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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 computationWed, 21 Oct 2009 11:40:47 -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/21/t12561470064phsfg8wv5ztmjw.htm/, Retrieved Thu, 02 May 2024 06:36:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49534, Retrieved Thu, 02 May 2024 06:36:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
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] [SHw WS3 V2] [2009-10-21 17:40:47] [d9efc2d105d810fc0b0ac636e31105d1] [Current]
- RMPD          [Univariate Explorative Data Analysis] [] [2009-10-24 17:51:12] [4d62210f0915d3a20cbf115865da7cd4]
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Dataseries X:
0,57
0,55
0,54
0,57
0,50
0,57
0,55
0,52
0,55
0,56
0,49
0,56
0,54
0,52
0,56
0,54
0,49
0,54
0,53
0,54
0,51
0,48
0,53
0,55
0,49
0,51
0,56
0,54
0,44
0,53
0,57
0,56
0,49
0,48
0,56
0,48
0,55
0,52
0,54
0,50
0,54
0,49
0,56
0,66
0,49
0,50
0,51
0,47
0,53
0,53
0,45
0,55
0,48
0,47
0,50
0,59
0,47
0,53
0,50
0,50




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49534&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49534&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49534&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5250.00494889133278645106.084366112844
Geometric Mean0.523637285511099
Harmonic Mean0.522284057589943
Quadratic Mean0.526374391474357
Winsorized Mean ( 1 / 20 )0.5240.00447970943367642116.971872340828
Winsorized Mean ( 2 / 20 )0.5240.00416604515138637125.778761621348
Winsorized Mean ( 3 / 20 )0.5240.00416604515138637125.778761621348
Winsorized Mean ( 4 / 20 )0.5240.00416604515138637125.778761621348
Winsorized Mean ( 5 / 20 )0.5248333333333330.00399499451408989131.372729419854
Winsorized Mean ( 6 / 20 )0.5238333333333330.00381856649728167137.180623594282
Winsorized Mean ( 7 / 20 )0.5238333333333330.00381856649728167137.180623594282
Winsorized Mean ( 8 / 20 )0.5238333333333330.00381856649728167137.180623594282
Winsorized Mean ( 9 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 10 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 11 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 12 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 13 / 20 )0.5231666666666670.00321095992710654162.931546498029
Winsorized Mean ( 14 / 20 )0.5231666666666670.00321095992710654162.931546498029
Winsorized Mean ( 15 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 16 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 17 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 18 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 19 / 20 )0.52250.00236051560009780221.349945739969
Winsorized Mean ( 20 / 20 )0.52250.00236051560009780221.349945739969
Trimmed Mean ( 1 / 20 )0.5241379310344830.00430277617411297121.813896383429
Trimmed Mean ( 2 / 20 )0.5242857142857140.00408399745965443128.375622038236
Trimmed Mean ( 3 / 20 )0.5244444444444440.00402357367522489130.342945544580
Trimmed Mean ( 4 / 20 )0.5246153846153850.00394591583404244132.951488749302
Trimmed Mean ( 5 / 20 )0.52480.0038464401777249136.437842719917
Trimmed Mean ( 6 / 20 )0.5247916666666670.00377784676529278138.912904432215
Trimmed Mean ( 7 / 20 )0.5250.00373972020963826140.384833776317
Trimmed Mean ( 8 / 20 )0.5252272727272730.00368541833224975142.514967196858
Trimmed Mean ( 9 / 20 )0.5254761904761910.00360993565294383145.56386622783
Trimmed Mean ( 10 / 20 )0.52550.00357967911468369146.800867665602
Trimmed Mean ( 11 / 20 )0.5255263157894740.00353195871296348148.791749422386
Trimmed Mean ( 12 / 20 )0.5255555555555560.00346053588942166151.871147229567
Trimmed Mean ( 13 / 20 )0.5255882352941180.00335619193824014156.602555803086
Trimmed Mean ( 14 / 20 )0.52593750.00329526098506286159.60420202953
Trimmed Mean ( 15 / 20 )0.5263333333333330.00319782013875808164.591287344179
Trimmed Mean ( 16 / 20 )0.5264285714285710.00317955962285875165.566504129669
Trimmed Mean ( 17 / 20 )0.5265384615384620.00313502828804844167.953336671878
Trimmed Mean ( 18 / 20 )0.5266666666666670.00304951092934795172.705289100007
Trimmed Mean ( 19 / 20 )0.5268181818181820.00289695792350304181.852203493914
Trimmed Mean ( 20 / 20 )0.52750.00279802561968633188.525793433991
Median0.53
Midrange0.55
Midmean - Weighted Average at Xnp0.521842105263158
Midmean - Weighted Average at X(n+1)p0.5278125
Midmean - Empirical Distribution Function0.521842105263158
Midmean - Empirical Distribution Function - Averaging0.5278125
Midmean - Empirical Distribution Function - Interpolation0.5278125
Midmean - Closest Observation0.521842105263158
Midmean - True Basic - Statistics Graphics Toolkit0.5278125
Midmean - MS Excel (old versions)0.521842105263158
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.525 & 0.00494889133278645 & 106.084366112844 \tabularnewline
Geometric Mean & 0.523637285511099 &  &  \tabularnewline
Harmonic Mean & 0.522284057589943 &  &  \tabularnewline
Quadratic Mean & 0.526374391474357 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.524 & 0.00447970943367642 & 116.971872340828 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.524 & 0.00416604515138637 & 125.778761621348 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.524 & 0.00416604515138637 & 125.778761621348 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.524 & 0.00416604515138637 & 125.778761621348 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.524833333333333 & 0.00399499451408989 & 131.372729419854 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.523833333333333 & 0.00381856649728167 & 137.180623594282 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.523833333333333 & 0.00381856649728167 & 137.180623594282 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.523833333333333 & 0.00381856649728167 & 137.180623594282 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.525333333333333 & 0.00354524163206899 & 148.179838739722 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.525333333333333 & 0.00354524163206899 & 148.179838739722 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.525333333333333 & 0.00354524163206899 & 148.179838739722 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.525333333333333 & 0.00354524163206899 & 148.179838739722 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.523166666666667 & 0.00321095992710654 & 162.931546498029 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.523166666666667 & 0.00321095992710654 & 162.931546498029 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.525666666666667 & 0.00279594810402065 & 188.010165822014 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.525666666666667 & 0.00279594810402065 & 188.010165822014 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.525666666666667 & 0.00279594810402065 & 188.010165822014 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.525666666666667 & 0.00279594810402065 & 188.010165822014 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.5225 & 0.00236051560009780 & 221.349945739969 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.5225 & 0.00236051560009780 & 221.349945739969 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.524137931034483 & 0.00430277617411297 & 121.813896383429 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.524285714285714 & 0.00408399745965443 & 128.375622038236 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.524444444444444 & 0.00402357367522489 & 130.342945544580 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.524615384615385 & 0.00394591583404244 & 132.951488749302 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.5248 & 0.0038464401777249 & 136.437842719917 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.524791666666667 & 0.00377784676529278 & 138.912904432215 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.525 & 0.00373972020963826 & 140.384833776317 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.525227272727273 & 0.00368541833224975 & 142.514967196858 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.525476190476191 & 0.00360993565294383 & 145.56386622783 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.5255 & 0.00357967911468369 & 146.800867665602 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.525526315789474 & 0.00353195871296348 & 148.791749422386 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.525555555555556 & 0.00346053588942166 & 151.871147229567 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.525588235294118 & 0.00335619193824014 & 156.602555803086 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.5259375 & 0.00329526098506286 & 159.60420202953 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.526333333333333 & 0.00319782013875808 & 164.591287344179 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.526428571428571 & 0.00317955962285875 & 165.566504129669 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.526538461538462 & 0.00313502828804844 & 167.953336671878 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.526666666666667 & 0.00304951092934795 & 172.705289100007 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.526818181818182 & 0.00289695792350304 & 181.852203493914 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.5275 & 0.00279802561968633 & 188.525793433991 \tabularnewline
Median & 0.53 &  &  \tabularnewline
Midrange & 0.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.521842105263158 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.5278125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.521842105263158 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.5278125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.5278125 &  &  \tabularnewline
Midmean - Closest Observation & 0.521842105263158 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.5278125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.521842105263158 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49534&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]0.525[/C][C]0.00494889133278645[/C][C]106.084366112844[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.523637285511099[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.522284057589943[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.526374391474357[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.524[/C][C]0.00447970943367642[/C][C]116.971872340828[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.524[/C][C]0.00416604515138637[/C][C]125.778761621348[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.524[/C][C]0.00416604515138637[/C][C]125.778761621348[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.524[/C][C]0.00416604515138637[/C][C]125.778761621348[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.524833333333333[/C][C]0.00399499451408989[/C][C]131.372729419854[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.523833333333333[/C][C]0.00381856649728167[/C][C]137.180623594282[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.523833333333333[/C][C]0.00381856649728167[/C][C]137.180623594282[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.523833333333333[/C][C]0.00381856649728167[/C][C]137.180623594282[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.525333333333333[/C][C]0.00354524163206899[/C][C]148.179838739722[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.525333333333333[/C][C]0.00354524163206899[/C][C]148.179838739722[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.525333333333333[/C][C]0.00354524163206899[/C][C]148.179838739722[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.525333333333333[/C][C]0.00354524163206899[/C][C]148.179838739722[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.523166666666667[/C][C]0.00321095992710654[/C][C]162.931546498029[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.523166666666667[/C][C]0.00321095992710654[/C][C]162.931546498029[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.525666666666667[/C][C]0.00279594810402065[/C][C]188.010165822014[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.525666666666667[/C][C]0.00279594810402065[/C][C]188.010165822014[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.525666666666667[/C][C]0.00279594810402065[/C][C]188.010165822014[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.525666666666667[/C][C]0.00279594810402065[/C][C]188.010165822014[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.5225[/C][C]0.00236051560009780[/C][C]221.349945739969[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.5225[/C][C]0.00236051560009780[/C][C]221.349945739969[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.524137931034483[/C][C]0.00430277617411297[/C][C]121.813896383429[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.524285714285714[/C][C]0.00408399745965443[/C][C]128.375622038236[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.524444444444444[/C][C]0.00402357367522489[/C][C]130.342945544580[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.524615384615385[/C][C]0.00394591583404244[/C][C]132.951488749302[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.5248[/C][C]0.0038464401777249[/C][C]136.437842719917[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.524791666666667[/C][C]0.00377784676529278[/C][C]138.912904432215[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.525[/C][C]0.00373972020963826[/C][C]140.384833776317[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.525227272727273[/C][C]0.00368541833224975[/C][C]142.514967196858[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.525476190476191[/C][C]0.00360993565294383[/C][C]145.56386622783[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.5255[/C][C]0.00357967911468369[/C][C]146.800867665602[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.525526315789474[/C][C]0.00353195871296348[/C][C]148.791749422386[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.525555555555556[/C][C]0.00346053588942166[/C][C]151.871147229567[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.525588235294118[/C][C]0.00335619193824014[/C][C]156.602555803086[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.5259375[/C][C]0.00329526098506286[/C][C]159.60420202953[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.526333333333333[/C][C]0.00319782013875808[/C][C]164.591287344179[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.526428571428571[/C][C]0.00317955962285875[/C][C]165.566504129669[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.526538461538462[/C][C]0.00313502828804844[/C][C]167.953336671878[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.526666666666667[/C][C]0.00304951092934795[/C][C]172.705289100007[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.526818181818182[/C][C]0.00289695792350304[/C][C]181.852203493914[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.5275[/C][C]0.00279802561968633[/C][C]188.525793433991[/C][/ROW]
[ROW][C]Median[/C][C]0.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.521842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.5278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.521842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.5278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.5278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.521842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.5278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.521842105263158[/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=49534&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49534&T=1

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5250.00494889133278645106.084366112844
Geometric Mean0.523637285511099
Harmonic Mean0.522284057589943
Quadratic Mean0.526374391474357
Winsorized Mean ( 1 / 20 )0.5240.00447970943367642116.971872340828
Winsorized Mean ( 2 / 20 )0.5240.00416604515138637125.778761621348
Winsorized Mean ( 3 / 20 )0.5240.00416604515138637125.778761621348
Winsorized Mean ( 4 / 20 )0.5240.00416604515138637125.778761621348
Winsorized Mean ( 5 / 20 )0.5248333333333330.00399499451408989131.372729419854
Winsorized Mean ( 6 / 20 )0.5238333333333330.00381856649728167137.180623594282
Winsorized Mean ( 7 / 20 )0.5238333333333330.00381856649728167137.180623594282
Winsorized Mean ( 8 / 20 )0.5238333333333330.00381856649728167137.180623594282
Winsorized Mean ( 9 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 10 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 11 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 12 / 20 )0.5253333333333330.00354524163206899148.179838739722
Winsorized Mean ( 13 / 20 )0.5231666666666670.00321095992710654162.931546498029
Winsorized Mean ( 14 / 20 )0.5231666666666670.00321095992710654162.931546498029
Winsorized Mean ( 15 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 16 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 17 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 18 / 20 )0.5256666666666670.00279594810402065188.010165822014
Winsorized Mean ( 19 / 20 )0.52250.00236051560009780221.349945739969
Winsorized Mean ( 20 / 20 )0.52250.00236051560009780221.349945739969
Trimmed Mean ( 1 / 20 )0.5241379310344830.00430277617411297121.813896383429
Trimmed Mean ( 2 / 20 )0.5242857142857140.00408399745965443128.375622038236
Trimmed Mean ( 3 / 20 )0.5244444444444440.00402357367522489130.342945544580
Trimmed Mean ( 4 / 20 )0.5246153846153850.00394591583404244132.951488749302
Trimmed Mean ( 5 / 20 )0.52480.0038464401777249136.437842719917
Trimmed Mean ( 6 / 20 )0.5247916666666670.00377784676529278138.912904432215
Trimmed Mean ( 7 / 20 )0.5250.00373972020963826140.384833776317
Trimmed Mean ( 8 / 20 )0.5252272727272730.00368541833224975142.514967196858
Trimmed Mean ( 9 / 20 )0.5254761904761910.00360993565294383145.56386622783
Trimmed Mean ( 10 / 20 )0.52550.00357967911468369146.800867665602
Trimmed Mean ( 11 / 20 )0.5255263157894740.00353195871296348148.791749422386
Trimmed Mean ( 12 / 20 )0.5255555555555560.00346053588942166151.871147229567
Trimmed Mean ( 13 / 20 )0.5255882352941180.00335619193824014156.602555803086
Trimmed Mean ( 14 / 20 )0.52593750.00329526098506286159.60420202953
Trimmed Mean ( 15 / 20 )0.5263333333333330.00319782013875808164.591287344179
Trimmed Mean ( 16 / 20 )0.5264285714285710.00317955962285875165.566504129669
Trimmed Mean ( 17 / 20 )0.5265384615384620.00313502828804844167.953336671878
Trimmed Mean ( 18 / 20 )0.5266666666666670.00304951092934795172.705289100007
Trimmed Mean ( 19 / 20 )0.5268181818181820.00289695792350304181.852203493914
Trimmed Mean ( 20 / 20 )0.52750.00279802561968633188.525793433991
Median0.53
Midrange0.55
Midmean - Weighted Average at Xnp0.521842105263158
Midmean - Weighted Average at X(n+1)p0.5278125
Midmean - Empirical Distribution Function0.521842105263158
Midmean - Empirical Distribution Function - Averaging0.5278125
Midmean - Empirical Distribution Function - Interpolation0.5278125
Midmean - Closest Observation0.521842105263158
Midmean - True Basic - Statistics Graphics Toolkit0.5278125
Midmean - MS Excel (old versions)0.521842105263158
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')