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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 11 Dec 2009 01:07:42 -0700
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/Dec/11/t12605189041u3ild2is29d86i.htm/, Retrieved Mon, 29 Apr 2024 03:59:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65862, Retrieved Mon, 29 Apr 2024 03:59:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [invoer] [2008-12-18 17:20:12] [5e74953d94072114d25d7276793b561e]
-  M D  [Central Tendency] [central tendency ...] [2009-12-06 18:30:17] [1433a524809eda02c3198b3ae6eebb69]
-    D      [Central Tendency] [central tendency ...] [2009-12-11 08:07:42] [a5c6be3c0aa55fdb2a703a08e16947ef] [Current]
-    D        [Central Tendency] [Univariate EDA Euro] [2009-12-11 08:24:19] [1433a524809eda02c3198b3ae6eebb69]
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Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,8600
2,5500
2,2700
2,2600
2,5700
3,0700
2,7600
2,5100
2,8700
3,1400
3,1100
3,1600
2,4700
2,5700
2,8900
2,6300
2,3800
1,6900
1,9600
2,1900
1,8700
1,6000
1,6300
1,2200
1,2100
1,4900
1,6400
1,6600
1,7700
1,8200
1,7800
1,2800
1,2900
1,3700
1,1200
1,5100
2,2400
2,9400
3,0900
3,4600
3,6400
4,3900
4,1500
5,2100
5,8000
5,9100
5,3900
5,4600
4,7200
3,1400
2,6300
2,3200
1,9300
0,6200
0,6000
-0,3700
-1,1000
-1,6800
-0,7800

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65862&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65862&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65862&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.370847457627120.20007863564214011.8495782921451
Geometric MeanNaN
Harmonic Mean2.75447060250339
Quadratic Mean2.81828713456975
Winsorized Mean ( 1 / 19 )2.378813559322030.19629443955085312.1185987986469
Winsorized Mean ( 2 / 19 )2.378135593220340.18973134203236512.5342263842453
Winsorized Mean ( 3 / 19 )2.395423728813560.18301892701749013.0883934675491
Winsorized Mean ( 4 / 19 )2.448983050847460.16447776037984814.8894479423342
Winsorized Mean ( 5 / 19 )2.409152542372880.15269377187096415.7776739211654
Winsorized Mean ( 6 / 19 )2.42644067796610.13464149482274918.0214924170326
Winsorized Mean ( 7 / 19 )2.408644067796610.12588980960703019.1329550446958
Winsorized Mean ( 8 / 19 )2.340847457627120.11031258072731721.2201313956519
Winsorized Mean ( 9 / 19 )2.322542372881360.10331489748951722.4802272403844
Winsorized Mean ( 10 / 19 )2.273389830508470.094022893542999524.1791094151850
Winsorized Mean ( 11 / 19 )2.284576271186440.090775708340161125.1672646015112
Winsorized Mean ( 12 / 19 )2.308983050847460.08666450319638126.6427772119725
Winsorized Mean ( 13 / 19 )2.306779661016950.084862952286812327.182411156528
Winsorized Mean ( 14 / 19 )2.323389830508470.080706483867481128.7881433953119
Winsorized Mean ( 15 / 19 )2.325932203389830.078704857700163829.5525876210941
Winsorized Mean ( 16 / 19 )2.293389830508470.072705345209706731.5436206773184
Winsorized Mean ( 17 / 19 )2.284745762711860.069628452004849832.8133930444515
Winsorized Mean ( 18 / 19 )2.287796610169490.067307344737099433.9902965880701
Winsorized Mean ( 19 / 19 )2.310338983050850.06294355922775636.7049307569513
Trimmed Mean ( 1 / 19 )2.379824561403510.18398275690632412.935041312677
Trimmed Mean ( 2 / 19 )2.380909090909090.16841632572144914.1370444979721
Trimmed Mean ( 3 / 19 )2.382452830188680.15330062520414215.5410509710322
Trimmed Mean ( 4 / 19 )2.377450980392160.13740789232613317.3021428401606
Trimmed Mean ( 5 / 19 )2.355918367346940.12532438127292318.7985637225399
Trimmed Mean ( 6 / 19 )2.342553191489360.11447158415362620.4640584718872
Trimmed Mean ( 7 / 19 )2.324222222222220.10690432279005821.7411434969436
Trimmed Mean ( 8 / 19 )2.307674418604650.09994950951784323.0884016313525
Trimmed Mean ( 9 / 19 )2.301707317073170.095898130935666324.0015868361114
Trimmed Mean ( 10 / 19 )2.298205128205130.092557653765439624.8299847144922
Trimmed Mean ( 11 / 19 )2.302162162162160.09061197934639425.4068190405751
Trimmed Mean ( 12 / 19 )2.304857142857140.088712898675201325.9810825401587
Trimmed Mean ( 13 / 19 )2.304242424242420.08705953020672926.4674346251449
Trimmed Mean ( 14 / 19 )2.303870967741940.085028366448712427.0953219962374
Trimmed Mean ( 15 / 19 )2.301034482758620.083120105437715227.6832478813789
Trimmed Mean ( 16 / 19 )2.297407407407410.08066778376105928.4798627195761
Trimmed Mean ( 17 / 19 )2.2980.078771822373231929.1728683019641
Trimmed Mean ( 18 / 19 )2.30.076553734776955230.0442559295274
Trimmed Mean ( 19 / 19 )2.301904761904760.073489937917082831.3227201865642
Median2.32
Midrange2.115
Midmean - Weighted Average at Xnp2.27766666666667
Midmean - Weighted Average at X(n+1)p2.30387096774193
Midmean - Empirical Distribution Function2.30387096774193
Midmean - Empirical Distribution Function - Averaging2.30387096774193
Midmean - Empirical Distribution Function - Interpolation2.30103448275862
Midmean - Closest Observation2.27766666666667
Midmean - True Basic - Statistics Graphics Toolkit2.30387096774193
Midmean - MS Excel (old versions)2.30387096774193
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.37084745762712 & 0.200078635642140 & 11.8495782921451 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 2.75447060250339 &  &  \tabularnewline
Quadratic Mean & 2.81828713456975 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 2.37881355932203 & 0.196294439550853 & 12.1185987986469 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 2.37813559322034 & 0.189731342032365 & 12.5342263842453 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 2.39542372881356 & 0.183018927017490 & 13.0883934675491 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 2.44898305084746 & 0.164477760379848 & 14.8894479423342 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 2.40915254237288 & 0.152693771870964 & 15.7776739211654 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 2.4264406779661 & 0.134641494822749 & 18.0214924170326 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 2.40864406779661 & 0.125889809607030 & 19.1329550446958 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 2.34084745762712 & 0.110312580727317 & 21.2201313956519 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 2.32254237288136 & 0.103314897489517 & 22.4802272403844 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 2.27338983050847 & 0.0940228935429995 & 24.1791094151850 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 2.28457627118644 & 0.0907757083401611 & 25.1672646015112 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 2.30898305084746 & 0.086664503196381 & 26.6427772119725 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 2.30677966101695 & 0.0848629522868123 & 27.182411156528 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 2.32338983050847 & 0.0807064838674811 & 28.7881433953119 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 2.32593220338983 & 0.0787048577001638 & 29.5525876210941 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 2.29338983050847 & 0.0727053452097067 & 31.5436206773184 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 2.28474576271186 & 0.0696284520048498 & 32.8133930444515 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 2.28779661016949 & 0.0673073447370994 & 33.9902965880701 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 2.31033898305085 & 0.062943559227756 & 36.7049307569513 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 2.37982456140351 & 0.183982756906324 & 12.935041312677 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 2.38090909090909 & 0.168416325721449 & 14.1370444979721 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 2.38245283018868 & 0.153300625204142 & 15.5410509710322 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 2.37745098039216 & 0.137407892326133 & 17.3021428401606 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 2.35591836734694 & 0.125324381272923 & 18.7985637225399 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 2.34255319148936 & 0.114471584153626 & 20.4640584718872 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 2.32422222222222 & 0.106904322790058 & 21.7411434969436 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 2.30767441860465 & 0.099949509517843 & 23.0884016313525 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 2.30170731707317 & 0.0958981309356663 & 24.0015868361114 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 2.29820512820513 & 0.0925576537654396 & 24.8299847144922 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 2.30216216216216 & 0.090611979346394 & 25.4068190405751 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 2.30485714285714 & 0.0887128986752013 & 25.9810825401587 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 2.30424242424242 & 0.087059530206729 & 26.4674346251449 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 2.30387096774194 & 0.0850283664487124 & 27.0953219962374 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 2.30103448275862 & 0.0831201054377152 & 27.6832478813789 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 2.29740740740741 & 0.080667783761059 & 28.4798627195761 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 2.298 & 0.0787718223732319 & 29.1728683019641 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 2.3 & 0.0765537347769552 & 30.0442559295274 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 2.30190476190476 & 0.0734899379170828 & 31.3227201865642 \tabularnewline
Median & 2.32 &  &  \tabularnewline
Midrange & 2.115 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.27766666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.30387096774193 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.30387096774193 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.30387096774193 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.30103448275862 &  &  \tabularnewline
Midmean - Closest Observation & 2.27766666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.30387096774193 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.30387096774193 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65862&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]2.37084745762712[/C][C]0.200078635642140[/C][C]11.8495782921451[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.75447060250339[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.81828713456975[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]2.37881355932203[/C][C]0.196294439550853[/C][C]12.1185987986469[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]2.37813559322034[/C][C]0.189731342032365[/C][C]12.5342263842453[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]2.39542372881356[/C][C]0.183018927017490[/C][C]13.0883934675491[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]2.44898305084746[/C][C]0.164477760379848[/C][C]14.8894479423342[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]2.40915254237288[/C][C]0.152693771870964[/C][C]15.7776739211654[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]2.4264406779661[/C][C]0.134641494822749[/C][C]18.0214924170326[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]2.40864406779661[/C][C]0.125889809607030[/C][C]19.1329550446958[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]2.34084745762712[/C][C]0.110312580727317[/C][C]21.2201313956519[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]2.32254237288136[/C][C]0.103314897489517[/C][C]22.4802272403844[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]2.27338983050847[/C][C]0.0940228935429995[/C][C]24.1791094151850[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]2.28457627118644[/C][C]0.0907757083401611[/C][C]25.1672646015112[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]2.30898305084746[/C][C]0.086664503196381[/C][C]26.6427772119725[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]2.30677966101695[/C][C]0.0848629522868123[/C][C]27.182411156528[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]2.32338983050847[/C][C]0.0807064838674811[/C][C]28.7881433953119[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]2.32593220338983[/C][C]0.0787048577001638[/C][C]29.5525876210941[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]2.29338983050847[/C][C]0.0727053452097067[/C][C]31.5436206773184[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]2.28474576271186[/C][C]0.0696284520048498[/C][C]32.8133930444515[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]2.28779661016949[/C][C]0.0673073447370994[/C][C]33.9902965880701[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]2.31033898305085[/C][C]0.062943559227756[/C][C]36.7049307569513[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]2.37982456140351[/C][C]0.183982756906324[/C][C]12.935041312677[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]2.38090909090909[/C][C]0.168416325721449[/C][C]14.1370444979721[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]2.38245283018868[/C][C]0.153300625204142[/C][C]15.5410509710322[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]2.37745098039216[/C][C]0.137407892326133[/C][C]17.3021428401606[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]2.35591836734694[/C][C]0.125324381272923[/C][C]18.7985637225399[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]2.34255319148936[/C][C]0.114471584153626[/C][C]20.4640584718872[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]2.32422222222222[/C][C]0.106904322790058[/C][C]21.7411434969436[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]2.30767441860465[/C][C]0.099949509517843[/C][C]23.0884016313525[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]2.30170731707317[/C][C]0.0958981309356663[/C][C]24.0015868361114[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]2.29820512820513[/C][C]0.0925576537654396[/C][C]24.8299847144922[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]2.30216216216216[/C][C]0.090611979346394[/C][C]25.4068190405751[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]2.30485714285714[/C][C]0.0887128986752013[/C][C]25.9810825401587[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]2.30424242424242[/C][C]0.087059530206729[/C][C]26.4674346251449[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]2.30387096774194[/C][C]0.0850283664487124[/C][C]27.0953219962374[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]2.30103448275862[/C][C]0.0831201054377152[/C][C]27.6832478813789[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]2.29740740740741[/C][C]0.080667783761059[/C][C]28.4798627195761[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]2.298[/C][C]0.0787718223732319[/C][C]29.1728683019641[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]2.3[/C][C]0.0765537347769552[/C][C]30.0442559295274[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]2.30190476190476[/C][C]0.0734899379170828[/C][C]31.3227201865642[/C][/ROW]
[ROW][C]Median[/C][C]2.32[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.27766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.30387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.30387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.30387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.30103448275862[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.27766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.30387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.30387096774193[/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=65862&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65862&T=1

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


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.370847457627120.20007863564214011.8495782921451
Geometric MeanNaN
Harmonic Mean2.75447060250339
Quadratic Mean2.81828713456975
Winsorized Mean ( 1 / 19 )2.378813559322030.19629443955085312.1185987986469
Winsorized Mean ( 2 / 19 )2.378135593220340.18973134203236512.5342263842453
Winsorized Mean ( 3 / 19 )2.395423728813560.18301892701749013.0883934675491
Winsorized Mean ( 4 / 19 )2.448983050847460.16447776037984814.8894479423342
Winsorized Mean ( 5 / 19 )2.409152542372880.15269377187096415.7776739211654
Winsorized Mean ( 6 / 19 )2.42644067796610.13464149482274918.0214924170326
Winsorized Mean ( 7 / 19 )2.408644067796610.12588980960703019.1329550446958
Winsorized Mean ( 8 / 19 )2.340847457627120.11031258072731721.2201313956519
Winsorized Mean ( 9 / 19 )2.322542372881360.10331489748951722.4802272403844
Winsorized Mean ( 10 / 19 )2.273389830508470.094022893542999524.1791094151850
Winsorized Mean ( 11 / 19 )2.284576271186440.090775708340161125.1672646015112
Winsorized Mean ( 12 / 19 )2.308983050847460.08666450319638126.6427772119725
Winsorized Mean ( 13 / 19 )2.306779661016950.084862952286812327.182411156528
Winsorized Mean ( 14 / 19 )2.323389830508470.080706483867481128.7881433953119
Winsorized Mean ( 15 / 19 )2.325932203389830.078704857700163829.5525876210941
Winsorized Mean ( 16 / 19 )2.293389830508470.072705345209706731.5436206773184
Winsorized Mean ( 17 / 19 )2.284745762711860.069628452004849832.8133930444515
Winsorized Mean ( 18 / 19 )2.287796610169490.067307344737099433.9902965880701
Winsorized Mean ( 19 / 19 )2.310338983050850.06294355922775636.7049307569513
Trimmed Mean ( 1 / 19 )2.379824561403510.18398275690632412.935041312677
Trimmed Mean ( 2 / 19 )2.380909090909090.16841632572144914.1370444979721
Trimmed Mean ( 3 / 19 )2.382452830188680.15330062520414215.5410509710322
Trimmed Mean ( 4 / 19 )2.377450980392160.13740789232613317.3021428401606
Trimmed Mean ( 5 / 19 )2.355918367346940.12532438127292318.7985637225399
Trimmed Mean ( 6 / 19 )2.342553191489360.11447158415362620.4640584718872
Trimmed Mean ( 7 / 19 )2.324222222222220.10690432279005821.7411434969436
Trimmed Mean ( 8 / 19 )2.307674418604650.09994950951784323.0884016313525
Trimmed Mean ( 9 / 19 )2.301707317073170.095898130935666324.0015868361114
Trimmed Mean ( 10 / 19 )2.298205128205130.092557653765439624.8299847144922
Trimmed Mean ( 11 / 19 )2.302162162162160.09061197934639425.4068190405751
Trimmed Mean ( 12 / 19 )2.304857142857140.088712898675201325.9810825401587
Trimmed Mean ( 13 / 19 )2.304242424242420.08705953020672926.4674346251449
Trimmed Mean ( 14 / 19 )2.303870967741940.085028366448712427.0953219962374
Trimmed Mean ( 15 / 19 )2.301034482758620.083120105437715227.6832478813789
Trimmed Mean ( 16 / 19 )2.297407407407410.08066778376105928.4798627195761
Trimmed Mean ( 17 / 19 )2.2980.078771822373231929.1728683019641
Trimmed Mean ( 18 / 19 )2.30.076553734776955230.0442559295274
Trimmed Mean ( 19 / 19 )2.301904761904760.073489937917082831.3227201865642
Median2.32
Midrange2.115
Midmean - Weighted Average at Xnp2.27766666666667
Midmean - Weighted Average at X(n+1)p2.30387096774193
Midmean - Empirical Distribution Function2.30387096774193
Midmean - Empirical Distribution Function - Averaging2.30387096774193
Midmean - Empirical Distribution Function - Interpolation2.30103448275862
Midmean - Closest Observation2.27766666666667
Midmean - True Basic - Statistics Graphics Toolkit2.30387096774193
Midmean - MS Excel (old versions)2.30387096774193
Number of observations59


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')