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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Oct 2009 09:15:54 -0600
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/Oct/21/t12561382230fl4aj89cnyess5.htm/, Retrieved Thu, 02 May 2024 03:44:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49409, Retrieved Thu, 02 May 2024 03:44:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsworkshop 3 deel 2.2 central tendency
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3 deel 2...] [2009-10-21 15:15:54] [6198946fb53eb5eb18db46bb758f7fde] [Current]
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Dataseries X:
-0.9136
-0.90493
-0.88768
-0.86839
-0.85537
-0.84792
-0.85478
-0.85791
-0.8659
-0.85207
-0.85173
-0.82897
-0.82805
-0.8237
-0.82727
-0.83431
-0.83506
-0.83021
-0.82573
-0.80499
-0.79763
-0.78695
-0.80738
-0.80228
-0.83886
-0.84715
-0.84081
-0.85047
-0.85087
-0.86622
-0.85244
-0.87355
-0.8965
-0.89576
-0.88938
-0.86843
-0.85492
-0.86124
-0.86928
-0.8618
-0.85116
-0.82298
-0.8414
-0.84823
-0.86042
-0.85707
-0.86457
-0.86081
-0.87015
-0.87024
-0.86753
-0.872
-0.86763
-0.86557
-0.86868
-0.86342
-0.87503
-0.87975
-0.88017
-0.8731
-0.87344
-0.88088
-0.90081
-0.90899
-0.91726
-0.91823
-0.92404
-0.95209
-0.9532
-0.93219
-0.95816
-0.96924
-0.97868
-0.9823
-0.96064
-0.95863
-0.97446
-0.93954
-0.93856
-0.87305




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49409&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49409&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.8745598750.00500173755092-174.851212422998
Geometric MeanNaN
Harmonic Mean-0.872367845787753
Quadratic Mean0.875689070311917
Winsorized Mean ( 1 / 26 )-0.8746481250.00496164068252231-176.28203672245
Winsorized Mean ( 2 / 26 )-0.8746588750.00491180520578219-178.072793678859
Winsorized Mean ( 3 / 26 )-0.874564750.00484369067942442-180.557514482722
Winsorized Mean ( 4 / 26 )-0.874254250.00471904829353093-185.260712673457
Winsorized Mean ( 5 / 26 )-0.8751036250.00453106826215642-193.134063397121
Winsorized Mean ( 6 / 26 )-0.8751223750.00451502824347303-193.824341246389
Winsorized Mean ( 7 / 26 )-0.8748660.00439008658329887-199.282174371740
Winsorized Mean ( 8 / 26 )-0.8749090.00434346656383346-201.431042956578
Winsorized Mean ( 9 / 26 )-0.8735848750.00402543199581943-217.016428524256
Winsorized Mean ( 10 / 26 )-0.8735773750.00398369760868724-219.288073747112
Winsorized Mean ( 11 / 26 )-0.8728720.00378198033651985-230.797603988394
Winsorized Mean ( 12 / 26 )-0.87226450.00345783955150091-252.257077579376
Winsorized Mean ( 13 / 26 )-0.871442250.00326558556002469-266.856352094297
Winsorized Mean ( 14 / 26 )-0.87193750.00314347511129267-277.380118858787
Winsorized Mean ( 15 / 26 )-0.8716168750.00297108899713828-293.366127988604
Winsorized Mean ( 16 / 26 )-0.8708128750.00279318459755254-311.763453000217
Winsorized Mean ( 17 / 26 )-0.8711720.00248793485735266-350.158685797340
Winsorized Mean ( 18 / 26 )-0.870418250.00230977372155336-376.841351114960
Winsorized Mean ( 19 / 26 )-0.869468250.00213312953352669-407.602180896401
Winsorized Mean ( 20 / 26 )-0.869843250.00203429823198990-427.588854142169
Winsorized Mean ( 21 / 26 )-0.86827350.00175858626962726-493.733810502248
Winsorized Mean ( 22 / 26 )-0.867885750.00167813383180148-517.173144092044
Winsorized Mean ( 23 / 26 )-0.8660946250.00137691830447826-629.009449713272
Winsorized Mean ( 24 / 26 )-0.8659836250.0013346457032798-648.84907123434
Winsorized Mean ( 25 / 26 )-0.8659680.00130178682460258-665.214905877059
Winsorized Mean ( 26 / 26 )-0.86519450.00100277936383416-862.796474682027
Trimmed Mean ( 1 / 26 )-0.8743017948717950.00480767667068164-181.855364817583
Trimmed Mean ( 2 / 26 )-0.8739372368421050.0046271081097812-188.873312684157
Trimmed Mean ( 3 / 26 )-0.8735471621621620.00444612516788781-196.473812404421
Trimmed Mean ( 4 / 26 )-0.8731702777777780.00426341806148404-204.805220878067
Trimmed Mean ( 5 / 26 )-0.8728605714285710.00409345877171916-213.233018849238
Trimmed Mean ( 6 / 26 )-0.8723327941176470.00394958425616645-220.866991951288
Trimmed Mean ( 7 / 26 )-0.8717692424242420.0037806280931942-230.588468618106
Trimmed Mean ( 8 / 26 )-0.871216250.00361006972201611-241.329480338528
Trimmed Mean ( 9 / 26 )-0.870620645161290.00341295113123019-255.093205758114
Trimmed Mean ( 10 / 26 )-0.87018150.00325385118040719-267.431253537264
Trimmed Mean ( 11 / 26 )-0.8697131034482760.00306676988181037-283.592554044149
Trimmed Mean ( 12 / 26 )-0.8693028571428570.00288412040333403-301.410043817154
Trimmed Mean ( 13 / 26 )-0.8689372222222220.00273395385164777-317.831707985308
Trimmed Mean ( 14 / 26 )-0.868640769230770.00259146523608666-335.192908295576
Trimmed Mean ( 15 / 26 )-0.8682640.00243714401272791-356.262902588241
Trimmed Mean ( 16 / 26 )-0.8678914583333330.00228086172960418-380.510333909608
Trimmed Mean ( 17 / 26 )-0.8675739130434780.00212427095714009-408.410193684281
Trimmed Mean ( 18 / 26 )-0.8671890909090910.00199388623735241-434.924056680681
Trimmed Mean ( 19 / 26 )-0.8668473809523810.00186900170423788-463.802349129399
Trimmed Mean ( 20 / 26 )-0.86657150.00175161191514618-494.72802308934
Trimmed Mean ( 21 / 26 )-0.8662271052631580.00161575000125541-536.114562642806
Trimmed Mean ( 22 / 26 )-0.8660105555555560.00151630968820579-571.130397894036
Trimmed Mean ( 23 / 26 )-0.865810.00140203391853921-617.538554917484
Trimmed Mean ( 24 / 26 )-0.86577906250.00133958515179374-646.303866044424
Trimmed Mean ( 25 / 26 )-0.8657563333333330.00126176281387091-686.148239443921
Trimmed Mean ( 26 / 26 )-0.8657321428571430.00115694113631375-748.294027832345
Median-0.866875
Midrange-0.884625
Midmean - Weighted Average at Xnp-0.867301463414634
Midmean - Weighted Average at X(n+1)p-0.8665715
Midmean - Empirical Distribution Function-0.867301463414634
Midmean - Empirical Distribution Function - Averaging-0.8665715
Midmean - Empirical Distribution Function - Interpolation-0.8665715
Midmean - Closest Observation-0.867301463414634
Midmean - True Basic - Statistics Graphics Toolkit-0.8665715
Midmean - MS Excel (old versions)-0.866847380952381
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.874559875 & 0.00500173755092 & -174.851212422998 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.872367845787753 &  &  \tabularnewline
Quadratic Mean & 0.875689070311917 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & -0.874648125 & 0.00496164068252231 & -176.28203672245 \tabularnewline
Winsorized Mean ( 2 / 26 ) & -0.874658875 & 0.00491180520578219 & -178.072793678859 \tabularnewline
Winsorized Mean ( 3 / 26 ) & -0.87456475 & 0.00484369067942442 & -180.557514482722 \tabularnewline
Winsorized Mean ( 4 / 26 ) & -0.87425425 & 0.00471904829353093 & -185.260712673457 \tabularnewline
Winsorized Mean ( 5 / 26 ) & -0.875103625 & 0.00453106826215642 & -193.134063397121 \tabularnewline
Winsorized Mean ( 6 / 26 ) & -0.875122375 & 0.00451502824347303 & -193.824341246389 \tabularnewline
Winsorized Mean ( 7 / 26 ) & -0.874866 & 0.00439008658329887 & -199.282174371740 \tabularnewline
Winsorized Mean ( 8 / 26 ) & -0.874909 & 0.00434346656383346 & -201.431042956578 \tabularnewline
Winsorized Mean ( 9 / 26 ) & -0.873584875 & 0.00402543199581943 & -217.016428524256 \tabularnewline
Winsorized Mean ( 10 / 26 ) & -0.873577375 & 0.00398369760868724 & -219.288073747112 \tabularnewline
Winsorized Mean ( 11 / 26 ) & -0.872872 & 0.00378198033651985 & -230.797603988394 \tabularnewline
Winsorized Mean ( 12 / 26 ) & -0.8722645 & 0.00345783955150091 & -252.257077579376 \tabularnewline
Winsorized Mean ( 13 / 26 ) & -0.87144225 & 0.00326558556002469 & -266.856352094297 \tabularnewline
Winsorized Mean ( 14 / 26 ) & -0.8719375 & 0.00314347511129267 & -277.380118858787 \tabularnewline
Winsorized Mean ( 15 / 26 ) & -0.871616875 & 0.00297108899713828 & -293.366127988604 \tabularnewline
Winsorized Mean ( 16 / 26 ) & -0.870812875 & 0.00279318459755254 & -311.763453000217 \tabularnewline
Winsorized Mean ( 17 / 26 ) & -0.871172 & 0.00248793485735266 & -350.158685797340 \tabularnewline
Winsorized Mean ( 18 / 26 ) & -0.87041825 & 0.00230977372155336 & -376.841351114960 \tabularnewline
Winsorized Mean ( 19 / 26 ) & -0.86946825 & 0.00213312953352669 & -407.602180896401 \tabularnewline
Winsorized Mean ( 20 / 26 ) & -0.86984325 & 0.00203429823198990 & -427.588854142169 \tabularnewline
Winsorized Mean ( 21 / 26 ) & -0.8682735 & 0.00175858626962726 & -493.733810502248 \tabularnewline
Winsorized Mean ( 22 / 26 ) & -0.86788575 & 0.00167813383180148 & -517.173144092044 \tabularnewline
Winsorized Mean ( 23 / 26 ) & -0.866094625 & 0.00137691830447826 & -629.009449713272 \tabularnewline
Winsorized Mean ( 24 / 26 ) & -0.865983625 & 0.0013346457032798 & -648.84907123434 \tabularnewline
Winsorized Mean ( 25 / 26 ) & -0.865968 & 0.00130178682460258 & -665.214905877059 \tabularnewline
Winsorized Mean ( 26 / 26 ) & -0.8651945 & 0.00100277936383416 & -862.796474682027 \tabularnewline
Trimmed Mean ( 1 / 26 ) & -0.874301794871795 & 0.00480767667068164 & -181.855364817583 \tabularnewline
Trimmed Mean ( 2 / 26 ) & -0.873937236842105 & 0.0046271081097812 & -188.873312684157 \tabularnewline
Trimmed Mean ( 3 / 26 ) & -0.873547162162162 & 0.00444612516788781 & -196.473812404421 \tabularnewline
Trimmed Mean ( 4 / 26 ) & -0.873170277777778 & 0.00426341806148404 & -204.805220878067 \tabularnewline
Trimmed Mean ( 5 / 26 ) & -0.872860571428571 & 0.00409345877171916 & -213.233018849238 \tabularnewline
Trimmed Mean ( 6 / 26 ) & -0.872332794117647 & 0.00394958425616645 & -220.866991951288 \tabularnewline
Trimmed Mean ( 7 / 26 ) & -0.871769242424242 & 0.0037806280931942 & -230.588468618106 \tabularnewline
Trimmed Mean ( 8 / 26 ) & -0.87121625 & 0.00361006972201611 & -241.329480338528 \tabularnewline
Trimmed Mean ( 9 / 26 ) & -0.87062064516129 & 0.00341295113123019 & -255.093205758114 \tabularnewline
Trimmed Mean ( 10 / 26 ) & -0.8701815 & 0.00325385118040719 & -267.431253537264 \tabularnewline
Trimmed Mean ( 11 / 26 ) & -0.869713103448276 & 0.00306676988181037 & -283.592554044149 \tabularnewline
Trimmed Mean ( 12 / 26 ) & -0.869302857142857 & 0.00288412040333403 & -301.410043817154 \tabularnewline
Trimmed Mean ( 13 / 26 ) & -0.868937222222222 & 0.00273395385164777 & -317.831707985308 \tabularnewline
Trimmed Mean ( 14 / 26 ) & -0.86864076923077 & 0.00259146523608666 & -335.192908295576 \tabularnewline
Trimmed Mean ( 15 / 26 ) & -0.868264 & 0.00243714401272791 & -356.262902588241 \tabularnewline
Trimmed Mean ( 16 / 26 ) & -0.867891458333333 & 0.00228086172960418 & -380.510333909608 \tabularnewline
Trimmed Mean ( 17 / 26 ) & -0.867573913043478 & 0.00212427095714009 & -408.410193684281 \tabularnewline
Trimmed Mean ( 18 / 26 ) & -0.867189090909091 & 0.00199388623735241 & -434.924056680681 \tabularnewline
Trimmed Mean ( 19 / 26 ) & -0.866847380952381 & 0.00186900170423788 & -463.802349129399 \tabularnewline
Trimmed Mean ( 20 / 26 ) & -0.8665715 & 0.00175161191514618 & -494.72802308934 \tabularnewline
Trimmed Mean ( 21 / 26 ) & -0.866227105263158 & 0.00161575000125541 & -536.114562642806 \tabularnewline
Trimmed Mean ( 22 / 26 ) & -0.866010555555556 & 0.00151630968820579 & -571.130397894036 \tabularnewline
Trimmed Mean ( 23 / 26 ) & -0.86581 & 0.00140203391853921 & -617.538554917484 \tabularnewline
Trimmed Mean ( 24 / 26 ) & -0.8657790625 & 0.00133958515179374 & -646.303866044424 \tabularnewline
Trimmed Mean ( 25 / 26 ) & -0.865756333333333 & 0.00126176281387091 & -686.148239443921 \tabularnewline
Trimmed Mean ( 26 / 26 ) & -0.865732142857143 & 0.00115694113631375 & -748.294027832345 \tabularnewline
Median & -0.866875 &  &  \tabularnewline
Midrange & -0.884625 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.867301463414634 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.8665715 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.867301463414634 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.8665715 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.8665715 &  &  \tabularnewline
Midmean - Closest Observation & -0.867301463414634 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.8665715 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.866847380952381 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49409&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]-0.874559875[/C][C]0.00500173755092[/C][C]-174.851212422998[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.872367845787753[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.875689070311917[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]-0.874648125[/C][C]0.00496164068252231[/C][C]-176.28203672245[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]-0.874658875[/C][C]0.00491180520578219[/C][C]-178.072793678859[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]-0.87456475[/C][C]0.00484369067942442[/C][C]-180.557514482722[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]-0.87425425[/C][C]0.00471904829353093[/C][C]-185.260712673457[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]-0.875103625[/C][C]0.00453106826215642[/C][C]-193.134063397121[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]-0.875122375[/C][C]0.00451502824347303[/C][C]-193.824341246389[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]-0.874866[/C][C]0.00439008658329887[/C][C]-199.282174371740[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]-0.874909[/C][C]0.00434346656383346[/C][C]-201.431042956578[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]-0.873584875[/C][C]0.00402543199581943[/C][C]-217.016428524256[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]-0.873577375[/C][C]0.00398369760868724[/C][C]-219.288073747112[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]-0.872872[/C][C]0.00378198033651985[/C][C]-230.797603988394[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]-0.8722645[/C][C]0.00345783955150091[/C][C]-252.257077579376[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]-0.87144225[/C][C]0.00326558556002469[/C][C]-266.856352094297[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]-0.8719375[/C][C]0.00314347511129267[/C][C]-277.380118858787[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]-0.871616875[/C][C]0.00297108899713828[/C][C]-293.366127988604[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]-0.870812875[/C][C]0.00279318459755254[/C][C]-311.763453000217[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]-0.871172[/C][C]0.00248793485735266[/C][C]-350.158685797340[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]-0.87041825[/C][C]0.00230977372155336[/C][C]-376.841351114960[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]-0.86946825[/C][C]0.00213312953352669[/C][C]-407.602180896401[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]-0.86984325[/C][C]0.00203429823198990[/C][C]-427.588854142169[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]-0.8682735[/C][C]0.00175858626962726[/C][C]-493.733810502248[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]-0.86788575[/C][C]0.00167813383180148[/C][C]-517.173144092044[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]-0.866094625[/C][C]0.00137691830447826[/C][C]-629.009449713272[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]-0.865983625[/C][C]0.0013346457032798[/C][C]-648.84907123434[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]-0.865968[/C][C]0.00130178682460258[/C][C]-665.214905877059[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]-0.8651945[/C][C]0.00100277936383416[/C][C]-862.796474682027[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]-0.874301794871795[/C][C]0.00480767667068164[/C][C]-181.855364817583[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]-0.873937236842105[/C][C]0.0046271081097812[/C][C]-188.873312684157[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]-0.873547162162162[/C][C]0.00444612516788781[/C][C]-196.473812404421[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]-0.873170277777778[/C][C]0.00426341806148404[/C][C]-204.805220878067[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]-0.872860571428571[/C][C]0.00409345877171916[/C][C]-213.233018849238[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]-0.872332794117647[/C][C]0.00394958425616645[/C][C]-220.866991951288[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]-0.871769242424242[/C][C]0.0037806280931942[/C][C]-230.588468618106[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]-0.87121625[/C][C]0.00361006972201611[/C][C]-241.329480338528[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]-0.87062064516129[/C][C]0.00341295113123019[/C][C]-255.093205758114[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]-0.8701815[/C][C]0.00325385118040719[/C][C]-267.431253537264[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]-0.869713103448276[/C][C]0.00306676988181037[/C][C]-283.592554044149[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]-0.869302857142857[/C][C]0.00288412040333403[/C][C]-301.410043817154[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]-0.868937222222222[/C][C]0.00273395385164777[/C][C]-317.831707985308[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]-0.86864076923077[/C][C]0.00259146523608666[/C][C]-335.192908295576[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]-0.868264[/C][C]0.00243714401272791[/C][C]-356.262902588241[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]-0.867891458333333[/C][C]0.00228086172960418[/C][C]-380.510333909608[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]-0.867573913043478[/C][C]0.00212427095714009[/C][C]-408.410193684281[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]-0.867189090909091[/C][C]0.00199388623735241[/C][C]-434.924056680681[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]-0.866847380952381[/C][C]0.00186900170423788[/C][C]-463.802349129399[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]-0.8665715[/C][C]0.00175161191514618[/C][C]-494.72802308934[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]-0.866227105263158[/C][C]0.00161575000125541[/C][C]-536.114562642806[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]-0.866010555555556[/C][C]0.00151630968820579[/C][C]-571.130397894036[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]-0.86581[/C][C]0.00140203391853921[/C][C]-617.538554917484[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]-0.8657790625[/C][C]0.00133958515179374[/C][C]-646.303866044424[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]-0.865756333333333[/C][C]0.00126176281387091[/C][C]-686.148239443921[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]-0.865732142857143[/C][C]0.00115694113631375[/C][C]-748.294027832345[/C][/ROW]
[ROW][C]Median[/C][C]-0.866875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.884625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.867301463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.8665715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.867301463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.8665715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.8665715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.867301463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.8665715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.866847380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49409&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.8745598750.00500173755092-174.851212422998
Geometric MeanNaN
Harmonic Mean-0.872367845787753
Quadratic Mean0.875689070311917
Winsorized Mean ( 1 / 26 )-0.8746481250.00496164068252231-176.28203672245
Winsorized Mean ( 2 / 26 )-0.8746588750.00491180520578219-178.072793678859
Winsorized Mean ( 3 / 26 )-0.874564750.00484369067942442-180.557514482722
Winsorized Mean ( 4 / 26 )-0.874254250.00471904829353093-185.260712673457
Winsorized Mean ( 5 / 26 )-0.8751036250.00453106826215642-193.134063397121
Winsorized Mean ( 6 / 26 )-0.8751223750.00451502824347303-193.824341246389
Winsorized Mean ( 7 / 26 )-0.8748660.00439008658329887-199.282174371740
Winsorized Mean ( 8 / 26 )-0.8749090.00434346656383346-201.431042956578
Winsorized Mean ( 9 / 26 )-0.8735848750.00402543199581943-217.016428524256
Winsorized Mean ( 10 / 26 )-0.8735773750.00398369760868724-219.288073747112
Winsorized Mean ( 11 / 26 )-0.8728720.00378198033651985-230.797603988394
Winsorized Mean ( 12 / 26 )-0.87226450.00345783955150091-252.257077579376
Winsorized Mean ( 13 / 26 )-0.871442250.00326558556002469-266.856352094297
Winsorized Mean ( 14 / 26 )-0.87193750.00314347511129267-277.380118858787
Winsorized Mean ( 15 / 26 )-0.8716168750.00297108899713828-293.366127988604
Winsorized Mean ( 16 / 26 )-0.8708128750.00279318459755254-311.763453000217
Winsorized Mean ( 17 / 26 )-0.8711720.00248793485735266-350.158685797340
Winsorized Mean ( 18 / 26 )-0.870418250.00230977372155336-376.841351114960
Winsorized Mean ( 19 / 26 )-0.869468250.00213312953352669-407.602180896401
Winsorized Mean ( 20 / 26 )-0.869843250.00203429823198990-427.588854142169
Winsorized Mean ( 21 / 26 )-0.86827350.00175858626962726-493.733810502248
Winsorized Mean ( 22 / 26 )-0.867885750.00167813383180148-517.173144092044
Winsorized Mean ( 23 / 26 )-0.8660946250.00137691830447826-629.009449713272
Winsorized Mean ( 24 / 26 )-0.8659836250.0013346457032798-648.84907123434
Winsorized Mean ( 25 / 26 )-0.8659680.00130178682460258-665.214905877059
Winsorized Mean ( 26 / 26 )-0.86519450.00100277936383416-862.796474682027
Trimmed Mean ( 1 / 26 )-0.8743017948717950.00480767667068164-181.855364817583
Trimmed Mean ( 2 / 26 )-0.8739372368421050.0046271081097812-188.873312684157
Trimmed Mean ( 3 / 26 )-0.8735471621621620.00444612516788781-196.473812404421
Trimmed Mean ( 4 / 26 )-0.8731702777777780.00426341806148404-204.805220878067
Trimmed Mean ( 5 / 26 )-0.8728605714285710.00409345877171916-213.233018849238
Trimmed Mean ( 6 / 26 )-0.8723327941176470.00394958425616645-220.866991951288
Trimmed Mean ( 7 / 26 )-0.8717692424242420.0037806280931942-230.588468618106
Trimmed Mean ( 8 / 26 )-0.871216250.00361006972201611-241.329480338528
Trimmed Mean ( 9 / 26 )-0.870620645161290.00341295113123019-255.093205758114
Trimmed Mean ( 10 / 26 )-0.87018150.00325385118040719-267.431253537264
Trimmed Mean ( 11 / 26 )-0.8697131034482760.00306676988181037-283.592554044149
Trimmed Mean ( 12 / 26 )-0.8693028571428570.00288412040333403-301.410043817154
Trimmed Mean ( 13 / 26 )-0.8689372222222220.00273395385164777-317.831707985308
Trimmed Mean ( 14 / 26 )-0.868640769230770.00259146523608666-335.192908295576
Trimmed Mean ( 15 / 26 )-0.8682640.00243714401272791-356.262902588241
Trimmed Mean ( 16 / 26 )-0.8678914583333330.00228086172960418-380.510333909608
Trimmed Mean ( 17 / 26 )-0.8675739130434780.00212427095714009-408.410193684281
Trimmed Mean ( 18 / 26 )-0.8671890909090910.00199388623735241-434.924056680681
Trimmed Mean ( 19 / 26 )-0.8668473809523810.00186900170423788-463.802349129399
Trimmed Mean ( 20 / 26 )-0.86657150.00175161191514618-494.72802308934
Trimmed Mean ( 21 / 26 )-0.8662271052631580.00161575000125541-536.114562642806
Trimmed Mean ( 22 / 26 )-0.8660105555555560.00151630968820579-571.130397894036
Trimmed Mean ( 23 / 26 )-0.865810.00140203391853921-617.538554917484
Trimmed Mean ( 24 / 26 )-0.86577906250.00133958515179374-646.303866044424
Trimmed Mean ( 25 / 26 )-0.8657563333333330.00126176281387091-686.148239443921
Trimmed Mean ( 26 / 26 )-0.8657321428571430.00115694113631375-748.294027832345
Median-0.866875
Midrange-0.884625
Midmean - Weighted Average at Xnp-0.867301463414634
Midmean - Weighted Average at X(n+1)p-0.8665715
Midmean - Empirical Distribution Function-0.867301463414634
Midmean - Empirical Distribution Function - Averaging-0.8665715
Midmean - Empirical Distribution Function - Interpolation-0.8665715
Midmean - Closest Observation-0.867301463414634
Midmean - True Basic - Statistics Graphics Toolkit-0.8665715
Midmean - MS Excel (old versions)-0.866847380952381
Number of observations80



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')