884380426144[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]-0.0146313001536504[/C][C]0.238330629044551[/C][C]-0.0613907671553007[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]0.0308184901360190[/C][C]0.230249766570986[/C][C]0.133848084169578[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]0.0615959974278174[/C][C]0.224563139309993[/C][C]0.27429255583566[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]0.0599807070643739[/C][C]0.222632158524076[/C][C]0.269416186152134[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]0.0604089706683212[/C][C]0.219363993470445[/C][C]0.275382343805024[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]0.0437439413481391[/C][C]0.216307604053310[/C][C]0.202230252327875[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]0.0716869226793626[/C][C]0.209821011034896[/C][C]0.341657502867719[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]0.0940879032180208[/C][C]0.206362200233027[/C][C]0.455935743618624[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]0.0935148168874216[/C][C]0.204159619170813[/C][C]0.458047567228175[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]0.121477226713289[/C][C]0.198588812459405[/C][C]0.611702266652714[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]0.125599820440518[/C][C]0.196423946639170[/C][C]0.639432322736312[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]0.153840846966852[/C][C]0.189212761869132[/C][C]0.813057456839274[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]0.145944570856589[/C][C]0.180462171104114[/C][C]0.80872667087879[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]0.121042377894827[/C][C]0.176412569416277[/C][C]0.686132390086137[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]0.0813927968674314[/C][C]0.168829968424170[/C][C]0.482099224605310[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]-0.0265047797551751[/C][C]0.154328387841984[/C][C]-0.171742737196952[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]0.00716456013128206[/C][C]0.302607350184260[/C][C]0.023676094208946[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]0.0181389827594056[/C][C]0.292730285083159[/C][C]0.0619648313950594[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]0.0325244348333859[/C][C]0.281717109625282[/C][C]0.115450690505264[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]0.0396688239756733[/C][C]0.271210107123316[/C][C]0.146266023771881[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]0.0480657266319479[/C][C]0.260379529835724[/C][C]0.184598715045968[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]0.0401809509340780[/C][C]0.253350403852208[/C][C]0.158598329914317[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]0.0381705465099725[/C][C]0.246892989574358[/C][C]0.154603606103917[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]0.0481016595156327[/C][C]0.242674045313345[/C][C]0.198215097348062[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]0.059392088219772[/C][C]0.237939799177210[/C][C]0.249609726599536[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]0.0641201258294259[/C][C]0.234746628094124[/C][C]0.273146099477587[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]0.0752641955440121[/C][C]0.232089418485960[/C][C]0.324289646787861[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]0.0812061347696797[/C][C]0.230247390142267[/C][C]0.352690793669815[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]0.0837074277979784[/C][C]0.228799041160112[/C][C]0.365855675677419[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]0.0866198730598775[/C][C]0.227026663632397[/C][C]0.381540527768724[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]0.0897402185826818[/C][C]0.225082259345222[/C][C]0.398699652490346[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]0.0950886229122798[/C][C]0.222830953623527[/C][C]0.426729865694206[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]0.097764122176714[/C][C]0.220870139016922[/C][C]0.442631686709011[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]0.0981799840498693[/C][C]0.218583936759227[/C][C]0.449163765213067[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]0.0987053407123071[/C][C]0.215555702649707[/C][C]0.457911061962069[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]0.0961370828926475[/C][C]0.212281723589418[/C][C]0.452874987385112[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]0.092789044534935[/C][C]0.207794718251641[/C][C]0.446541881890216[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]0.0857554267432394[/C][C]0.202912279595977[/C][C]0.422623149835923[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]0.0786799003976263[/C][C]0.197902490866694[/C][C]0.397569025296526[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]0.073563659154003[/C][C]0.191220118028865[/C][C]0.384706692540051[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]0.0725850169398245[/C][C]0.183242055608517[/C][C]0.396115491603615[/C][/ROW]
[ROW][C]Median[/C][C]0.0911415552623357[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.261506444791795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.0428670751043052[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0981799840498692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.0981799840498692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0981799840498692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.098705340712307[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.0428670751043052[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0981799840498692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0981799840498692[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70046&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-2.75712612463064e-180.323411487124367-8.52513356636089e-18
Geometric MeanNaN
Harmonic Mean-1.45747101473654
Quadratic Mean2.78209080734178
Winsorized Mean ( 1 / 25 )-0.003224559956674920.310969286159803-0.0103693840523461
Winsorized Mean ( 2 / 25 )-0.008330249056718150.309843102614015-0.0268853783945467
Winsorized Mean ( 3 / 25 )0.01337747193205580.3042332389342590.0439711057835681
Winsorized Mean ( 4 / 25 )0.01055956143392140.2995693768476310.0352491350919767
Winsorized Mean ( 5 / 25 )0.08118178456300150.2811055500897260.288794669963254
Winsorized Mean ( 6 / 25 )0.04999172452371270.2739039010272180.182515562342228
Winsorized Mean ( 7 / 25 )-0.01651678244119660.259543377234315-0.0636378497390256
Winsorized Mean ( 8 / 25 )-0.02054414700553380.257351187327505-0.0798292295399021
Winsorized Mean ( 9 / 25 )0.02818703999605630.2453513688414500.114884380426144
Winsorized Mean ( 10 / 25 )-0.01463130015365040.238330629044551-0.0613907671553007
Winsorized Mean ( 11 / 25 )0.03081849013601900.2302497665709860.133848084169578
Winsorized Mean ( 12 / 25 )0.06159599742781740.2245631393099930.27429255583566
Winsorized Mean ( 13 / 25 )0.05998070706437390.2226321585240760.269416186152134
Winsorized Mean ( 14 / 25 )0.06040897066832120.2193639934704450.275382343805024
Winsorized Mean ( 15 / 25 )0.04374394134813910.2163076040533100.202230252327875
Winsorized Mean ( 16 / 25 )0.07168692267936260.2098210110348960.341657502867719
Winsorized Mean ( 17 / 25 )0.09408790321802080.2063622002330270.455935743618624
Winsorized Mean ( 18 / 25 )0.09351481688742160.2041596191708130.458047567228175
Winsorized Mean ( 19 / 25 )0.1214772267132890.1985888124594050.611702266652714
Winsorized Mean ( 20 / 25 )0.1255998204405180.1964239466391700.639432322736312
Winsorized Mean ( 21 / 25 )0.1538408469668520.1892127618691320.813057456839274
Winsorized Mean ( 22 / 25 )0.1459445708565890.1804621711041140.80872667087879
Winsorized Mean ( 23 / 25 )0.1210423778948270.1764125694162770.686132390086137
Winsorized Mean ( 24 / 25 )0.08139279686743140.1688299684241700.482099224605310
Winsorized Mean ( 25 / 25 )-0.02650477975517510.154328387841984-0.171742737196952
Trimmed Mean ( 1 / 25 )0.007164560131282060.3026073501842600.023676094208946
Trimmed Mean ( 2 / 25 )0.01813898275940560.2927302850831590.0619648313950594
Trimmed Mean ( 3 / 25 )0.03252443483338590.2817171096252820.115450690505264
Trimmed Mean ( 4 / 25 )0.03966882397567330.2712101071233160.146266023771881
Trimmed Mean ( 5 / 25 )0.04806572663194790.2603795298357240.184598715045968
Trimmed Mean ( 6 / 25 )0.04018095093407800.2533504038522080.158598329914317
Trimmed Mean ( 7 / 25 )0.03817054650997250.2468929895743580.154603606103917
Trimmed Mean ( 8 / 25 )0.04810165951563270.2426740453133450.198215097348062
Trimmed Mean ( 9 / 25 )0.0593920882197720.2379397991772100.249609726599536
Trimmed Mean ( 10 / 25 )0.06412012582942590.2347466280941240.273146099477587
Trimmed Mean ( 11 / 25 )0.07526419554401210.2320894184859600.324289646787861
Trimmed Mean ( 12 / 25 )0.08120613476967970.2302473901422670.352690793669815
Trimmed Mean ( 13 / 25 )0.08370742779797840.2287990411601120.365855675677419
Trimmed Mean ( 14 / 25 )0.08661987305987750.2270266636323970.381540527768724
Trimmed Mean ( 15 / 25 )0.08974021858268180.2250822593452220.398699652490346
Trimmed Mean ( 16 / 25 )0.09508862291227980.2228309536235270.426729865694206
Trimmed Mean ( 17 / 25 )0.0977641221767140.2208701390169220.442631686709011
Trimmed Mean ( 18 / 25 )0.09817998404986930.2185839367592270.449163765213067
Trimmed Mean ( 19 / 25 )0.09870534071230710.2155557026497070.457911061962069
Trimmed Mean ( 20 / 25 )0.09613708289264750.2122817235894180.452874987385112
Trimmed Mean ( 21 / 25 )0.0927890445349350.2077947182516410.446541881890216
Trimmed Mean ( 22 / 25 )0.08575542674323940.2029122795959770.422623149835923
Trimmed Mean ( 23 / 25 )0.07867990039762630.1979024908666940.397569025296526
Trimmed Mean ( 24 / 25 )0.0735636591540030.1912201180288650.384706692540051
Trimmed Mean ( 25 / 25 )0.07258501693982450.1832420556085170.396115491603615
Median0.0911415552623357
Midrange-0.261506444791795
Midmean - Weighted Average at Xnp0.0428670751043052
Midmean - Weighted Average at X(n+1)p0.0981799840498692
Midmean - Empirical Distribution Function0.0981799840498692
Midmean - Empirical Distribution Function - Averaging0.0981799840498692
Midmean - Empirical Distribution Function - Interpolation0.098705340712307
Midmean - Closest Observation0.0428670751043052
Midmean - True Basic - Statistics Graphics Toolkit0.0981799840498692
Midmean - MS Excel (old versions)0.0981799840498692
Number of observations75



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')