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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 25 Oct 2009 17:51:56 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/26/t1256514783yhddhbqbu5q5yn8.htm/, Retrieved Thu, 02 May 2024 22:12:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50437, Retrieved Thu, 02 May 2024 22:12:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [totaal aanbod ele...] [2009-10-12 16:10:35] [12f02da0296cb21dc23d82ae014a8b71]
-   PD  [Univariate Data Series] [werkloosheid mannen] [2009-10-12 21:38:09] [4a2be4899cba879e4eea9daa25281df8]
- RMPD      [Central Tendency] [WS deel 3.2] [2009-10-25 23:51:56] [71c065898bd1c08eef04509b4bcee039] [Current]
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Dataseries X:
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50437&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50437&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.1650.084064308178944385.232367400778
Geometric Mean7.13517666382079
Harmonic Mean7.10466177304988
Quadratic Mean7.1940368824928
Winsorized Mean ( 1 / 20 )7.1650.084064308178944385.232367400778
Winsorized Mean ( 2 / 20 )7.1750.0815674480878987.9640122156188
Winsorized Mean ( 3 / 20 )7.170.080545456864238689.0180561280472
Winsorized Mean ( 4 / 20 )7.170.080545456864238689.0180561280472
Winsorized Mean ( 5 / 20 )7.170.077141736159015292.9457950650761
Winsorized Mean ( 6 / 20 )7.160.075397253018341994.9636719292437
Winsorized Mean ( 7 / 20 )7.171666666666670.072955820803258898.3015006575914
Winsorized Mean ( 8 / 20 )7.1850.0703431861789606102.142089238332
Winsorized Mean ( 9 / 20 )7.170.0678690996644683105.644542736637
Winsorized Mean ( 10 / 20 )7.170.0678690996644683105.644542736637
Winsorized Mean ( 11 / 20 )7.188333333333330.0644442415088694111.543454698648
Winsorized Mean ( 12 / 20 )7.188333333333330.0577884152890490124.390559896449
Winsorized Mean ( 13 / 20 )7.188333333333330.0577884152890490124.390559896449
Winsorized Mean ( 14 / 20 )7.211666666666670.0538931599837309133.814136503477
Winsorized Mean ( 15 / 20 )7.211666666666670.0538931599837309133.814136503477
Winsorized Mean ( 16 / 20 )7.238333333333330.0497503182096212145.493206753671
Winsorized Mean ( 17 / 20 )7.210.0454543913710794158.620537697649
Winsorized Mean ( 18 / 20 )7.210.0454543913710794158.620537697649
Winsorized Mean ( 19 / 20 )7.241666666666670.0407757867297186177.597227361127
Winsorized Mean ( 20 / 20 )7.208333333333330.0359921261529437200.275285286079
Trimmed Mean ( 1 / 20 )7.170689655172410.081724035827902887.7427256562891
Trimmed Mean ( 2 / 20 )7.176785714285710.078830373185398391.0408694553163
Trimmed Mean ( 3 / 20 )7.177777777777780.07691949318821493.3154585433175
Trimmed Mean ( 4 / 20 )7.180769230769230.075008217827231295.7331001692232
Trimmed Mean ( 5 / 20 )7.1840.072582676293721698.9767857405585
Trimmed Mean ( 6 / 20 )7.18750.0706871666705838101.680408743714
Trimmed Mean ( 7 / 20 )7.193478260869560.0687642597535209104.610713278292
Trimmed Mean ( 8 / 20 )7.197727272727270.0669865276571705107.450371357722
Trimmed Mean ( 9 / 20 )7.20.0653766004305514110.131147116596
Trimmed Mean ( 10 / 20 )7.2050.0638457676849613112.850080142385
Trimmed Mean ( 11 / 20 )7.210526315789470.0617190294923889116.828251757890
Trimmed Mean ( 12 / 20 )7.213888888888890.0597817163982457120.670487960439
Trimmed Mean ( 13 / 20 )7.217647058823530.0588769810624224122.588606422793
Trimmed Mean ( 14 / 20 )7.2218750.057455167480056125.695830623188
Trimmed Mean ( 15 / 20 )7.223333333333330.056463462569736127.929337036531
Trimmed Mean ( 16 / 20 )7.2250.0548265663793783131.779180735227
Trimmed Mean ( 17 / 20 )7.223076923076920.0535817685146708134.804750259395
Trimmed Mean ( 18 / 20 )7.2250.0529047544505998136.566175857529
Trimmed Mean ( 19 / 20 )7.227272727272730.0514641968523212140.433022748061
Trimmed Mean ( 20 / 20 )7.2250.0507185214793632142.452890763777
Median7.2
Midrange7
Midmean - Weighted Average at Xnp7.25
Midmean - Weighted Average at X(n+1)p7.25
Midmean - Empirical Distribution Function7.25
Midmean - Empirical Distribution Function - Averaging7.25
Midmean - Empirical Distribution Function - Interpolation7.25
Midmean - Closest Observation7.25
Midmean - True Basic - Statistics Graphics Toolkit7.25
Midmean - MS Excel (old versions)7.25
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.165 & 0.0840643081789443 & 85.232367400778 \tabularnewline
Geometric Mean & 7.13517666382079 &  &  \tabularnewline
Harmonic Mean & 7.10466177304988 &  &  \tabularnewline
Quadratic Mean & 7.1940368824928 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.165 & 0.0840643081789443 & 85.232367400778 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.175 & 0.08156744808789 & 87.9640122156188 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.17 & 0.0805454568642386 & 89.0180561280472 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.17 & 0.0805454568642386 & 89.0180561280472 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.17 & 0.0771417361590152 & 92.9457950650761 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.16 & 0.0753972530183419 & 94.9636719292437 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.17166666666667 & 0.0729558208032588 & 98.3015006575914 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.185 & 0.0703431861789606 & 102.142089238332 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.17 & 0.0678690996644683 & 105.644542736637 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.17 & 0.0678690996644683 & 105.644542736637 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.18833333333333 & 0.0644442415088694 & 111.543454698648 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.18833333333333 & 0.0577884152890490 & 124.390559896449 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.18833333333333 & 0.0577884152890490 & 124.390559896449 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.21166666666667 & 0.0538931599837309 & 133.814136503477 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.21166666666667 & 0.0538931599837309 & 133.814136503477 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.23833333333333 & 0.0497503182096212 & 145.493206753671 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.21 & 0.0454543913710794 & 158.620537697649 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.21 & 0.0454543913710794 & 158.620537697649 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.24166666666667 & 0.0407757867297186 & 177.597227361127 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.20833333333333 & 0.0359921261529437 & 200.275285286079 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.17068965517241 & 0.0817240358279028 & 87.7427256562891 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.17678571428571 & 0.0788303731853983 & 91.0408694553163 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.17777777777778 & 0.076919493188214 & 93.3154585433175 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.18076923076923 & 0.0750082178272312 & 95.7331001692232 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.184 & 0.0725826762937216 & 98.9767857405585 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.1875 & 0.0706871666705838 & 101.680408743714 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.19347826086956 & 0.0687642597535209 & 104.610713278292 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.19772727272727 & 0.0669865276571705 & 107.450371357722 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.2 & 0.0653766004305514 & 110.131147116596 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.205 & 0.0638457676849613 & 112.850080142385 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.21052631578947 & 0.0617190294923889 & 116.828251757890 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.21388888888889 & 0.0597817163982457 & 120.670487960439 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.21764705882353 & 0.0588769810624224 & 122.588606422793 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.221875 & 0.057455167480056 & 125.695830623188 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.22333333333333 & 0.056463462569736 & 127.929337036531 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.225 & 0.0548265663793783 & 131.779180735227 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.22307692307692 & 0.0535817685146708 & 134.804750259395 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.225 & 0.0529047544505998 & 136.566175857529 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.22727272727273 & 0.0514641968523212 & 140.433022748061 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.225 & 0.0507185214793632 & 142.452890763777 \tabularnewline
Median & 7.2 &  &  \tabularnewline
Midrange & 7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.25 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.25 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.25 &  &  \tabularnewline
Midmean - Closest Observation & 7.25 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.25 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.25 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50437&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]7.165[/C][C]0.0840643081789443[/C][C]85.232367400778[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.13517666382079[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.10466177304988[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.1940368824928[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.165[/C][C]0.0840643081789443[/C][C]85.232367400778[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.175[/C][C]0.08156744808789[/C][C]87.9640122156188[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.17[/C][C]0.0805454568642386[/C][C]89.0180561280472[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.17[/C][C]0.0805454568642386[/C][C]89.0180561280472[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.17[/C][C]0.0771417361590152[/C][C]92.9457950650761[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.16[/C][C]0.0753972530183419[/C][C]94.9636719292437[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.17166666666667[/C][C]0.0729558208032588[/C][C]98.3015006575914[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.185[/C][C]0.0703431861789606[/C][C]102.142089238332[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.17[/C][C]0.0678690996644683[/C][C]105.644542736637[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.17[/C][C]0.0678690996644683[/C][C]105.644542736637[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.18833333333333[/C][C]0.0644442415088694[/C][C]111.543454698648[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.18833333333333[/C][C]0.0577884152890490[/C][C]124.390559896449[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.18833333333333[/C][C]0.0577884152890490[/C][C]124.390559896449[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.21166666666667[/C][C]0.0538931599837309[/C][C]133.814136503477[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.21166666666667[/C][C]0.0538931599837309[/C][C]133.814136503477[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.23833333333333[/C][C]0.0497503182096212[/C][C]145.493206753671[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.21[/C][C]0.0454543913710794[/C][C]158.620537697649[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.21[/C][C]0.0454543913710794[/C][C]158.620537697649[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.24166666666667[/C][C]0.0407757867297186[/C][C]177.597227361127[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.20833333333333[/C][C]0.0359921261529437[/C][C]200.275285286079[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.17068965517241[/C][C]0.0817240358279028[/C][C]87.7427256562891[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.17678571428571[/C][C]0.0788303731853983[/C][C]91.0408694553163[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.17777777777778[/C][C]0.076919493188214[/C][C]93.3154585433175[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.18076923076923[/C][C]0.0750082178272312[/C][C]95.7331001692232[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.184[/C][C]0.0725826762937216[/C][C]98.9767857405585[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.1875[/C][C]0.0706871666705838[/C][C]101.680408743714[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.19347826086956[/C][C]0.0687642597535209[/C][C]104.610713278292[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.19772727272727[/C][C]0.0669865276571705[/C][C]107.450371357722[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.2[/C][C]0.0653766004305514[/C][C]110.131147116596[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.205[/C][C]0.0638457676849613[/C][C]112.850080142385[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.21052631578947[/C][C]0.0617190294923889[/C][C]116.828251757890[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.21388888888889[/C][C]0.0597817163982457[/C][C]120.670487960439[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.21764705882353[/C][C]0.0588769810624224[/C][C]122.588606422793[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.221875[/C][C]0.057455167480056[/C][C]125.695830623188[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.22333333333333[/C][C]0.056463462569736[/C][C]127.929337036531[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.225[/C][C]0.0548265663793783[/C][C]131.779180735227[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.22307692307692[/C][C]0.0535817685146708[/C][C]134.804750259395[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.225[/C][C]0.0529047544505998[/C][C]136.566175857529[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.22727272727273[/C][C]0.0514641968523212[/C][C]140.433022748061[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.225[/C][C]0.0507185214793632[/C][C]142.452890763777[/C][/ROW]
[ROW][C]Median[/C][C]7.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.25[/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=50437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50437&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 Mean7.1650.084064308178944385.232367400778
Geometric Mean7.13517666382079
Harmonic Mean7.10466177304988
Quadratic Mean7.1940368824928
Winsorized Mean ( 1 / 20 )7.1650.084064308178944385.232367400778
Winsorized Mean ( 2 / 20 )7.1750.0815674480878987.9640122156188
Winsorized Mean ( 3 / 20 )7.170.080545456864238689.0180561280472
Winsorized Mean ( 4 / 20 )7.170.080545456864238689.0180561280472
Winsorized Mean ( 5 / 20 )7.170.077141736159015292.9457950650761
Winsorized Mean ( 6 / 20 )7.160.075397253018341994.9636719292437
Winsorized Mean ( 7 / 20 )7.171666666666670.072955820803258898.3015006575914
Winsorized Mean ( 8 / 20 )7.1850.0703431861789606102.142089238332
Winsorized Mean ( 9 / 20 )7.170.0678690996644683105.644542736637
Winsorized Mean ( 10 / 20 )7.170.0678690996644683105.644542736637
Winsorized Mean ( 11 / 20 )7.188333333333330.0644442415088694111.543454698648
Winsorized Mean ( 12 / 20 )7.188333333333330.0577884152890490124.390559896449
Winsorized Mean ( 13 / 20 )7.188333333333330.0577884152890490124.390559896449
Winsorized Mean ( 14 / 20 )7.211666666666670.0538931599837309133.814136503477
Winsorized Mean ( 15 / 20 )7.211666666666670.0538931599837309133.814136503477
Winsorized Mean ( 16 / 20 )7.238333333333330.0497503182096212145.493206753671
Winsorized Mean ( 17 / 20 )7.210.0454543913710794158.620537697649
Winsorized Mean ( 18 / 20 )7.210.0454543913710794158.620537697649
Winsorized Mean ( 19 / 20 )7.241666666666670.0407757867297186177.597227361127
Winsorized Mean ( 20 / 20 )7.208333333333330.0359921261529437200.275285286079
Trimmed Mean ( 1 / 20 )7.170689655172410.081724035827902887.7427256562891
Trimmed Mean ( 2 / 20 )7.176785714285710.078830373185398391.0408694553163
Trimmed Mean ( 3 / 20 )7.177777777777780.07691949318821493.3154585433175
Trimmed Mean ( 4 / 20 )7.180769230769230.075008217827231295.7331001692232
Trimmed Mean ( 5 / 20 )7.1840.072582676293721698.9767857405585
Trimmed Mean ( 6 / 20 )7.18750.0706871666705838101.680408743714
Trimmed Mean ( 7 / 20 )7.193478260869560.0687642597535209104.610713278292
Trimmed Mean ( 8 / 20 )7.197727272727270.0669865276571705107.450371357722
Trimmed Mean ( 9 / 20 )7.20.0653766004305514110.131147116596
Trimmed Mean ( 10 / 20 )7.2050.0638457676849613112.850080142385
Trimmed Mean ( 11 / 20 )7.210526315789470.0617190294923889116.828251757890
Trimmed Mean ( 12 / 20 )7.213888888888890.0597817163982457120.670487960439
Trimmed Mean ( 13 / 20 )7.217647058823530.0588769810624224122.588606422793
Trimmed Mean ( 14 / 20 )7.2218750.057455167480056125.695830623188
Trimmed Mean ( 15 / 20 )7.223333333333330.056463462569736127.929337036531
Trimmed Mean ( 16 / 20 )7.2250.0548265663793783131.779180735227
Trimmed Mean ( 17 / 20 )7.223076923076920.0535817685146708134.804750259395
Trimmed Mean ( 18 / 20 )7.2250.0529047544505998136.566175857529
Trimmed Mean ( 19 / 20 )7.227272727272730.0514641968523212140.433022748061
Trimmed Mean ( 20 / 20 )7.2250.0507185214793632142.452890763777
Median7.2
Midrange7
Midmean - Weighted Average at Xnp7.25
Midmean - Weighted Average at X(n+1)p7.25
Midmean - Empirical Distribution Function7.25
Midmean - Empirical Distribution Function - Averaging7.25
Midmean - Empirical Distribution Function - Interpolation7.25
Midmean - Closest Observation7.25
Midmean - True Basic - Statistics Graphics Toolkit7.25
Midmean - MS Excel (old versions)7.25
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')