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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, 18 Oct 2009 04:48:53 -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/18/t1255863026aifek813zafplb9.htm/, Retrieved Mon, 29 Apr 2024 08:21:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47264, Retrieved Mon, 29 Apr 2024 08:21:03 +0000
QR Codes:

Original text written by user:Central Tendency (Part 3)
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Shw3: Central Ten...] [2009-10-18 10:48:53] [7a39e26d7a09dd77604df90cb29f8d39] [Current]
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Dataseries X:
1.086873163
0.918367347
0.905546834
0.882839397
0.988825045
1.108747531
1.012523191
0.927841294
0.988926353
1.023809524
0.983446712
0.958638648
0.855721844
0.839932158
0.925036882
0.887076885
0.866378197
0.807465091
0.834866341
0.84416485
0.862305879
1.25170068
0.897295918
0.896462585
0.745609872
0.779679187
0.772067863
0.755821559
0.884005272
0.921075539
0.854550017
0.736900165
0.738350832
0.760546907
0.730656133
0.802425318
0.97675244
1.112677274
1.203421784
1.185972981
1.167635769
1.537528615
1.403892835
1.384984922
1.546262221
2.291625187
1.544590439
1.364795918
1.226145372
0.978131844
0.802147462
0.771691423
1.098628726
0.717737095
0.689795918
0.383167676
0.206290764
0
0.297677692




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47264&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47264&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9479328028813560.044216034896172921.438665975076
Geometric Mean0
Harmonic Mean0
Quadratic Mean1.00596717034454
Winsorized Mean ( 1 / 19 )0.9387959858983050.037798982965161224.8365408869223
Winsorized Mean ( 2 / 19 )0.9418371772881360.036797432325354625.5951874294006
Winsorized Mean ( 3 / 19 )0.9458250498305080.035443030640012426.6857837140695
Winsorized Mean ( 4 / 19 )0.9575533523389830.028220928085181133.930611688203
Winsorized Mean ( 5 / 19 )0.958318883186440.027414392402546434.9567799685186
Winsorized Mean ( 6 / 19 )0.957579564610170.026672848270263035.9009114777501
Winsorized Mean ( 7 / 19 )0.9449023028813560.023252979745710740.6357513408859
Winsorized Mean ( 8 / 19 )0.941633876983050.022449482879411841.944568703033
Winsorized Mean ( 9 / 19 )0.9392748781355930.021531625974637343.6230352153615
Winsorized Mean ( 10 / 19 )0.9380482483050850.020646628209881545.4334838003299
Winsorized Mean ( 11 / 19 )0.9355104431525420.019813157032232947.2166268924539
Winsorized Mean ( 12 / 19 )0.926599125389830.017293689380282253.5801878369756
Winsorized Mean ( 13 / 19 )0.9258161942203390.017120788213868354.0755590604412
Winsorized Mean ( 14 / 19 )0.9252211987288140.016402745667265456.4064832496463
Winsorized Mean ( 15 / 19 )0.9279447695762710.015006714739274061.8353041087504
Winsorized Mean ( 16 / 19 )0.9109181165593220.012031115587970075.7135204876721
Winsorized Mean ( 17 / 19 )0.9091182602881360.011285338109385580.5574677051157
Winsorized Mean ( 18 / 19 )0.9102789283559320.00890175798154452102.258332594883
Winsorized Mean ( 19 / 19 )0.9118776685423730.00866077571410166105.288221129850
Trimmed Mean ( 1 / 19 )0.9409896523333330.035325970200813226.6373335816173
Trimmed Mean ( 2 / 19 )0.9433428581454550.032187016889150429.3081791765374
Trimmed Mean ( 3 / 19 )0.9441809257924530.028879112570885232.6942499869036
Trimmed Mean ( 4 / 19 )0.943546917176470.025295855777287637.30045448882
Trimmed Mean ( 5 / 19 )0.9393306943469390.023997907991361639.1421908395125
Trimmed Mean ( 6 / 19 )0.934563446936170.022615069764497441.3248093712852
Trimmed Mean ( 7 / 19 )0.9295339990.021056919039828644.1438748585115
Trimmed Mean ( 8 / 19 )0.9265216072093020.020196027619423745.8764280119232
Trimmed Mean ( 9 / 19 )0.9238032416097560.019304126044403947.8552222195813
Trimmed Mean ( 10 / 19 )0.9212025961538460.018385246936739350.1055329484319
Trimmed Mean ( 11 / 19 )0.9185163975675680.017398794059029552.7919575604657
Trimmed Mean ( 12 / 19 )0.9159121152571430.016294769512819856.2089641425461
Trimmed Mean ( 13 / 19 )0.914319858696970.015581178580001858.6810461097265
Trimmed Mean ( 14 / 19 )0.9126367723548390.014600149313900762.5087286940225
Trimmed Mean ( 15 / 19 )0.9108080010344830.013403327500849667.9538719752051
Trimmed Mean ( 16 / 19 )0.9083115335185190.012107120016761475.0229230618869
Trimmed Mean ( 17 / 19 )0.907927062520.01142697403730779.4547234951075
Trimmed Mean ( 18 / 19 )0.9077473165652170.010642570612538785.2939904853199
Trimmed Mean ( 19 / 19 )0.9073521708095240.010397663310931087.265007884572
Median0.897295918
Midrange1.1458125935
Midmean - Weighted Average at Xnp0.906437040566667
Midmean - Weighted Average at X(n+1)p0.912636772354839
Midmean - Empirical Distribution Function0.912636772354839
Midmean - Empirical Distribution Function - Averaging0.912636772354839
Midmean - Empirical Distribution Function - Interpolation0.910808001034483
Midmean - Closest Observation0.906437040566667
Midmean - True Basic - Statistics Graphics Toolkit0.912636772354839
Midmean - MS Excel (old versions)0.912636772354839
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.947932802881356 & 0.0442160348961729 & 21.438665975076 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.00596717034454 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 0.938795985898305 & 0.0377989829651612 & 24.8365408869223 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 0.941837177288136 & 0.0367974323253546 & 25.5951874294006 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 0.945825049830508 & 0.0354430306400124 & 26.6857837140695 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 0.957553352338983 & 0.0282209280851811 & 33.930611688203 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 0.95831888318644 & 0.0274143924025464 & 34.9567799685186 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 0.95757956461017 & 0.0266728482702630 & 35.9009114777501 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 0.944902302881356 & 0.0232529797457107 & 40.6357513408859 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 0.94163387698305 & 0.0224494828794118 & 41.944568703033 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 0.939274878135593 & 0.0215316259746373 & 43.6230352153615 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 0.938048248305085 & 0.0206466282098815 & 45.4334838003299 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 0.935510443152542 & 0.0198131570322329 & 47.2166268924539 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 0.92659912538983 & 0.0172936893802822 & 53.5801878369756 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 0.925816194220339 & 0.0171207882138683 & 54.0755590604412 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 0.925221198728814 & 0.0164027456672654 & 56.4064832496463 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 0.927944769576271 & 0.0150067147392740 & 61.8353041087504 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 0.910918116559322 & 0.0120311155879700 & 75.7135204876721 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 0.909118260288136 & 0.0112853381093855 & 80.5574677051157 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 0.910278928355932 & 0.00890175798154452 & 102.258332594883 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 0.911877668542373 & 0.00866077571410166 & 105.288221129850 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 0.940989652333333 & 0.0353259702008132 & 26.6373335816173 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 0.943342858145455 & 0.0321870168891504 & 29.3081791765374 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 0.944180925792453 & 0.0288791125708852 & 32.6942499869036 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 0.94354691717647 & 0.0252958557772876 & 37.30045448882 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 0.939330694346939 & 0.0239979079913616 & 39.1421908395125 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 0.93456344693617 & 0.0226150697644974 & 41.3248093712852 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 0.929533999 & 0.0210569190398286 & 44.1438748585115 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 0.926521607209302 & 0.0201960276194237 & 45.8764280119232 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 0.923803241609756 & 0.0193041260444039 & 47.8552222195813 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 0.921202596153846 & 0.0183852469367393 & 50.1055329484319 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 0.918516397567568 & 0.0173987940590295 & 52.7919575604657 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 0.915912115257143 & 0.0162947695128198 & 56.2089641425461 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 0.91431985869697 & 0.0155811785800018 & 58.6810461097265 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 0.912636772354839 & 0.0146001493139007 & 62.5087286940225 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 0.910808001034483 & 0.0134033275008496 & 67.9538719752051 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 0.908311533518519 & 0.0121071200167614 & 75.0229230618869 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 0.90792706252 & 0.011426974037307 & 79.4547234951075 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 0.907747316565217 & 0.0106425706125387 & 85.2939904853199 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 0.907352170809524 & 0.0103976633109310 & 87.265007884572 \tabularnewline
Median & 0.897295918 &  &  \tabularnewline
Midrange & 1.1458125935 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.906437040566667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.912636772354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.912636772354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.912636772354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.910808001034483 &  &  \tabularnewline
Midmean - Closest Observation & 0.906437040566667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.912636772354839 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.912636772354839 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47264&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]0.947932802881356[/C][C]0.0442160348961729[/C][C]21.438665975076[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.00596717034454[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]0.938795985898305[/C][C]0.0377989829651612[/C][C]24.8365408869223[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]0.941837177288136[/C][C]0.0367974323253546[/C][C]25.5951874294006[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]0.945825049830508[/C][C]0.0354430306400124[/C][C]26.6857837140695[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]0.957553352338983[/C][C]0.0282209280851811[/C][C]33.930611688203[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]0.95831888318644[/C][C]0.0274143924025464[/C][C]34.9567799685186[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]0.95757956461017[/C][C]0.0266728482702630[/C][C]35.9009114777501[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]0.944902302881356[/C][C]0.0232529797457107[/C][C]40.6357513408859[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]0.94163387698305[/C][C]0.0224494828794118[/C][C]41.944568703033[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]0.939274878135593[/C][C]0.0215316259746373[/C][C]43.6230352153615[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]0.938048248305085[/C][C]0.0206466282098815[/C][C]45.4334838003299[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]0.935510443152542[/C][C]0.0198131570322329[/C][C]47.2166268924539[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]0.92659912538983[/C][C]0.0172936893802822[/C][C]53.5801878369756[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]0.925816194220339[/C][C]0.0171207882138683[/C][C]54.0755590604412[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]0.925221198728814[/C][C]0.0164027456672654[/C][C]56.4064832496463[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]0.927944769576271[/C][C]0.0150067147392740[/C][C]61.8353041087504[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]0.910918116559322[/C][C]0.0120311155879700[/C][C]75.7135204876721[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]0.909118260288136[/C][C]0.0112853381093855[/C][C]80.5574677051157[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]0.910278928355932[/C][C]0.00890175798154452[/C][C]102.258332594883[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]0.911877668542373[/C][C]0.00866077571410166[/C][C]105.288221129850[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]0.940989652333333[/C][C]0.0353259702008132[/C][C]26.6373335816173[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]0.943342858145455[/C][C]0.0321870168891504[/C][C]29.3081791765374[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]0.944180925792453[/C][C]0.0288791125708852[/C][C]32.6942499869036[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]0.94354691717647[/C][C]0.0252958557772876[/C][C]37.30045448882[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]0.939330694346939[/C][C]0.0239979079913616[/C][C]39.1421908395125[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]0.93456344693617[/C][C]0.0226150697644974[/C][C]41.3248093712852[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]0.929533999[/C][C]0.0210569190398286[/C][C]44.1438748585115[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]0.926521607209302[/C][C]0.0201960276194237[/C][C]45.8764280119232[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]0.923803241609756[/C][C]0.0193041260444039[/C][C]47.8552222195813[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]0.921202596153846[/C][C]0.0183852469367393[/C][C]50.1055329484319[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]0.918516397567568[/C][C]0.0173987940590295[/C][C]52.7919575604657[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]0.915912115257143[/C][C]0.0162947695128198[/C][C]56.2089641425461[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]0.91431985869697[/C][C]0.0155811785800018[/C][C]58.6810461097265[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]0.912636772354839[/C][C]0.0146001493139007[/C][C]62.5087286940225[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]0.910808001034483[/C][C]0.0134033275008496[/C][C]67.9538719752051[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]0.908311533518519[/C][C]0.0121071200167614[/C][C]75.0229230618869[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]0.90792706252[/C][C]0.011426974037307[/C][C]79.4547234951075[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]0.907747316565217[/C][C]0.0106425706125387[/C][C]85.2939904853199[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]0.907352170809524[/C][C]0.0103976633109310[/C][C]87.265007884572[/C][/ROW]
[ROW][C]Median[/C][C]0.897295918[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.1458125935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.906437040566667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.912636772354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.912636772354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.912636772354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.910808001034483[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.906437040566667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.912636772354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.912636772354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47264&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 Mean0.9479328028813560.044216034896172921.438665975076
Geometric Mean0
Harmonic Mean0
Quadratic Mean1.00596717034454
Winsorized Mean ( 1 / 19 )0.9387959858983050.037798982965161224.8365408869223
Winsorized Mean ( 2 / 19 )0.9418371772881360.036797432325354625.5951874294006
Winsorized Mean ( 3 / 19 )0.9458250498305080.035443030640012426.6857837140695
Winsorized Mean ( 4 / 19 )0.9575533523389830.028220928085181133.930611688203
Winsorized Mean ( 5 / 19 )0.958318883186440.027414392402546434.9567799685186
Winsorized Mean ( 6 / 19 )0.957579564610170.026672848270263035.9009114777501
Winsorized Mean ( 7 / 19 )0.9449023028813560.023252979745710740.6357513408859
Winsorized Mean ( 8 / 19 )0.941633876983050.022449482879411841.944568703033
Winsorized Mean ( 9 / 19 )0.9392748781355930.021531625974637343.6230352153615
Winsorized Mean ( 10 / 19 )0.9380482483050850.020646628209881545.4334838003299
Winsorized Mean ( 11 / 19 )0.9355104431525420.019813157032232947.2166268924539
Winsorized Mean ( 12 / 19 )0.926599125389830.017293689380282253.5801878369756
Winsorized Mean ( 13 / 19 )0.9258161942203390.017120788213868354.0755590604412
Winsorized Mean ( 14 / 19 )0.9252211987288140.016402745667265456.4064832496463
Winsorized Mean ( 15 / 19 )0.9279447695762710.015006714739274061.8353041087504
Winsorized Mean ( 16 / 19 )0.9109181165593220.012031115587970075.7135204876721
Winsorized Mean ( 17 / 19 )0.9091182602881360.011285338109385580.5574677051157
Winsorized Mean ( 18 / 19 )0.9102789283559320.00890175798154452102.258332594883
Winsorized Mean ( 19 / 19 )0.9118776685423730.00866077571410166105.288221129850
Trimmed Mean ( 1 / 19 )0.9409896523333330.035325970200813226.6373335816173
Trimmed Mean ( 2 / 19 )0.9433428581454550.032187016889150429.3081791765374
Trimmed Mean ( 3 / 19 )0.9441809257924530.028879112570885232.6942499869036
Trimmed Mean ( 4 / 19 )0.943546917176470.025295855777287637.30045448882
Trimmed Mean ( 5 / 19 )0.9393306943469390.023997907991361639.1421908395125
Trimmed Mean ( 6 / 19 )0.934563446936170.022615069764497441.3248093712852
Trimmed Mean ( 7 / 19 )0.9295339990.021056919039828644.1438748585115
Trimmed Mean ( 8 / 19 )0.9265216072093020.020196027619423745.8764280119232
Trimmed Mean ( 9 / 19 )0.9238032416097560.019304126044403947.8552222195813
Trimmed Mean ( 10 / 19 )0.9212025961538460.018385246936739350.1055329484319
Trimmed Mean ( 11 / 19 )0.9185163975675680.017398794059029552.7919575604657
Trimmed Mean ( 12 / 19 )0.9159121152571430.016294769512819856.2089641425461
Trimmed Mean ( 13 / 19 )0.914319858696970.015581178580001858.6810461097265
Trimmed Mean ( 14 / 19 )0.9126367723548390.014600149313900762.5087286940225
Trimmed Mean ( 15 / 19 )0.9108080010344830.013403327500849667.9538719752051
Trimmed Mean ( 16 / 19 )0.9083115335185190.012107120016761475.0229230618869
Trimmed Mean ( 17 / 19 )0.907927062520.01142697403730779.4547234951075
Trimmed Mean ( 18 / 19 )0.9077473165652170.010642570612538785.2939904853199
Trimmed Mean ( 19 / 19 )0.9073521708095240.010397663310931087.265007884572
Median0.897295918
Midrange1.1458125935
Midmean - Weighted Average at Xnp0.906437040566667
Midmean - Weighted Average at X(n+1)p0.912636772354839
Midmean - Empirical Distribution Function0.912636772354839
Midmean - Empirical Distribution Function - Averaging0.912636772354839
Midmean - Empirical Distribution Function - Interpolation0.910808001034483
Midmean - Closest Observation0.906437040566667
Midmean - True Basic - Statistics Graphics Toolkit0.912636772354839
Midmean - MS Excel (old versions)0.912636772354839
Number of observations59



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')