Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 03:18:14 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318836311qbm06svhpoj7jtx.htm/, Retrieved Wed, 15 May 2024 06:54:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130276, Retrieved Wed, 15 May 2024 06:54:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W51a
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2011-10-17 07:18:14] [3a5148fa0f21767f499340b81dfb0928] [Current]
Feedback Forum

Post a new message
Dataseries X:
101,16
101,16
101,16
101,16
101,16
101,16
101,16
101,16
101,16
101,21
101,21
101,21
103,16
103,16
103,16
103,16
101,13
101,13
100,53
100,53
100,53
100,53
100,53
100,53
100,53
100,53
100,53
99,42
99,42
99,42
99,42
100,31
100,31
102,25
102,25
102,25
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,81
101,94
101,94
101,94
101,94
101,94




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130276&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130276&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.3813333333330.112535359582261900.884252822114
Geometric Mean101.377641710411
Harmonic Mean101.373943398972
Quadratic Mean101.38501830481
Winsorized Mean ( 1 / 20 )101.3813333333330.112535359582261900.884252822114
Winsorized Mean ( 2 / 20 )101.3813333333330.112535359582261900.884252822114
Winsorized Mean ( 3 / 20 )101.3813333333330.112535359582261900.884252822114
Winsorized Mean ( 4 / 20 )101.380.08301963555090841221.15689050252
Winsorized Mean ( 5 / 20 )101.380.08301963555090841221.15689050252
Winsorized Mean ( 6 / 20 )101.4020.07853740697136181291.12997118654
Winsorized Mean ( 7 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 8 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 9 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 10 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 11 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 12 / 20 )101.3398333333330.06954228550093141457.24047755054
Winsorized Mean ( 13 / 20 )101.3398333333330.06954228550093141457.24047755054
Winsorized Mean ( 14 / 20 )101.3398333333330.06954228550093141457.24047755054
Winsorized Mean ( 15 / 20 )101.4898333333330.04315554030635872351.72199473956
Winsorized Mean ( 16 / 20 )101.4898333333330.04315554030635872351.72199473956
Winsorized Mean ( 17 / 20 )101.4983333333330.04197400774051022418.12347204993
Winsorized Mean ( 18 / 20 )101.4983333333330.04197400774051022418.12347204993
Winsorized Mean ( 19 / 20 )101.4983333333330.04197400774051022418.12347204994
Winsorized Mean ( 20 / 20 )101.4983333333330.04197400774051022418.12347204993
Trimmed Mean ( 1 / 20 )101.3844827586210.106957362247802947.896251627172
Trimmed Mean ( 2 / 20 )101.3878571428570.1000128934174071013.74786468492
Trimmed Mean ( 3 / 20 )101.3914814814810.09118039782818861111.98770674958
Trimmed Mean ( 4 / 20 )101.3953846153850.07954217676016431274.73736255813
Trimmed Mean ( 5 / 20 )101.40.07790522761532711301.58146126834
Trimmed Mean ( 6 / 20 )101.4050.07578723951800121338.02208188245
Trimmed Mean ( 7 / 20 )101.4056521739130.07446469329960461361.79506932115
Trimmed Mean ( 8 / 20 )101.4134090909090.07422321000159341366.33014240063
Trimmed Mean ( 9 / 20 )101.4219047619050.07373575422579731375.47795946218
Trimmed Mean ( 10 / 20 )101.431250.07292003655216631390.99285732581
Trimmed Mean ( 11 / 20 )101.4415789473680.07165938706642271415.6076837964
Trimmed Mean ( 12 / 20 )101.4530555555560.06978290535704711453.83822924063
Trimmed Mean ( 13 / 20 )101.4697058823530.06772925719798971498.16652478162
Trimmed Mean ( 14 / 20 )101.48843750.06457695673948981571.58904080003
Trimmed Mean ( 15 / 20 )101.5096666666670.05970518245730941700.18183495626
Trimmed Mean ( 16 / 20 )101.51250.06157892728616151648.49412735406
Trimmed Mean ( 17 / 20 )101.5157692307690.06362914928751861595.42867329648
Trimmed Mean ( 18 / 20 )101.5183333333330.06618941491917791533.75480743099
Trimmed Mean ( 19 / 20 )101.5213636363640.06907958724733521469.62898421603
Trimmed Mean ( 20 / 20 )101.5250.07237511930723811402.76107275234
Median101.81
Midrange101.29
Midmean - Weighted Average at Xnp101.32119047619
Midmean - Weighted Average at X(n+1)p101.53696969697
Midmean - Empirical Distribution Function101.32119047619
Midmean - Empirical Distribution Function - Averaging101.53696969697
Midmean - Empirical Distribution Function - Interpolation101.53696969697
Midmean - Closest Observation101.32119047619
Midmean - True Basic - Statistics Graphics Toolkit101.53696969697
Midmean - MS Excel (old versions)101.32119047619
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.381333333333 & 0.112535359582261 & 900.884252822114 \tabularnewline
Geometric Mean & 101.377641710411 &  &  \tabularnewline
Harmonic Mean & 101.373943398972 &  &  \tabularnewline
Quadratic Mean & 101.38501830481 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.381333333333 & 0.112535359582261 & 900.884252822114 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.381333333333 & 0.112535359582261 & 900.884252822114 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.381333333333 & 0.112535359582261 & 900.884252822114 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.38 & 0.0830196355509084 & 1221.15689050252 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.38 & 0.0830196355509084 & 1221.15689050252 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.402 & 0.0785374069713618 & 1291.12997118654 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.365833333333 & 0.0727759861627348 & 1392.84726567179 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.365833333333 & 0.0727759861627348 & 1392.84726567179 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.365833333333 & 0.0727759861627348 & 1392.84726567179 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.365833333333 & 0.0727759861627348 & 1392.84726567179 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.365833333333 & 0.0727759861627348 & 1392.84726567179 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.339833333333 & 0.0695422855009314 & 1457.24047755054 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.339833333333 & 0.0695422855009314 & 1457.24047755054 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.339833333333 & 0.0695422855009314 & 1457.24047755054 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.489833333333 & 0.0431555403063587 & 2351.72199473956 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.489833333333 & 0.0431555403063587 & 2351.72199473956 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.498333333333 & 0.0419740077405102 & 2418.12347204993 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.498333333333 & 0.0419740077405102 & 2418.12347204993 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.498333333333 & 0.0419740077405102 & 2418.12347204994 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.498333333333 & 0.0419740077405102 & 2418.12347204993 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.384482758621 & 0.106957362247802 & 947.896251627172 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.387857142857 & 0.100012893417407 & 1013.74786468492 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.391481481481 & 0.0911803978281886 & 1111.98770674958 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.395384615385 & 0.0795421767601643 & 1274.73736255813 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.4 & 0.0779052276153271 & 1301.58146126834 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.405 & 0.0757872395180012 & 1338.02208188245 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.405652173913 & 0.0744646932996046 & 1361.79506932115 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.413409090909 & 0.0742232100015934 & 1366.33014240063 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.421904761905 & 0.0737357542257973 & 1375.47795946218 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.43125 & 0.0729200365521663 & 1390.99285732581 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.441578947368 & 0.0716593870664227 & 1415.6076837964 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.453055555556 & 0.0697829053570471 & 1453.83822924063 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.469705882353 & 0.0677292571979897 & 1498.16652478162 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.4884375 & 0.0645769567394898 & 1571.58904080003 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.509666666667 & 0.0597051824573094 & 1700.18183495626 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.5125 & 0.0615789272861615 & 1648.49412735406 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.515769230769 & 0.0636291492875186 & 1595.42867329648 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.518333333333 & 0.0661894149191779 & 1533.75480743099 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.521363636364 & 0.0690795872473352 & 1469.62898421603 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.525 & 0.0723751193072381 & 1402.76107275234 \tabularnewline
Median & 101.81 &  &  \tabularnewline
Midrange & 101.29 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.32119047619 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.53696969697 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.32119047619 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.53696969697 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.53696969697 &  &  \tabularnewline
Midmean - Closest Observation & 101.32119047619 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.53696969697 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.32119047619 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130276&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]101.381333333333[/C][C]0.112535359582261[/C][C]900.884252822114[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.377641710411[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.373943398972[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.38501830481[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.381333333333[/C][C]0.112535359582261[/C][C]900.884252822114[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.381333333333[/C][C]0.112535359582261[/C][C]900.884252822114[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.381333333333[/C][C]0.112535359582261[/C][C]900.884252822114[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.38[/C][C]0.0830196355509084[/C][C]1221.15689050252[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.38[/C][C]0.0830196355509084[/C][C]1221.15689050252[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.402[/C][C]0.0785374069713618[/C][C]1291.12997118654[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.365833333333[/C][C]0.0727759861627348[/C][C]1392.84726567179[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.365833333333[/C][C]0.0727759861627348[/C][C]1392.84726567179[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.365833333333[/C][C]0.0727759861627348[/C][C]1392.84726567179[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.365833333333[/C][C]0.0727759861627348[/C][C]1392.84726567179[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.365833333333[/C][C]0.0727759861627348[/C][C]1392.84726567179[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.339833333333[/C][C]0.0695422855009314[/C][C]1457.24047755054[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.339833333333[/C][C]0.0695422855009314[/C][C]1457.24047755054[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.339833333333[/C][C]0.0695422855009314[/C][C]1457.24047755054[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.489833333333[/C][C]0.0431555403063587[/C][C]2351.72199473956[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.489833333333[/C][C]0.0431555403063587[/C][C]2351.72199473956[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.498333333333[/C][C]0.0419740077405102[/C][C]2418.12347204993[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.498333333333[/C][C]0.0419740077405102[/C][C]2418.12347204993[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.498333333333[/C][C]0.0419740077405102[/C][C]2418.12347204994[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.498333333333[/C][C]0.0419740077405102[/C][C]2418.12347204993[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.384482758621[/C][C]0.106957362247802[/C][C]947.896251627172[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.387857142857[/C][C]0.100012893417407[/C][C]1013.74786468492[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.391481481481[/C][C]0.0911803978281886[/C][C]1111.98770674958[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.395384615385[/C][C]0.0795421767601643[/C][C]1274.73736255813[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.4[/C][C]0.0779052276153271[/C][C]1301.58146126834[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.405[/C][C]0.0757872395180012[/C][C]1338.02208188245[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.405652173913[/C][C]0.0744646932996046[/C][C]1361.79506932115[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.413409090909[/C][C]0.0742232100015934[/C][C]1366.33014240063[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.421904761905[/C][C]0.0737357542257973[/C][C]1375.47795946218[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.43125[/C][C]0.0729200365521663[/C][C]1390.99285732581[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.441578947368[/C][C]0.0716593870664227[/C][C]1415.6076837964[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.453055555556[/C][C]0.0697829053570471[/C][C]1453.83822924063[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.469705882353[/C][C]0.0677292571979897[/C][C]1498.16652478162[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.4884375[/C][C]0.0645769567394898[/C][C]1571.58904080003[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.509666666667[/C][C]0.0597051824573094[/C][C]1700.18183495626[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.5125[/C][C]0.0615789272861615[/C][C]1648.49412735406[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.515769230769[/C][C]0.0636291492875186[/C][C]1595.42867329648[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.518333333333[/C][C]0.0661894149191779[/C][C]1533.75480743099[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.521363636364[/C][C]0.0690795872473352[/C][C]1469.62898421603[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.525[/C][C]0.0723751193072381[/C][C]1402.76107275234[/C][/ROW]
[ROW][C]Median[/C][C]101.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.29[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.32119047619[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.53696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.32119047619[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.53696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.53696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.32119047619[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.53696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.32119047619[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130276&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 Mean101.3813333333330.112535359582261900.884252822114
Geometric Mean101.377641710411
Harmonic Mean101.373943398972
Quadratic Mean101.38501830481
Winsorized Mean ( 1 / 20 )101.3813333333330.112535359582261900.884252822114
Winsorized Mean ( 2 / 20 )101.3813333333330.112535359582261900.884252822114
Winsorized Mean ( 3 / 20 )101.3813333333330.112535359582261900.884252822114
Winsorized Mean ( 4 / 20 )101.380.08301963555090841221.15689050252
Winsorized Mean ( 5 / 20 )101.380.08301963555090841221.15689050252
Winsorized Mean ( 6 / 20 )101.4020.07853740697136181291.12997118654
Winsorized Mean ( 7 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 8 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 9 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 10 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 11 / 20 )101.3658333333330.07277598616273481392.84726567179
Winsorized Mean ( 12 / 20 )101.3398333333330.06954228550093141457.24047755054
Winsorized Mean ( 13 / 20 )101.3398333333330.06954228550093141457.24047755054
Winsorized Mean ( 14 / 20 )101.3398333333330.06954228550093141457.24047755054
Winsorized Mean ( 15 / 20 )101.4898333333330.04315554030635872351.72199473956
Winsorized Mean ( 16 / 20 )101.4898333333330.04315554030635872351.72199473956
Winsorized Mean ( 17 / 20 )101.4983333333330.04197400774051022418.12347204993
Winsorized Mean ( 18 / 20 )101.4983333333330.04197400774051022418.12347204993
Winsorized Mean ( 19 / 20 )101.4983333333330.04197400774051022418.12347204994
Winsorized Mean ( 20 / 20 )101.4983333333330.04197400774051022418.12347204993
Trimmed Mean ( 1 / 20 )101.3844827586210.106957362247802947.896251627172
Trimmed Mean ( 2 / 20 )101.3878571428570.1000128934174071013.74786468492
Trimmed Mean ( 3 / 20 )101.3914814814810.09118039782818861111.98770674958
Trimmed Mean ( 4 / 20 )101.3953846153850.07954217676016431274.73736255813
Trimmed Mean ( 5 / 20 )101.40.07790522761532711301.58146126834
Trimmed Mean ( 6 / 20 )101.4050.07578723951800121338.02208188245
Trimmed Mean ( 7 / 20 )101.4056521739130.07446469329960461361.79506932115
Trimmed Mean ( 8 / 20 )101.4134090909090.07422321000159341366.33014240063
Trimmed Mean ( 9 / 20 )101.4219047619050.07373575422579731375.47795946218
Trimmed Mean ( 10 / 20 )101.431250.07292003655216631390.99285732581
Trimmed Mean ( 11 / 20 )101.4415789473680.07165938706642271415.6076837964
Trimmed Mean ( 12 / 20 )101.4530555555560.06978290535704711453.83822924063
Trimmed Mean ( 13 / 20 )101.4697058823530.06772925719798971498.16652478162
Trimmed Mean ( 14 / 20 )101.48843750.06457695673948981571.58904080003
Trimmed Mean ( 15 / 20 )101.5096666666670.05970518245730941700.18183495626
Trimmed Mean ( 16 / 20 )101.51250.06157892728616151648.49412735406
Trimmed Mean ( 17 / 20 )101.5157692307690.06362914928751861595.42867329648
Trimmed Mean ( 18 / 20 )101.5183333333330.06618941491917791533.75480743099
Trimmed Mean ( 19 / 20 )101.5213636363640.06907958724733521469.62898421603
Trimmed Mean ( 20 / 20 )101.5250.07237511930723811402.76107275234
Median101.81
Midrange101.29
Midmean - Weighted Average at Xnp101.32119047619
Midmean - Weighted Average at X(n+1)p101.53696969697
Midmean - Empirical Distribution Function101.32119047619
Midmean - Empirical Distribution Function - Averaging101.53696969697
Midmean - Empirical Distribution Function - Interpolation101.53696969697
Midmean - Closest Observation101.32119047619
Midmean - True Basic - Statistics Graphics Toolkit101.53696969697
Midmean - MS Excel (old versions)101.32119047619
Number of observations60



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