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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 15:01:49 -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/Mar/05/t1362513736chl8m1n1079uqp4.htm/, Retrieved Sat, 04 May 2024 17:32:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207500, Retrieved Sat, 04 May 2024 17:32:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 20:01:49] [8e6f8740463a1fe0a9188e5ce9dc522d] [Current]
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Dataseries X:
1,01
1,02
1,04
1,06
1,06
1,06
1,06
1,06
1,02
0,98
0,99
0,99
0,94
0,96
0,98
1,01
1,01
1,02
1,04
1,03
1,05
1,08
1,17
1,11
1,11
1,11
1,2
1,21
1,31
1,37
1,37
1,26
1,23
1,17
1,06
0,95
0,92
0,92
0,9
0,93
0,93
0,97
0,96
0,99
0,98
0,96
1
0,99
1,03
1,02
1,07
1,13
1,15
1,16
1,14
1,15
1,15
1,16
1,17
1,22
1,26
1,29
1,36
1,38
1,37
1,37
1,37
1,36
1,38
1,4
1,44
1,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207500&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207500&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207500&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.118055555555560.017836458074811162.6837206616984
Geometric Mean1.10839288776869
Harmonic Mean1.09920158224409
Quadratic Mean1.12811174584396
Winsorized Mean ( 1 / 24 )1.118055555555560.017722030895597563.0884553887842
Winsorized Mean ( 2 / 24 )1.11750.017592534250239663.5212632872823
Winsorized Mean ( 3 / 24 )1.117083333333330.01734470273116764.4048705041239
Winsorized Mean ( 4 / 24 )1.117083333333330.01734470273116764.4048705041239
Winsorized Mean ( 5 / 24 )1.117083333333330.01709478031694265.3464573760117
Winsorized Mean ( 6 / 24 )1.117916666666670.016975930557994765.8530419200018
Winsorized Mean ( 7 / 24 )1.118888888888890.016843609511021266.4280947713002
Winsorized Mean ( 8 / 24 )1.118888888888890.016843609511021266.4280947713002
Winsorized Mean ( 9 / 24 )1.118888888888890.016843609511021266.4280947713002
Winsorized Mean ( 10 / 24 )1.118888888888890.016372468631534968.3396569002311
Winsorized Mean ( 11 / 24 )1.120416666666670.016181237686025269.2417161410528
Winsorized Mean ( 12 / 24 )1.112083333333330.014508021498241176.652997341378
Winsorized Mean ( 13 / 24 )1.108472222222220.013826925551129980.1676568028997
Winsorized Mean ( 14 / 24 )1.104583333333330.01252374505253388.1991232414879
Winsorized Mean ( 15 / 24 )1.104583333333330.01252374505253388.1991232414879
Winsorized Mean ( 16 / 24 )1.097916666666670.011395125491916596.3496775393573
Winsorized Mean ( 17 / 24 )1.095555555555560.011014446497517399.4653299920702
Winsorized Mean ( 18 / 24 )1.095555555555560.0102871314709296106.49767222782
Winsorized Mean ( 19 / 24 )1.095555555555560.00953719530283821114.871880124917
Winsorized Mean ( 20 / 24 )1.087222222222220.00830563995225647130.901679879206
Winsorized Mean ( 21 / 24 )1.087222222222220.00830563995225647130.901679879206
Winsorized Mean ( 22 / 24 )1.090277777777780.00791428113853915137.760809692316
Winsorized Mean ( 23 / 24 )1.087083333333330.00746781696999461145.569091703933
Winsorized Mean ( 24 / 24 )1.087083333333330.00746781696999461145.569091703933
Trimmed Mean ( 1 / 24 )1.116571428571430.017475076264400563.8950818684587
Trimmed Mean ( 2 / 24 )1.1150.017176075199605764.9158778732871
Trimmed Mean ( 3 / 24 )1.113636363636360.01689627807408965.9101583646497
Trimmed Mean ( 4 / 24 )1.112343750.016666283012697466.7421613537073
Trimmed Mean ( 5 / 24 )1.110967741935480.016381732738013467.8174744822633
Trimmed Mean ( 6 / 24 )1.10950.01610773229067468.879962739533
Trimmed Mean ( 7 / 24 )1.107758620689660.015797116416642670.1241031257201
Trimmed Mean ( 8 / 24 )1.105714285714290.015439149812692971.6175630866183
Trimmed Mean ( 9 / 24 )1.103518518518520.014986967101704673.631877018867
Trimmed Mean ( 10 / 24 )1.101153846153850.014413244511802476.3987487516886
Trimmed Mean ( 11 / 24 )1.09860.013797396974259579.6237146796277
Trimmed Mean ( 12 / 24 )1.0956250.013039445917012584.0238923473382
Trimmed Mean ( 13 / 24 )1.093478260869570.012511704245273487.3964281310958
Trimmed Mean ( 14 / 24 )1.091590909090910.011998692590063590.9758209819372
Trimmed Mean ( 15 / 24 )1.090.011647154747190293.5850878312542
Trimmed Mean ( 16 / 24 )1.088250.011168221284818297.4416580981735
Trimmed Mean ( 17 / 24 )1.087105263157890.010825841632247100.417621103908
Trimmed Mean ( 18 / 24 )1.086111111111110.0104522935720878103.91127111197
Trimmed Mean ( 19 / 24 )1.0850.0101174035123861107.240953538297
Trimmed Mean ( 20 / 24 )1.083750.00983482538343109110.195144066901
Trimmed Mean ( 21 / 24 )1.083333333333330.00977133190527601110.86854318687
Trimmed Mean ( 22 / 24 )1.082857142857140.00963427993999588112.396271397695
Trimmed Mean ( 23 / 24 )1.081923076923080.00949524951297275113.943617326213
Trimmed Mean ( 24 / 24 )1.081250.00938918009724761115.159150085636
Median1.06
Midrange1.17
Midmean - Weighted Average at Xnp1.0765
Midmean - Weighted Average at X(n+1)p1.08611111111111
Midmean - Empirical Distribution Function1.0765
Midmean - Empirical Distribution Function - Averaging1.08611111111111
Midmean - Empirical Distribution Function - Interpolation1.08611111111111
Midmean - Closest Observation1.0765
Midmean - True Basic - Statistics Graphics Toolkit1.08611111111111
Midmean - MS Excel (old versions)1.08
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.11805555555556 & 0.0178364580748111 & 62.6837206616984 \tabularnewline
Geometric Mean & 1.10839288776869 &  &  \tabularnewline
Harmonic Mean & 1.09920158224409 &  &  \tabularnewline
Quadratic Mean & 1.12811174584396 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.11805555555556 & 0.0177220308955975 & 63.0884553887842 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.1175 & 0.0175925342502396 & 63.5212632872823 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.11708333333333 & 0.017344702731167 & 64.4048705041239 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.11708333333333 & 0.017344702731167 & 64.4048705041239 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.11708333333333 & 0.017094780316942 & 65.3464573760117 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.11791666666667 & 0.0169759305579947 & 65.8530419200018 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.11888888888889 & 0.0168436095110212 & 66.4280947713002 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.11888888888889 & 0.0168436095110212 & 66.4280947713002 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.11888888888889 & 0.0168436095110212 & 66.4280947713002 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.11888888888889 & 0.0163724686315349 & 68.3396569002311 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.12041666666667 & 0.0161812376860252 & 69.2417161410528 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.11208333333333 & 0.0145080214982411 & 76.652997341378 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.10847222222222 & 0.0138269255511299 & 80.1676568028997 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.10458333333333 & 0.012523745052533 & 88.1991232414879 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.10458333333333 & 0.012523745052533 & 88.1991232414879 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.09791666666667 & 0.0113951254919165 & 96.3496775393573 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.09555555555556 & 0.0110144464975173 & 99.4653299920702 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.09555555555556 & 0.0102871314709296 & 106.49767222782 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.09555555555556 & 0.00953719530283821 & 114.871880124917 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.08722222222222 & 0.00830563995225647 & 130.901679879206 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.08722222222222 & 0.00830563995225647 & 130.901679879206 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.09027777777778 & 0.00791428113853915 & 137.760809692316 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.08708333333333 & 0.00746781696999461 & 145.569091703933 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.08708333333333 & 0.00746781696999461 & 145.569091703933 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.11657142857143 & 0.0174750762644005 & 63.8950818684587 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.115 & 0.0171760751996057 & 64.9158778732871 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.11363636363636 & 0.016896278074089 & 65.9101583646497 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.11234375 & 0.0166662830126974 & 66.7421613537073 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.11096774193548 & 0.0163817327380134 & 67.8174744822633 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.1095 & 0.016107732290674 & 68.879962739533 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.10775862068966 & 0.0157971164166426 & 70.1241031257201 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.10571428571429 & 0.0154391498126929 & 71.6175630866183 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.10351851851852 & 0.0149869671017046 & 73.631877018867 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.10115384615385 & 0.0144132445118024 & 76.3987487516886 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.0986 & 0.0137973969742595 & 79.6237146796277 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.095625 & 0.0130394459170125 & 84.0238923473382 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.09347826086957 & 0.0125117042452734 & 87.3964281310958 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.09159090909091 & 0.0119986925900635 & 90.9758209819372 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.09 & 0.0116471547471902 & 93.5850878312542 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.08825 & 0.0111682212848182 & 97.4416580981735 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.08710526315789 & 0.010825841632247 & 100.417621103908 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.08611111111111 & 0.0104522935720878 & 103.91127111197 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.085 & 0.0101174035123861 & 107.240953538297 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.08375 & 0.00983482538343109 & 110.195144066901 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.08333333333333 & 0.00977133190527601 & 110.86854318687 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.08285714285714 & 0.00963427993999588 & 112.396271397695 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.08192307692308 & 0.00949524951297275 & 113.943617326213 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.08125 & 0.00938918009724761 & 115.159150085636 \tabularnewline
Median & 1.06 &  &  \tabularnewline
Midrange & 1.17 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.0765 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.08611111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.0765 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.08611111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.08611111111111 &  &  \tabularnewline
Midmean - Closest Observation & 1.0765 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.08611111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.08 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207500&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.11805555555556[/C][C]0.0178364580748111[/C][C]62.6837206616984[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.10839288776869[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.09920158224409[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.12811174584396[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.11805555555556[/C][C]0.0177220308955975[/C][C]63.0884553887842[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.1175[/C][C]0.0175925342502396[/C][C]63.5212632872823[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.11708333333333[/C][C]0.017344702731167[/C][C]64.4048705041239[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.11708333333333[/C][C]0.017344702731167[/C][C]64.4048705041239[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.11708333333333[/C][C]0.017094780316942[/C][C]65.3464573760117[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.11791666666667[/C][C]0.0169759305579947[/C][C]65.8530419200018[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.11888888888889[/C][C]0.0168436095110212[/C][C]66.4280947713002[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.11888888888889[/C][C]0.0168436095110212[/C][C]66.4280947713002[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.11888888888889[/C][C]0.0168436095110212[/C][C]66.4280947713002[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.11888888888889[/C][C]0.0163724686315349[/C][C]68.3396569002311[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.12041666666667[/C][C]0.0161812376860252[/C][C]69.2417161410528[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.11208333333333[/C][C]0.0145080214982411[/C][C]76.652997341378[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.10847222222222[/C][C]0.0138269255511299[/C][C]80.1676568028997[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.10458333333333[/C][C]0.012523745052533[/C][C]88.1991232414879[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.10458333333333[/C][C]0.012523745052533[/C][C]88.1991232414879[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.09791666666667[/C][C]0.0113951254919165[/C][C]96.3496775393573[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.09555555555556[/C][C]0.0110144464975173[/C][C]99.4653299920702[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.09555555555556[/C][C]0.0102871314709296[/C][C]106.49767222782[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.09555555555556[/C][C]0.00953719530283821[/C][C]114.871880124917[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.08722222222222[/C][C]0.00830563995225647[/C][C]130.901679879206[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.08722222222222[/C][C]0.00830563995225647[/C][C]130.901679879206[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.09027777777778[/C][C]0.00791428113853915[/C][C]137.760809692316[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.08708333333333[/C][C]0.00746781696999461[/C][C]145.569091703933[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.08708333333333[/C][C]0.00746781696999461[/C][C]145.569091703933[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.11657142857143[/C][C]0.0174750762644005[/C][C]63.8950818684587[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.115[/C][C]0.0171760751996057[/C][C]64.9158778732871[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.11363636363636[/C][C]0.016896278074089[/C][C]65.9101583646497[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.11234375[/C][C]0.0166662830126974[/C][C]66.7421613537073[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.11096774193548[/C][C]0.0163817327380134[/C][C]67.8174744822633[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.1095[/C][C]0.016107732290674[/C][C]68.879962739533[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.10775862068966[/C][C]0.0157971164166426[/C][C]70.1241031257201[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.10571428571429[/C][C]0.0154391498126929[/C][C]71.6175630866183[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.10351851851852[/C][C]0.0149869671017046[/C][C]73.631877018867[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.10115384615385[/C][C]0.0144132445118024[/C][C]76.3987487516886[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.0986[/C][C]0.0137973969742595[/C][C]79.6237146796277[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.095625[/C][C]0.0130394459170125[/C][C]84.0238923473382[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.09347826086957[/C][C]0.0125117042452734[/C][C]87.3964281310958[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.09159090909091[/C][C]0.0119986925900635[/C][C]90.9758209819372[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.09[/C][C]0.0116471547471902[/C][C]93.5850878312542[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.08825[/C][C]0.0111682212848182[/C][C]97.4416580981735[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.08710526315789[/C][C]0.010825841632247[/C][C]100.417621103908[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.08611111111111[/C][C]0.0104522935720878[/C][C]103.91127111197[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.085[/C][C]0.0101174035123861[/C][C]107.240953538297[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.08375[/C][C]0.00983482538343109[/C][C]110.195144066901[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.08333333333333[/C][C]0.00977133190527601[/C][C]110.86854318687[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.08285714285714[/C][C]0.00963427993999588[/C][C]112.396271397695[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.08192307692308[/C][C]0.00949524951297275[/C][C]113.943617326213[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.08125[/C][C]0.00938918009724761[/C][C]115.159150085636[/C][/ROW]
[ROW][C]Median[/C][C]1.06[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.17[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.0765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.08611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.0765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.08611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.08611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.0765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.08611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207500&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207500&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.118055555555560.017836458074811162.6837206616984
Geometric Mean1.10839288776869
Harmonic Mean1.09920158224409
Quadratic Mean1.12811174584396
Winsorized Mean ( 1 / 24 )1.118055555555560.017722030895597563.0884553887842
Winsorized Mean ( 2 / 24 )1.11750.017592534250239663.5212632872823
Winsorized Mean ( 3 / 24 )1.117083333333330.01734470273116764.4048705041239
Winsorized Mean ( 4 / 24 )1.117083333333330.01734470273116764.4048705041239
Winsorized Mean ( 5 / 24 )1.117083333333330.01709478031694265.3464573760117
Winsorized Mean ( 6 / 24 )1.117916666666670.016975930557994765.8530419200018
Winsorized Mean ( 7 / 24 )1.118888888888890.016843609511021266.4280947713002
Winsorized Mean ( 8 / 24 )1.118888888888890.016843609511021266.4280947713002
Winsorized Mean ( 9 / 24 )1.118888888888890.016843609511021266.4280947713002
Winsorized Mean ( 10 / 24 )1.118888888888890.016372468631534968.3396569002311
Winsorized Mean ( 11 / 24 )1.120416666666670.016181237686025269.2417161410528
Winsorized Mean ( 12 / 24 )1.112083333333330.014508021498241176.652997341378
Winsorized Mean ( 13 / 24 )1.108472222222220.013826925551129980.1676568028997
Winsorized Mean ( 14 / 24 )1.104583333333330.01252374505253388.1991232414879
Winsorized Mean ( 15 / 24 )1.104583333333330.01252374505253388.1991232414879
Winsorized Mean ( 16 / 24 )1.097916666666670.011395125491916596.3496775393573
Winsorized Mean ( 17 / 24 )1.095555555555560.011014446497517399.4653299920702
Winsorized Mean ( 18 / 24 )1.095555555555560.0102871314709296106.49767222782
Winsorized Mean ( 19 / 24 )1.095555555555560.00953719530283821114.871880124917
Winsorized Mean ( 20 / 24 )1.087222222222220.00830563995225647130.901679879206
Winsorized Mean ( 21 / 24 )1.087222222222220.00830563995225647130.901679879206
Winsorized Mean ( 22 / 24 )1.090277777777780.00791428113853915137.760809692316
Winsorized Mean ( 23 / 24 )1.087083333333330.00746781696999461145.569091703933
Winsorized Mean ( 24 / 24 )1.087083333333330.00746781696999461145.569091703933
Trimmed Mean ( 1 / 24 )1.116571428571430.017475076264400563.8950818684587
Trimmed Mean ( 2 / 24 )1.1150.017176075199605764.9158778732871
Trimmed Mean ( 3 / 24 )1.113636363636360.01689627807408965.9101583646497
Trimmed Mean ( 4 / 24 )1.112343750.016666283012697466.7421613537073
Trimmed Mean ( 5 / 24 )1.110967741935480.016381732738013467.8174744822633
Trimmed Mean ( 6 / 24 )1.10950.01610773229067468.879962739533
Trimmed Mean ( 7 / 24 )1.107758620689660.015797116416642670.1241031257201
Trimmed Mean ( 8 / 24 )1.105714285714290.015439149812692971.6175630866183
Trimmed Mean ( 9 / 24 )1.103518518518520.014986967101704673.631877018867
Trimmed Mean ( 10 / 24 )1.101153846153850.014413244511802476.3987487516886
Trimmed Mean ( 11 / 24 )1.09860.013797396974259579.6237146796277
Trimmed Mean ( 12 / 24 )1.0956250.013039445917012584.0238923473382
Trimmed Mean ( 13 / 24 )1.093478260869570.012511704245273487.3964281310958
Trimmed Mean ( 14 / 24 )1.091590909090910.011998692590063590.9758209819372
Trimmed Mean ( 15 / 24 )1.090.011647154747190293.5850878312542
Trimmed Mean ( 16 / 24 )1.088250.011168221284818297.4416580981735
Trimmed Mean ( 17 / 24 )1.087105263157890.010825841632247100.417621103908
Trimmed Mean ( 18 / 24 )1.086111111111110.0104522935720878103.91127111197
Trimmed Mean ( 19 / 24 )1.0850.0101174035123861107.240953538297
Trimmed Mean ( 20 / 24 )1.083750.00983482538343109110.195144066901
Trimmed Mean ( 21 / 24 )1.083333333333330.00977133190527601110.86854318687
Trimmed Mean ( 22 / 24 )1.082857142857140.00963427993999588112.396271397695
Trimmed Mean ( 23 / 24 )1.081923076923080.00949524951297275113.943617326213
Trimmed Mean ( 24 / 24 )1.081250.00938918009724761115.159150085636
Median1.06
Midrange1.17
Midmean - Weighted Average at Xnp1.0765
Midmean - Weighted Average at X(n+1)p1.08611111111111
Midmean - Empirical Distribution Function1.0765
Midmean - Empirical Distribution Function - Averaging1.08611111111111
Midmean - Empirical Distribution Function - Interpolation1.08611111111111
Midmean - Closest Observation1.0765
Midmean - True Basic - Statistics Graphics Toolkit1.08611111111111
Midmean - MS Excel (old versions)1.08
Number of observations72



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')