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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 computationSat, 25 Dec 2010 16:25:22 +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/Dec/25/t1293294358hle8tr6bc5irso8.htm/, Retrieved Sun, 28 Apr 2024 19:53:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115417, Retrieved Sun, 28 Apr 2024 19:53:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [EONIA Central ten...] [2010-12-25 16:25:22] [f593aab944ee27cf123b0a348e80fa81] [Current]
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Dataseries X:
2,08
2,09
2,07
2,04
2,35
2,33
2,37
2,59
2,62
2,6
2,83
2,78
3,01
3,06
3,33
3,32
3,6
3,57
3,57
3,83
3,84
3,8
4,07
4,05
4,272
3,858
4,067
3,964
3,782
4,114
4,009
4,025
4,082
4,044
3,916
4,289
4,296
4,193
3,48
2,934
2,221
1,211
1,28
0,96
0,5
0,687
0,344
0,346
0,334
0,34
0,328
0,344
0,341
0,32
0,314
0,325
0,339
0,329
0,48
0,399
0,37




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=115417&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=115417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115417&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 Mean2.413721311475410.19143815524805912.6083606914608
Geometric Mean1.68788296777972
Harmonic Mean0.978018915633025
Quadratic Mean2.83283684785365
Winsorized Mean ( 1 / 20 )2.413704918032790.19140142684695512.6106944853801
Winsorized Mean ( 2 / 20 )2.413311475409840.1912809259841312.6165819356712
Winsorized Mean ( 3 / 20 )2.40957377049180.19063655728149312.639620673247
Winsorized Mean ( 4 / 20 )2.404459016393440.189831965635212.6662493766413
Winsorized Mean ( 5 / 20 )2.402245901639340.18936658965181612.6856902585419
Winsorized Mean ( 6 / 20 )2.401557377049180.18910309375597812.6997254743394
Winsorized Mean ( 7 / 20 )2.401327868852460.18903164467686712.7033115167427
Winsorized Mean ( 8 / 20 )2.399229508196720.18868154191311812.715761615418
Winsorized Mean ( 9 / 20 )2.39878688524590.18847215462282912.7275399914983
Winsorized Mean ( 10 / 20 )2.395672131147540.18802064576979112.7415376185909
Winsorized Mean ( 11 / 20 )2.393147540983610.18753952419280112.7607636378736
Winsorized Mean ( 12 / 20 )2.389016393442620.18541934527464612.8843966626243
Winsorized Mean ( 13 / 20 )2.384967213114750.1828612809468313.0424942927542
Winsorized Mean ( 14 / 20 )2.390245901639340.17766754373275813.4534752460735
Winsorized Mean ( 15 / 20 )2.390737704918030.17617891567598213.5699422132609
Winsorized Mean ( 16 / 20 )2.437163934426230.16714777366335614.5808937864456
Winsorized Mean ( 17 / 20 )2.504885245901640.15292350153429216.3799888229733
Winsorized Mean ( 18 / 20 )2.57363934426230.13991016249661418.3949421424236
Winsorized Mean ( 19 / 20 )2.538442622950820.12841865985607219.7669297109612
Winsorized Mean ( 20 / 20 )2.77778688524590.088865647701435731.2582753526819
Trimmed Mean ( 1 / 20 )2.417406779661020.1920247648020412.589036534705
Trimmed Mean ( 2 / 20 )2.421368421052630.19249571266191912.5788174062105
Trimmed Mean ( 3 / 20 )2.425836363636360.19284995783805312.5788794087965
Trimmed Mean ( 4 / 20 )2.432075471698110.19325691640797412.5846749337752
Trimmed Mean ( 5 / 20 )2.440333333333330.19370126922492412.5984374965538
Trimmed Mean ( 6 / 20 )2.449816326530610.19402243557035112.6264589934102
Trimmed Mean ( 7 / 20 )2.460255319148940.19410207998444512.6750590171218
Trimmed Mean ( 8 / 20 )2.471666666666670.19380782160989212.7531832623442
Trimmed Mean ( 9 / 20 )2.484511627906980.19308898726030612.8671845202522
Trimmed Mean ( 10 / 20 )2.498682926829270.19176922563656913.0296345439943
Trimmed Mean ( 11 / 20 )2.514794871794870.18969627040628813.256954743542
Trimmed Mean ( 12 / 20 )2.533027027027030.18660204192822113.5744871859515
Trimmed Mean ( 13 / 20 )2.553942857142860.18251047601039613.9934041758643
Trimmed Mean ( 14 / 20 )2.57796969696970.17710037966893214.5565452868532
Trimmed Mean ( 15 / 20 )2.604354838709680.17057594750579315.2680074582099
Trimmed Mean ( 16 / 20 )2.634310344827590.16111630367217916.3503648283018
Trimmed Mean ( 17 / 20 )2.662148148148150.15019293104127217.7248564875307
Trimmed Mean ( 18 / 20 )2.684720.13922945713222219.2827010554986
Trimmed Mean ( 19 / 20 )2.701086956521740.12767973324221921.155173870841
Trimmed Mean ( 20 / 20 )2.725952380952380.11347700577210524.0220682807484
Median2.62
Midrange2.305
Midmean - Weighted Average at Xnp2.56316666666667
Midmean - Weighted Average at X(n+1)p2.60435483870968
Midmean - Empirical Distribution Function2.60435483870968
Midmean - Empirical Distribution Function - Averaging2.60435483870968
Midmean - Empirical Distribution Function - Interpolation2.60435483870968
Midmean - Closest Observation2.53796875
Midmean - True Basic - Statistics Graphics Toolkit2.60435483870968
Midmean - MS Excel (old versions)2.60435483870968
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.41372131147541 & 0.191438155248059 & 12.6083606914608 \tabularnewline
Geometric Mean & 1.68788296777972 &  &  \tabularnewline
Harmonic Mean & 0.978018915633025 &  &  \tabularnewline
Quadratic Mean & 2.83283684785365 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.41370491803279 & 0.191401426846955 & 12.6106944853801 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.41331147540984 & 0.19128092598413 & 12.6165819356712 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.4095737704918 & 0.190636557281493 & 12.639620673247 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.40445901639344 & 0.1898319656352 & 12.6662493766413 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.40224590163934 & 0.189366589651816 & 12.6856902585419 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.40155737704918 & 0.189103093755978 & 12.6997254743394 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.40132786885246 & 0.189031644676867 & 12.7033115167427 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.39922950819672 & 0.188681541913118 & 12.715761615418 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.3987868852459 & 0.188472154622829 & 12.7275399914983 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.39567213114754 & 0.188020645769791 & 12.7415376185909 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.39314754098361 & 0.187539524192801 & 12.7607636378736 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.38901639344262 & 0.185419345274646 & 12.8843966626243 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.38496721311475 & 0.18286128094683 & 13.0424942927542 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.39024590163934 & 0.177667543732758 & 13.4534752460735 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.39073770491803 & 0.176178915675982 & 13.5699422132609 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.43716393442623 & 0.167147773663356 & 14.5808937864456 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.50488524590164 & 0.152923501534292 & 16.3799888229733 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.5736393442623 & 0.139910162496614 & 18.3949421424236 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.53844262295082 & 0.128418659856072 & 19.7669297109612 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.7777868852459 & 0.0888656477014357 & 31.2582753526819 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.41740677966102 & 0.19202476480204 & 12.589036534705 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.42136842105263 & 0.192495712661919 & 12.5788174062105 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.42583636363636 & 0.192849957838053 & 12.5788794087965 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.43207547169811 & 0.193256916407974 & 12.5846749337752 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.44033333333333 & 0.193701269224924 & 12.5984374965538 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.44981632653061 & 0.194022435570351 & 12.6264589934102 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.46025531914894 & 0.194102079984445 & 12.6750590171218 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.47166666666667 & 0.193807821609892 & 12.7531832623442 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.48451162790698 & 0.193088987260306 & 12.8671845202522 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.49868292682927 & 0.191769225636569 & 13.0296345439943 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.51479487179487 & 0.189696270406288 & 13.256954743542 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.53302702702703 & 0.186602041928221 & 13.5744871859515 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.55394285714286 & 0.182510476010396 & 13.9934041758643 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.5779696969697 & 0.177100379668932 & 14.5565452868532 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.60435483870968 & 0.170575947505793 & 15.2680074582099 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.63431034482759 & 0.161116303672179 & 16.3503648283018 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.66214814814815 & 0.150192931041272 & 17.7248564875307 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.68472 & 0.139229457132222 & 19.2827010554986 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.70108695652174 & 0.127679733242219 & 21.155173870841 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.72595238095238 & 0.113477005772105 & 24.0220682807484 \tabularnewline
Median & 2.62 &  &  \tabularnewline
Midrange & 2.305 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.56316666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.60435483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.60435483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.60435483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.60435483870968 &  &  \tabularnewline
Midmean - Closest Observation & 2.53796875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.60435483870968 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.60435483870968 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115417&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]2.41372131147541[/C][C]0.191438155248059[/C][C]12.6083606914608[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.68788296777972[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.978018915633025[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.83283684785365[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.41370491803279[/C][C]0.191401426846955[/C][C]12.6106944853801[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.41331147540984[/C][C]0.19128092598413[/C][C]12.6165819356712[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.4095737704918[/C][C]0.190636557281493[/C][C]12.639620673247[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.40445901639344[/C][C]0.1898319656352[/C][C]12.6662493766413[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.40224590163934[/C][C]0.189366589651816[/C][C]12.6856902585419[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.40155737704918[/C][C]0.189103093755978[/C][C]12.6997254743394[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.40132786885246[/C][C]0.189031644676867[/C][C]12.7033115167427[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.39922950819672[/C][C]0.188681541913118[/C][C]12.715761615418[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.3987868852459[/C][C]0.188472154622829[/C][C]12.7275399914983[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.39567213114754[/C][C]0.188020645769791[/C][C]12.7415376185909[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.39314754098361[/C][C]0.187539524192801[/C][C]12.7607636378736[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.38901639344262[/C][C]0.185419345274646[/C][C]12.8843966626243[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.38496721311475[/C][C]0.18286128094683[/C][C]13.0424942927542[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.39024590163934[/C][C]0.177667543732758[/C][C]13.4534752460735[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.39073770491803[/C][C]0.176178915675982[/C][C]13.5699422132609[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.43716393442623[/C][C]0.167147773663356[/C][C]14.5808937864456[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.50488524590164[/C][C]0.152923501534292[/C][C]16.3799888229733[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.5736393442623[/C][C]0.139910162496614[/C][C]18.3949421424236[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.53844262295082[/C][C]0.128418659856072[/C][C]19.7669297109612[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.7777868852459[/C][C]0.0888656477014357[/C][C]31.2582753526819[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.41740677966102[/C][C]0.19202476480204[/C][C]12.589036534705[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.42136842105263[/C][C]0.192495712661919[/C][C]12.5788174062105[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.42583636363636[/C][C]0.192849957838053[/C][C]12.5788794087965[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.43207547169811[/C][C]0.193256916407974[/C][C]12.5846749337752[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.44033333333333[/C][C]0.193701269224924[/C][C]12.5984374965538[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.44981632653061[/C][C]0.194022435570351[/C][C]12.6264589934102[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.46025531914894[/C][C]0.194102079984445[/C][C]12.6750590171218[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.47166666666667[/C][C]0.193807821609892[/C][C]12.7531832623442[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.48451162790698[/C][C]0.193088987260306[/C][C]12.8671845202522[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.49868292682927[/C][C]0.191769225636569[/C][C]13.0296345439943[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.51479487179487[/C][C]0.189696270406288[/C][C]13.256954743542[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.53302702702703[/C][C]0.186602041928221[/C][C]13.5744871859515[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.55394285714286[/C][C]0.182510476010396[/C][C]13.9934041758643[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.5779696969697[/C][C]0.177100379668932[/C][C]14.5565452868532[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.60435483870968[/C][C]0.170575947505793[/C][C]15.2680074582099[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.63431034482759[/C][C]0.161116303672179[/C][C]16.3503648283018[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.66214814814815[/C][C]0.150192931041272[/C][C]17.7248564875307[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.68472[/C][C]0.139229457132222[/C][C]19.2827010554986[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.70108695652174[/C][C]0.127679733242219[/C][C]21.155173870841[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.72595238095238[/C][C]0.113477005772105[/C][C]24.0220682807484[/C][/ROW]
[ROW][C]Median[/C][C]2.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.56316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.60435483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.60435483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.60435483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.60435483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.53796875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.60435483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.60435483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115417&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 Mean2.413721311475410.19143815524805912.6083606914608
Geometric Mean1.68788296777972
Harmonic Mean0.978018915633025
Quadratic Mean2.83283684785365
Winsorized Mean ( 1 / 20 )2.413704918032790.19140142684695512.6106944853801
Winsorized Mean ( 2 / 20 )2.413311475409840.1912809259841312.6165819356712
Winsorized Mean ( 3 / 20 )2.40957377049180.19063655728149312.639620673247
Winsorized Mean ( 4 / 20 )2.404459016393440.189831965635212.6662493766413
Winsorized Mean ( 5 / 20 )2.402245901639340.18936658965181612.6856902585419
Winsorized Mean ( 6 / 20 )2.401557377049180.18910309375597812.6997254743394
Winsorized Mean ( 7 / 20 )2.401327868852460.18903164467686712.7033115167427
Winsorized Mean ( 8 / 20 )2.399229508196720.18868154191311812.715761615418
Winsorized Mean ( 9 / 20 )2.39878688524590.18847215462282912.7275399914983
Winsorized Mean ( 10 / 20 )2.395672131147540.18802064576979112.7415376185909
Winsorized Mean ( 11 / 20 )2.393147540983610.18753952419280112.7607636378736
Winsorized Mean ( 12 / 20 )2.389016393442620.18541934527464612.8843966626243
Winsorized Mean ( 13 / 20 )2.384967213114750.1828612809468313.0424942927542
Winsorized Mean ( 14 / 20 )2.390245901639340.17766754373275813.4534752460735
Winsorized Mean ( 15 / 20 )2.390737704918030.17617891567598213.5699422132609
Winsorized Mean ( 16 / 20 )2.437163934426230.16714777366335614.5808937864456
Winsorized Mean ( 17 / 20 )2.504885245901640.15292350153429216.3799888229733
Winsorized Mean ( 18 / 20 )2.57363934426230.13991016249661418.3949421424236
Winsorized Mean ( 19 / 20 )2.538442622950820.12841865985607219.7669297109612
Winsorized Mean ( 20 / 20 )2.77778688524590.088865647701435731.2582753526819
Trimmed Mean ( 1 / 20 )2.417406779661020.1920247648020412.589036534705
Trimmed Mean ( 2 / 20 )2.421368421052630.19249571266191912.5788174062105
Trimmed Mean ( 3 / 20 )2.425836363636360.19284995783805312.5788794087965
Trimmed Mean ( 4 / 20 )2.432075471698110.19325691640797412.5846749337752
Trimmed Mean ( 5 / 20 )2.440333333333330.19370126922492412.5984374965538
Trimmed Mean ( 6 / 20 )2.449816326530610.19402243557035112.6264589934102
Trimmed Mean ( 7 / 20 )2.460255319148940.19410207998444512.6750590171218
Trimmed Mean ( 8 / 20 )2.471666666666670.19380782160989212.7531832623442
Trimmed Mean ( 9 / 20 )2.484511627906980.19308898726030612.8671845202522
Trimmed Mean ( 10 / 20 )2.498682926829270.19176922563656913.0296345439943
Trimmed Mean ( 11 / 20 )2.514794871794870.18969627040628813.256954743542
Trimmed Mean ( 12 / 20 )2.533027027027030.18660204192822113.5744871859515
Trimmed Mean ( 13 / 20 )2.553942857142860.18251047601039613.9934041758643
Trimmed Mean ( 14 / 20 )2.57796969696970.17710037966893214.5565452868532
Trimmed Mean ( 15 / 20 )2.604354838709680.17057594750579315.2680074582099
Trimmed Mean ( 16 / 20 )2.634310344827590.16111630367217916.3503648283018
Trimmed Mean ( 17 / 20 )2.662148148148150.15019293104127217.7248564875307
Trimmed Mean ( 18 / 20 )2.684720.13922945713222219.2827010554986
Trimmed Mean ( 19 / 20 )2.701086956521740.12767973324221921.155173870841
Trimmed Mean ( 20 / 20 )2.725952380952380.11347700577210524.0220682807484
Median2.62
Midrange2.305
Midmean - Weighted Average at Xnp2.56316666666667
Midmean - Weighted Average at X(n+1)p2.60435483870968
Midmean - Empirical Distribution Function2.60435483870968
Midmean - Empirical Distribution Function - Averaging2.60435483870968
Midmean - Empirical Distribution Function - Interpolation2.60435483870968
Midmean - Closest Observation2.53796875
Midmean - True Basic - Statistics Graphics Toolkit2.60435483870968
Midmean - MS Excel (old versions)2.60435483870968
Number of observations61



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')