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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 14:04:13 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476277636s0bxzuunpq5oc2e.htm/, Retrieved Sun, 05 May 2024 20:34:22 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 20:34:22 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
106
106,8
106,5
107,6
107,6
107,6
108,9
108,5
108,9
108,7
108,4
108,4
109,2
109,3
109,4
109,3
109
108,8
108,7
106,1
106,2
109,7
108,4
108,3
108,1
110,6
111,8
111,7
112,2
111,1
111
111
113,6
114
116,1
115,5
115,8
115,6
114,1
114,2
113,4
112
110,9
111
112,8
113,8
114,7
113,9
114,5
113,8
113,8
113,7
113
113,1
112,4
112,8
113,2
112,9
113,9
113,2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ yule.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.0916666666670.363265880329651305.813655182411
Geometric Mean111.056557338233
Harmonic Mean111.02138828814
Quadratic Mean111.126703211544
Winsorized Mean ( 1 / 20 )111.0883333333330.361736955860754307.096998339576
Winsorized Mean ( 2 / 20 )111.0850.359518078248606308.983071285737
Winsorized Mean ( 3 / 20 )111.0950.355087520046334312.866529315093
Winsorized Mean ( 4 / 20 )111.0616666666670.340314673813525326.349920272679
Winsorized Mean ( 5 / 20 )111.1116666666670.324107567993845342.823425427624
Winsorized Mean ( 6 / 20 )111.0816666666670.318962758099773348.259048574944
Winsorized Mean ( 7 / 20 )111.070.317051208681742350.321957332428
Winsorized Mean ( 8 / 20 )111.1233333333330.303066872472409366.662751447538
Winsorized Mean ( 9 / 20 )111.1383333333330.295695022175484375.854596792559
Winsorized Mean ( 10 / 20 )111.1550.293011106401406379.354220954768
Winsorized Mean ( 11 / 20 )111.1366666666670.290129200390137383.059225052911
Winsorized Mean ( 12 / 20 )111.1366666666670.290129200390137383.059225052911
Winsorized Mean ( 13 / 20 )111.1583333333330.286694503312769387.723978133147
Winsorized Mean ( 14 / 20 )111.1816666666670.275839669990539403.066269150046
Winsorized Mean ( 15 / 20 )111.1566666666670.272002063246855408.661115801121
Winsorized Mean ( 16 / 20 )111.130.2599250217835427.546371786261
Winsorized Mean ( 17 / 20 )111.1016666666670.247364545672463449.141433606162
Winsorized Mean ( 18 / 20 )111.1016666666670.247364545672463449.141433606162
Winsorized Mean ( 19 / 20 )111.1016666666670.238077180509751466.662392543397
Winsorized Mean ( 20 / 20 )111.1350.223465577677591497.324917577874
Trimmed Mean ( 1 / 20 )111.0931034482760.354786321256256313.1267943333
Trimmed Mean ( 2 / 20 )111.0982142857140.346152236152956320.951889609122
Trimmed Mean ( 3 / 20 )111.1055555555560.336872372827144329.8149819266
Trimmed Mean ( 4 / 20 )111.1096153846150.327397291591366339.372432937822
Trimmed Mean ( 5 / 20 )111.1240.321216565003508345.947289482989
Trimmed Mean ( 6 / 20 )111.1270833333330.318584240495292348.815381327613
Trimmed Mean ( 7 / 20 )111.1369565217390.316294345509796351.371935981376
Trimmed Mean ( 8 / 20 )111.150.313365081683656354.698102937348
Trimmed Mean ( 9 / 20 )111.1547619047620.312685761391393355.483925491664
Trimmed Mean ( 10 / 20 )111.15750.312842376547843355.314715437858
Trimmed Mean ( 11 / 20 )111.1578947368420.312782028160309355.384532131337
Trimmed Mean ( 12 / 20 )111.1611111111110.312396720146639355.833156823581
Trimmed Mean ( 13 / 20 )111.1647058823530.310794575762467357.67904124335
Trimmed Mean ( 14 / 20 )111.1656250.308371417202666360.492635823444
Trimmed Mean ( 15 / 20 )111.1633333333330.306687280666488362.464765711036
Trimmed Mean ( 16 / 20 )111.1642857142860.303908154363679365.782504082659
Trimmed Mean ( 17 / 20 )111.1692307692310.301879712711447368.256713148169
Trimmed Mean ( 18 / 20 )111.1791666666670.300842968250703369.558801101899
Trimmed Mean ( 19 / 20 )111.1909090909090.296728853658466374.72226822569
Trimmed Mean ( 20 / 20 )111.2050.291229245928719381.846952373795
Median111.05
Midrange111.05
Midmean - Weighted Average at Xnp111.083870967742
Midmean - Weighted Average at X(n+1)p111.083870967742
Midmean - Empirical Distribution Function111.083870967742
Midmean - Empirical Distribution Function - Averaging111.083870967742
Midmean - Empirical Distribution Function - Interpolation111.083870967742
Midmean - Closest Observation111.083870967742
Midmean - True Basic - Statistics Graphics Toolkit111.083870967742
Midmean - MS Excel (old versions)111.165625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.091666666667 & 0.363265880329651 & 305.813655182411 \tabularnewline
Geometric Mean & 111.056557338233 &  &  \tabularnewline
Harmonic Mean & 111.02138828814 &  &  \tabularnewline
Quadratic Mean & 111.126703211544 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.088333333333 & 0.361736955860754 & 307.096998339576 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 111.085 & 0.359518078248606 & 308.983071285737 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 111.095 & 0.355087520046334 & 312.866529315093 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 111.061666666667 & 0.340314673813525 & 326.349920272679 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.111666666667 & 0.324107567993845 & 342.823425427624 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.081666666667 & 0.318962758099773 & 348.259048574944 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.07 & 0.317051208681742 & 350.321957332428 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.123333333333 & 0.303066872472409 & 366.662751447538 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.138333333333 & 0.295695022175484 & 375.854596792559 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.155 & 0.293011106401406 & 379.354220954768 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.136666666667 & 0.290129200390137 & 383.059225052911 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.136666666667 & 0.290129200390137 & 383.059225052911 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.158333333333 & 0.286694503312769 & 387.723978133147 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.181666666667 & 0.275839669990539 & 403.066269150046 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.156666666667 & 0.272002063246855 & 408.661115801121 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.13 & 0.2599250217835 & 427.546371786261 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111.101666666667 & 0.247364545672463 & 449.141433606162 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.101666666667 & 0.247364545672463 & 449.141433606162 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111.101666666667 & 0.238077180509751 & 466.662392543397 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 111.135 & 0.223465577677591 & 497.324917577874 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 111.093103448276 & 0.354786321256256 & 313.1267943333 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 111.098214285714 & 0.346152236152956 & 320.951889609122 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 111.105555555556 & 0.336872372827144 & 329.8149819266 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.109615384615 & 0.327397291591366 & 339.372432937822 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.124 & 0.321216565003508 & 345.947289482989 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.127083333333 & 0.318584240495292 & 348.815381327613 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.136956521739 & 0.316294345509796 & 351.371935981376 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.15 & 0.313365081683656 & 354.698102937348 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.154761904762 & 0.312685761391393 & 355.483925491664 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.1575 & 0.312842376547843 & 355.314715437858 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.157894736842 & 0.312782028160309 & 355.384532131337 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.161111111111 & 0.312396720146639 & 355.833156823581 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.164705882353 & 0.310794575762467 & 357.67904124335 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.165625 & 0.308371417202666 & 360.492635823444 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.163333333333 & 0.306687280666488 & 362.464765711036 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.164285714286 & 0.303908154363679 & 365.782504082659 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.169230769231 & 0.301879712711447 & 368.256713148169 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.179166666667 & 0.300842968250703 & 369.558801101899 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.190909090909 & 0.296728853658466 & 374.72226822569 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111.205 & 0.291229245928719 & 381.846952373795 \tabularnewline
Median & 111.05 &  &  \tabularnewline
Midrange & 111.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.083870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.083870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.083870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.083870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.083870967742 &  &  \tabularnewline
Midmean - Closest Observation & 111.083870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.083870967742 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.165625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]111.091666666667[/C][C]0.363265880329651[/C][C]305.813655182411[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.056557338233[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.02138828814[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.126703211544[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.088333333333[/C][C]0.361736955860754[/C][C]307.096998339576[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]111.085[/C][C]0.359518078248606[/C][C]308.983071285737[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]111.095[/C][C]0.355087520046334[/C][C]312.866529315093[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]111.061666666667[/C][C]0.340314673813525[/C][C]326.349920272679[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.111666666667[/C][C]0.324107567993845[/C][C]342.823425427624[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.081666666667[/C][C]0.318962758099773[/C][C]348.259048574944[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.07[/C][C]0.317051208681742[/C][C]350.321957332428[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.123333333333[/C][C]0.303066872472409[/C][C]366.662751447538[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.138333333333[/C][C]0.295695022175484[/C][C]375.854596792559[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.155[/C][C]0.293011106401406[/C][C]379.354220954768[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.136666666667[/C][C]0.290129200390137[/C][C]383.059225052911[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.136666666667[/C][C]0.290129200390137[/C][C]383.059225052911[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.158333333333[/C][C]0.286694503312769[/C][C]387.723978133147[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.181666666667[/C][C]0.275839669990539[/C][C]403.066269150046[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.156666666667[/C][C]0.272002063246855[/C][C]408.661115801121[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.13[/C][C]0.2599250217835[/C][C]427.546371786261[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111.101666666667[/C][C]0.247364545672463[/C][C]449.141433606162[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.101666666667[/C][C]0.247364545672463[/C][C]449.141433606162[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111.101666666667[/C][C]0.238077180509751[/C][C]466.662392543397[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]111.135[/C][C]0.223465577677591[/C][C]497.324917577874[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]111.093103448276[/C][C]0.354786321256256[/C][C]313.1267943333[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]111.098214285714[/C][C]0.346152236152956[/C][C]320.951889609122[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]111.105555555556[/C][C]0.336872372827144[/C][C]329.8149819266[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.109615384615[/C][C]0.327397291591366[/C][C]339.372432937822[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.124[/C][C]0.321216565003508[/C][C]345.947289482989[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.127083333333[/C][C]0.318584240495292[/C][C]348.815381327613[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.136956521739[/C][C]0.316294345509796[/C][C]351.371935981376[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.15[/C][C]0.313365081683656[/C][C]354.698102937348[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.154761904762[/C][C]0.312685761391393[/C][C]355.483925491664[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.1575[/C][C]0.312842376547843[/C][C]355.314715437858[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.157894736842[/C][C]0.312782028160309[/C][C]355.384532131337[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.161111111111[/C][C]0.312396720146639[/C][C]355.833156823581[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.164705882353[/C][C]0.310794575762467[/C][C]357.67904124335[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.165625[/C][C]0.308371417202666[/C][C]360.492635823444[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.163333333333[/C][C]0.306687280666488[/C][C]362.464765711036[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.164285714286[/C][C]0.303908154363679[/C][C]365.782504082659[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.169230769231[/C][C]0.301879712711447[/C][C]368.256713148169[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.179166666667[/C][C]0.300842968250703[/C][C]369.558801101899[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.190909090909[/C][C]0.296728853658466[/C][C]374.72226822569[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111.205[/C][C]0.291229245928719[/C][C]381.846952373795[/C][/ROW]
[ROW][C]Median[/C][C]111.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.165625[/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=&T=1

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

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.0916666666670.363265880329651305.813655182411
Geometric Mean111.056557338233
Harmonic Mean111.02138828814
Quadratic Mean111.126703211544
Winsorized Mean ( 1 / 20 )111.0883333333330.361736955860754307.096998339576
Winsorized Mean ( 2 / 20 )111.0850.359518078248606308.983071285737
Winsorized Mean ( 3 / 20 )111.0950.355087520046334312.866529315093
Winsorized Mean ( 4 / 20 )111.0616666666670.340314673813525326.349920272679
Winsorized Mean ( 5 / 20 )111.1116666666670.324107567993845342.823425427624
Winsorized Mean ( 6 / 20 )111.0816666666670.318962758099773348.259048574944
Winsorized Mean ( 7 / 20 )111.070.317051208681742350.321957332428
Winsorized Mean ( 8 / 20 )111.1233333333330.303066872472409366.662751447538
Winsorized Mean ( 9 / 20 )111.1383333333330.295695022175484375.854596792559
Winsorized Mean ( 10 / 20 )111.1550.293011106401406379.354220954768
Winsorized Mean ( 11 / 20 )111.1366666666670.290129200390137383.059225052911
Winsorized Mean ( 12 / 20 )111.1366666666670.290129200390137383.059225052911
Winsorized Mean ( 13 / 20 )111.1583333333330.286694503312769387.723978133147
Winsorized Mean ( 14 / 20 )111.1816666666670.275839669990539403.066269150046
Winsorized Mean ( 15 / 20 )111.1566666666670.272002063246855408.661115801121
Winsorized Mean ( 16 / 20 )111.130.2599250217835427.546371786261
Winsorized Mean ( 17 / 20 )111.1016666666670.247364545672463449.141433606162
Winsorized Mean ( 18 / 20 )111.1016666666670.247364545672463449.141433606162
Winsorized Mean ( 19 / 20 )111.1016666666670.238077180509751466.662392543397
Winsorized Mean ( 20 / 20 )111.1350.223465577677591497.324917577874
Trimmed Mean ( 1 / 20 )111.0931034482760.354786321256256313.1267943333
Trimmed Mean ( 2 / 20 )111.0982142857140.346152236152956320.951889609122
Trimmed Mean ( 3 / 20 )111.1055555555560.336872372827144329.8149819266
Trimmed Mean ( 4 / 20 )111.1096153846150.327397291591366339.372432937822
Trimmed Mean ( 5 / 20 )111.1240.321216565003508345.947289482989
Trimmed Mean ( 6 / 20 )111.1270833333330.318584240495292348.815381327613
Trimmed Mean ( 7 / 20 )111.1369565217390.316294345509796351.371935981376
Trimmed Mean ( 8 / 20 )111.150.313365081683656354.698102937348
Trimmed Mean ( 9 / 20 )111.1547619047620.312685761391393355.483925491664
Trimmed Mean ( 10 / 20 )111.15750.312842376547843355.314715437858
Trimmed Mean ( 11 / 20 )111.1578947368420.312782028160309355.384532131337
Trimmed Mean ( 12 / 20 )111.1611111111110.312396720146639355.833156823581
Trimmed Mean ( 13 / 20 )111.1647058823530.310794575762467357.67904124335
Trimmed Mean ( 14 / 20 )111.1656250.308371417202666360.492635823444
Trimmed Mean ( 15 / 20 )111.1633333333330.306687280666488362.464765711036
Trimmed Mean ( 16 / 20 )111.1642857142860.303908154363679365.782504082659
Trimmed Mean ( 17 / 20 )111.1692307692310.301879712711447368.256713148169
Trimmed Mean ( 18 / 20 )111.1791666666670.300842968250703369.558801101899
Trimmed Mean ( 19 / 20 )111.1909090909090.296728853658466374.72226822569
Trimmed Mean ( 20 / 20 )111.2050.291229245928719381.846952373795
Median111.05
Midrange111.05
Midmean - Weighted Average at Xnp111.083870967742
Midmean - Weighted Average at X(n+1)p111.083870967742
Midmean - Empirical Distribution Function111.083870967742
Midmean - Empirical Distribution Function - Averaging111.083870967742
Midmean - Empirical Distribution Function - Interpolation111.083870967742
Midmean - Closest Observation111.083870967742
Midmean - True Basic - Statistics Graphics Toolkit111.083870967742
Midmean - MS Excel (old versions)111.165625
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')