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of Irreproducible Research!

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 18:17:01 -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/t1256516287u3d2q14844zp556.htm/, Retrieved Thu, 02 May 2024 18:44:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50443, Retrieved Thu, 02 May 2024 18:44:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [WS3, part 1-3] [2009-10-20 14:26:04] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P   [Harrell-Davis Quantiles] [WS3 part 1 -3] [2009-10-20 14:31:26] [ed603017d2bee8fbd82b6d5ec04e12c3]
- RMPD    [Univariate Explorative Data Analysis] [WS part 2y(t)- co...] [2009-10-20 15:38:58] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D      [Univariate Explorative Data Analysis] [WS 3 deel III.3] [2009-10-25 23:57:54] [4a2be4899cba879e4eea9daa25281df8]
- RMPD          [Central Tendency] [WS 3 deel III.6] [2009-10-26 00:17:01] [71c065898bd1c08eef04509b4bcee039] [Current]
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Dataseries X:
2.4
2.8
2.9
2.5
2.3
2.4
2.6
2.6
2.6
2.3
2.3
1.9
2.3
2.3
2.4
2.5
2.5
2.7
2.9
3
3
3
2.7
2.1
1.7
1.4
1.5
1.7
1.8
1.9
2
1.9
1.7
1.8
1.6
1.2
1.5
1.4
1.2
1.1
1
1.3
1.6
1.6
1.2
0.9
0.6
0.9
2
2.1
1.7
0.9
0.6
1
1.9
2.5
2.7
2.5
2.2
2.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50443&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50443&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.9650.084064308178944323.3749618900947
Geometric Mean1.83710329843613
Harmonic Mean1.68404101578230
Quadratic Mean2.06837295154106
Winsorized Mean ( 1 / 20 )1.9650.084064308178944323.3749618900947
Winsorized Mean ( 2 / 20 )1.9750.0815674480878924.2130904705013
Winsorized Mean ( 3 / 20 )1.970.080545456864238624.458238573536
Winsorized Mean ( 4 / 20 )1.970.080545456864238624.458238573536
Winsorized Mean ( 5 / 20 )1.970.077141736159015225.5374081280614
Winsorized Mean ( 6 / 20 )1.960.075397253018341925.9956420364969
Winsorized Mean ( 7 / 20 )1.971666666666670.072955820803258827.0254880961958
Winsorized Mean ( 8 / 20 )1.9850.070343186178960628.2187957046749
Winsorized Mean ( 9 / 20 )1.970.067869099664468329.0264643223396
Winsorized Mean ( 10 / 20 )1.970.067869099664468329.0264643223396
Winsorized Mean ( 11 / 20 )1.988333333333330.064444241508869430.853545433686
Winsorized Mean ( 12 / 20 )1.988333333333330.057788415289048934.4071268157812
Winsorized Mean ( 13 / 20 )1.988333333333330.057788415289048934.4071268157812
Winsorized Mean ( 14 / 20 )2.011666666666670.053893159983730937.3269384700014
Winsorized Mean ( 15 / 20 )2.011666666666670.053893159983730937.3269384700014
Winsorized Mean ( 16 / 20 )2.038333333333330.049750318209621240.9712622288140
Winsorized Mean ( 17 / 20 )2.010.045454391371079444.2201498990673
Winsorized Mean ( 18 / 20 )2.010.045454391371079444.2201498990673
Winsorized Mean ( 19 / 20 )2.041666666666670.040775786729718650.070564676037
Winsorized Mean ( 20 / 20 )2.008333333333330.035992126152943755.7992413340404
Trimmed Mean ( 1 / 20 )1.970689655172410.081724035827902824.1139541777202
Trimmed Mean ( 2 / 20 )1.976785714285710.078830373185398325.0764474961521
Trimmed Mean ( 3 / 20 )1.977777777777780.07691949318821425.7123090103878
Trimmed Mean ( 4 / 20 )1.980769230769230.075008217827231226.4073629283074
Trimmed Mean ( 5 / 20 )1.9840.072582676293721627.3343461733391
Trimmed Mean ( 6 / 20 )1.98750.070687166670583828.1168434613053
Trimmed Mean ( 7 / 20 )1.993478260869570.068764259753520928.9900344745221
Trimmed Mean ( 8 / 20 )1.997727272727270.066986527657170529.8228217314296
Trimmed Mean ( 9 / 20 )20.065376600430551530.5919853101657
Trimmed Mean ( 10 / 20 )2.0050.063845767684961331.4038043977075
Trimmed Mean ( 11 / 20 )2.010526315789470.061719029492388932.5754687383315
Trimmed Mean ( 12 / 20 )2.013888888888890.059781716398245733.6873714945392
Trimmed Mean ( 13 / 20 )2.017647058823530.058876981062422434.2688606381564
Trimmed Mean ( 14 / 20 )2.0218750.05745516748005635.1904813557777
Trimmed Mean ( 15 / 20 )2.023333333333330.05646346256973635.8343828247229
Trimmed Mean ( 16 / 20 )2.0250.054826566379378336.9346492718109
Trimmed Mean ( 17 / 20 )2.023076923076920.053581768514670837.7568150353791
Trimmed Mean ( 18 / 20 )2.0250.052904754450599838.2763330258126
Trimmed Mean ( 19 / 20 )2.027272727272730.051464196852321239.3919044941103
Trimmed Mean ( 20 / 20 )2.0250.050718521479363239.9262427400205
Median2
Midrange1.8
Midmean - Weighted Average at Xnp2.05
Midmean - Weighted Average at X(n+1)p2.05
Midmean - Empirical Distribution Function2.05
Midmean - Empirical Distribution Function - Averaging2.05
Midmean - Empirical Distribution Function - Interpolation2.05
Midmean - Closest Observation2.05
Midmean - True Basic - Statistics Graphics Toolkit2.05
Midmean - MS Excel (old versions)2.05
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.965 & 0.0840643081789443 & 23.3749618900947 \tabularnewline
Geometric Mean & 1.83710329843613 &  &  \tabularnewline
Harmonic Mean & 1.68404101578230 &  &  \tabularnewline
Quadratic Mean & 2.06837295154106 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.965 & 0.0840643081789443 & 23.3749618900947 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.975 & 0.08156744808789 & 24.2130904705013 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.97 & 0.0805454568642386 & 24.458238573536 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.97 & 0.0805454568642386 & 24.458238573536 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.97 & 0.0771417361590152 & 25.5374081280614 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.96 & 0.0753972530183419 & 25.9956420364969 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.97166666666667 & 0.0729558208032588 & 27.0254880961958 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.985 & 0.0703431861789606 & 28.2187957046749 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.97 & 0.0678690996644683 & 29.0264643223396 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.97 & 0.0678690996644683 & 29.0264643223396 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.98833333333333 & 0.0644442415088694 & 30.853545433686 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.98833333333333 & 0.0577884152890489 & 34.4071268157812 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.98833333333333 & 0.0577884152890489 & 34.4071268157812 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.01166666666667 & 0.0538931599837309 & 37.3269384700014 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.01166666666667 & 0.0538931599837309 & 37.3269384700014 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.03833333333333 & 0.0497503182096212 & 40.9712622288140 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.01 & 0.0454543913710794 & 44.2201498990673 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.01 & 0.0454543913710794 & 44.2201498990673 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.04166666666667 & 0.0407757867297186 & 50.070564676037 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.00833333333333 & 0.0359921261529437 & 55.7992413340404 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.97068965517241 & 0.0817240358279028 & 24.1139541777202 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.97678571428571 & 0.0788303731853983 & 25.0764474961521 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.97777777777778 & 0.076919493188214 & 25.7123090103878 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.98076923076923 & 0.0750082178272312 & 26.4073629283074 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.984 & 0.0725826762937216 & 27.3343461733391 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.9875 & 0.0706871666705838 & 28.1168434613053 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.99347826086957 & 0.0687642597535209 & 28.9900344745221 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.99772727272727 & 0.0669865276571705 & 29.8228217314296 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2 & 0.0653766004305515 & 30.5919853101657 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.005 & 0.0638457676849613 & 31.4038043977075 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.01052631578947 & 0.0617190294923889 & 32.5754687383315 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.01388888888889 & 0.0597817163982457 & 33.6873714945392 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.01764705882353 & 0.0588769810624224 & 34.2688606381564 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.021875 & 0.057455167480056 & 35.1904813557777 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.02333333333333 & 0.056463462569736 & 35.8343828247229 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.025 & 0.0548265663793783 & 36.9346492718109 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.02307692307692 & 0.0535817685146708 & 37.7568150353791 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.025 & 0.0529047544505998 & 38.2763330258126 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.02727272727273 & 0.0514641968523212 & 39.3919044941103 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.025 & 0.0507185214793632 & 39.9262427400205 \tabularnewline
Median & 2 &  &  \tabularnewline
Midrange & 1.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.05 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.05 &  &  \tabularnewline
Midmean - Closest Observation & 2.05 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.05 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.05 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50443&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.965[/C][C]0.0840643081789443[/C][C]23.3749618900947[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.83710329843613[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.68404101578230[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.06837295154106[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.965[/C][C]0.0840643081789443[/C][C]23.3749618900947[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.975[/C][C]0.08156744808789[/C][C]24.2130904705013[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.97[/C][C]0.0805454568642386[/C][C]24.458238573536[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.97[/C][C]0.0805454568642386[/C][C]24.458238573536[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.97[/C][C]0.0771417361590152[/C][C]25.5374081280614[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.96[/C][C]0.0753972530183419[/C][C]25.9956420364969[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.97166666666667[/C][C]0.0729558208032588[/C][C]27.0254880961958[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.985[/C][C]0.0703431861789606[/C][C]28.2187957046749[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.97[/C][C]0.0678690996644683[/C][C]29.0264643223396[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.97[/C][C]0.0678690996644683[/C][C]29.0264643223396[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.98833333333333[/C][C]0.0644442415088694[/C][C]30.853545433686[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.98833333333333[/C][C]0.0577884152890489[/C][C]34.4071268157812[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.98833333333333[/C][C]0.0577884152890489[/C][C]34.4071268157812[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.01166666666667[/C][C]0.0538931599837309[/C][C]37.3269384700014[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.01166666666667[/C][C]0.0538931599837309[/C][C]37.3269384700014[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.03833333333333[/C][C]0.0497503182096212[/C][C]40.9712622288140[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.01[/C][C]0.0454543913710794[/C][C]44.2201498990673[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.01[/C][C]0.0454543913710794[/C][C]44.2201498990673[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.04166666666667[/C][C]0.0407757867297186[/C][C]50.070564676037[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.00833333333333[/C][C]0.0359921261529437[/C][C]55.7992413340404[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.97068965517241[/C][C]0.0817240358279028[/C][C]24.1139541777202[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.97678571428571[/C][C]0.0788303731853983[/C][C]25.0764474961521[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.97777777777778[/C][C]0.076919493188214[/C][C]25.7123090103878[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.98076923076923[/C][C]0.0750082178272312[/C][C]26.4073629283074[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.984[/C][C]0.0725826762937216[/C][C]27.3343461733391[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.9875[/C][C]0.0706871666705838[/C][C]28.1168434613053[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.99347826086957[/C][C]0.0687642597535209[/C][C]28.9900344745221[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.99772727272727[/C][C]0.0669865276571705[/C][C]29.8228217314296[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2[/C][C]0.0653766004305515[/C][C]30.5919853101657[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.005[/C][C]0.0638457676849613[/C][C]31.4038043977075[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.01052631578947[/C][C]0.0617190294923889[/C][C]32.5754687383315[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.01388888888889[/C][C]0.0597817163982457[/C][C]33.6873714945392[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.01764705882353[/C][C]0.0588769810624224[/C][C]34.2688606381564[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.021875[/C][C]0.057455167480056[/C][C]35.1904813557777[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.02333333333333[/C][C]0.056463462569736[/C][C]35.8343828247229[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.025[/C][C]0.0548265663793783[/C][C]36.9346492718109[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.02307692307692[/C][C]0.0535817685146708[/C][C]37.7568150353791[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.025[/C][C]0.0529047544505998[/C][C]38.2763330258126[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.02727272727273[/C][C]0.0514641968523212[/C][C]39.3919044941103[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.025[/C][C]0.0507185214793632[/C][C]39.9262427400205[/C][/ROW]
[ROW][C]Median[/C][C]2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.05[/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=50443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50443&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.9650.084064308178944323.3749618900947
Geometric Mean1.83710329843613
Harmonic Mean1.68404101578230
Quadratic Mean2.06837295154106
Winsorized Mean ( 1 / 20 )1.9650.084064308178944323.3749618900947
Winsorized Mean ( 2 / 20 )1.9750.0815674480878924.2130904705013
Winsorized Mean ( 3 / 20 )1.970.080545456864238624.458238573536
Winsorized Mean ( 4 / 20 )1.970.080545456864238624.458238573536
Winsorized Mean ( 5 / 20 )1.970.077141736159015225.5374081280614
Winsorized Mean ( 6 / 20 )1.960.075397253018341925.9956420364969
Winsorized Mean ( 7 / 20 )1.971666666666670.072955820803258827.0254880961958
Winsorized Mean ( 8 / 20 )1.9850.070343186178960628.2187957046749
Winsorized Mean ( 9 / 20 )1.970.067869099664468329.0264643223396
Winsorized Mean ( 10 / 20 )1.970.067869099664468329.0264643223396
Winsorized Mean ( 11 / 20 )1.988333333333330.064444241508869430.853545433686
Winsorized Mean ( 12 / 20 )1.988333333333330.057788415289048934.4071268157812
Winsorized Mean ( 13 / 20 )1.988333333333330.057788415289048934.4071268157812
Winsorized Mean ( 14 / 20 )2.011666666666670.053893159983730937.3269384700014
Winsorized Mean ( 15 / 20 )2.011666666666670.053893159983730937.3269384700014
Winsorized Mean ( 16 / 20 )2.038333333333330.049750318209621240.9712622288140
Winsorized Mean ( 17 / 20 )2.010.045454391371079444.2201498990673
Winsorized Mean ( 18 / 20 )2.010.045454391371079444.2201498990673
Winsorized Mean ( 19 / 20 )2.041666666666670.040775786729718650.070564676037
Winsorized Mean ( 20 / 20 )2.008333333333330.035992126152943755.7992413340404
Trimmed Mean ( 1 / 20 )1.970689655172410.081724035827902824.1139541777202
Trimmed Mean ( 2 / 20 )1.976785714285710.078830373185398325.0764474961521
Trimmed Mean ( 3 / 20 )1.977777777777780.07691949318821425.7123090103878
Trimmed Mean ( 4 / 20 )1.980769230769230.075008217827231226.4073629283074
Trimmed Mean ( 5 / 20 )1.9840.072582676293721627.3343461733391
Trimmed Mean ( 6 / 20 )1.98750.070687166670583828.1168434613053
Trimmed Mean ( 7 / 20 )1.993478260869570.068764259753520928.9900344745221
Trimmed Mean ( 8 / 20 )1.997727272727270.066986527657170529.8228217314296
Trimmed Mean ( 9 / 20 )20.065376600430551530.5919853101657
Trimmed Mean ( 10 / 20 )2.0050.063845767684961331.4038043977075
Trimmed Mean ( 11 / 20 )2.010526315789470.061719029492388932.5754687383315
Trimmed Mean ( 12 / 20 )2.013888888888890.059781716398245733.6873714945392
Trimmed Mean ( 13 / 20 )2.017647058823530.058876981062422434.2688606381564
Trimmed Mean ( 14 / 20 )2.0218750.05745516748005635.1904813557777
Trimmed Mean ( 15 / 20 )2.023333333333330.05646346256973635.8343828247229
Trimmed Mean ( 16 / 20 )2.0250.054826566379378336.9346492718109
Trimmed Mean ( 17 / 20 )2.023076923076920.053581768514670837.7568150353791
Trimmed Mean ( 18 / 20 )2.0250.052904754450599838.2763330258126
Trimmed Mean ( 19 / 20 )2.027272727272730.051464196852321239.3919044941103
Trimmed Mean ( 20 / 20 )2.0250.050718521479363239.9262427400205
Median2
Midrange1.8
Midmean - Weighted Average at Xnp2.05
Midmean - Weighted Average at X(n+1)p2.05
Midmean - Empirical Distribution Function2.05
Midmean - Empirical Distribution Function - Averaging2.05
Midmean - Empirical Distribution Function - Interpolation2.05
Midmean - Closest Observation2.05
Midmean - True Basic - Statistics Graphics Toolkit2.05
Midmean - MS Excel (old versions)2.05
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')