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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Dec 2007 14:54:01 -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/2007/Dec/16/t1197841048zid2d1565ixblls.htm/, Retrieved Thu, 02 May 2024 09:35:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4274, Retrieved Thu, 02 May 2024 09:35:37 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper] [2007-12-16 21:54:01] [3463f71ebce131edf0c83e066f45702c] [Current]
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Dataseries X:
0.00462688879263115 
0.0703142211119144 
0.0260868629642251 
0.0254011575549011 
0.0693359456203217 
-0.0975630863684548 
-0.0543312516101782 
-0.0215349672009734 
0.0540158291707738 
0.0245500449446185 
0.0765469234760861 
0.0233421971972810 
0.0176074485180608 
-0.0190235392186886 
-0.0291330935155393 
0.0179249311620706 
0.0539146589519815 
0.0483328780076326 
-0.0332622856503486 
-0.0276668079464368 
0.0084397755453432 
0.0608148983838934 
0.00713350726032488 
-0.085878546085382 
-0.0217172930163510 
0.064354270734894 
0.00244805628783018 
0.0302778459397813 
-0.0148076448126125 
-0.0305464740305135 
0.00310945439016042 
0.0977140428152255 
-0.0072460534732927 
0.0569400433985821 
0.0190901097993433 
-0.000535953823312061 
-0.0206933994341181 
-0.049920735350657 
0.0369689239861515 
0.0274026122000065 
-0.00503157125906739 
0.0431723500241272 
-0.0226812549324880 
-0.0119562327657929 
-0.0364276186086352 
0.0281020656022255 
-0.0185020740169399 
0.0127940833434153 
-0.0278448333224306 
-0.0677637400382904 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4274&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4274&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.0061338714140660.005983257985189721.02517247781210
Geometric MeanNaN
Harmonic Mean-0.0503450211179155
Quadratic Mean0.0423295854961254
Winsorized Mean ( 1 / 16 )0.005944219832944660.005784954769510071.02753090901834
Winsorized Mean ( 2 / 16 )0.006419503980261460.005506955564676481.16570833101294
Winsorized Mean ( 3 / 16 )0.007166756756452630.005286196300500061.35574926640062
Winsorized Mean ( 4 / 16 )0.00712106406638010.005110689162095561.39336669488626
Winsorized Mean ( 5 / 16 )0.008116438505482230.004746337255076891.71004251684823
Winsorized Mean ( 6 / 16 )0.008031295862239260.004571446431910351.75683910592891
Winsorized Mean ( 7 / 16 )0.008002119497123020.004414240902643531.81279628221714
Winsorized Mean ( 8 / 16 )0.008212073144512120.004370922705221211.87879624013999
Winsorized Mean ( 9 / 16 )0.007439239409288880.004121364265601271.80504292507704
Winsorized Mean ( 10 / 16 )0.006442738887786560.0039115484995461.64710699318553
Winsorized Mean ( 11 / 16 )0.006174806822500650.003465559612824431.78176326837678
Winsorized Mean ( 12 / 16 )0.004800298951244680.003147139882220851.52528935188519
Winsorized Mean ( 13 / 16 )0.004282000775478350.003047083839658491.40527829255865
Winsorized Mean ( 14 / 16 )0.004321792797576510.002975367728958091.45252392015756
Winsorized Mean ( 15 / 16 )0.004428026091470940.002827879350328761.56584689193199
Winsorized Mean ( 16 / 16 )0.004375469225046840.002765498849697921.58216273549518
Trimmed Mean ( 1 / 16 )0.006386304463677690.005512937152498131.15842141621074
Trimmed Mean ( 2 / 16 )0.006866831236213580.005160210514226041.33072695722057
Trimmed Mean ( 3 / 16 )0.007120994449822750.004905090410249871.45175600330270
Trimmed Mean ( 4 / 16 )0.00710283480433470.00468981281812451.51452415688846
Trimmed Mean ( 5 / 16 )0.007097138159945510.004482504813152051.58329738746111
Trimmed Mean ( 6 / 16 )0.006828901226909530.004346489297073841.57113034455346
Trimmed Mean ( 7 / 16 )0.006550569135398020.004220216837746531.5521878110168
Trimmed Mean ( 8 / 16 )0.006245621580413780.004094318779655561.52543607777878
Trimmed Mean ( 9 / 16 )0.005861549009300820.00392467839920171.49351065567387
Trimmed Mean ( 10 / 16 )0.005569384120414140.003765753260181961.47895619697214
Trimmed Mean ( 11 / 16 )0.005413427911954780.003603729768558651.50217365330363
Trimmed Mean ( 12 / 16 )0.00528031971081040.003515362153096171.50206990940030
Trimmed Mean ( 13 / 16 )0.0053636566482350.003478358845435631.54200785099366
Trimmed Mean ( 14 / 16 )0.005552757325290360.003430597992882951.61859749723226
Trimmed Mean ( 15 / 16 )0.005772572419524970.003352154028544941.72204867985456
Trimmed Mean ( 16 / 16 )0.006021562480275720.003254661030811931.85013505961742
Median0.00588019802647801
Midrange7.54782233853488e-05
Midmean - Weighted Average at Xnp0.00428041866165156
Midmean - Weighted Average at X(n+1)p0.00528031971081039
Midmean - Empirical Distribution Function0.00528031971081039
Midmean - Empirical Distribution Function - Averaging0.00528031971081039
Midmean - Empirical Distribution Function - Interpolation0.005363656648235
Midmean - Closest Observation0.00528031971081039
Midmean - True Basic - Statistics Graphics Toolkit0.00528031971081039
Midmean - MS Excel (old versions)0.00528031971081039
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.006133871414066 & 0.00598325798518972 & 1.02517247781210 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.0503450211179155 &  &  \tabularnewline
Quadratic Mean & 0.0423295854961254 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 0.00594421983294466 & 0.00578495476951007 & 1.02753090901834 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 0.00641950398026146 & 0.00550695556467648 & 1.16570833101294 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 0.00716675675645263 & 0.00528619630050006 & 1.35574926640062 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 0.0071210640663801 & 0.00511068916209556 & 1.39336669488626 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 0.00811643850548223 & 0.00474633725507689 & 1.71004251684823 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 0.00803129586223926 & 0.00457144643191035 & 1.75683910592891 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 0.00800211949712302 & 0.00441424090264353 & 1.81279628221714 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 0.00821207314451212 & 0.00437092270522121 & 1.87879624013999 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 0.00743923940928888 & 0.00412136426560127 & 1.80504292507704 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 0.00644273888778656 & 0.003911548499546 & 1.64710699318553 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 0.00617480682250065 & 0.00346555961282443 & 1.78176326837678 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.00480029895124468 & 0.00314713988222085 & 1.52528935188519 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.00428200077547835 & 0.00304708383965849 & 1.40527829255865 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.00432179279757651 & 0.00297536772895809 & 1.45252392015756 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.00442802609147094 & 0.00282787935032876 & 1.56584689193199 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.00437546922504684 & 0.00276549884969792 & 1.58216273549518 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 0.00638630446367769 & 0.00551293715249813 & 1.15842141621074 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 0.00686683123621358 & 0.00516021051422604 & 1.33072695722057 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 0.00712099444982275 & 0.00490509041024987 & 1.45175600330270 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 0.0071028348043347 & 0.0046898128181245 & 1.51452415688846 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 0.00709713815994551 & 0.00448250481315205 & 1.58329738746111 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 0.00682890122690953 & 0.00434648929707384 & 1.57113034455346 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 0.00655056913539802 & 0.00422021683774653 & 1.5521878110168 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0.00624562158041378 & 0.00409431877965556 & 1.52543607777878 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.00586154900930082 & 0.0039246783992017 & 1.49351065567387 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.00556938412041414 & 0.00376575326018196 & 1.47895619697214 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.00541342791195478 & 0.00360372976855865 & 1.50217365330363 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.0052803197108104 & 0.00351536215309617 & 1.50206990940030 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.005363656648235 & 0.00347835884543563 & 1.54200785099366 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.00555275732529036 & 0.00343059799288295 & 1.61859749723226 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.00577257241952497 & 0.00335215402854494 & 1.72204867985456 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.00602156248027572 & 0.00325466103081193 & 1.85013505961742 \tabularnewline
Median & 0.00588019802647801 &  &  \tabularnewline
Midrange & 7.54782233853488e-05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.00428041866165156 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.00528031971081039 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.00528031971081039 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.00528031971081039 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.005363656648235 &  &  \tabularnewline
Midmean - Closest Observation & 0.00528031971081039 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.00528031971081039 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.00528031971081039 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4274&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]0.006133871414066[/C][C]0.00598325798518972[/C][C]1.02517247781210[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.0503450211179155[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.0423295854961254[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]0.00594421983294466[/C][C]0.00578495476951007[/C][C]1.02753090901834[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]0.00641950398026146[/C][C]0.00550695556467648[/C][C]1.16570833101294[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]0.00716675675645263[/C][C]0.00528619630050006[/C][C]1.35574926640062[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]0.0071210640663801[/C][C]0.00511068916209556[/C][C]1.39336669488626[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]0.00811643850548223[/C][C]0.00474633725507689[/C][C]1.71004251684823[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]0.00803129586223926[/C][C]0.00457144643191035[/C][C]1.75683910592891[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]0.00800211949712302[/C][C]0.00441424090264353[/C][C]1.81279628221714[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]0.00821207314451212[/C][C]0.00437092270522121[/C][C]1.87879624013999[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]0.00743923940928888[/C][C]0.00412136426560127[/C][C]1.80504292507704[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]0.00644273888778656[/C][C]0.003911548499546[/C][C]1.64710699318553[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]0.00617480682250065[/C][C]0.00346555961282443[/C][C]1.78176326837678[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.00480029895124468[/C][C]0.00314713988222085[/C][C]1.52528935188519[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.00428200077547835[/C][C]0.00304708383965849[/C][C]1.40527829255865[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.00432179279757651[/C][C]0.00297536772895809[/C][C]1.45252392015756[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.00442802609147094[/C][C]0.00282787935032876[/C][C]1.56584689193199[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.00437546922504684[/C][C]0.00276549884969792[/C][C]1.58216273549518[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]0.00638630446367769[/C][C]0.00551293715249813[/C][C]1.15842141621074[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]0.00686683123621358[/C][C]0.00516021051422604[/C][C]1.33072695722057[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]0.00712099444982275[/C][C]0.00490509041024987[/C][C]1.45175600330270[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]0.0071028348043347[/C][C]0.0046898128181245[/C][C]1.51452415688846[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]0.00709713815994551[/C][C]0.00448250481315205[/C][C]1.58329738746111[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]0.00682890122690953[/C][C]0.00434648929707384[/C][C]1.57113034455346[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]0.00655056913539802[/C][C]0.00422021683774653[/C][C]1.5521878110168[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0.00624562158041378[/C][C]0.00409431877965556[/C][C]1.52543607777878[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.00586154900930082[/C][C]0.0039246783992017[/C][C]1.49351065567387[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.00556938412041414[/C][C]0.00376575326018196[/C][C]1.47895619697214[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.00541342791195478[/C][C]0.00360372976855865[/C][C]1.50217365330363[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.0052803197108104[/C][C]0.00351536215309617[/C][C]1.50206990940030[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.005363656648235[/C][C]0.00347835884543563[/C][C]1.54200785099366[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.00555275732529036[/C][C]0.00343059799288295[/C][C]1.61859749723226[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.00577257241952497[/C][C]0.00335215402854494[/C][C]1.72204867985456[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.00602156248027572[/C][C]0.00325466103081193[/C][C]1.85013505961742[/C][/ROW]
[ROW][C]Median[/C][C]0.00588019802647801[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.54782233853488e-05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.00428041866165156[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.00528031971081039[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.00528031971081039[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.00528031971081039[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.005363656648235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.00528031971081039[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.00528031971081039[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.00528031971081039[/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=4274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4274&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 Mean0.0061338714140660.005983257985189721.02517247781210
Geometric MeanNaN
Harmonic Mean-0.0503450211179155
Quadratic Mean0.0423295854961254
Winsorized Mean ( 1 / 16 )0.005944219832944660.005784954769510071.02753090901834
Winsorized Mean ( 2 / 16 )0.006419503980261460.005506955564676481.16570833101294
Winsorized Mean ( 3 / 16 )0.007166756756452630.005286196300500061.35574926640062
Winsorized Mean ( 4 / 16 )0.00712106406638010.005110689162095561.39336669488626
Winsorized Mean ( 5 / 16 )0.008116438505482230.004746337255076891.71004251684823
Winsorized Mean ( 6 / 16 )0.008031295862239260.004571446431910351.75683910592891
Winsorized Mean ( 7 / 16 )0.008002119497123020.004414240902643531.81279628221714
Winsorized Mean ( 8 / 16 )0.008212073144512120.004370922705221211.87879624013999
Winsorized Mean ( 9 / 16 )0.007439239409288880.004121364265601271.80504292507704
Winsorized Mean ( 10 / 16 )0.006442738887786560.0039115484995461.64710699318553
Winsorized Mean ( 11 / 16 )0.006174806822500650.003465559612824431.78176326837678
Winsorized Mean ( 12 / 16 )0.004800298951244680.003147139882220851.52528935188519
Winsorized Mean ( 13 / 16 )0.004282000775478350.003047083839658491.40527829255865
Winsorized Mean ( 14 / 16 )0.004321792797576510.002975367728958091.45252392015756
Winsorized Mean ( 15 / 16 )0.004428026091470940.002827879350328761.56584689193199
Winsorized Mean ( 16 / 16 )0.004375469225046840.002765498849697921.58216273549518
Trimmed Mean ( 1 / 16 )0.006386304463677690.005512937152498131.15842141621074
Trimmed Mean ( 2 / 16 )0.006866831236213580.005160210514226041.33072695722057
Trimmed Mean ( 3 / 16 )0.007120994449822750.004905090410249871.45175600330270
Trimmed Mean ( 4 / 16 )0.00710283480433470.00468981281812451.51452415688846
Trimmed Mean ( 5 / 16 )0.007097138159945510.004482504813152051.58329738746111
Trimmed Mean ( 6 / 16 )0.006828901226909530.004346489297073841.57113034455346
Trimmed Mean ( 7 / 16 )0.006550569135398020.004220216837746531.5521878110168
Trimmed Mean ( 8 / 16 )0.006245621580413780.004094318779655561.52543607777878
Trimmed Mean ( 9 / 16 )0.005861549009300820.00392467839920171.49351065567387
Trimmed Mean ( 10 / 16 )0.005569384120414140.003765753260181961.47895619697214
Trimmed Mean ( 11 / 16 )0.005413427911954780.003603729768558651.50217365330363
Trimmed Mean ( 12 / 16 )0.00528031971081040.003515362153096171.50206990940030
Trimmed Mean ( 13 / 16 )0.0053636566482350.003478358845435631.54200785099366
Trimmed Mean ( 14 / 16 )0.005552757325290360.003430597992882951.61859749723226
Trimmed Mean ( 15 / 16 )0.005772572419524970.003352154028544941.72204867985456
Trimmed Mean ( 16 / 16 )0.006021562480275720.003254661030811931.85013505961742
Median0.00588019802647801
Midrange7.54782233853488e-05
Midmean - Weighted Average at Xnp0.00428041866165156
Midmean - Weighted Average at X(n+1)p0.00528031971081039
Midmean - Empirical Distribution Function0.00528031971081039
Midmean - Empirical Distribution Function - Averaging0.00528031971081039
Midmean - Empirical Distribution Function - Interpolation0.005363656648235
Midmean - Closest Observation0.00528031971081039
Midmean - True Basic - Statistics Graphics Toolkit0.00528031971081039
Midmean - MS Excel (old versions)0.00528031971081039
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')