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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 17 Dec 2008 16:19:42 -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/Dec/18/t1229556077f4amh5frebob2n0.htm/, Retrieved Sat, 11 May 2024 05:18:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34602, Retrieved Sat, 11 May 2024 05:18:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2008-12-17 12:54:04] [ca30429b07824e7c5d48293114d35d71]
- RMP   [ARIMA Backward Selection] [] [2008-12-17 13:46:44] [ca30429b07824e7c5d48293114d35d71]
- RMPD      [Central Tendency] [] [2008-12-17 23:19:42] [c66d07e79164cd7acb2569833ec5bcd8] [Current]
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Dataseries X:
15.4691282859677 
34.2996675106348 
-238.209522954599 
387.020317650704 
-98.5176697145262 
-44.3694576648198 
783.987858756855 
11.1862348135376 
172.651805196371 
1020.32327869547 
800.593565020378 
-484.343985425235 
737.457677839988 
55.5609422808023 
822.189704277798 
-116.132771305324 
-98.586734276139 
465.188518947078 
581.544809079795 
-111.080374662329 
-735.880531457096 
-131.555749782164 
295.376771032459 
353.720857097988 
-269.780936411349 
-1013.91960500132 
75.1837769724952 
830.836991051352 
-783.56420833338 
446.58677270943 
943.811327734552 
890.546384991281 
-491.633709949806 
881.630403124671 
-1509.65208842739 
627.931421750767 
467.791508841453 
499.317207939511 
-413.690774702081 
-631.993062988557 
571.140686045693 
472.976253932897 
-920.513799147452 
4.46328359127034 
14.5445053225582 
541.889750009112 
24.9035548828124 
586.484226837517 
631.907811031939 
539.941413883246 




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34602&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34602&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34602&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean149.90066869869680.79488464753351.85532375412919
Geometric MeanNaN
Harmonic Mean98.8314868184396
Quadratic Mean585.09235711255
Winsorized Mean ( 1 / 16 )158.28507934799976.83177692667652.06015122491644
Winsorized Mean ( 2 / 16 )159.89071387242375.26908606289352.12425475365572
Winsorized Mean ( 3 / 16 )167.57273040927172.86279277944742.29983952051504
Winsorized Mean ( 4 / 16 )167.32395159350871.06606229387972.35448463292609
Winsorized Mean ( 5 / 16 )176.84796976300768.29573500539272.58944383202030
Winsorized Mean ( 6 / 16 )191.09955541676663.9158155286972.98986336693093
Winsorized Mean ( 7 / 16 )189.79531797331363.24446274156273.00097921218618
Winsorized Mean ( 8 / 16 )193.65500274231959.4248789904963.25882031284053
Winsorized Mean ( 9 / 16 )200.55979760920250.82813917538373.94584182822758
Winsorized Mean ( 10 / 16 )206.07880244431849.51555699887724.16190011654298
Winsorized Mean ( 11 / 16 )220.42424966133843.86196703170975.02540730792999
Winsorized Mean ( 12 / 16 )222.94030423392743.05969546125855.17747052889655
Winsorized Mean ( 13 / 16 )221.54885537223942.39143288848035.22626484353738
Winsorized Mean ( 14 / 16 )216.85681259012940.47226088854995.35815909042731
Winsorized Mean ( 15 / 16 )216.29303112085340.37325289706545.35733476002809
Winsorized Mean ( 16 / 16 )220.62071307476435.56918805264656.20257939956966
Trimmed Mean ( 1 / 16 )166.34088009722474.34232461694522.23749904182185
Trimmed Mean ( 2 / 16 )175.09718525942471.1106384056262.46232053579160
Trimmed Mean ( 3 / 16 )183.7372258202268.01279567978962.70150967893264
Trimmed Mean ( 4 / 16 )190.15170812615265.2318554290322.91501302355296
Trimmed Mean ( 5 / 16 )197.28538204260362.31329452929343.16602393651100
Trimmed Mean ( 6 / 16 )202.66364843197159.50297626543983.4059413688468
Trimmed Mean ( 7 / 16 )205.3405218151257.30912080711923.58303388576171
Trimmed Mean ( 8 / 16 )208.6063209415554.45731642016933.83063901518821
Trimmed Mean ( 9 / 16 )211.52650027733751.78460464932184.08473718607616
Trimmed Mean ( 10 / 16 )213.55737114180750.87387026980784.19778110077359
Trimmed Mean ( 11 / 16 )214.89282983778749.81237244713364.31404527190217
Trimmed Mean ( 12 / 16 )213.92579840010349.88773354338274.28814426324001
Trimmed Mean ( 13 / 16 )212.36078002617549.88337292205754.25714556948641
Trimmed Mean ( 14 / 16 )210.75447314749349.67809204584624.24240272659817
Trimmed Mean ( 15 / 16 )209.66476967559349.59863707481574.22722844902634
Trimmed Mean ( 16 / 16 )208.43731385239748.86700728020594.26539961117748
Median123.917791084433
Midrange-244.66440486596
Midmean - Weighted Average at Xnp199.221037972915
Midmean - Weighted Average at X(n+1)p213.925798400103
Midmean - Empirical Distribution Function213.925798400103
Midmean - Empirical Distribution Function - Averaging213.925798400103
Midmean - Empirical Distribution Function - Interpolation212.360780026175
Midmean - Closest Observation213.925798400103
Midmean - True Basic - Statistics Graphics Toolkit213.925798400103
Midmean - MS Excel (old versions)213.925798400103
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 149.900668698696 & 80.7948846475335 & 1.85532375412919 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 98.8314868184396 &  &  \tabularnewline
Quadratic Mean & 585.09235711255 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 158.285079347999 & 76.8317769266765 & 2.06015122491644 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 159.890713872423 & 75.2690860628935 & 2.12425475365572 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 167.572730409271 & 72.8627927794474 & 2.29983952051504 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 167.323951593508 & 71.0660622938797 & 2.35448463292609 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 176.847969763007 & 68.2957350053927 & 2.58944383202030 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 191.099555416766 & 63.915815528697 & 2.98986336693093 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 189.795317973313 & 63.2444627415627 & 3.00097921218618 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 193.655002742319 & 59.424878990496 & 3.25882031284053 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 200.559797609202 & 50.8281391753837 & 3.94584182822758 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 206.078802444318 & 49.5155569988772 & 4.16190011654298 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 220.424249661338 & 43.8619670317097 & 5.02540730792999 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 222.940304233927 & 43.0596954612585 & 5.17747052889655 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 221.548855372239 & 42.3914328884803 & 5.22626484353738 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 216.856812590129 & 40.4722608885499 & 5.35815909042731 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 216.293031120853 & 40.3732528970654 & 5.35733476002809 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 220.620713074764 & 35.5691880526465 & 6.20257939956966 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 166.340880097224 & 74.3423246169452 & 2.23749904182185 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 175.097185259424 & 71.110638405626 & 2.46232053579160 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 183.73722582022 & 68.0127956797896 & 2.70150967893264 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 190.151708126152 & 65.231855429032 & 2.91501302355296 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 197.285382042603 & 62.3132945292934 & 3.16602393651100 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 202.663648431971 & 59.5029762654398 & 3.4059413688468 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 205.34052181512 & 57.3091208071192 & 3.58303388576171 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 208.60632094155 & 54.4573164201693 & 3.83063901518821 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 211.526500277337 & 51.7846046493218 & 4.08473718607616 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 213.557371141807 & 50.8738702698078 & 4.19778110077359 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 214.892829837787 & 49.8123724471336 & 4.31404527190217 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 213.925798400103 & 49.8877335433827 & 4.28814426324001 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 212.360780026175 & 49.8833729220575 & 4.25714556948641 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 210.754473147493 & 49.6780920458462 & 4.24240272659817 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 209.664769675593 & 49.5986370748157 & 4.22722844902634 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 208.437313852397 & 48.8670072802059 & 4.26539961117748 \tabularnewline
Median & 123.917791084433 &  &  \tabularnewline
Midrange & -244.66440486596 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 199.221037972915 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 213.925798400103 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 213.925798400103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 213.925798400103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 212.360780026175 &  &  \tabularnewline
Midmean - Closest Observation & 213.925798400103 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 213.925798400103 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 213.925798400103 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34602&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]149.900668698696[/C][C]80.7948846475335[/C][C]1.85532375412919[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.8314868184396[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]585.09235711255[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]158.285079347999[/C][C]76.8317769266765[/C][C]2.06015122491644[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]159.890713872423[/C][C]75.2690860628935[/C][C]2.12425475365572[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]167.572730409271[/C][C]72.8627927794474[/C][C]2.29983952051504[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]167.323951593508[/C][C]71.0660622938797[/C][C]2.35448463292609[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]176.847969763007[/C][C]68.2957350053927[/C][C]2.58944383202030[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]191.099555416766[/C][C]63.915815528697[/C][C]2.98986336693093[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]189.795317973313[/C][C]63.2444627415627[/C][C]3.00097921218618[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]193.655002742319[/C][C]59.424878990496[/C][C]3.25882031284053[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]200.559797609202[/C][C]50.8281391753837[/C][C]3.94584182822758[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]206.078802444318[/C][C]49.5155569988772[/C][C]4.16190011654298[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]220.424249661338[/C][C]43.8619670317097[/C][C]5.02540730792999[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]222.940304233927[/C][C]43.0596954612585[/C][C]5.17747052889655[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]221.548855372239[/C][C]42.3914328884803[/C][C]5.22626484353738[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]216.856812590129[/C][C]40.4722608885499[/C][C]5.35815909042731[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]216.293031120853[/C][C]40.3732528970654[/C][C]5.35733476002809[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]220.620713074764[/C][C]35.5691880526465[/C][C]6.20257939956966[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]166.340880097224[/C][C]74.3423246169452[/C][C]2.23749904182185[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]175.097185259424[/C][C]71.110638405626[/C][C]2.46232053579160[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]183.73722582022[/C][C]68.0127956797896[/C][C]2.70150967893264[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]190.151708126152[/C][C]65.231855429032[/C][C]2.91501302355296[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]197.285382042603[/C][C]62.3132945292934[/C][C]3.16602393651100[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]202.663648431971[/C][C]59.5029762654398[/C][C]3.4059413688468[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]205.34052181512[/C][C]57.3091208071192[/C][C]3.58303388576171[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]208.60632094155[/C][C]54.4573164201693[/C][C]3.83063901518821[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]211.526500277337[/C][C]51.7846046493218[/C][C]4.08473718607616[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]213.557371141807[/C][C]50.8738702698078[/C][C]4.19778110077359[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]214.892829837787[/C][C]49.8123724471336[/C][C]4.31404527190217[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]213.925798400103[/C][C]49.8877335433827[/C][C]4.28814426324001[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]212.360780026175[/C][C]49.8833729220575[/C][C]4.25714556948641[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]210.754473147493[/C][C]49.6780920458462[/C][C]4.24240272659817[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]209.664769675593[/C][C]49.5986370748157[/C][C]4.22722844902634[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]208.437313852397[/C][C]48.8670072802059[/C][C]4.26539961117748[/C][/ROW]
[ROW][C]Median[/C][C]123.917791084433[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-244.66440486596[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]199.221037972915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]213.925798400103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]213.925798400103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]213.925798400103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]212.360780026175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]213.925798400103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]213.925798400103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]213.925798400103[/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=34602&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34602&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 Mean149.90066869869680.79488464753351.85532375412919
Geometric MeanNaN
Harmonic Mean98.8314868184396
Quadratic Mean585.09235711255
Winsorized Mean ( 1 / 16 )158.28507934799976.83177692667652.06015122491644
Winsorized Mean ( 2 / 16 )159.89071387242375.26908606289352.12425475365572
Winsorized Mean ( 3 / 16 )167.57273040927172.86279277944742.29983952051504
Winsorized Mean ( 4 / 16 )167.32395159350871.06606229387972.35448463292609
Winsorized Mean ( 5 / 16 )176.84796976300768.29573500539272.58944383202030
Winsorized Mean ( 6 / 16 )191.09955541676663.9158155286972.98986336693093
Winsorized Mean ( 7 / 16 )189.79531797331363.24446274156273.00097921218618
Winsorized Mean ( 8 / 16 )193.65500274231959.4248789904963.25882031284053
Winsorized Mean ( 9 / 16 )200.55979760920250.82813917538373.94584182822758
Winsorized Mean ( 10 / 16 )206.07880244431849.51555699887724.16190011654298
Winsorized Mean ( 11 / 16 )220.42424966133843.86196703170975.02540730792999
Winsorized Mean ( 12 / 16 )222.94030423392743.05969546125855.17747052889655
Winsorized Mean ( 13 / 16 )221.54885537223942.39143288848035.22626484353738
Winsorized Mean ( 14 / 16 )216.85681259012940.47226088854995.35815909042731
Winsorized Mean ( 15 / 16 )216.29303112085340.37325289706545.35733476002809
Winsorized Mean ( 16 / 16 )220.62071307476435.56918805264656.20257939956966
Trimmed Mean ( 1 / 16 )166.34088009722474.34232461694522.23749904182185
Trimmed Mean ( 2 / 16 )175.09718525942471.1106384056262.46232053579160
Trimmed Mean ( 3 / 16 )183.7372258202268.01279567978962.70150967893264
Trimmed Mean ( 4 / 16 )190.15170812615265.2318554290322.91501302355296
Trimmed Mean ( 5 / 16 )197.28538204260362.31329452929343.16602393651100
Trimmed Mean ( 6 / 16 )202.66364843197159.50297626543983.4059413688468
Trimmed Mean ( 7 / 16 )205.3405218151257.30912080711923.58303388576171
Trimmed Mean ( 8 / 16 )208.6063209415554.45731642016933.83063901518821
Trimmed Mean ( 9 / 16 )211.52650027733751.78460464932184.08473718607616
Trimmed Mean ( 10 / 16 )213.55737114180750.87387026980784.19778110077359
Trimmed Mean ( 11 / 16 )214.89282983778749.81237244713364.31404527190217
Trimmed Mean ( 12 / 16 )213.92579840010349.88773354338274.28814426324001
Trimmed Mean ( 13 / 16 )212.36078002617549.88337292205754.25714556948641
Trimmed Mean ( 14 / 16 )210.75447314749349.67809204584624.24240272659817
Trimmed Mean ( 15 / 16 )209.66476967559349.59863707481574.22722844902634
Trimmed Mean ( 16 / 16 )208.43731385239748.86700728020594.26539961117748
Median123.917791084433
Midrange-244.66440486596
Midmean - Weighted Average at Xnp199.221037972915
Midmean - Weighted Average at X(n+1)p213.925798400103
Midmean - Empirical Distribution Function213.925798400103
Midmean - Empirical Distribution Function - Averaging213.925798400103
Midmean - Empirical Distribution Function - Interpolation212.360780026175
Midmean - Closest Observation213.925798400103
Midmean - True Basic - Statistics Graphics Toolkit213.925798400103
Midmean - MS Excel (old versions)213.925798400103
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')