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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 computationThu, 12 Dec 2013 04:07:57 -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/2013/Dec/12/t1386839332cwsgay51v4a0vdw.htm/, Retrieved Sun, 05 Dec 2021 18:13:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232226, Retrieved Sun, 05 Dec 2021 18:13:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-12-12 09:07:57] [9e6a405f514733ea23d87e4507d39d29] [Current]
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Dataseries X:
0.00509985932295509
-0.320818222286888
-0.197117196687452
-0.273021303154159
-0.259307390005561
0.117630375827139
0.555831262688101
0.010351517675088
0.186684058005416
0.364862612399688
0.208424913402032
0.0647618673786489
0.0525051410399968
0.321269449652341
-0.350838864527021
0.0658651693688728
0.149554375196613
-0.114936607453198
-0.0612678864901738
-0.00290255501150305
0.299406072944713
-0.236384620475663
0.0015162047029825
-0.0938556758527673
0.124750000263356
-0.471783613685228
0.234820874083843
-0.0203883669827977
-0.129022235700457
0.041076861804919
-0.29004767860936
0.314346990835869
0.191624455541518
0.303417989902342
-0.268503945062622
0.289915006795012
-0.0448823511961261
0.213557197426895
-0.0820876439224611
0.236085417896762
0.173065057049405
0.251710933962102
-0.160389171911666
0.40817566275154
0.0820190953928902
0.0173582939155595
-0.0866614148161779
0.000536593053893895
0.329911858162196
0.115744305385573
0.0621722848647087
-0.0861085957245128
0.0753749365683205
-0.250523461798932
-0.228666727370203
0.0163675459851644
-0.129247437631836
0.0984376599509383
0.100778218291185
-0.0302527053025421
-0.1037533234522
-0.218990024090205
0.187279008866825
0.330481842656331
-0.412290770407357
0.0545177145540067
-0.122307642656818
-0.0956975808541104
0.143309956329961
0.0187572159841698
0.0916514301580276
-0.114220581652296
0.0100967146974866
-0.318283738127712
0.2145351886932
-0.141165358157766
0.131873070807267




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232226&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232226&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.02015308533997510.02384452396179820.845187153757514
Geometric MeanNaN
Harmonic Mean0.0281062848649855
Quadratic Mean0.208846372709805
Winsorized Mean ( 1 / 25 )0.01900811447427780.02314822036839640.821147983377116
Winsorized Mean ( 2 / 25 )0.01947925357891380.02254176360780790.86414061995427
Winsorized Mean ( 3 / 25 )0.01930937848138560.02203691227588760.876228858183256
Winsorized Mean ( 4 / 25 )0.0194114304120370.02200475054973540.882147260345583
Winsorized Mean ( 5 / 25 )0.02068374541258880.0215418967482410.960163612996509
Winsorized Mean ( 6 / 25 )0.021471063592230.02119612754317381.01297105089107
Winsorized Mean ( 7 / 25 )0.02088818697023090.02094274385181190.997394950634597
Winsorized Mean ( 8 / 25 )0.02142685066887320.02069677918721811.03527464225477
Winsorized Mean ( 9 / 25 )0.02134419818202060.02032027818256861.05038907392175
Winsorized Mean ( 10 / 25 )0.01821884344050880.01916813050005770.950475761861805
Winsorized Mean ( 11 / 25 )0.01708918301766880.0186243979026790.917569690411877
Winsorized Mean ( 12 / 25 )0.01840016890864220.01833445219237171.00358432941333
Winsorized Mean ( 13 / 25 )0.01866812794964780.01719166063585371.08588276287369
Winsorized Mean ( 14 / 25 )0.02516813404228070.0161055812543211.56269641218495
Winsorized Mean ( 15 / 25 )0.02791323723624890.01539682123946421.81292208320919
Winsorized Mean ( 16 / 25 )0.02689868402386780.0145122867421951.8535110628471
Winsorized Mean ( 17 / 25 )0.02598901960001930.01436271045595411.80947876654058
Winsorized Mean ( 18 / 25 )0.02741958530495620.01412115458607671.94173820120853
Winsorized Mean ( 19 / 25 )0.02587787946995060.01337547178209611.9347264822905
Winsorized Mean ( 20 / 25 )0.01995718958634280.01248961276493951.59790299042465
Winsorized Mean ( 21 / 25 )0.02110887304091840.01185824772658511.78010052814078
Winsorized Mean ( 22 / 25 )0.02014283220531720.01110271835553541.81422526991102
Winsorized Mean ( 23 / 25 )0.01856534119909560.01074789523362391.72734668468069
Winsorized Mean ( 24 / 25 )0.01858860455505580.01015394274459381.83067848840814
Winsorized Mean ( 25 / 25 )0.01815573074015290.01005104101838561.80635326300449
Trimmed Mean ( 1 / 25 )0.01956986562900280.02245412751464020.871548699286717
Trimmed Mean ( 2 / 25 )0.02016239766891820.02163722455685860.93183844424848
Trimmed Mean ( 3 / 25 )0.020532834957160.0210596016502910.974986863385244
Trimmed Mean ( 4 / 25 )0.0209879371244770.02060273407858521.01869669551733
Trimmed Mean ( 5 / 25 )0.0209879371244770.02006926425547991.04577511448863
Trimmed Mean ( 6 / 25 )0.02162027339248390.01957571770877441.10444345970483
Trimmed Mean ( 7 / 25 )0.02165066798142450.01907785570691451.13485856660387
Trimmed Mean ( 8 / 25 )0.02178816455721350.01854003176360321.17519564340698
Trimmed Mean ( 9 / 25 )0.02184710771272660.01794510223710711.2174412507693
Trimmed Mean ( 10 / 25 )0.02184710771272660.01730538851435571.26244537616727
Trimmed Mean ( 11 / 25 )0.02244111811942450.01678131086807851.3372684825303
Trimmed Mean ( 12 / 25 )0.02314797747248660.0162489621547361.42458190572742
Trimmed Mean ( 13 / 25 )0.02374533247153240.01564569561459851.51769106701631
Trimmed Mean ( 14 / 25 )0.02435906049066130.01513838356622041.60909256817986
Trimmed Mean ( 15 / 25 )0.0242643816707910.01472977563523711.6473015116907
Trimmed Mean ( 16 / 25 )0.02384814185073130.0143511380392531.66175963087403
Trimmed Mean ( 17 / 25 )0.02350672942728440.0140438930404081.67380436177128
Trimmed Mean ( 18 / 25 )0.02323250224894780.013662069950991.70051114745349
Trimmed Mean ( 19 / 25 )0.0227732353040580.01319947049886951.72531430757079
Trimmed Mean ( 20 / 25 )0.0227732353040580.01275335005061751.78566691996
Trimmed Mean ( 21 / 25 )0.02270554096336390.01236049574788541.83694419920401
Trimmed Mean ( 22 / 25 )0.02288294851030230.01196871314339681.91189714684798
Trimmed Mean ( 23 / 25 )0.023192316480220.01160871678064961.99783636024947
Trimmed Mean ( 24 / 25 )0.02372646505090450.01116967625649652.12418556331073
Trimmed Mean ( 25 / 25 )0.02433698242463970.01069474016165122.27560296526945
Median0.0173582939155595
Midrange0.0420238245014365
Midmean - Weighted Average at Xnp0.018818187363391
Midmean - Weighted Average at X(n+1)p0.022773235304058
Midmean - Empirical Distribution Function0.022773235304058
Midmean - Empirical Distribution Function - Averaging0.022773235304058
Midmean - Empirical Distribution Function - Interpolation0.022773235304058
Midmean - Closest Observation0.0191462133550361
Midmean - True Basic - Statistics Graphics Toolkit0.022773235304058
Midmean - MS Excel (old versions)0.022773235304058
Number of observations77

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0201530853399751 & 0.0238445239617982 & 0.845187153757514 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.0281062848649855 &  &  \tabularnewline
Quadratic Mean & 0.208846372709805 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 0.0190081144742778 & 0.0231482203683964 & 0.821147983377116 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 0.0194792535789138 & 0.0225417636078079 & 0.86414061995427 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 0.0193093784813856 & 0.0220369122758876 & 0.876228858183256 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 0.019411430412037 & 0.0220047505497354 & 0.882147260345583 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 0.0206837454125888 & 0.021541896748241 & 0.960163612996509 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 0.02147106359223 & 0.0211961275431738 & 1.01297105089107 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 0.0208881869702309 & 0.0209427438518119 & 0.997394950634597 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 0.0214268506688732 & 0.0206967791872181 & 1.03527464225477 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 0.0213441981820206 & 0.0203202781825686 & 1.05038907392175 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 0.0182188434405088 & 0.0191681305000577 & 0.950475761861805 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 0.0170891830176688 & 0.018624397902679 & 0.917569690411877 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 0.0184001689086422 & 0.0183344521923717 & 1.00358432941333 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 0.0186681279496478 & 0.0171916606358537 & 1.08588276287369 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 0.0251681340422807 & 0.016105581254321 & 1.56269641218495 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 0.0279132372362489 & 0.0153968212394642 & 1.81292208320919 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 0.0268986840238678 & 0.014512286742195 & 1.8535110628471 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 0.0259890196000193 & 0.0143627104559541 & 1.80947876654058 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 0.0274195853049562 & 0.0141211545860767 & 1.94173820120853 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 0.0258778794699506 & 0.0133754717820961 & 1.9347264822905 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 0.0199571895863428 & 0.0124896127649395 & 1.59790299042465 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 0.0211088730409184 & 0.0118582477265851 & 1.78010052814078 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 0.0201428322053172 & 0.0111027183555354 & 1.81422526991102 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 0.0185653411990956 & 0.0107478952336239 & 1.72734668468069 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 0.0185886045550558 & 0.0101539427445938 & 1.83067848840814 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 0.0181557307401529 & 0.0100510410183856 & 1.80635326300449 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 0.0195698656290028 & 0.0224541275146402 & 0.871548699286717 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 0.0201623976689182 & 0.0216372245568586 & 0.93183844424848 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 0.02053283495716 & 0.021059601650291 & 0.974986863385244 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 0.020987937124477 & 0.0206027340785852 & 1.01869669551733 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 0.020987937124477 & 0.0200692642554799 & 1.04577511448863 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 0.0216202733924839 & 0.0195757177087744 & 1.10444345970483 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 0.0216506679814245 & 0.0190778557069145 & 1.13485856660387 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 0.0217881645572135 & 0.0185400317636032 & 1.17519564340698 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 0.0218471077127266 & 0.0179451022371071 & 1.2174412507693 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 0.0218471077127266 & 0.0173053885143557 & 1.26244537616727 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 0.0224411181194245 & 0.0167813108680785 & 1.3372684825303 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 0.0231479774724866 & 0.016248962154736 & 1.42458190572742 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 0.0237453324715324 & 0.0156456956145985 & 1.51769106701631 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 0.0243590604906613 & 0.0151383835662204 & 1.60909256817986 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 0.024264381670791 & 0.0147297756352371 & 1.6473015116907 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 0.0238481418507313 & 0.014351138039253 & 1.66175963087403 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 0.0235067294272844 & 0.014043893040408 & 1.67380436177128 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 0.0232325022489478 & 0.01366206995099 & 1.70051114745349 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 0.022773235304058 & 0.0131994704988695 & 1.72531430757079 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 0.022773235304058 & 0.0127533500506175 & 1.78566691996 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 0.0227055409633639 & 0.0123604957478854 & 1.83694419920401 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 0.0228829485103023 & 0.0119687131433968 & 1.91189714684798 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 0.02319231648022 & 0.0116087167806496 & 1.99783636024947 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 0.0237264650509045 & 0.0111696762564965 & 2.12418556331073 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 0.0243369824246397 & 0.0106947401616512 & 2.27560296526945 \tabularnewline
Median & 0.0173582939155595 &  &  \tabularnewline
Midrange & 0.0420238245014365 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.018818187363391 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.022773235304058 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.022773235304058 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.022773235304058 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.022773235304058 &  &  \tabularnewline
Midmean - Closest Observation & 0.0191462133550361 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.022773235304058 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.022773235304058 &  &  \tabularnewline
Number of observations & 77 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232226&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.0201530853399751[/C][C]0.0238445239617982[/C][C]0.845187153757514[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.0281062848649855[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.208846372709805[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]0.0190081144742778[/C][C]0.0231482203683964[/C][C]0.821147983377116[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]0.0194792535789138[/C][C]0.0225417636078079[/C][C]0.86414061995427[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]0.0193093784813856[/C][C]0.0220369122758876[/C][C]0.876228858183256[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]0.019411430412037[/C][C]0.0220047505497354[/C][C]0.882147260345583[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]0.0206837454125888[/C][C]0.021541896748241[/C][C]0.960163612996509[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]0.02147106359223[/C][C]0.0211961275431738[/C][C]1.01297105089107[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]0.0208881869702309[/C][C]0.0209427438518119[/C][C]0.997394950634597[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]0.0214268506688732[/C][C]0.0206967791872181[/C][C]1.03527464225477[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]0.0213441981820206[/C][C]0.0203202781825686[/C][C]1.05038907392175[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]0.0182188434405088[/C][C]0.0191681305000577[/C][C]0.950475761861805[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]0.0170891830176688[/C][C]0.018624397902679[/C][C]0.917569690411877[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]0.0184001689086422[/C][C]0.0183344521923717[/C][C]1.00358432941333[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]0.0186681279496478[/C][C]0.0171916606358537[/C][C]1.08588276287369[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]0.0251681340422807[/C][C]0.016105581254321[/C][C]1.56269641218495[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]0.0279132372362489[/C][C]0.0153968212394642[/C][C]1.81292208320919[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]0.0268986840238678[/C][C]0.014512286742195[/C][C]1.8535110628471[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]0.0259890196000193[/C][C]0.0143627104559541[/C][C]1.80947876654058[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]0.0274195853049562[/C][C]0.0141211545860767[/C][C]1.94173820120853[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]0.0258778794699506[/C][C]0.0133754717820961[/C][C]1.9347264822905[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]0.0199571895863428[/C][C]0.0124896127649395[/C][C]1.59790299042465[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]0.0211088730409184[/C][C]0.0118582477265851[/C][C]1.78010052814078[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]0.0201428322053172[/C][C]0.0111027183555354[/C][C]1.81422526991102[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]0.0185653411990956[/C][C]0.0107478952336239[/C][C]1.72734668468069[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]0.0185886045550558[/C][C]0.0101539427445938[/C][C]1.83067848840814[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]0.0181557307401529[/C][C]0.0100510410183856[/C][C]1.80635326300449[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]0.0195698656290028[/C][C]0.0224541275146402[/C][C]0.871548699286717[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]0.0201623976689182[/C][C]0.0216372245568586[/C][C]0.93183844424848[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]0.02053283495716[/C][C]0.021059601650291[/C][C]0.974986863385244[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]0.020987937124477[/C][C]0.0206027340785852[/C][C]1.01869669551733[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]0.020987937124477[/C][C]0.0200692642554799[/C][C]1.04577511448863[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]0.0216202733924839[/C][C]0.0195757177087744[/C][C]1.10444345970483[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]0.0216506679814245[/C][C]0.0190778557069145[/C][C]1.13485856660387[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]0.0217881645572135[/C][C]0.0185400317636032[/C][C]1.17519564340698[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]0.0218471077127266[/C][C]0.0179451022371071[/C][C]1.2174412507693[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]0.0218471077127266[/C][C]0.0173053885143557[/C][C]1.26244537616727[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]0.0224411181194245[/C][C]0.0167813108680785[/C][C]1.3372684825303[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]0.0231479774724866[/C][C]0.016248962154736[/C][C]1.42458190572742[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]0.0237453324715324[/C][C]0.0156456956145985[/C][C]1.51769106701631[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]0.0243590604906613[/C][C]0.0151383835662204[/C][C]1.60909256817986[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]0.024264381670791[/C][C]0.0147297756352371[/C][C]1.6473015116907[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]0.0238481418507313[/C][C]0.014351138039253[/C][C]1.66175963087403[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]0.0235067294272844[/C][C]0.014043893040408[/C][C]1.67380436177128[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]0.0232325022489478[/C][C]0.01366206995099[/C][C]1.70051114745349[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]0.022773235304058[/C][C]0.0131994704988695[/C][C]1.72531430757079[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]0.022773235304058[/C][C]0.0127533500506175[/C][C]1.78566691996[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]0.0227055409633639[/C][C]0.0123604957478854[/C][C]1.83694419920401[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]0.0228829485103023[/C][C]0.0119687131433968[/C][C]1.91189714684798[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]0.02319231648022[/C][C]0.0116087167806496[/C][C]1.99783636024947[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]0.0237264650509045[/C][C]0.0111696762564965[/C][C]2.12418556331073[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]0.0243369824246397[/C][C]0.0106947401616512[/C][C]2.27560296526945[/C][/ROW]
[ROW][C]Median[/C][C]0.0173582939155595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.0420238245014365[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.018818187363391[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.022773235304058[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.022773235304058[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.022773235304058[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.022773235304058[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.0191462133550361[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.022773235304058[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.022773235304058[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]77[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232226&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 Mean0.02015308533997510.02384452396179820.845187153757514
Geometric MeanNaN
Harmonic Mean0.0281062848649855
Quadratic Mean0.208846372709805
Winsorized Mean ( 1 / 25 )0.01900811447427780.02314822036839640.821147983377116
Winsorized Mean ( 2 / 25 )0.01947925357891380.02254176360780790.86414061995427
Winsorized Mean ( 3 / 25 )0.01930937848138560.02203691227588760.876228858183256
Winsorized Mean ( 4 / 25 )0.0194114304120370.02200475054973540.882147260345583
Winsorized Mean ( 5 / 25 )0.02068374541258880.0215418967482410.960163612996509
Winsorized Mean ( 6 / 25 )0.021471063592230.02119612754317381.01297105089107
Winsorized Mean ( 7 / 25 )0.02088818697023090.02094274385181190.997394950634597
Winsorized Mean ( 8 / 25 )0.02142685066887320.02069677918721811.03527464225477
Winsorized Mean ( 9 / 25 )0.02134419818202060.02032027818256861.05038907392175
Winsorized Mean ( 10 / 25 )0.01821884344050880.01916813050005770.950475761861805
Winsorized Mean ( 11 / 25 )0.01708918301766880.0186243979026790.917569690411877
Winsorized Mean ( 12 / 25 )0.01840016890864220.01833445219237171.00358432941333
Winsorized Mean ( 13 / 25 )0.01866812794964780.01719166063585371.08588276287369
Winsorized Mean ( 14 / 25 )0.02516813404228070.0161055812543211.56269641218495
Winsorized Mean ( 15 / 25 )0.02791323723624890.01539682123946421.81292208320919
Winsorized Mean ( 16 / 25 )0.02689868402386780.0145122867421951.8535110628471
Winsorized Mean ( 17 / 25 )0.02598901960001930.01436271045595411.80947876654058
Winsorized Mean ( 18 / 25 )0.02741958530495620.01412115458607671.94173820120853
Winsorized Mean ( 19 / 25 )0.02587787946995060.01337547178209611.9347264822905
Winsorized Mean ( 20 / 25 )0.01995718958634280.01248961276493951.59790299042465
Winsorized Mean ( 21 / 25 )0.02110887304091840.01185824772658511.78010052814078
Winsorized Mean ( 22 / 25 )0.02014283220531720.01110271835553541.81422526991102
Winsorized Mean ( 23 / 25 )0.01856534119909560.01074789523362391.72734668468069
Winsorized Mean ( 24 / 25 )0.01858860455505580.01015394274459381.83067848840814
Winsorized Mean ( 25 / 25 )0.01815573074015290.01005104101838561.80635326300449
Trimmed Mean ( 1 / 25 )0.01956986562900280.02245412751464020.871548699286717
Trimmed Mean ( 2 / 25 )0.02016239766891820.02163722455685860.93183844424848
Trimmed Mean ( 3 / 25 )0.020532834957160.0210596016502910.974986863385244
Trimmed Mean ( 4 / 25 )0.0209879371244770.02060273407858521.01869669551733
Trimmed Mean ( 5 / 25 )0.0209879371244770.02006926425547991.04577511448863
Trimmed Mean ( 6 / 25 )0.02162027339248390.01957571770877441.10444345970483
Trimmed Mean ( 7 / 25 )0.02165066798142450.01907785570691451.13485856660387
Trimmed Mean ( 8 / 25 )0.02178816455721350.01854003176360321.17519564340698
Trimmed Mean ( 9 / 25 )0.02184710771272660.01794510223710711.2174412507693
Trimmed Mean ( 10 / 25 )0.02184710771272660.01730538851435571.26244537616727
Trimmed Mean ( 11 / 25 )0.02244111811942450.01678131086807851.3372684825303
Trimmed Mean ( 12 / 25 )0.02314797747248660.0162489621547361.42458190572742
Trimmed Mean ( 13 / 25 )0.02374533247153240.01564569561459851.51769106701631
Trimmed Mean ( 14 / 25 )0.02435906049066130.01513838356622041.60909256817986
Trimmed Mean ( 15 / 25 )0.0242643816707910.01472977563523711.6473015116907
Trimmed Mean ( 16 / 25 )0.02384814185073130.0143511380392531.66175963087403
Trimmed Mean ( 17 / 25 )0.02350672942728440.0140438930404081.67380436177128
Trimmed Mean ( 18 / 25 )0.02323250224894780.013662069950991.70051114745349
Trimmed Mean ( 19 / 25 )0.0227732353040580.01319947049886951.72531430757079
Trimmed Mean ( 20 / 25 )0.0227732353040580.01275335005061751.78566691996
Trimmed Mean ( 21 / 25 )0.02270554096336390.01236049574788541.83694419920401
Trimmed Mean ( 22 / 25 )0.02288294851030230.01196871314339681.91189714684798
Trimmed Mean ( 23 / 25 )0.023192316480220.01160871678064961.99783636024947
Trimmed Mean ( 24 / 25 )0.02372646505090450.01116967625649652.12418556331073
Trimmed Mean ( 25 / 25 )0.02433698242463970.01069474016165122.27560296526945
Median0.0173582939155595
Midrange0.0420238245014365
Midmean - Weighted Average at Xnp0.018818187363391
Midmean - Weighted Average at X(n+1)p0.022773235304058
Midmean - Empirical Distribution Function0.022773235304058
Midmean - Empirical Distribution Function - Averaging0.022773235304058
Midmean - Empirical Distribution Function - Interpolation0.022773235304058
Midmean - Closest Observation0.0191462133550361
Midmean - True Basic - Statistics Graphics Toolkit0.022773235304058
Midmean - MS Excel (old versions)0.022773235304058
Number of observations77



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')