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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 22:23:46 -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/t1256099055ppvonehw70w1jny.htm/, Retrieved Thu, 02 May 2024 08:48:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49246, Retrieved Thu, 02 May 2024 08:48:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS 3 part 3] [2009-10-21 04:23:46] [87085ce7f5378f281469a8b1f0969170] [Current]
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Dataseries X:
0.76
0.7625
0.759493671
0.756410256
0.753246753
0.75
0.756756757
0.75
0.739726027
0.743243243
0.746666667
0.75
0.7375
0.734939759
0.722891566
0.707317073
0.743589744
0.7125
0.6875
0.670886076
0.702702703
0.693333333
0.675675676
0.698630137
0.68
0.693333333
0.653333333
0.676056338
0.661764706
0.652173913
0.666666667
0.656716418
0.646153846
0.621212121
0.6
0.584615385
0.582089552
0.617647059
0.672131148
0.655172414
0.620689655
0.606557377
0.625
0.62962963
0.607843137
0.596153846
0.62
0.615384615
0.611111111
0.636363636
0.705882353
0.729166667
0.66
0.653061224
0.673913043
0.744186047
0.697674419
0.681818182
0.704545455
0.755555556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49246&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49246&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49246&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.6834851937833330.0069487175925734298.3613428920787
Geometric Mean0.681378486998671
Harmonic Mean0.67925325573099
Quadratic Mean0.685566047887248
Winsorized Mean ( 1 / 20 )0.6834856243333330.0069305084264936198.6198388736586
Winsorized Mean ( 2 / 20 )0.6838533620666670.006839019741029899.9928919584744
Winsorized Mean ( 3 / 20 )0.6839088240666670.00677262396572001100.981366679784
Winsorized Mean ( 4 / 20 )0.6843228824666670.00667935393486141102.453454202359
Winsorized Mean ( 5 / 20 )0.6843588041333330.00664534531252176102.98318175337
Winsorized Mean ( 6 / 20 )0.6844547212333330.0065408520287594104.643052346065
Winsorized Mean ( 7 / 20 )0.684574508850.00638095457394938107.284027948548
Winsorized Mean ( 8 / 20 )0.684876168050.00632606425418145108.262600652104
Winsorized Mean ( 9 / 20 )0.68522910920.00626312356692242109.406928009359
Winsorized Mean ( 10 / 20 )0.68478849620.00614672357449959111.407075314225
Winsorized Mean ( 11 / 20 )0.68442950130.0060529280139978113.074118792956
Winsorized Mean ( 12 / 20 )0.68506781650.00590049476773624116.103452924988
Winsorized Mean ( 13 / 20 )0.6859958277833330.00571742752895849119.983300935394
Winsorized Mean ( 14 / 20 )0.6867464121166670.00532098004699312129.063895382345
Winsorized Mean ( 15 / 20 )0.6886374578666670.00484765482891964142.055794434551
Winsorized Mean ( 16 / 20 )0.6895600781333330.00449844523020792153.288534781485
Winsorized Mean ( 17 / 20 )0.6881757735166670.00418718863867655164.352703663759
Winsorized Mean ( 18 / 20 )0.6863748759166670.00386848683391236177.427222938874
Winsorized Mean ( 19 / 20 )0.6836665890.00327306469557124208.876588942792
Winsorized Mean ( 20 / 20 )0.6824536146666670.00294406631442913231.806468258511
Trimmed Mean ( 1 / 20 )0.6838710702586210.00683383945279903100.071281302712
Trimmed Mean ( 2 / 20 )0.6842840480357140.00671153895473563101.956354965784
Trimmed Mean ( 3 / 20 )0.6845233180185190.00661698823815154103.449378082882
Trimmed Mean ( 4 / 20 )0.6847596618461540.00652604044735074104.927278243293
Trimmed Mean ( 5 / 20 )0.684890695660.00644272427187277106.304517585837
Trimmed Mean ( 6 / 20 )0.6850236685416670.00634294743632892107.997689625840
Trimmed Mean ( 7 / 20 )0.685147352739130.00624180423736784109.767517000510
Trimmed Mean ( 8 / 20 )0.6852589457045450.00615060265012167111.413301213823
Trimmed Mean ( 9 / 20 )0.6853272988571430.00603951504821052113.473895401619
Trimmed Mean ( 10 / 20 )0.68534366380.00590311753753801116.098596960316
Trimmed Mean ( 11 / 20 )0.6854313218421050.00574592806701208119.289923898844
Trimmed Mean ( 12 / 20 )0.6855831128333330.00555227725942295123.477823746969
Trimmed Mean ( 13 / 20 )0.6856588917058820.00532439047098382128.776973710418
Trimmed Mean ( 14 / 20 )0.685610295156250.00505538049449023135.619919391524
Trimmed Mean ( 15 / 20 )0.6854479927333330.00479437899268552142.969088129887
Trimmed Mean ( 16 / 20 )0.6849923548571430.00456270631811842150.128521780385
Trimmed Mean ( 17 / 20 )0.6843335486153850.00432444722459707158.247635610618
Trimmed Mean ( 18 / 20 )0.6837685155416670.00407358034775481167.854432015446
Trimmed Mean ( 19 / 20 )0.6833736124545450.00380805000081321179.454999884091
Trimmed Mean ( 20 / 20 )0.6833273530.00364759410872175187.336455930252
Median0.680909091
Midrange0.672294776
Midmean - Weighted Average at Xnp0.683864626387097
Midmean - Weighted Average at X(n+1)p0.685447992733333
Midmean - Empirical Distribution Function0.683864626387097
Midmean - Empirical Distribution Function - Averaging0.685447992733333
Midmean - Empirical Distribution Function - Interpolation0.685447992733333
Midmean - Closest Observation0.683864626387097
Midmean - True Basic - Statistics Graphics Toolkit0.685447992733333
Midmean - MS Excel (old versions)0.68561029515625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.683485193783333 & 0.00694871759257342 & 98.3613428920787 \tabularnewline
Geometric Mean & 0.681378486998671 &  &  \tabularnewline
Harmonic Mean & 0.67925325573099 &  &  \tabularnewline
Quadratic Mean & 0.685566047887248 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.683485624333333 & 0.00693050842649361 & 98.6198388736586 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.683853362066667 & 0.0068390197410298 & 99.9928919584744 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.683908824066667 & 0.00677262396572001 & 100.981366679784 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.684322882466667 & 0.00667935393486141 & 102.453454202359 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.684358804133333 & 0.00664534531252176 & 102.98318175337 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.684454721233333 & 0.0065408520287594 & 104.643052346065 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.68457450885 & 0.00638095457394938 & 107.284027948548 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.68487616805 & 0.00632606425418145 & 108.262600652104 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.6852291092 & 0.00626312356692242 & 109.406928009359 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.6847884962 & 0.00614672357449959 & 111.407075314225 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.6844295013 & 0.0060529280139978 & 113.074118792956 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.6850678165 & 0.00590049476773624 & 116.103452924988 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.685995827783333 & 0.00571742752895849 & 119.983300935394 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.686746412116667 & 0.00532098004699312 & 129.063895382345 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.688637457866667 & 0.00484765482891964 & 142.055794434551 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.689560078133333 & 0.00449844523020792 & 153.288534781485 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.688175773516667 & 0.00418718863867655 & 164.352703663759 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.686374875916667 & 0.00386848683391236 & 177.427222938874 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.683666589 & 0.00327306469557124 & 208.876588942792 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.682453614666667 & 0.00294406631442913 & 231.806468258511 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.683871070258621 & 0.00683383945279903 & 100.071281302712 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.684284048035714 & 0.00671153895473563 & 101.956354965784 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.684523318018519 & 0.00661698823815154 & 103.449378082882 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.684759661846154 & 0.00652604044735074 & 104.927278243293 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.68489069566 & 0.00644272427187277 & 106.304517585837 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.685023668541667 & 0.00634294743632892 & 107.997689625840 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.68514735273913 & 0.00624180423736784 & 109.767517000510 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.685258945704545 & 0.00615060265012167 & 111.413301213823 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.685327298857143 & 0.00603951504821052 & 113.473895401619 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.6853436638 & 0.00590311753753801 & 116.098596960316 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.685431321842105 & 0.00574592806701208 & 119.289923898844 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.685583112833333 & 0.00555227725942295 & 123.477823746969 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.685658891705882 & 0.00532439047098382 & 128.776973710418 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.68561029515625 & 0.00505538049449023 & 135.619919391524 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.685447992733333 & 0.00479437899268552 & 142.969088129887 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.684992354857143 & 0.00456270631811842 & 150.128521780385 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.684333548615385 & 0.00432444722459707 & 158.247635610618 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.683768515541667 & 0.00407358034775481 & 167.854432015446 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.683373612454545 & 0.00380805000081321 & 179.454999884091 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.683327353 & 0.00364759410872175 & 187.336455930252 \tabularnewline
Median & 0.680909091 &  &  \tabularnewline
Midrange & 0.672294776 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.683864626387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.685447992733333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.683864626387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.685447992733333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.685447992733333 &  &  \tabularnewline
Midmean - Closest Observation & 0.683864626387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.685447992733333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.68561029515625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49246&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]0.683485193783333[/C][C]0.00694871759257342[/C][C]98.3613428920787[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.681378486998671[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.67925325573099[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.685566047887248[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.683485624333333[/C][C]0.00693050842649361[/C][C]98.6198388736586[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.683853362066667[/C][C]0.0068390197410298[/C][C]99.9928919584744[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.683908824066667[/C][C]0.00677262396572001[/C][C]100.981366679784[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.684322882466667[/C][C]0.00667935393486141[/C][C]102.453454202359[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.684358804133333[/C][C]0.00664534531252176[/C][C]102.98318175337[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.684454721233333[/C][C]0.0065408520287594[/C][C]104.643052346065[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.68457450885[/C][C]0.00638095457394938[/C][C]107.284027948548[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.68487616805[/C][C]0.00632606425418145[/C][C]108.262600652104[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.6852291092[/C][C]0.00626312356692242[/C][C]109.406928009359[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.6847884962[/C][C]0.00614672357449959[/C][C]111.407075314225[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.6844295013[/C][C]0.0060529280139978[/C][C]113.074118792956[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.6850678165[/C][C]0.00590049476773624[/C][C]116.103452924988[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.685995827783333[/C][C]0.00571742752895849[/C][C]119.983300935394[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.686746412116667[/C][C]0.00532098004699312[/C][C]129.063895382345[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.688637457866667[/C][C]0.00484765482891964[/C][C]142.055794434551[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.689560078133333[/C][C]0.00449844523020792[/C][C]153.288534781485[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.688175773516667[/C][C]0.00418718863867655[/C][C]164.352703663759[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.686374875916667[/C][C]0.00386848683391236[/C][C]177.427222938874[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.683666589[/C][C]0.00327306469557124[/C][C]208.876588942792[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.682453614666667[/C][C]0.00294406631442913[/C][C]231.806468258511[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.683871070258621[/C][C]0.00683383945279903[/C][C]100.071281302712[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.684284048035714[/C][C]0.00671153895473563[/C][C]101.956354965784[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.684523318018519[/C][C]0.00661698823815154[/C][C]103.449378082882[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.684759661846154[/C][C]0.00652604044735074[/C][C]104.927278243293[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.68489069566[/C][C]0.00644272427187277[/C][C]106.304517585837[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.685023668541667[/C][C]0.00634294743632892[/C][C]107.997689625840[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.68514735273913[/C][C]0.00624180423736784[/C][C]109.767517000510[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.685258945704545[/C][C]0.00615060265012167[/C][C]111.413301213823[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.685327298857143[/C][C]0.00603951504821052[/C][C]113.473895401619[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.6853436638[/C][C]0.00590311753753801[/C][C]116.098596960316[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.685431321842105[/C][C]0.00574592806701208[/C][C]119.289923898844[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.685583112833333[/C][C]0.00555227725942295[/C][C]123.477823746969[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.685658891705882[/C][C]0.00532439047098382[/C][C]128.776973710418[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.68561029515625[/C][C]0.00505538049449023[/C][C]135.619919391524[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.685447992733333[/C][C]0.00479437899268552[/C][C]142.969088129887[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.684992354857143[/C][C]0.00456270631811842[/C][C]150.128521780385[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.684333548615385[/C][C]0.00432444722459707[/C][C]158.247635610618[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.683768515541667[/C][C]0.00407358034775481[/C][C]167.854432015446[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.683373612454545[/C][C]0.00380805000081321[/C][C]179.454999884091[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.683327353[/C][C]0.00364759410872175[/C][C]187.336455930252[/C][/ROW]
[ROW][C]Median[/C][C]0.680909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.672294776[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.683864626387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.685447992733333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.683864626387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.685447992733333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.685447992733333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.683864626387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.685447992733333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.68561029515625[/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=49246&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49246&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.6834851937833330.0069487175925734298.3613428920787
Geometric Mean0.681378486998671
Harmonic Mean0.67925325573099
Quadratic Mean0.685566047887248
Winsorized Mean ( 1 / 20 )0.6834856243333330.0069305084264936198.6198388736586
Winsorized Mean ( 2 / 20 )0.6838533620666670.006839019741029899.9928919584744
Winsorized Mean ( 3 / 20 )0.6839088240666670.00677262396572001100.981366679784
Winsorized Mean ( 4 / 20 )0.6843228824666670.00667935393486141102.453454202359
Winsorized Mean ( 5 / 20 )0.6843588041333330.00664534531252176102.98318175337
Winsorized Mean ( 6 / 20 )0.6844547212333330.0065408520287594104.643052346065
Winsorized Mean ( 7 / 20 )0.684574508850.00638095457394938107.284027948548
Winsorized Mean ( 8 / 20 )0.684876168050.00632606425418145108.262600652104
Winsorized Mean ( 9 / 20 )0.68522910920.00626312356692242109.406928009359
Winsorized Mean ( 10 / 20 )0.68478849620.00614672357449959111.407075314225
Winsorized Mean ( 11 / 20 )0.68442950130.0060529280139978113.074118792956
Winsorized Mean ( 12 / 20 )0.68506781650.00590049476773624116.103452924988
Winsorized Mean ( 13 / 20 )0.6859958277833330.00571742752895849119.983300935394
Winsorized Mean ( 14 / 20 )0.6867464121166670.00532098004699312129.063895382345
Winsorized Mean ( 15 / 20 )0.6886374578666670.00484765482891964142.055794434551
Winsorized Mean ( 16 / 20 )0.6895600781333330.00449844523020792153.288534781485
Winsorized Mean ( 17 / 20 )0.6881757735166670.00418718863867655164.352703663759
Winsorized Mean ( 18 / 20 )0.6863748759166670.00386848683391236177.427222938874
Winsorized Mean ( 19 / 20 )0.6836665890.00327306469557124208.876588942792
Winsorized Mean ( 20 / 20 )0.6824536146666670.00294406631442913231.806468258511
Trimmed Mean ( 1 / 20 )0.6838710702586210.00683383945279903100.071281302712
Trimmed Mean ( 2 / 20 )0.6842840480357140.00671153895473563101.956354965784
Trimmed Mean ( 3 / 20 )0.6845233180185190.00661698823815154103.449378082882
Trimmed Mean ( 4 / 20 )0.6847596618461540.00652604044735074104.927278243293
Trimmed Mean ( 5 / 20 )0.684890695660.00644272427187277106.304517585837
Trimmed Mean ( 6 / 20 )0.6850236685416670.00634294743632892107.997689625840
Trimmed Mean ( 7 / 20 )0.685147352739130.00624180423736784109.767517000510
Trimmed Mean ( 8 / 20 )0.6852589457045450.00615060265012167111.413301213823
Trimmed Mean ( 9 / 20 )0.6853272988571430.00603951504821052113.473895401619
Trimmed Mean ( 10 / 20 )0.68534366380.00590311753753801116.098596960316
Trimmed Mean ( 11 / 20 )0.6854313218421050.00574592806701208119.289923898844
Trimmed Mean ( 12 / 20 )0.6855831128333330.00555227725942295123.477823746969
Trimmed Mean ( 13 / 20 )0.6856588917058820.00532439047098382128.776973710418
Trimmed Mean ( 14 / 20 )0.685610295156250.00505538049449023135.619919391524
Trimmed Mean ( 15 / 20 )0.6854479927333330.00479437899268552142.969088129887
Trimmed Mean ( 16 / 20 )0.6849923548571430.00456270631811842150.128521780385
Trimmed Mean ( 17 / 20 )0.6843335486153850.00432444722459707158.247635610618
Trimmed Mean ( 18 / 20 )0.6837685155416670.00407358034775481167.854432015446
Trimmed Mean ( 19 / 20 )0.6833736124545450.00380805000081321179.454999884091
Trimmed Mean ( 20 / 20 )0.6833273530.00364759410872175187.336455930252
Median0.680909091
Midrange0.672294776
Midmean - Weighted Average at Xnp0.683864626387097
Midmean - Weighted Average at X(n+1)p0.685447992733333
Midmean - Empirical Distribution Function0.683864626387097
Midmean - Empirical Distribution Function - Averaging0.685447992733333
Midmean - Empirical Distribution Function - Interpolation0.685447992733333
Midmean - Closest Observation0.683864626387097
Midmean - True Basic - Statistics Graphics Toolkit0.685447992733333
Midmean - MS Excel (old versions)0.68561029515625
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')