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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 computationTue, 20 Oct 2009 13:37:22 -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/20/t1256067493rx1y82qb8v6e5ga.htm/, Retrieved Fri, 03 May 2024 03:45:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49076, Retrieved Fri, 03 May 2024 03:45:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
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] [Workshop 3: Part ...] [2009-10-20 17:47:21] [03d5b865e91ca35b5a5d21b8d6da5aba]
-    D          [Central Tendency] [WS3-Part2] [2009-10-20 19:37:22] [b32ceebc68d054278e6bda97f3d57f91] [Current]
Feedback Forum

Post a new message
Dataseries X:
7,7
7,5
7,6
7,8
7,8
7,8
7,5
7,5
7,1
7,5
7,5
7,6
7,7
7,7
7,9
8,1
8,2
8,2
8,2
7,9
7,3
6,9
6,6
6,7
6,9
7
7,1
7,2
7,1
6,9
7
6,8
6,4
6,7
6,6
6,4
6,3
6,2
6,5
6,8
6,8
6,4
6,1
5,8
6,1
7,2
7,3
6,9
6,1
5,8
6,2
7,1
7,7
7,9
7,7
7,4
7,5
8
8,1




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=49076&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=49076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49076&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 Mean7.157627118644070.085171926713676484.0373981758797
Geometric Mean7.12754837460732
Harmonic Mean7.09682206016793
Quadratic Mean7.18695852787227
Winsorized Mean ( 1 / 19 )7.157627118644070.085171926713676484.0373981758797
Winsorized Mean ( 2 / 19 )7.167796610169490.082637720550482786.7375886268637
Winsorized Mean ( 3 / 19 )7.162711864406780.081586343311076687.7930248337816
Winsorized Mean ( 4 / 19 )7.162711864406780.081586343311076687.7930248337816
Winsorized Mean ( 5 / 19 )7.162711864406780.078109542027374391.7008559837226
Winsorized Mean ( 6 / 19 )7.152542372881360.076310140062441593.7299075460839
Winsorized Mean ( 7 / 19 )7.164406779661020.07383471169753297.0330433334718
Winsorized Mean ( 8 / 19 )7.177966101694920.0711871364525848100.832347800307
Winsorized Mean ( 9 / 19 )7.162711864406780.0686301766002368104.366799259876
Winsorized Mean ( 10 / 19 )7.162711864406780.0686301766002368104.366799259876
Winsorized Mean ( 11 / 19 )7.181355932203390.0651606196160715110.210062066877
Winsorized Mean ( 12 / 19 )7.181355932203390.0583463217091802123.081553760971
Winsorized Mean ( 13 / 19 )7.181355932203390.0583463217091802123.081553760971
Winsorized Mean ( 14 / 19 )7.205084745762710.0544041486461258132.436310926001
Winsorized Mean ( 15 / 19 )7.205084745762710.0544041486461258132.436310926001
Winsorized Mean ( 16 / 19 )7.232203389830510.0502152396974582144.024073835031
Winsorized Mean ( 17 / 19 )7.203389830508470.0457399774686919157.485644487671
Winsorized Mean ( 18 / 19 )7.203389830508470.0457399774686919157.485644487671
Winsorized Mean ( 19 / 19 )7.203389830508470.0362604789823723198.656775438911
Trimmed Mean ( 1 / 19 )7.163157894736840.082816627877822286.4941990309544
Trimmed Mean ( 2 / 19 )7.169090909090910.079893562496836289.733023350596
Trimmed Mean ( 3 / 19 )7.169811320754720.077963227984156591.964013114128
Trimmed Mean ( 4 / 19 )7.172549019607840.076032935658717994.3347637108557
Trimmed Mean ( 5 / 19 )7.175510204081630.073570886050062797.5319258653338
Trimmed Mean ( 6 / 19 )7.178723404255320.0716487584701393100.193270023613
Trimmed Mean ( 7 / 19 )7.184444444444440.069700336619012103.076180014958
Trimmed Mean ( 8 / 19 )7.188372093023260.0678909703673924105.881121659086
Trimmed Mean ( 9 / 19 )7.190243902439020.0662409568654359108.546800086924
Trimmed Mean ( 10 / 19 )7.19487179487180.0646749077851197111.246726764212
Trimmed Mean ( 11 / 19 )7.20.0624812284122512115.234610185549
Trimmed Mean ( 12 / 19 )7.202857142857140.0604584327355211119.137344733471
Trimmed Mean ( 13 / 19 )7.20606060606060.0595022589874513121.105664367807
Trimmed Mean ( 14 / 19 )7.209677419354840.0579868058240017124.333067098699
Trimmed Mean ( 15 / 19 )7.21034482758620.0568778891619787126.768854010253
Trimmed Mean ( 16 / 19 )7.211111111111110.0550403460754596131.015003089275
Trimmed Mean ( 17 / 19 )7.2080.0535163526410386134.687803713899
Trimmed Mean ( 18 / 19 )7.208695652173910.0525676840112136137.131695789302
Trimmed Mean ( 19 / 19 )7.209523809523810.050664518393411142.299266590116
Median7.2
Midrange7
Midmean - Weighted Average at Xnp7.23939393939394
Midmean - Weighted Average at X(n+1)p7.23939393939394
Midmean - Empirical Distribution Function7.23939393939394
Midmean - Empirical Distribution Function - Averaging7.23939393939394
Midmean - Empirical Distribution Function - Interpolation7.23939393939394
Midmean - Closest Observation7.23939393939394
Midmean - True Basic - Statistics Graphics Toolkit7.23939393939394
Midmean - MS Excel (old versions)7.23939393939394
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.15762711864407 & 0.0851719267136764 & 84.0373981758797 \tabularnewline
Geometric Mean & 7.12754837460732 &  &  \tabularnewline
Harmonic Mean & 7.09682206016793 &  &  \tabularnewline
Quadratic Mean & 7.18695852787227 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 7.15762711864407 & 0.0851719267136764 & 84.0373981758797 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 7.16779661016949 & 0.0826377205504827 & 86.7375886268637 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 7.16271186440678 & 0.0815863433110766 & 87.7930248337816 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 7.16271186440678 & 0.0815863433110766 & 87.7930248337816 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 7.16271186440678 & 0.0781095420273743 & 91.7008559837226 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 7.15254237288136 & 0.0763101400624415 & 93.7299075460839 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 7.16440677966102 & 0.073834711697532 & 97.0330433334718 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 7.17796610169492 & 0.0711871364525848 & 100.832347800307 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 7.16271186440678 & 0.0686301766002368 & 104.366799259876 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 7.16271186440678 & 0.0686301766002368 & 104.366799259876 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 7.18135593220339 & 0.0651606196160715 & 110.210062066877 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 7.18135593220339 & 0.0583463217091802 & 123.081553760971 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 7.18135593220339 & 0.0583463217091802 & 123.081553760971 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 7.20508474576271 & 0.0544041486461258 & 132.436310926001 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 7.20508474576271 & 0.0544041486461258 & 132.436310926001 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 7.23220338983051 & 0.0502152396974582 & 144.024073835031 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 7.20338983050847 & 0.0457399774686919 & 157.485644487671 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 7.20338983050847 & 0.0457399774686919 & 157.485644487671 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 7.20338983050847 & 0.0362604789823723 & 198.656775438911 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 7.16315789473684 & 0.0828166278778222 & 86.4941990309544 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 7.16909090909091 & 0.0798935624968362 & 89.733023350596 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 7.16981132075472 & 0.0779632279841565 & 91.964013114128 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 7.17254901960784 & 0.0760329356587179 & 94.3347637108557 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 7.17551020408163 & 0.0735708860500627 & 97.5319258653338 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 7.17872340425532 & 0.0716487584701393 & 100.193270023613 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 7.18444444444444 & 0.069700336619012 & 103.076180014958 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 7.18837209302326 & 0.0678909703673924 & 105.881121659086 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 7.19024390243902 & 0.0662409568654359 & 108.546800086924 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 7.1948717948718 & 0.0646749077851197 & 111.246726764212 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 7.2 & 0.0624812284122512 & 115.234610185549 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 7.20285714285714 & 0.0604584327355211 & 119.137344733471 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 7.2060606060606 & 0.0595022589874513 & 121.105664367807 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 7.20967741935484 & 0.0579868058240017 & 124.333067098699 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 7.2103448275862 & 0.0568778891619787 & 126.768854010253 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 7.21111111111111 & 0.0550403460754596 & 131.015003089275 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 7.208 & 0.0535163526410386 & 134.687803713899 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 7.20869565217391 & 0.0525676840112136 & 137.131695789302 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 7.20952380952381 & 0.050664518393411 & 142.299266590116 \tabularnewline
Median & 7.2 &  &  \tabularnewline
Midrange & 7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.23939393939394 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.23939393939394 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.23939393939394 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.23939393939394 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.23939393939394 &  &  \tabularnewline
Midmean - Closest Observation & 7.23939393939394 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.23939393939394 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.23939393939394 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49076&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]7.15762711864407[/C][C]0.0851719267136764[/C][C]84.0373981758797[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.12754837460732[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.09682206016793[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.18695852787227[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]7.15762711864407[/C][C]0.0851719267136764[/C][C]84.0373981758797[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]7.16779661016949[/C][C]0.0826377205504827[/C][C]86.7375886268637[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]7.16271186440678[/C][C]0.0815863433110766[/C][C]87.7930248337816[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]7.16271186440678[/C][C]0.0815863433110766[/C][C]87.7930248337816[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]7.16271186440678[/C][C]0.0781095420273743[/C][C]91.7008559837226[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]7.15254237288136[/C][C]0.0763101400624415[/C][C]93.7299075460839[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]7.16440677966102[/C][C]0.073834711697532[/C][C]97.0330433334718[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]7.17796610169492[/C][C]0.0711871364525848[/C][C]100.832347800307[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]7.16271186440678[/C][C]0.0686301766002368[/C][C]104.366799259876[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]7.16271186440678[/C][C]0.0686301766002368[/C][C]104.366799259876[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]7.18135593220339[/C][C]0.0651606196160715[/C][C]110.210062066877[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]7.18135593220339[/C][C]0.0583463217091802[/C][C]123.081553760971[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]7.18135593220339[/C][C]0.0583463217091802[/C][C]123.081553760971[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]7.20508474576271[/C][C]0.0544041486461258[/C][C]132.436310926001[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]7.20508474576271[/C][C]0.0544041486461258[/C][C]132.436310926001[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]7.23220338983051[/C][C]0.0502152396974582[/C][C]144.024073835031[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]7.20338983050847[/C][C]0.0457399774686919[/C][C]157.485644487671[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]7.20338983050847[/C][C]0.0457399774686919[/C][C]157.485644487671[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]7.20338983050847[/C][C]0.0362604789823723[/C][C]198.656775438911[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]7.16315789473684[/C][C]0.0828166278778222[/C][C]86.4941990309544[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]7.16909090909091[/C][C]0.0798935624968362[/C][C]89.733023350596[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]7.16981132075472[/C][C]0.0779632279841565[/C][C]91.964013114128[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]7.17254901960784[/C][C]0.0760329356587179[/C][C]94.3347637108557[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]7.17551020408163[/C][C]0.0735708860500627[/C][C]97.5319258653338[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]7.17872340425532[/C][C]0.0716487584701393[/C][C]100.193270023613[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]7.18444444444444[/C][C]0.069700336619012[/C][C]103.076180014958[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]7.18837209302326[/C][C]0.0678909703673924[/C][C]105.881121659086[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]7.19024390243902[/C][C]0.0662409568654359[/C][C]108.546800086924[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]7.1948717948718[/C][C]0.0646749077851197[/C][C]111.246726764212[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]7.2[/C][C]0.0624812284122512[/C][C]115.234610185549[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]7.20285714285714[/C][C]0.0604584327355211[/C][C]119.137344733471[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]7.2060606060606[/C][C]0.0595022589874513[/C][C]121.105664367807[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]7.20967741935484[/C][C]0.0579868058240017[/C][C]124.333067098699[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]7.2103448275862[/C][C]0.0568778891619787[/C][C]126.768854010253[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]7.21111111111111[/C][C]0.0550403460754596[/C][C]131.015003089275[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]7.208[/C][C]0.0535163526410386[/C][C]134.687803713899[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]7.20869565217391[/C][C]0.0525676840112136[/C][C]137.131695789302[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]7.20952380952381[/C][C]0.050664518393411[/C][C]142.299266590116[/C][/ROW]
[ROW][C]Median[/C][C]7.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.23939393939394[/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=49076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49076&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 Mean7.157627118644070.085171926713676484.0373981758797
Geometric Mean7.12754837460732
Harmonic Mean7.09682206016793
Quadratic Mean7.18695852787227
Winsorized Mean ( 1 / 19 )7.157627118644070.085171926713676484.0373981758797
Winsorized Mean ( 2 / 19 )7.167796610169490.082637720550482786.7375886268637
Winsorized Mean ( 3 / 19 )7.162711864406780.081586343311076687.7930248337816
Winsorized Mean ( 4 / 19 )7.162711864406780.081586343311076687.7930248337816
Winsorized Mean ( 5 / 19 )7.162711864406780.078109542027374391.7008559837226
Winsorized Mean ( 6 / 19 )7.152542372881360.076310140062441593.7299075460839
Winsorized Mean ( 7 / 19 )7.164406779661020.07383471169753297.0330433334718
Winsorized Mean ( 8 / 19 )7.177966101694920.0711871364525848100.832347800307
Winsorized Mean ( 9 / 19 )7.162711864406780.0686301766002368104.366799259876
Winsorized Mean ( 10 / 19 )7.162711864406780.0686301766002368104.366799259876
Winsorized Mean ( 11 / 19 )7.181355932203390.0651606196160715110.210062066877
Winsorized Mean ( 12 / 19 )7.181355932203390.0583463217091802123.081553760971
Winsorized Mean ( 13 / 19 )7.181355932203390.0583463217091802123.081553760971
Winsorized Mean ( 14 / 19 )7.205084745762710.0544041486461258132.436310926001
Winsorized Mean ( 15 / 19 )7.205084745762710.0544041486461258132.436310926001
Winsorized Mean ( 16 / 19 )7.232203389830510.0502152396974582144.024073835031
Winsorized Mean ( 17 / 19 )7.203389830508470.0457399774686919157.485644487671
Winsorized Mean ( 18 / 19 )7.203389830508470.0457399774686919157.485644487671
Winsorized Mean ( 19 / 19 )7.203389830508470.0362604789823723198.656775438911
Trimmed Mean ( 1 / 19 )7.163157894736840.082816627877822286.4941990309544
Trimmed Mean ( 2 / 19 )7.169090909090910.079893562496836289.733023350596
Trimmed Mean ( 3 / 19 )7.169811320754720.077963227984156591.964013114128
Trimmed Mean ( 4 / 19 )7.172549019607840.076032935658717994.3347637108557
Trimmed Mean ( 5 / 19 )7.175510204081630.073570886050062797.5319258653338
Trimmed Mean ( 6 / 19 )7.178723404255320.0716487584701393100.193270023613
Trimmed Mean ( 7 / 19 )7.184444444444440.069700336619012103.076180014958
Trimmed Mean ( 8 / 19 )7.188372093023260.0678909703673924105.881121659086
Trimmed Mean ( 9 / 19 )7.190243902439020.0662409568654359108.546800086924
Trimmed Mean ( 10 / 19 )7.19487179487180.0646749077851197111.246726764212
Trimmed Mean ( 11 / 19 )7.20.0624812284122512115.234610185549
Trimmed Mean ( 12 / 19 )7.202857142857140.0604584327355211119.137344733471
Trimmed Mean ( 13 / 19 )7.20606060606060.0595022589874513121.105664367807
Trimmed Mean ( 14 / 19 )7.209677419354840.0579868058240017124.333067098699
Trimmed Mean ( 15 / 19 )7.21034482758620.0568778891619787126.768854010253
Trimmed Mean ( 16 / 19 )7.211111111111110.0550403460754596131.015003089275
Trimmed Mean ( 17 / 19 )7.2080.0535163526410386134.687803713899
Trimmed Mean ( 18 / 19 )7.208695652173910.0525676840112136137.131695789302
Trimmed Mean ( 19 / 19 )7.209523809523810.050664518393411142.299266590116
Median7.2
Midrange7
Midmean - Weighted Average at Xnp7.23939393939394
Midmean - Weighted Average at X(n+1)p7.23939393939394
Midmean - Empirical Distribution Function7.23939393939394
Midmean - Empirical Distribution Function - Averaging7.23939393939394
Midmean - Empirical Distribution Function - Interpolation7.23939393939394
Midmean - Closest Observation7.23939393939394
Midmean - True Basic - Statistics Graphics Toolkit7.23939393939394
Midmean - MS Excel (old versions)7.23939393939394
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')