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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 08:59:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t136249210036sad9t7omvijgk.htm/, Retrieved Sat, 04 May 2024 06:57:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207392, Retrieved Sat, 04 May 2024 06:57:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [eigen centrummaten] [2013-03-05 13:59:17] [69bb275cfc110db963587bebba58b9f3] [Current]
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Dataseries X:
85,3
85,65
85,15
84,94
85,15
85,15
85,15
85,14
85,37
85,61
85,59
85,54
85,54
85,5
85,78
86,16
86,38
86,49
86,49
86
85,9
85,66
85,64
85,6
85,6
85,57
85,81
86,29
86,37
86,41
86,41
86,38
86,62
87,08
87,19
87,21
87,21
87,24
87,16
87,05
87,04
86,98
86,98
86,94
86,96
86,98
86,86
86,82
86,82
86,84
86,91
86,85
86,61
86,65
86,65
86,36
86,33
86,43
86,36
86,29
86,29
86,44
86,51
86,72
86,93
86,79
86,79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207392&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207392&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.29268656716420.07989380731501431080.09230586445
Geometric Mean86.2902404980554
Harmonic Mean86.2877893898097
Quadratic Mean86.295127523681
Winsorized Mean ( 1 / 22 )86.2952238805970.07910094033035731090.95067037375
Winsorized Mean ( 2 / 22 )86.29552238805970.0790351368259851091.86275691608
Winsorized Mean ( 3 / 22 )86.29462686567160.07887962889864581094.00396617679
Winsorized Mean ( 4 / 22 )86.29283582089550.07857586019877141098.21051405104
Winsorized Mean ( 5 / 22 )86.28686567164180.07761430605586151111.73918902964
Winsorized Mean ( 6 / 22 )86.29761194029850.07434139882951751160.82846568706
Winsorized Mean ( 7 / 22 )86.30388059701490.07272587367103791186.70118680725
Winsorized Mean ( 8 / 22 )86.31223880597020.06874589610563621255.52569237502
Winsorized Mean ( 9 / 22 )86.31761194029850.06779798442168861273.15896890713
Winsorized Mean ( 10 / 22 )86.31761194029850.06779798442168861273.15896890713
Winsorized Mean ( 11 / 22 )86.31925373134330.0664664497217781298.68909942787
Winsorized Mean ( 12 / 22 )86.31925373134330.06533818139583911321.11503392472
Winsorized Mean ( 13 / 22 )86.31925373134330.0647324498943751333.47731890562
Winsorized Mean ( 14 / 22 )86.31507462686570.0641400594365851345.72801124709
Winsorized Mean ( 15 / 22 )86.30611940298510.06221923103238621387.12931630514
Winsorized Mean ( 16 / 22 )86.31089552238810.06069018510613751422.15574678911
Winsorized Mean ( 17 / 22 )86.31089552238810.05992522528288931440.30990480119
Winsorized Mean ( 18 / 22 )86.30820895522390.05876226947263511468.76915629367
Winsorized Mean ( 19 / 22 )86.34223880597020.05318733730115531623.36080704861
Winsorized Mean ( 20 / 22 )86.34223880597020.0505451157319531708.22121100392
Winsorized Mean ( 21 / 22 )86.3704477611940.04611130068070951873.08634729809
Winsorized Mean ( 22 / 22 )86.38029850746270.03792859710074272277.44512347838
Trimmed Mean ( 1 / 22 )86.29892307692310.078286985323271102.34060898589
Trimmed Mean ( 2 / 22 )86.30285714285710.07727085396893841116.88758063357
Trimmed Mean ( 3 / 22 )86.30688524590160.07605165809210031134.84554329351
Trimmed Mean ( 4 / 22 )86.31152542372880.07461054682290861156.82740710362
Trimmed Mean ( 5 / 22 )86.31701754385960.07293221563349471183.5238624537
Trimmed Mean ( 6 / 22 )86.32436363636360.07114161134245971213.41591801762
Trimmed Mean ( 7 / 22 )86.330.06986925380305451235.59355941234
Trimmed Mean ( 8 / 22 )86.33490196078430.06867677779108631257.11928744551
Trimmed Mean ( 9 / 22 )86.33877551020410.06811706650619921267.50577995526
Trimmed Mean ( 10 / 22 )86.34212765957450.06754375439410741278.31401191858
Trimmed Mean ( 11 / 22 )86.34577777777780.06671398993781681294.26793178252
Trimmed Mean ( 12 / 22 )86.34953488372090.06585661249688611311.17486323494
Trimmed Mean ( 13 / 22 )86.35365853658540.06489462010995021330.6751528906
Trimmed Mean ( 14 / 22 )86.35820512820510.0636580267662891356.59569601892
Trimmed Mean ( 15 / 22 )86.36378378378380.06202943134557781392.30332940882
Trimmed Mean ( 16 / 22 )86.37114285714290.06017309964401281435.37799063234
Trimmed Mean ( 17 / 22 )86.37878787878790.05792294642610431491.27061395239
Trimmed Mean ( 18 / 22 )86.38741935483870.05483889943041171575.29454916324
Trimmed Mean ( 19 / 22 )86.39758620689650.05058197066892671708.07078222383
Trimmed Mean ( 20 / 22 )86.40481481481480.04647509632537741859.16375965926
Trimmed Mean ( 21 / 22 )86.41320.04107602707176052103.73802337394
Trimmed Mean ( 22 / 22 )86.41913043478260.03461198268300062496.79803743883
Median86.41
Midrange86.09
Midmean - Weighted Average at Xnp86.3570588235294
Midmean - Weighted Average at X(n+1)p86.3711428571429
Midmean - Empirical Distribution Function86.3711428571429
Midmean - Empirical Distribution Function - Averaging86.3711428571429
Midmean - Empirical Distribution Function - Interpolation86.3787878787879
Midmean - Closest Observation86.3570588235294
Midmean - True Basic - Statistics Graphics Toolkit86.3711428571429
Midmean - MS Excel (old versions)86.3711428571429
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 86.2926865671642 & 0.0798938073150143 & 1080.09230586445 \tabularnewline
Geometric Mean & 86.2902404980554 &  &  \tabularnewline
Harmonic Mean & 86.2877893898097 &  &  \tabularnewline
Quadratic Mean & 86.295127523681 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 86.295223880597 & 0.0791009403303573 & 1090.95067037375 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 86.2955223880597 & 0.079035136825985 & 1091.86275691608 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 86.2946268656716 & 0.0788796288986458 & 1094.00396617679 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 86.2928358208955 & 0.0785758601987714 & 1098.21051405104 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 86.2868656716418 & 0.0776143060558615 & 1111.73918902964 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 86.2976119402985 & 0.0743413988295175 & 1160.82846568706 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 86.3038805970149 & 0.0727258736710379 & 1186.70118680725 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 86.3122388059702 & 0.0687458961056362 & 1255.52569237502 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 86.3176119402985 & 0.0677979844216886 & 1273.15896890713 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 86.3176119402985 & 0.0677979844216886 & 1273.15896890713 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 86.3192537313433 & 0.066466449721778 & 1298.68909942787 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 86.3192537313433 & 0.0653381813958391 & 1321.11503392472 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 86.3192537313433 & 0.064732449894375 & 1333.47731890562 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 86.3150746268657 & 0.064140059436585 & 1345.72801124709 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 86.3061194029851 & 0.0622192310323862 & 1387.12931630514 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 86.3108955223881 & 0.0606901851061375 & 1422.15574678911 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 86.3108955223881 & 0.0599252252828893 & 1440.30990480119 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 86.3082089552239 & 0.0587622694726351 & 1468.76915629367 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 86.3422388059702 & 0.0531873373011553 & 1623.36080704861 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 86.3422388059702 & 0.050545115731953 & 1708.22121100392 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 86.370447761194 & 0.0461113006807095 & 1873.08634729809 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 86.3802985074627 & 0.0379285971007427 & 2277.44512347838 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 86.2989230769231 & 0.07828698532327 & 1102.34060898589 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 86.3028571428571 & 0.0772708539689384 & 1116.88758063357 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 86.3068852459016 & 0.0760516580921003 & 1134.84554329351 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 86.3115254237288 & 0.0746105468229086 & 1156.82740710362 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 86.3170175438596 & 0.0729322156334947 & 1183.5238624537 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 86.3243636363636 & 0.0711416113424597 & 1213.41591801762 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 86.33 & 0.0698692538030545 & 1235.59355941234 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 86.3349019607843 & 0.0686767777910863 & 1257.11928744551 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 86.3387755102041 & 0.0681170665061992 & 1267.50577995526 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 86.3421276595745 & 0.0675437543941074 & 1278.31401191858 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 86.3457777777778 & 0.0667139899378168 & 1294.26793178252 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 86.3495348837209 & 0.0658566124968861 & 1311.17486323494 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 86.3536585365854 & 0.0648946201099502 & 1330.6751528906 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 86.3582051282051 & 0.063658026766289 & 1356.59569601892 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 86.3637837837838 & 0.0620294313455778 & 1392.30332940882 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 86.3711428571429 & 0.0601730996440128 & 1435.37799063234 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 86.3787878787879 & 0.0579229464261043 & 1491.27061395239 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 86.3874193548387 & 0.0548388994304117 & 1575.29454916324 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 86.3975862068965 & 0.0505819706689267 & 1708.07078222383 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 86.4048148148148 & 0.0464750963253774 & 1859.16375965926 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 86.4132 & 0.0410760270717605 & 2103.73802337394 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 86.4191304347826 & 0.0346119826830006 & 2496.79803743883 \tabularnewline
Median & 86.41 &  &  \tabularnewline
Midrange & 86.09 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 86.3570588235294 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 86.3711428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 86.3711428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 86.3711428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 86.3787878787879 &  &  \tabularnewline
Midmean - Closest Observation & 86.3570588235294 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 86.3711428571429 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 86.3711428571429 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207392&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]86.2926865671642[/C][C]0.0798938073150143[/C][C]1080.09230586445[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.2902404980554[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.2877893898097[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]86.295127523681[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]86.295223880597[/C][C]0.0791009403303573[/C][C]1090.95067037375[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]86.2955223880597[/C][C]0.079035136825985[/C][C]1091.86275691608[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]86.2946268656716[/C][C]0.0788796288986458[/C][C]1094.00396617679[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]86.2928358208955[/C][C]0.0785758601987714[/C][C]1098.21051405104[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]86.2868656716418[/C][C]0.0776143060558615[/C][C]1111.73918902964[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]86.2976119402985[/C][C]0.0743413988295175[/C][C]1160.82846568706[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]86.3038805970149[/C][C]0.0727258736710379[/C][C]1186.70118680725[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]86.3122388059702[/C][C]0.0687458961056362[/C][C]1255.52569237502[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]86.3176119402985[/C][C]0.0677979844216886[/C][C]1273.15896890713[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]86.3176119402985[/C][C]0.0677979844216886[/C][C]1273.15896890713[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]86.3192537313433[/C][C]0.066466449721778[/C][C]1298.68909942787[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]86.3192537313433[/C][C]0.0653381813958391[/C][C]1321.11503392472[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]86.3192537313433[/C][C]0.064732449894375[/C][C]1333.47731890562[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]86.3150746268657[/C][C]0.064140059436585[/C][C]1345.72801124709[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]86.3061194029851[/C][C]0.0622192310323862[/C][C]1387.12931630514[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]86.3108955223881[/C][C]0.0606901851061375[/C][C]1422.15574678911[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]86.3108955223881[/C][C]0.0599252252828893[/C][C]1440.30990480119[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]86.3082089552239[/C][C]0.0587622694726351[/C][C]1468.76915629367[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]86.3422388059702[/C][C]0.0531873373011553[/C][C]1623.36080704861[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]86.3422388059702[/C][C]0.050545115731953[/C][C]1708.22121100392[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]86.370447761194[/C][C]0.0461113006807095[/C][C]1873.08634729809[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]86.3802985074627[/C][C]0.0379285971007427[/C][C]2277.44512347838[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]86.2989230769231[/C][C]0.07828698532327[/C][C]1102.34060898589[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]86.3028571428571[/C][C]0.0772708539689384[/C][C]1116.88758063357[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]86.3068852459016[/C][C]0.0760516580921003[/C][C]1134.84554329351[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]86.3115254237288[/C][C]0.0746105468229086[/C][C]1156.82740710362[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]86.3170175438596[/C][C]0.0729322156334947[/C][C]1183.5238624537[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]86.3243636363636[/C][C]0.0711416113424597[/C][C]1213.41591801762[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]86.33[/C][C]0.0698692538030545[/C][C]1235.59355941234[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]86.3349019607843[/C][C]0.0686767777910863[/C][C]1257.11928744551[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]86.3387755102041[/C][C]0.0681170665061992[/C][C]1267.50577995526[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]86.3421276595745[/C][C]0.0675437543941074[/C][C]1278.31401191858[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]86.3457777777778[/C][C]0.0667139899378168[/C][C]1294.26793178252[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]86.3495348837209[/C][C]0.0658566124968861[/C][C]1311.17486323494[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]86.3536585365854[/C][C]0.0648946201099502[/C][C]1330.6751528906[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]86.3582051282051[/C][C]0.063658026766289[/C][C]1356.59569601892[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]86.3637837837838[/C][C]0.0620294313455778[/C][C]1392.30332940882[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]86.3711428571429[/C][C]0.0601730996440128[/C][C]1435.37799063234[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]86.3787878787879[/C][C]0.0579229464261043[/C][C]1491.27061395239[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]86.3874193548387[/C][C]0.0548388994304117[/C][C]1575.29454916324[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]86.3975862068965[/C][C]0.0505819706689267[/C][C]1708.07078222383[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]86.4048148148148[/C][C]0.0464750963253774[/C][C]1859.16375965926[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]86.4132[/C][C]0.0410760270717605[/C][C]2103.73802337394[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]86.4191304347826[/C][C]0.0346119826830006[/C][C]2496.79803743883[/C][/ROW]
[ROW][C]Median[/C][C]86.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]86.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]86.3570588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]86.3711428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]86.3711428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]86.3711428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]86.3787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]86.3570588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]86.3711428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]86.3711428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]67[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207392&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 Mean86.29268656716420.07989380731501431080.09230586445
Geometric Mean86.2902404980554
Harmonic Mean86.2877893898097
Quadratic Mean86.295127523681
Winsorized Mean ( 1 / 22 )86.2952238805970.07910094033035731090.95067037375
Winsorized Mean ( 2 / 22 )86.29552238805970.0790351368259851091.86275691608
Winsorized Mean ( 3 / 22 )86.29462686567160.07887962889864581094.00396617679
Winsorized Mean ( 4 / 22 )86.29283582089550.07857586019877141098.21051405104
Winsorized Mean ( 5 / 22 )86.28686567164180.07761430605586151111.73918902964
Winsorized Mean ( 6 / 22 )86.29761194029850.07434139882951751160.82846568706
Winsorized Mean ( 7 / 22 )86.30388059701490.07272587367103791186.70118680725
Winsorized Mean ( 8 / 22 )86.31223880597020.06874589610563621255.52569237502
Winsorized Mean ( 9 / 22 )86.31761194029850.06779798442168861273.15896890713
Winsorized Mean ( 10 / 22 )86.31761194029850.06779798442168861273.15896890713
Winsorized Mean ( 11 / 22 )86.31925373134330.0664664497217781298.68909942787
Winsorized Mean ( 12 / 22 )86.31925373134330.06533818139583911321.11503392472
Winsorized Mean ( 13 / 22 )86.31925373134330.0647324498943751333.47731890562
Winsorized Mean ( 14 / 22 )86.31507462686570.0641400594365851345.72801124709
Winsorized Mean ( 15 / 22 )86.30611940298510.06221923103238621387.12931630514
Winsorized Mean ( 16 / 22 )86.31089552238810.06069018510613751422.15574678911
Winsorized Mean ( 17 / 22 )86.31089552238810.05992522528288931440.30990480119
Winsorized Mean ( 18 / 22 )86.30820895522390.05876226947263511468.76915629367
Winsorized Mean ( 19 / 22 )86.34223880597020.05318733730115531623.36080704861
Winsorized Mean ( 20 / 22 )86.34223880597020.0505451157319531708.22121100392
Winsorized Mean ( 21 / 22 )86.3704477611940.04611130068070951873.08634729809
Winsorized Mean ( 22 / 22 )86.38029850746270.03792859710074272277.44512347838
Trimmed Mean ( 1 / 22 )86.29892307692310.078286985323271102.34060898589
Trimmed Mean ( 2 / 22 )86.30285714285710.07727085396893841116.88758063357
Trimmed Mean ( 3 / 22 )86.30688524590160.07605165809210031134.84554329351
Trimmed Mean ( 4 / 22 )86.31152542372880.07461054682290861156.82740710362
Trimmed Mean ( 5 / 22 )86.31701754385960.07293221563349471183.5238624537
Trimmed Mean ( 6 / 22 )86.32436363636360.07114161134245971213.41591801762
Trimmed Mean ( 7 / 22 )86.330.06986925380305451235.59355941234
Trimmed Mean ( 8 / 22 )86.33490196078430.06867677779108631257.11928744551
Trimmed Mean ( 9 / 22 )86.33877551020410.06811706650619921267.50577995526
Trimmed Mean ( 10 / 22 )86.34212765957450.06754375439410741278.31401191858
Trimmed Mean ( 11 / 22 )86.34577777777780.06671398993781681294.26793178252
Trimmed Mean ( 12 / 22 )86.34953488372090.06585661249688611311.17486323494
Trimmed Mean ( 13 / 22 )86.35365853658540.06489462010995021330.6751528906
Trimmed Mean ( 14 / 22 )86.35820512820510.0636580267662891356.59569601892
Trimmed Mean ( 15 / 22 )86.36378378378380.06202943134557781392.30332940882
Trimmed Mean ( 16 / 22 )86.37114285714290.06017309964401281435.37799063234
Trimmed Mean ( 17 / 22 )86.37878787878790.05792294642610431491.27061395239
Trimmed Mean ( 18 / 22 )86.38741935483870.05483889943041171575.29454916324
Trimmed Mean ( 19 / 22 )86.39758620689650.05058197066892671708.07078222383
Trimmed Mean ( 20 / 22 )86.40481481481480.04647509632537741859.16375965926
Trimmed Mean ( 21 / 22 )86.41320.04107602707176052103.73802337394
Trimmed Mean ( 22 / 22 )86.41913043478260.03461198268300062496.79803743883
Median86.41
Midrange86.09
Midmean - Weighted Average at Xnp86.3570588235294
Midmean - Weighted Average at X(n+1)p86.3711428571429
Midmean - Empirical Distribution Function86.3711428571429
Midmean - Empirical Distribution Function - Averaging86.3711428571429
Midmean - Empirical Distribution Function - Interpolation86.3787878787879
Midmean - Closest Observation86.3570588235294
Midmean - True Basic - Statistics Graphics Toolkit86.3711428571429
Midmean - MS Excel (old versions)86.3711428571429
Number of observations67



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')