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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 22 Oct 2011 08:21:05 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/22/t13192862288o43kls0c3y2b9f.htm/, Retrieved Thu, 16 May 2024 00:56:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=133754, Retrieved Thu, 16 May 2024 00:56:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a, verbeterd
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [Decielen gem. pri...] [2011-10-22 12:09:49] [73b366456746118303ac4651ed29b8f6]
- RMP     [Central Tendency] [Gem. prijs reis n...] [2011-10-22 12:21:05] [a207ad521877ea2910ca3b39cbf26b1e] [Current]
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Dataseries X:
104.77
111.04
104.5
102.42
103.05
105.84
107.92
108.22
104.26
105.19
103.25
108.16
105.27
113.99
109.84
104.33
105.48
109.68
111.54
110.63
107.8
108.02
105.59
111.64
107
116.14
117.18
102.28
109.43
114.28
117.39
116.66
114.29
114.18
114.12
122.62
115.7
127.91
119.55
115.08
116.63
121.38
123.41
120.7
119.4
116.83
116.4
121.67
116.54
129.61
119.93
117.64
121.01
124.2
125.23
123.24
121.58
120.89
117.77
110.91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=133754&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=133754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=133754&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.6868333333330.915876490194995124.129000526183
Geometric Mean113.469842047672
Harmonic Mean113.253733619283
Quadratic Mean113.904288893497
Winsorized Mean ( 1 / 20 )113.6608333333330.90743844763838125.254592891823
Winsorized Mean ( 2 / 20 )113.59250.881189829456016128.90809244828
Winsorized Mean ( 3 / 20 )113.5510.868049104940251130.811724076158
Winsorized Mean ( 4 / 20 )113.5656666666670.844298403840094134.508920246846
Winsorized Mean ( 5 / 20 )113.5573333333330.840427718206147135.118500822077
Winsorized Mean ( 6 / 20 )113.5123333333330.82541957715016137.520766984042
Winsorized Mean ( 7 / 20 )113.4330.799561225011802141.869060744317
Winsorized Mean ( 8 / 20 )113.4770.787328792258129144.129112406188
Winsorized Mean ( 9 / 20 )113.4590.779992166410033145.461717291601
Winsorized Mean ( 10 / 20 )113.4323333333330.763291059199971148.609540182778
Winsorized Mean ( 11 / 20 )113.43050.756047648372885150.030887926333
Winsorized Mean ( 12 / 20 )113.44250.740973692321033153.099227645521
Winsorized Mean ( 13 / 20 )113.5270.670987605870361169.193885262218
Winsorized Mean ( 14 / 20 )113.6250.626592186642622181.338041587816
Winsorized Mean ( 15 / 20 )113.61750.615887702774929184.47762390463
Winsorized Mean ( 16 / 20 )113.20950.546074818708131207.314998094627
Winsorized Mean ( 17 / 20 )113.2123333333330.534509774168567211.805917879492
Winsorized Mean ( 18 / 20 )113.1553333333330.521193028788763217.108301690648
Winsorized Mean ( 19 / 20 )113.4720.452092798333577250.992717464777
Winsorized Mean ( 20 / 20 )113.4386666666670.423475829036059267.8751864655
Trimmed Mean ( 1 / 20 )113.6089655172410.884333384400011128.46847978528
Trimmed Mean ( 2 / 20 )113.5533928571430.85575914793346132.693168552575
Trimmed Mean ( 3 / 20 )113.5316666666670.837800844512816135.511520918418
Trimmed Mean ( 4 / 20 )113.5242307692310.82140901577908138.206701641273
Trimmed Mean ( 5 / 20 )113.51180.80957941663356140.210827582563
Trimmed Mean ( 6 / 20 )113.5004166666670.795272654878141142.718872540711
Trimmed Mean ( 7 / 20 )113.4978260869570.781010117215268145.321838456637
Trimmed Mean ( 8 / 20 )113.5104545454550.7692853795537147.55311560881
Trimmed Mean ( 9 / 20 )113.5164285714290.756442159827675150.066237182349
Trimmed Mean ( 10 / 20 )113.5260.740535824719039153.302509089377
Trimmed Mean ( 11 / 20 )113.5407894736840.722891733430108157.064722451501
Trimmed Mean ( 12 / 20 )113.55750.700057183038507162.211748913308
Trimmed Mean ( 13 / 20 )113.5744117647060.672158333669718168.969729415738
Trimmed Mean ( 14 / 20 )113.581250.65323184609912173.875861500429
Trimmed Mean ( 15 / 20 )113.5750.638107970181532177.987120216802
Trimmed Mean ( 16 / 20 )113.5689285714290.617574908012625183.894985204138
Trimmed Mean ( 17 / 20 )113.6207692307690.607425822777987187.052912421699
Trimmed Mean ( 18 / 20 )113.6808333333330.592475742995987191.874240721621
Trimmed Mean ( 19 / 20 )113.7604545454550.569896123774285199.616122657663
Trimmed Mean ( 20 / 20 )113.8060.56092376815768202.890314977718
Median114.23
Midrange115.945
Midmean - Weighted Average at Xnp113.388709677419
Midmean - Weighted Average at X(n+1)p113.575
Midmean - Empirical Distribution Function113.388709677419
Midmean - Empirical Distribution Function - Averaging113.575
Midmean - Empirical Distribution Function - Interpolation113.575
Midmean - Closest Observation113.388709677419
Midmean - True Basic - Statistics Graphics Toolkit113.575
Midmean - MS Excel (old versions)113.58125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.686833333333 & 0.915876490194995 & 124.129000526183 \tabularnewline
Geometric Mean & 113.469842047672 &  &  \tabularnewline
Harmonic Mean & 113.253733619283 &  &  \tabularnewline
Quadratic Mean & 113.904288893497 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 113.660833333333 & 0.90743844763838 & 125.254592891823 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 113.5925 & 0.881189829456016 & 128.90809244828 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 113.551 & 0.868049104940251 & 130.811724076158 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 113.565666666667 & 0.844298403840094 & 134.508920246846 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 113.557333333333 & 0.840427718206147 & 135.118500822077 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 113.512333333333 & 0.82541957715016 & 137.520766984042 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 113.433 & 0.799561225011802 & 141.869060744317 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 113.477 & 0.787328792258129 & 144.129112406188 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 113.459 & 0.779992166410033 & 145.461717291601 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 113.432333333333 & 0.763291059199971 & 148.609540182778 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 113.4305 & 0.756047648372885 & 150.030887926333 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 113.4425 & 0.740973692321033 & 153.099227645521 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 113.527 & 0.670987605870361 & 169.193885262218 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 113.625 & 0.626592186642622 & 181.338041587816 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 113.6175 & 0.615887702774929 & 184.47762390463 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 113.2095 & 0.546074818708131 & 207.314998094627 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 113.212333333333 & 0.534509774168567 & 211.805917879492 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 113.155333333333 & 0.521193028788763 & 217.108301690648 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 113.472 & 0.452092798333577 & 250.992717464777 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 113.438666666667 & 0.423475829036059 & 267.8751864655 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 113.608965517241 & 0.884333384400011 & 128.46847978528 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 113.553392857143 & 0.85575914793346 & 132.693168552575 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 113.531666666667 & 0.837800844512816 & 135.511520918418 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 113.524230769231 & 0.82140901577908 & 138.206701641273 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 113.5118 & 0.80957941663356 & 140.210827582563 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 113.500416666667 & 0.795272654878141 & 142.718872540711 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 113.497826086957 & 0.781010117215268 & 145.321838456637 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 113.510454545455 & 0.7692853795537 & 147.55311560881 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 113.516428571429 & 0.756442159827675 & 150.066237182349 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 113.526 & 0.740535824719039 & 153.302509089377 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 113.540789473684 & 0.722891733430108 & 157.064722451501 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 113.5575 & 0.700057183038507 & 162.211748913308 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 113.574411764706 & 0.672158333669718 & 168.969729415738 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 113.58125 & 0.65323184609912 & 173.875861500429 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 113.575 & 0.638107970181532 & 177.987120216802 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 113.568928571429 & 0.617574908012625 & 183.894985204138 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 113.620769230769 & 0.607425822777987 & 187.052912421699 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 113.680833333333 & 0.592475742995987 & 191.874240721621 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 113.760454545455 & 0.569896123774285 & 199.616122657663 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 113.806 & 0.56092376815768 & 202.890314977718 \tabularnewline
Median & 114.23 &  &  \tabularnewline
Midrange & 115.945 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 113.388709677419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 113.575 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 113.388709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 113.575 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 113.575 &  &  \tabularnewline
Midmean - Closest Observation & 113.388709677419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 113.575 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 113.58125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=133754&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]113.686833333333[/C][C]0.915876490194995[/C][C]124.129000526183[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.469842047672[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.253733619283[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.904288893497[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]113.660833333333[/C][C]0.90743844763838[/C][C]125.254592891823[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]113.5925[/C][C]0.881189829456016[/C][C]128.90809244828[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]113.551[/C][C]0.868049104940251[/C][C]130.811724076158[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]113.565666666667[/C][C]0.844298403840094[/C][C]134.508920246846[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]113.557333333333[/C][C]0.840427718206147[/C][C]135.118500822077[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]113.512333333333[/C][C]0.82541957715016[/C][C]137.520766984042[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]113.433[/C][C]0.799561225011802[/C][C]141.869060744317[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]113.477[/C][C]0.787328792258129[/C][C]144.129112406188[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]113.459[/C][C]0.779992166410033[/C][C]145.461717291601[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]113.432333333333[/C][C]0.763291059199971[/C][C]148.609540182778[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]113.4305[/C][C]0.756047648372885[/C][C]150.030887926333[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]113.4425[/C][C]0.740973692321033[/C][C]153.099227645521[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]113.527[/C][C]0.670987605870361[/C][C]169.193885262218[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]113.625[/C][C]0.626592186642622[/C][C]181.338041587816[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]113.6175[/C][C]0.615887702774929[/C][C]184.47762390463[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]113.2095[/C][C]0.546074818708131[/C][C]207.314998094627[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]113.212333333333[/C][C]0.534509774168567[/C][C]211.805917879492[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]113.155333333333[/C][C]0.521193028788763[/C][C]217.108301690648[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]113.472[/C][C]0.452092798333577[/C][C]250.992717464777[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]113.438666666667[/C][C]0.423475829036059[/C][C]267.8751864655[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]113.608965517241[/C][C]0.884333384400011[/C][C]128.46847978528[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]113.553392857143[/C][C]0.85575914793346[/C][C]132.693168552575[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]113.531666666667[/C][C]0.837800844512816[/C][C]135.511520918418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]113.524230769231[/C][C]0.82140901577908[/C][C]138.206701641273[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]113.5118[/C][C]0.80957941663356[/C][C]140.210827582563[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]113.500416666667[/C][C]0.795272654878141[/C][C]142.718872540711[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]113.497826086957[/C][C]0.781010117215268[/C][C]145.321838456637[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]113.510454545455[/C][C]0.7692853795537[/C][C]147.55311560881[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]113.516428571429[/C][C]0.756442159827675[/C][C]150.066237182349[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]113.526[/C][C]0.740535824719039[/C][C]153.302509089377[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]113.540789473684[/C][C]0.722891733430108[/C][C]157.064722451501[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]113.5575[/C][C]0.700057183038507[/C][C]162.211748913308[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]113.574411764706[/C][C]0.672158333669718[/C][C]168.969729415738[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]113.58125[/C][C]0.65323184609912[/C][C]173.875861500429[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]113.575[/C][C]0.638107970181532[/C][C]177.987120216802[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]113.568928571429[/C][C]0.617574908012625[/C][C]183.894985204138[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]113.620769230769[/C][C]0.607425822777987[/C][C]187.052912421699[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]113.680833333333[/C][C]0.592475742995987[/C][C]191.874240721621[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]113.760454545455[/C][C]0.569896123774285[/C][C]199.616122657663[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]113.806[/C][C]0.56092376815768[/C][C]202.890314977718[/C][/ROW]
[ROW][C]Median[/C][C]114.23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]115.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]113.388709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]113.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]113.388709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]113.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]113.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.388709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]113.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]113.58125[/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=133754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=133754&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 Mean113.6868333333330.915876490194995124.129000526183
Geometric Mean113.469842047672
Harmonic Mean113.253733619283
Quadratic Mean113.904288893497
Winsorized Mean ( 1 / 20 )113.6608333333330.90743844763838125.254592891823
Winsorized Mean ( 2 / 20 )113.59250.881189829456016128.90809244828
Winsorized Mean ( 3 / 20 )113.5510.868049104940251130.811724076158
Winsorized Mean ( 4 / 20 )113.5656666666670.844298403840094134.508920246846
Winsorized Mean ( 5 / 20 )113.5573333333330.840427718206147135.118500822077
Winsorized Mean ( 6 / 20 )113.5123333333330.82541957715016137.520766984042
Winsorized Mean ( 7 / 20 )113.4330.799561225011802141.869060744317
Winsorized Mean ( 8 / 20 )113.4770.787328792258129144.129112406188
Winsorized Mean ( 9 / 20 )113.4590.779992166410033145.461717291601
Winsorized Mean ( 10 / 20 )113.4323333333330.763291059199971148.609540182778
Winsorized Mean ( 11 / 20 )113.43050.756047648372885150.030887926333
Winsorized Mean ( 12 / 20 )113.44250.740973692321033153.099227645521
Winsorized Mean ( 13 / 20 )113.5270.670987605870361169.193885262218
Winsorized Mean ( 14 / 20 )113.6250.626592186642622181.338041587816
Winsorized Mean ( 15 / 20 )113.61750.615887702774929184.47762390463
Winsorized Mean ( 16 / 20 )113.20950.546074818708131207.314998094627
Winsorized Mean ( 17 / 20 )113.2123333333330.534509774168567211.805917879492
Winsorized Mean ( 18 / 20 )113.1553333333330.521193028788763217.108301690648
Winsorized Mean ( 19 / 20 )113.4720.452092798333577250.992717464777
Winsorized Mean ( 20 / 20 )113.4386666666670.423475829036059267.8751864655
Trimmed Mean ( 1 / 20 )113.6089655172410.884333384400011128.46847978528
Trimmed Mean ( 2 / 20 )113.5533928571430.85575914793346132.693168552575
Trimmed Mean ( 3 / 20 )113.5316666666670.837800844512816135.511520918418
Trimmed Mean ( 4 / 20 )113.5242307692310.82140901577908138.206701641273
Trimmed Mean ( 5 / 20 )113.51180.80957941663356140.210827582563
Trimmed Mean ( 6 / 20 )113.5004166666670.795272654878141142.718872540711
Trimmed Mean ( 7 / 20 )113.4978260869570.781010117215268145.321838456637
Trimmed Mean ( 8 / 20 )113.5104545454550.7692853795537147.55311560881
Trimmed Mean ( 9 / 20 )113.5164285714290.756442159827675150.066237182349
Trimmed Mean ( 10 / 20 )113.5260.740535824719039153.302509089377
Trimmed Mean ( 11 / 20 )113.5407894736840.722891733430108157.064722451501
Trimmed Mean ( 12 / 20 )113.55750.700057183038507162.211748913308
Trimmed Mean ( 13 / 20 )113.5744117647060.672158333669718168.969729415738
Trimmed Mean ( 14 / 20 )113.581250.65323184609912173.875861500429
Trimmed Mean ( 15 / 20 )113.5750.638107970181532177.987120216802
Trimmed Mean ( 16 / 20 )113.5689285714290.617574908012625183.894985204138
Trimmed Mean ( 17 / 20 )113.6207692307690.607425822777987187.052912421699
Trimmed Mean ( 18 / 20 )113.6808333333330.592475742995987191.874240721621
Trimmed Mean ( 19 / 20 )113.7604545454550.569896123774285199.616122657663
Trimmed Mean ( 20 / 20 )113.8060.56092376815768202.890314977718
Median114.23
Midrange115.945
Midmean - Weighted Average at Xnp113.388709677419
Midmean - Weighted Average at X(n+1)p113.575
Midmean - Empirical Distribution Function113.388709677419
Midmean - Empirical Distribution Function - Averaging113.575
Midmean - Empirical Distribution Function - Interpolation113.575
Midmean - Closest Observation113.388709677419
Midmean - True Basic - Statistics Graphics Toolkit113.575
Midmean - MS Excel (old versions)113.58125
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')