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Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 20 Oct 2010 13:41:55 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/20/t12875821094whrifjyz5kj60e.htm/, Retrieved Fri, 03 May 2024 23:49:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87204, Retrieved Fri, 03 May 2024 23:49:48 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-10-20 13:41:55] [9d49b4c553d27c097eebc753f5e7db7d] [Current]
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Dataseries X:
98,1
98,0
98,3
98,5
98,7
99,3
99,5
99,8
100,3
99,3
99,6
99,3



99,4
99,7
100,0
99,3
100,3
100,8
101,4
101,1
100,6
99,5
99,1
98,8



99,1
98,8
98,5
99,0
99,0
100,6
101,0
101,8
101,8
101,8
101,8
102,4



103,0
103,3
103,6
104,1
104,5
105,6
105,9
106,0
106,3
107,3
107,1
107,3



107,7
108,0
108,9
108,5
109,0
108,9
109,0
108,9
110,3
109,4
108,6
108,0



108,4
108,0
108,0
107,6
107,5
107,9
108,0
107,5
106,8
106,7
107,2
107,8



106,6
106,3
105,7
105,9
106,5
107,2
108,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=87204&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=87204&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87204&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.8151898734180.443083412145813234.301684575936
Geometric Mean103.741300831928
Harmonic Mean103.667334435127
Quadratic Mean103.888915844969
Winsorized Mean ( 1 / 26 )103.8050632911390.440875978568057235.451846635629
Winsorized Mean ( 2 / 26 )103.80.438454990071647236.740377804888
Winsorized Mean ( 3 / 26 )103.8075949367090.43725328148688237.408383954744
Winsorized Mean ( 4 / 26 )103.8025316455700.436488803340428237.812587290152
Winsorized Mean ( 5 / 26 )103.8151898734180.434547852131683238.903930520310
Winsorized Mean ( 6 / 26 )103.8227848101270.433410534282638239.548364882200
Winsorized Mean ( 7 / 26 )103.7962025316460.429508157672495241.662936262066
Winsorized Mean ( 8 / 26 )103.8063291139240.425086973066753244.200212405998
Winsorized Mean ( 9 / 26 )103.7949367088610.423486474794159245.096225940419
Winsorized Mean ( 10 / 26 )103.7949367088610.419907482484808247.185251605075
Winsorized Mean ( 11 / 26 )103.7531645569620.414288906947154250.43674309676
Winsorized Mean ( 12 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 13 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 14 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 15 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 16 / 26 )103.7835443037970.404488089651277256.579975922833
Winsorized Mean ( 17 / 26 )103.7835443037970.39871763926075260.293335645293
Winsorized Mean ( 18 / 26 )103.7607594936710.395792614847636262.159412786453
Winsorized Mean ( 19 / 26 )103.7607594936710.389431203830794266.441822003443
Winsorized Mean ( 20 / 26 )103.7607594936710.382790356969577271.064193766818
Winsorized Mean ( 21 / 26 )103.7873417721520.379190818738968273.707422867742
Winsorized Mean ( 22 / 26 )103.7873417721520.36479428290033284.509233387599
Winsorized Mean ( 23 / 26 )103.8746835443040.353314478781558294.000641871588
Winsorized Mean ( 24 / 26 )103.8443037974680.349556898703907297.074107770449
Winsorized Mean ( 25 / 26 )103.9392405063290.337360055357369308.095872216481
Winsorized Mean ( 26 / 26 )103.9063291139240.333299292835797311.750823801221
Trimmed Mean ( 1 / 26 )103.8064935064940.440178526132144235.828163674051
Trimmed Mean ( 2 / 26 )103.8080.439084879643483236.418981414909
Trimmed Mean ( 3 / 26 )103.8123287671230.438951745325209236.500549030079
Trimmed Mean ( 4 / 26 )103.8140845070420.438945580263876236.507870621760
Trimmed Mean ( 5 / 26 )103.8173913043480.438813581635417236.586549845221
Trimmed Mean ( 6 / 26 )103.8179104477610.43880581631112236.591919679918
Trimmed Mean ( 7 / 26 )103.8169230769230.438652707987597236.672249336390
Trimmed Mean ( 8 / 26 )103.8206349206350.438893541603232236.550837684667
Trimmed Mean ( 9 / 26 )103.8229508196720.439593661371679236.179362768130
Trimmed Mean ( 10 / 26 )103.8271186440680.440185063549713235.871516872452
Trimmed Mean ( 11 / 26 )103.8315789473680.440971514424049235.460966414083
Trimmed Mean ( 12 / 26 )103.8418181818180.442267579845539234.794099576742
Trimmed Mean ( 13 / 26 )103.8490566037740.44387970429299233.957659247304
Trimmed Mean ( 14 / 26 )103.8568627450980.445053465851418233.358170902934
Trimmed Mean ( 15 / 26 )103.8653061224490.445666502135756233.056120719637
Trimmed Mean ( 16 / 26 )103.8744680851060.445560567267422233.132094076812
Trimmed Mean ( 17 / 26 )103.8844444444440.445504543793849233.183804501252
Trimmed Mean ( 18 / 26 )103.8953488372090.445488688432474233.216581105083
Trimmed Mean ( 19 / 26 )103.9097560975610.444900713479146233.557180173934
Trimmed Mean ( 20 / 26 )103.9256410256410.444196615910046233.963153484913
Trimmed Mean ( 21 / 26 )103.9256410256410.443310988743624234.430554767375
Trimmed Mean ( 22 / 26 )103.960.441487173505356235.476829767375
Trimmed Mean ( 23 / 26 )103.9787878787880.440702726880896235.938607901760
Trimmed Mean ( 24 / 26 )103.9903225806450.440585017700005236.027823014745
Trimmed Mean ( 25 / 26 )104.0068965517240.439153098815303236.835164848665
Trimmed Mean ( 26 / 26 )104.0148148148150.438194420928506237.371380937288
Median104.1
Midrange104.15
Midmean - Weighted Average at Xnp103.8175
Midmean - Weighted Average at X(n+1)p103.909756097561
Midmean - Empirical Distribution Function103.909756097561
Midmean - Empirical Distribution Function - Averaging103.909756097561
Midmean - Empirical Distribution Function - Interpolation103.925641025641
Midmean - Closest Observation103.8175
Midmean - True Basic - Statistics Graphics Toolkit103.909756097561
Midmean - MS Excel (old versions)103.909756097561
Number of observations79

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.815189873418 & 0.443083412145813 & 234.301684575936 \tabularnewline
Geometric Mean & 103.741300831928 &  &  \tabularnewline
Harmonic Mean & 103.667334435127 &  &  \tabularnewline
Quadratic Mean & 103.888915844969 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 103.805063291139 & 0.440875978568057 & 235.451846635629 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 103.8 & 0.438454990071647 & 236.740377804888 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 103.807594936709 & 0.43725328148688 & 237.408383954744 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 103.802531645570 & 0.436488803340428 & 237.812587290152 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 103.815189873418 & 0.434547852131683 & 238.903930520310 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 103.822784810127 & 0.433410534282638 & 239.548364882200 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 103.796202531646 & 0.429508157672495 & 241.662936262066 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 103.806329113924 & 0.425086973066753 & 244.200212405998 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 103.794936708861 & 0.423486474794159 & 245.096225940419 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 103.794936708861 & 0.419907482484808 & 247.185251605075 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 103.753164556962 & 0.414288906947154 & 250.43674309676 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 103.783544303797 & 0.409971580857144 & 253.148142822029 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 103.783544303797 & 0.409971580857144 & 253.148142822029 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 103.783544303797 & 0.409971580857144 & 253.148142822029 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 103.783544303797 & 0.409971580857144 & 253.148142822029 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 103.783544303797 & 0.404488089651277 & 256.579975922833 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 103.783544303797 & 0.39871763926075 & 260.293335645293 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 103.760759493671 & 0.395792614847636 & 262.159412786453 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 103.760759493671 & 0.389431203830794 & 266.441822003443 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 103.760759493671 & 0.382790356969577 & 271.064193766818 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 103.787341772152 & 0.379190818738968 & 273.707422867742 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 103.787341772152 & 0.36479428290033 & 284.509233387599 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 103.874683544304 & 0.353314478781558 & 294.000641871588 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 103.844303797468 & 0.349556898703907 & 297.074107770449 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 103.939240506329 & 0.337360055357369 & 308.095872216481 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 103.906329113924 & 0.333299292835797 & 311.750823801221 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 103.806493506494 & 0.440178526132144 & 235.828163674051 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 103.808 & 0.439084879643483 & 236.418981414909 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 103.812328767123 & 0.438951745325209 & 236.500549030079 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 103.814084507042 & 0.438945580263876 & 236.507870621760 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 103.817391304348 & 0.438813581635417 & 236.586549845221 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 103.817910447761 & 0.43880581631112 & 236.591919679918 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 103.816923076923 & 0.438652707987597 & 236.672249336390 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 103.820634920635 & 0.438893541603232 & 236.550837684667 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 103.822950819672 & 0.439593661371679 & 236.179362768130 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 103.827118644068 & 0.440185063549713 & 235.871516872452 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 103.831578947368 & 0.440971514424049 & 235.460966414083 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 103.841818181818 & 0.442267579845539 & 234.794099576742 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 103.849056603774 & 0.44387970429299 & 233.957659247304 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 103.856862745098 & 0.445053465851418 & 233.358170902934 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 103.865306122449 & 0.445666502135756 & 233.056120719637 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 103.874468085106 & 0.445560567267422 & 233.132094076812 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 103.884444444444 & 0.445504543793849 & 233.183804501252 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 103.895348837209 & 0.445488688432474 & 233.216581105083 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 103.909756097561 & 0.444900713479146 & 233.557180173934 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 103.925641025641 & 0.444196615910046 & 233.963153484913 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 103.925641025641 & 0.443310988743624 & 234.430554767375 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 103.96 & 0.441487173505356 & 235.476829767375 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 103.978787878788 & 0.440702726880896 & 235.938607901760 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 103.990322580645 & 0.440585017700005 & 236.027823014745 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 104.006896551724 & 0.439153098815303 & 236.835164848665 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 104.014814814815 & 0.438194420928506 & 237.371380937288 \tabularnewline
Median & 104.1 &  &  \tabularnewline
Midrange & 104.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.8175 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.909756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.909756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.909756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.925641025641 &  &  \tabularnewline
Midmean - Closest Observation & 103.8175 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.909756097561 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.909756097561 &  &  \tabularnewline
Number of observations & 79 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87204&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]103.815189873418[/C][C]0.443083412145813[/C][C]234.301684575936[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.741300831928[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.667334435127[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.888915844969[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]103.805063291139[/C][C]0.440875978568057[/C][C]235.451846635629[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]103.8[/C][C]0.438454990071647[/C][C]236.740377804888[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]103.807594936709[/C][C]0.43725328148688[/C][C]237.408383954744[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]103.802531645570[/C][C]0.436488803340428[/C][C]237.812587290152[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]103.815189873418[/C][C]0.434547852131683[/C][C]238.903930520310[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]103.822784810127[/C][C]0.433410534282638[/C][C]239.548364882200[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]103.796202531646[/C][C]0.429508157672495[/C][C]241.662936262066[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]103.806329113924[/C][C]0.425086973066753[/C][C]244.200212405998[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]103.794936708861[/C][C]0.423486474794159[/C][C]245.096225940419[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]103.794936708861[/C][C]0.419907482484808[/C][C]247.185251605075[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]103.753164556962[/C][C]0.414288906947154[/C][C]250.43674309676[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]103.783544303797[/C][C]0.409971580857144[/C][C]253.148142822029[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]103.783544303797[/C][C]0.409971580857144[/C][C]253.148142822029[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]103.783544303797[/C][C]0.409971580857144[/C][C]253.148142822029[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]103.783544303797[/C][C]0.409971580857144[/C][C]253.148142822029[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]103.783544303797[/C][C]0.404488089651277[/C][C]256.579975922833[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]103.783544303797[/C][C]0.39871763926075[/C][C]260.293335645293[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]103.760759493671[/C][C]0.395792614847636[/C][C]262.159412786453[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]103.760759493671[/C][C]0.389431203830794[/C][C]266.441822003443[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]103.760759493671[/C][C]0.382790356969577[/C][C]271.064193766818[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]103.787341772152[/C][C]0.379190818738968[/C][C]273.707422867742[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]103.787341772152[/C][C]0.36479428290033[/C][C]284.509233387599[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]103.874683544304[/C][C]0.353314478781558[/C][C]294.000641871588[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]103.844303797468[/C][C]0.349556898703907[/C][C]297.074107770449[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]103.939240506329[/C][C]0.337360055357369[/C][C]308.095872216481[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]103.906329113924[/C][C]0.333299292835797[/C][C]311.750823801221[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]103.806493506494[/C][C]0.440178526132144[/C][C]235.828163674051[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]103.808[/C][C]0.439084879643483[/C][C]236.418981414909[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]103.812328767123[/C][C]0.438951745325209[/C][C]236.500549030079[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]103.814084507042[/C][C]0.438945580263876[/C][C]236.507870621760[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]103.817391304348[/C][C]0.438813581635417[/C][C]236.586549845221[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]103.817910447761[/C][C]0.43880581631112[/C][C]236.591919679918[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]103.816923076923[/C][C]0.438652707987597[/C][C]236.672249336390[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]103.820634920635[/C][C]0.438893541603232[/C][C]236.550837684667[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]103.822950819672[/C][C]0.439593661371679[/C][C]236.179362768130[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]103.827118644068[/C][C]0.440185063549713[/C][C]235.871516872452[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]103.831578947368[/C][C]0.440971514424049[/C][C]235.460966414083[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]103.841818181818[/C][C]0.442267579845539[/C][C]234.794099576742[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]103.849056603774[/C][C]0.44387970429299[/C][C]233.957659247304[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]103.856862745098[/C][C]0.445053465851418[/C][C]233.358170902934[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]103.865306122449[/C][C]0.445666502135756[/C][C]233.056120719637[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]103.874468085106[/C][C]0.445560567267422[/C][C]233.132094076812[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]103.884444444444[/C][C]0.445504543793849[/C][C]233.183804501252[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]103.895348837209[/C][C]0.445488688432474[/C][C]233.216581105083[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]103.909756097561[/C][C]0.444900713479146[/C][C]233.557180173934[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]103.925641025641[/C][C]0.444196615910046[/C][C]233.963153484913[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]103.925641025641[/C][C]0.443310988743624[/C][C]234.430554767375[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]103.96[/C][C]0.441487173505356[/C][C]235.476829767375[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]103.978787878788[/C][C]0.440702726880896[/C][C]235.938607901760[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]103.990322580645[/C][C]0.440585017700005[/C][C]236.027823014745[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]104.006896551724[/C][C]0.439153098815303[/C][C]236.835164848665[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]104.014814814815[/C][C]0.438194420928506[/C][C]237.371380937288[/C][/ROW]
[ROW][C]Median[/C][C]104.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.8175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.925641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.8175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.909756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]79[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87204&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87204&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 Mean103.8151898734180.443083412145813234.301684575936
Geometric Mean103.741300831928
Harmonic Mean103.667334435127
Quadratic Mean103.888915844969
Winsorized Mean ( 1 / 26 )103.8050632911390.440875978568057235.451846635629
Winsorized Mean ( 2 / 26 )103.80.438454990071647236.740377804888
Winsorized Mean ( 3 / 26 )103.8075949367090.43725328148688237.408383954744
Winsorized Mean ( 4 / 26 )103.8025316455700.436488803340428237.812587290152
Winsorized Mean ( 5 / 26 )103.8151898734180.434547852131683238.903930520310
Winsorized Mean ( 6 / 26 )103.8227848101270.433410534282638239.548364882200
Winsorized Mean ( 7 / 26 )103.7962025316460.429508157672495241.662936262066
Winsorized Mean ( 8 / 26 )103.8063291139240.425086973066753244.200212405998
Winsorized Mean ( 9 / 26 )103.7949367088610.423486474794159245.096225940419
Winsorized Mean ( 10 / 26 )103.7949367088610.419907482484808247.185251605075
Winsorized Mean ( 11 / 26 )103.7531645569620.414288906947154250.43674309676
Winsorized Mean ( 12 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 13 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 14 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 15 / 26 )103.7835443037970.409971580857144253.148142822029
Winsorized Mean ( 16 / 26 )103.7835443037970.404488089651277256.579975922833
Winsorized Mean ( 17 / 26 )103.7835443037970.39871763926075260.293335645293
Winsorized Mean ( 18 / 26 )103.7607594936710.395792614847636262.159412786453
Winsorized Mean ( 19 / 26 )103.7607594936710.389431203830794266.441822003443
Winsorized Mean ( 20 / 26 )103.7607594936710.382790356969577271.064193766818
Winsorized Mean ( 21 / 26 )103.7873417721520.379190818738968273.707422867742
Winsorized Mean ( 22 / 26 )103.7873417721520.36479428290033284.509233387599
Winsorized Mean ( 23 / 26 )103.8746835443040.353314478781558294.000641871588
Winsorized Mean ( 24 / 26 )103.8443037974680.349556898703907297.074107770449
Winsorized Mean ( 25 / 26 )103.9392405063290.337360055357369308.095872216481
Winsorized Mean ( 26 / 26 )103.9063291139240.333299292835797311.750823801221
Trimmed Mean ( 1 / 26 )103.8064935064940.440178526132144235.828163674051
Trimmed Mean ( 2 / 26 )103.8080.439084879643483236.418981414909
Trimmed Mean ( 3 / 26 )103.8123287671230.438951745325209236.500549030079
Trimmed Mean ( 4 / 26 )103.8140845070420.438945580263876236.507870621760
Trimmed Mean ( 5 / 26 )103.8173913043480.438813581635417236.586549845221
Trimmed Mean ( 6 / 26 )103.8179104477610.43880581631112236.591919679918
Trimmed Mean ( 7 / 26 )103.8169230769230.438652707987597236.672249336390
Trimmed Mean ( 8 / 26 )103.8206349206350.438893541603232236.550837684667
Trimmed Mean ( 9 / 26 )103.8229508196720.439593661371679236.179362768130
Trimmed Mean ( 10 / 26 )103.8271186440680.440185063549713235.871516872452
Trimmed Mean ( 11 / 26 )103.8315789473680.440971514424049235.460966414083
Trimmed Mean ( 12 / 26 )103.8418181818180.442267579845539234.794099576742
Trimmed Mean ( 13 / 26 )103.8490566037740.44387970429299233.957659247304
Trimmed Mean ( 14 / 26 )103.8568627450980.445053465851418233.358170902934
Trimmed Mean ( 15 / 26 )103.8653061224490.445666502135756233.056120719637
Trimmed Mean ( 16 / 26 )103.8744680851060.445560567267422233.132094076812
Trimmed Mean ( 17 / 26 )103.8844444444440.445504543793849233.183804501252
Trimmed Mean ( 18 / 26 )103.8953488372090.445488688432474233.216581105083
Trimmed Mean ( 19 / 26 )103.9097560975610.444900713479146233.557180173934
Trimmed Mean ( 20 / 26 )103.9256410256410.444196615910046233.963153484913
Trimmed Mean ( 21 / 26 )103.9256410256410.443310988743624234.430554767375
Trimmed Mean ( 22 / 26 )103.960.441487173505356235.476829767375
Trimmed Mean ( 23 / 26 )103.9787878787880.440702726880896235.938607901760
Trimmed Mean ( 24 / 26 )103.9903225806450.440585017700005236.027823014745
Trimmed Mean ( 25 / 26 )104.0068965517240.439153098815303236.835164848665
Trimmed Mean ( 26 / 26 )104.0148148148150.438194420928506237.371380937288
Median104.1
Midrange104.15
Midmean - Weighted Average at Xnp103.8175
Midmean - Weighted Average at X(n+1)p103.909756097561
Midmean - Empirical Distribution Function103.909756097561
Midmean - Empirical Distribution Function - Averaging103.909756097561
Midmean - Empirical Distribution Function - Interpolation103.925641025641
Midmean - Closest Observation103.8175
Midmean - True Basic - Statistics Graphics Toolkit103.909756097561
Midmean - MS Excel (old versions)103.909756097561
Number of observations79



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')