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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Jan 2008 16:22:56 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jan/16/t1200439197ihv6kxknkhtm734.htm/, Retrieved Thu, 16 May 2024 00:52:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7971, Retrieved Thu, 16 May 2024 00:52:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact270
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-01-15 23:22:56] [44cf2be50bc8700e14714598feda9df9] [Current]
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Dataseries X:
0.0903990067094626
1.47161810527303
-0.997067679494978
-1.93263218930345
4.0295440758445
-1.20192099065840
-0.911697751677917
4.70380860209899
2.97679498629855
-1.96034289188267
2.08520562238665
1.68065228020409
3.71625076749611
2.03722178261712
-2.75176003144595
-0.431081537831379
1.85415000315757
-0.0266938822924724
-4.24372746659652
-5.61403284325217
-1.71946239578839
0.771571241051611
6.76073119849922
-4.39818066182222
-2.10769633494198
0.967901247982025
-1.15733368715735
5.97314658573289
6.24212949842583
3.96255296875433
-0.563081363081936
6.45855118341927
-3.40545942545380
5.35890694571811
-0.365895237258271
-0.557610297827308
-1.19389479178954
0.232448357023645
3.75671034635943
1.63762120924211
-1.99745023931488
1.16502272733602
0.524603683619043
2.16418906501836
-2.07768541243117
-0.104697151044226
1.02295461736532
1.24551221338642
0.884436849076284
-7.20467667389068




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7971&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7971&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5370110846771670.4372153023569771.22825317819894
Geometric MeanNaN
Harmonic Mean-1.42272348291449
Quadratic Mean3.10726321949174
Winsorized Mean ( 1 / 16 )0.5627803609883380.4250011019745121.32418565122235
Winsorized Mean ( 2 / 16 )0.6027575808457980.4092599831590611.47279872366982
Winsorized Mean ( 3 / 16 )0.5958857977977640.4024973449621551.48047137516843
Winsorized Mean ( 4 / 16 )0.6138080698879990.3738030647117091.64206270047944
Winsorized Mean ( 5 / 16 )0.6136681749268720.343605601341921.78596673782455
Winsorized Mean ( 6 / 16 )0.610044075356810.3099507462215871.96819682737813
Winsorized Mean ( 7 / 16 )0.6048668495156990.3070980942078021.96962098080103
Winsorized Mean ( 8 / 16 )0.5847696576311220.2975585508521851.96522551933522
Winsorized Mean ( 9 / 16 )0.5841662559735220.2947970562520541.98158781977135
Winsorized Mean ( 10 / 16 )0.4418172402498540.2631438640041171.67899503156548
Winsorized Mean ( 11 / 16 )0.3099412921415250.2213955994629121.39994332720893
Winsorized Mean ( 12 / 16 )0.4151952031411120.1959823307975312.11853385686106
Winsorized Mean ( 13 / 16 )0.4048062165069380.1934716885711012.09232792403201
Winsorized Mean ( 14 / 16 )0.3637832275552770.1830646909712221.98718401470693
Winsorized Mean ( 15 / 16 )0.3598137129679450.1664409232444582.16181036462694
Winsorized Mean ( 16 / 16 )0.3733621471615710.1596971797251212.33793826418363
Trimmed Mean ( 1 / 16 )0.5686354106093710.4047691994037441.40483863754212
Trimmed Mean ( 2 / 16 )0.5749995949800580.3785941492093751.51877570263788
Trimmed Mean ( 3 / 16 )0.5592280121017970.3560416178317801.57068158353897
Trimmed Mean ( 4 / 16 )0.5446812717462550.3299357587586041.6508706840254
Trimmed Mean ( 5 / 16 )0.523079147326960.3086921846752381.69450077875237
Trimmed Mean ( 6 / 16 )0.4992399295375100.2926665105509971.70583210425273
Trimmed Mean ( 7 / 16 )0.4735908217089680.2833280608205031.67152812304391
Trimmed Mean ( 8 / 16 )0.4460118242705790.2710619962780991.64542366836621
Trimmed Mean ( 9 / 16 )0.4189106849423480.256927748647041.63046104264057
Trimmed Mean ( 10 / 16 )0.3883078014180560.2371341775067971.63750247012338
Trimmed Mean ( 11 / 16 )0.3787525444838070.2207274917200801.71592827668304
Trimmed Mean ( 12 / 16 )0.3907824837044850.2120912022422491.84252095123746
Trimmed Mean ( 13 / 16 )0.3865441643578490.2077769475973931.86038041672867
Trimmed Mean ( 14 / 16 )0.3833514978982180.2006902987183551.91016456872290
Trimmed Mean ( 15 / 16 )0.3868458318880290.1924262268884582.01035918098768
Trimmed Mean ( 16 / 16 )0.3918517798361920.1850718042772402.11729594017029
Median0.378526020321344
Midrange-0.22197273769573
Midmean - Weighted Average at Xnp0.323005558157199
Midmean - Weighted Average at X(n+1)p0.390782483704485
Midmean - Empirical Distribution Function0.390782483704485
Midmean - Empirical Distribution Function - Averaging0.390782483704485
Midmean - Empirical Distribution Function - Interpolation0.386544164357849
Midmean - Closest Observation0.390782483704485
Midmean - True Basic - Statistics Graphics Toolkit0.390782483704485
Midmean - MS Excel (old versions)0.390782483704485
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.537011084677167 & 0.437215302356977 & 1.22825317819894 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -1.42272348291449 &  &  \tabularnewline
Quadratic Mean & 3.10726321949174 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.562780360988338 & 0.425001101974512 & 1.32418565122235 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.602757580845798 & 0.409259983159061 & 1.47279872366982 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.595885797797764 & 0.402497344962155 & 1.48047137516843 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.613808069887999 & 0.373803064711709 & 1.64206270047944 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.613668174926872 & 0.34360560134192 & 1.78596673782455 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.61004407535681 & 0.309950746221587 & 1.96819682737813 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.604866849515699 & 0.307098094207802 & 1.96962098080103 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.584769657631122 & 0.297558550852185 & 1.96522551933522 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.584166255973522 & 0.294797056252054 & 1.98158781977135 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.441817240249854 & 0.263143864004117 & 1.67899503156548 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.309941292141525 & 0.221395599462912 & 1.39994332720893 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.415195203141112 & 0.195982330797531 & 2.11853385686106 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.404806216506938 & 0.193471688571101 & 2.09232792403201 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.363783227555277 & 0.183064690971222 & 1.98718401470693 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.359813712967945 & 0.166440923244458 & 2.16181036462694 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.373362147161571 & 0.159697179725121 & 2.33793826418363 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.568635410609371 & 0.404769199403744 & 1.40483863754212 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.574999594980058 & 0.378594149209375 & 1.51877570263788 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.559228012101797 & 0.356041617831780 & 1.57068158353897 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.544681271746255 & 0.329935758758604 & 1.6508706840254 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.52307914732696 & 0.308692184675238 & 1.69450077875237 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.499239929537510 & 0.292666510550997 & 1.70583210425273 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.473590821708968 & 0.283328060820503 & 1.67152812304391 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.446011824270579 & 0.271061996278099 & 1.64542366836621 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.418910684942348 & 0.25692774864704 & 1.63046104264057 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.388307801418056 & 0.237134177506797 & 1.63750247012338 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.378752544483807 & 0.220727491720080 & 1.71592827668304 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.390782483704485 & 0.212091202242249 & 1.84252095123746 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.386544164357849 & 0.207776947597393 & 1.86038041672867 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.383351497898218 & 0.200690298718355 & 1.91016456872290 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.386845831888029 & 0.192426226888458 & 2.01035918098768 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.391851779836192 & 0.185071804277240 & 2.11729594017029 \tabularnewline
Median & 0.378526020321344 &  &  \tabularnewline
Midrange & -0.22197273769573 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.323005558157199 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.390782483704485 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.390782483704485 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.390782483704485 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.386544164357849 &  &  \tabularnewline
Midmean - Closest Observation & 0.390782483704485 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.390782483704485 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.390782483704485 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7971&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]0.537011084677167[/C][C]0.437215302356977[/C][C]1.22825317819894[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-1.42272348291449[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.10726321949174[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.562780360988338[/C][C]0.425001101974512[/C][C]1.32418565122235[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.602757580845798[/C][C]0.409259983159061[/C][C]1.47279872366982[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.595885797797764[/C][C]0.402497344962155[/C][C]1.48047137516843[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.613808069887999[/C][C]0.373803064711709[/C][C]1.64206270047944[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.613668174926872[/C][C]0.34360560134192[/C][C]1.78596673782455[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.61004407535681[/C][C]0.309950746221587[/C][C]1.96819682737813[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.604866849515699[/C][C]0.307098094207802[/C][C]1.96962098080103[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.584769657631122[/C][C]0.297558550852185[/C][C]1.96522551933522[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.584166255973522[/C][C]0.294797056252054[/C][C]1.98158781977135[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.441817240249854[/C][C]0.263143864004117[/C][C]1.67899503156548[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.309941292141525[/C][C]0.221395599462912[/C][C]1.39994332720893[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.415195203141112[/C][C]0.195982330797531[/C][C]2.11853385686106[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.404806216506938[/C][C]0.193471688571101[/C][C]2.09232792403201[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.363783227555277[/C][C]0.183064690971222[/C][C]1.98718401470693[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.359813712967945[/C][C]0.166440923244458[/C][C]2.16181036462694[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.373362147161571[/C][C]0.159697179725121[/C][C]2.33793826418363[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.568635410609371[/C][C]0.404769199403744[/C][C]1.40483863754212[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.574999594980058[/C][C]0.378594149209375[/C][C]1.51877570263788[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.559228012101797[/C][C]0.356041617831780[/C][C]1.57068158353897[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.544681271746255[/C][C]0.329935758758604[/C][C]1.6508706840254[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.52307914732696[/C][C]0.308692184675238[/C][C]1.69450077875237[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.499239929537510[/C][C]0.292666510550997[/C][C]1.70583210425273[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.473590821708968[/C][C]0.283328060820503[/C][C]1.67152812304391[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.446011824270579[/C][C]0.271061996278099[/C][C]1.64542366836621[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.418910684942348[/C][C]0.25692774864704[/C][C]1.63046104264057[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.388307801418056[/C][C]0.237134177506797[/C][C]1.63750247012338[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.378752544483807[/C][C]0.220727491720080[/C][C]1.71592827668304[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.390782483704485[/C][C]0.212091202242249[/C][C]1.84252095123746[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.386544164357849[/C][C]0.207776947597393[/C][C]1.86038041672867[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.383351497898218[/C][C]0.200690298718355[/C][C]1.91016456872290[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.386845831888029[/C][C]0.192426226888458[/C][C]2.01035918098768[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.391851779836192[/C][C]0.185071804277240[/C][C]2.11729594017029[/C][/ROW]
[ROW][C]Median[/C][C]0.378526020321344[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.22197273769573[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.323005558157199[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.390782483704485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.390782483704485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.390782483704485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.386544164357849[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.390782483704485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.390782483704485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.390782483704485[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7971&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 Mean0.5370110846771670.4372153023569771.22825317819894
Geometric MeanNaN
Harmonic Mean-1.42272348291449
Quadratic Mean3.10726321949174
Winsorized Mean ( 1 / 16 )0.5627803609883380.4250011019745121.32418565122235
Winsorized Mean ( 2 / 16 )0.6027575808457980.4092599831590611.47279872366982
Winsorized Mean ( 3 / 16 )0.5958857977977640.4024973449621551.48047137516843
Winsorized Mean ( 4 / 16 )0.6138080698879990.3738030647117091.64206270047944
Winsorized Mean ( 5 / 16 )0.6136681749268720.343605601341921.78596673782455
Winsorized Mean ( 6 / 16 )0.610044075356810.3099507462215871.96819682737813
Winsorized Mean ( 7 / 16 )0.6048668495156990.3070980942078021.96962098080103
Winsorized Mean ( 8 / 16 )0.5847696576311220.2975585508521851.96522551933522
Winsorized Mean ( 9 / 16 )0.5841662559735220.2947970562520541.98158781977135
Winsorized Mean ( 10 / 16 )0.4418172402498540.2631438640041171.67899503156548
Winsorized Mean ( 11 / 16 )0.3099412921415250.2213955994629121.39994332720893
Winsorized Mean ( 12 / 16 )0.4151952031411120.1959823307975312.11853385686106
Winsorized Mean ( 13 / 16 )0.4048062165069380.1934716885711012.09232792403201
Winsorized Mean ( 14 / 16 )0.3637832275552770.1830646909712221.98718401470693
Winsorized Mean ( 15 / 16 )0.3598137129679450.1664409232444582.16181036462694
Winsorized Mean ( 16 / 16 )0.3733621471615710.1596971797251212.33793826418363
Trimmed Mean ( 1 / 16 )0.5686354106093710.4047691994037441.40483863754212
Trimmed Mean ( 2 / 16 )0.5749995949800580.3785941492093751.51877570263788
Trimmed Mean ( 3 / 16 )0.5592280121017970.3560416178317801.57068158353897
Trimmed Mean ( 4 / 16 )0.5446812717462550.3299357587586041.6508706840254
Trimmed Mean ( 5 / 16 )0.523079147326960.3086921846752381.69450077875237
Trimmed Mean ( 6 / 16 )0.4992399295375100.2926665105509971.70583210425273
Trimmed Mean ( 7 / 16 )0.4735908217089680.2833280608205031.67152812304391
Trimmed Mean ( 8 / 16 )0.4460118242705790.2710619962780991.64542366836621
Trimmed Mean ( 9 / 16 )0.4189106849423480.256927748647041.63046104264057
Trimmed Mean ( 10 / 16 )0.3883078014180560.2371341775067971.63750247012338
Trimmed Mean ( 11 / 16 )0.3787525444838070.2207274917200801.71592827668304
Trimmed Mean ( 12 / 16 )0.3907824837044850.2120912022422491.84252095123746
Trimmed Mean ( 13 / 16 )0.3865441643578490.2077769475973931.86038041672867
Trimmed Mean ( 14 / 16 )0.3833514978982180.2006902987183551.91016456872290
Trimmed Mean ( 15 / 16 )0.3868458318880290.1924262268884582.01035918098768
Trimmed Mean ( 16 / 16 )0.3918517798361920.1850718042772402.11729594017029
Median0.378526020321344
Midrange-0.22197273769573
Midmean - Weighted Average at Xnp0.323005558157199
Midmean - Weighted Average at X(n+1)p0.390782483704485
Midmean - Empirical Distribution Function0.390782483704485
Midmean - Empirical Distribution Function - Averaging0.390782483704485
Midmean - Empirical Distribution Function - Interpolation0.386544164357849
Midmean - Closest Observation0.390782483704485
Midmean - True Basic - Statistics Graphics Toolkit0.390782483704485
Midmean - MS Excel (old versions)0.390782483704485
Number of observations50



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')