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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 computationMon, 17 Dec 2012 09:18:50 -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/2012/Dec/17/t1355753963qktmkza6vcpxfa7.htm/, Retrieved Thu, 28 Mar 2024 10:29:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200946, Retrieved Thu, 28 Mar 2024 10:29:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact276
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-12-17 14:18:50] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
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Dataseries X:
0.00509986101484714
-0.367556066315499
-0.0537354466224309
-0.166704772282988
-0.126300049308617
0.327023686536905
0.692054233801963
-0.417564341193504
-0.232739197967506
0.158028515484774
0.141962601907719
0.0977015093305773
0.178499162542409
0.354710779485382
-0.354746935306964
0.0473075914423155
0.12548482811567
0.049678532976494
0.399090003338055
-0.246526990945034
0.21685291463498
-0.219593868435001
0.0652702639292979
-0.0665262770468571
0.308815292012484
-0.424601314868768
0.145355814680874
-0.0441183515794435
-0.221659463846152
0.122084195491148
0.0536801423020546
0.148492555999408
0.24474869125267
0.278323125606182
-0.309036135905256
0.264314084072332
0.17628378438955
0.241921702176668
-0.0565203845695072
0.238898007832185
0.108691572225452
0.343634820779181
0.0945164374426331
0.286201922339716
0.169943261563564
0.0957444165846209
-0.0751006897446516
0.135229078535882
0.636783916469131
0.143957130800366
-0.0621808412835195
-0.179444688104042
-0.0242396923945499
-0.0669552206506127
0.122304332221848
0.122161018305001
0.0441032730401381
0.193670631917222
-0.00500574026816254
-0.0808552739975925
0.0558677003038862
-0.250407187862639
0.193849819804146
0.414954798600835
-0.461344114086046
0.155266476855029
0.119974629604623
-0.0358831783828276
0.33240331269403
0.13904839615431
0.0356716080180407
-0.130743874142015
0.203701793870735
-0.332119742643951
0.2858057337555
-0.00330579177147433
0.05277378155592




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200946&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200946&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200946&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.05912241704250840.02610707828477072.26461254674357
Geometric MeanNaN
Harmonic Mean-0.410728483454046
Quadratic Mean0.235149962738784
Winsorized Mean ( 1 / 25 )0.05888179992412450.02576509489273742.28533215845915
Winsorized Mean ( 2 / 25 )0.0533027831918380.02429638684258442.19385637614289
Winsorized Mean ( 3 / 25 )0.05463304863139220.02369972110776082.30521905228252
Winsorized Mean ( 4 / 25 )0.05299304380832010.02312594020213812.29149791727909
Winsorized Mean ( 5 / 25 )0.05374312393538580.02266865355814092.37081235537632
Winsorized Mean ( 6 / 25 )0.05466666409020740.02212670387213152.47061941110262
Winsorized Mean ( 7 / 25 )0.05950751153434310.02094854012065922.84065195911468
Winsorized Mean ( 8 / 25 )0.05801886762714140.02055918774930552.82204084784922
Winsorized Mean ( 9 / 25 )0.05698730671471070.01983393631045892.87322222995442
Winsorized Mean ( 10 / 25 )0.05837478016109230.01955219821693892.98558655724551
Winsorized Mean ( 11 / 25 )0.0576009211984970.01933446676537012.97918333603416
Winsorized Mean ( 12 / 25 )0.06167470906298150.01786022033375183.45318858952878
Winsorized Mean ( 13 / 25 )0.06052235580347630.01699758890314593.56064358000062
Winsorized Mean ( 14 / 25 )0.06654670290619830.0158102617123894.20908294351964
Winsorized Mean ( 15 / 25 )0.06682335170274020.01558282630540734.28826904651771
Winsorized Mean ( 16 / 25 )0.07168562331080660.01344447962102095.33197455993192
Winsorized Mean ( 17 / 25 )0.07005262174337580.01285012091526495.45151459704623
Winsorized Mean ( 18 / 25 )0.06965369850303940.01225775789726675.68241754216498
Winsorized Mean ( 19 / 25 )0.06971532653706280.01223635025553535.69739547178504
Winsorized Mean ( 20 / 25 )0.06690336975486140.01155744050774125.78877042110227
Winsorized Mean ( 21 / 25 )0.06784293663517590.01125508630026926.02775801315298
Winsorized Mean ( 22 / 25 )0.06682705524120170.0109119145476626.12422824146107
Winsorized Mean ( 23 / 25 )0.06614074389284510.01006049746837776.57430152939651
Winsorized Mean ( 24 / 25 )0.0678466559656360.009589331337060727.07522282637405
Winsorized Mean ( 25 / 25 )0.0694276836061090.008793101318815997.89569926341501
Trimmed Mean ( 1 / 25 )0.0576228799007630.02444684141954082.35706850271071
Trimmed Mean ( 2 / 25 )0.05629497795831320.02286903644892712.46162439261644
Trimmed Mean ( 3 / 25 )0.05791750610633140.02195424118463882.6381010219955
Trimmed Mean ( 4 / 25 )0.05913926081923150.02114555189266222.79677074022143
Trimmed Mean ( 5 / 25 )0.05913926081923150.02039346790110672.89991192797681
Trimmed Mean ( 6 / 25 )0.06260200114174350.0196391082027093.18761934073504
Trimmed Mean ( 7 / 25 )0.06421845868927860.01888749906817293.40005092561421
Trimmed Mean ( 8 / 25 )0.06506797375000470.01829716183569123.55617851196355
Trimmed Mean ( 9 / 25 )0.06621793385903120.01767237920799753.74697334635422
Trimmed Mean ( 10 / 25 )0.06621793385903120.0170769424052123.87762236867539
Trimmed Mean ( 11 / 25 )0.06889543824365960.01640686627027384.19918326319788
Trimmed Mean ( 12 / 25 )0.07038716691000190.01561831859844174.50670579335119
Trimmed Mean ( 13 / 25 )0.07148334216199630.01497961180722394.77204236544526
Trimmed Mean ( 14 / 25 )0.07280829655698220.01436511985914355.06840856678543
Trimmed Mean ( 15 / 25 )0.07354103623952070.01385955755588995.30616045591355
Trimmed Mean ( 16 / 25 )0.07430734988297570.01325711180381615.60509340062941
Trimmed Mean ( 17 / 25 )0.07460076986270970.01296533897283435.75386189431818
Trimmed Mean ( 18 / 25 )0.0751032195114740.01269964168936765.91380618040209
Trimmed Mean ( 19 / 25 )0.07570095899530520.01246331687605186.07390149413307
Trimmed Mean ( 20 / 25 )0.07570095899530520.01213178544896616.23988606736829
Trimmed Mean ( 21 / 25 )0.07739642070536140.01182436176069516.54550514198844
Trimmed Mean ( 22 / 25 )0.0784579189353820.01145771527913796.84760591653361
Trimmed Mean ( 23 / 25 )0.07977108096537010.01100990593954837.24539168666532
Trimmed Mean ( 24 / 25 )0.081344598138660.0105972011882387.6760454665092
Trimmed Mean ( 25 / 25 )0.08294852027959040.01012119517803868.19552620223901
Median0.0957444165846209
Midrange0.115355059857958
Midmean - Weighted Average at Xnp0.0725964939184126
Midmean - Weighted Average at X(n+1)p0.0757009589953052
Midmean - Empirical Distribution Function0.0757009589953052
Midmean - Empirical Distribution Function - Averaging0.0757009589953052
Midmean - Empirical Distribution Function - Interpolation0.0757009589953052
Midmean - Closest Observation0.0721345545041572
Midmean - True Basic - Statistics Graphics Toolkit0.0757009589953052
Midmean - MS Excel (old versions)0.0757009589953052
Number of observations77

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0591224170425084 & 0.0261070782847707 & 2.26461254674357 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.410728483454046 &  &  \tabularnewline
Quadratic Mean & 0.235149962738784 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 0.0588817999241245 & 0.0257650948927374 & 2.28533215845915 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 0.053302783191838 & 0.0242963868425844 & 2.19385637614289 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 0.0546330486313922 & 0.0236997211077608 & 2.30521905228252 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 0.0529930438083201 & 0.0231259402021381 & 2.29149791727909 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 0.0537431239353858 & 0.0226686535581409 & 2.37081235537632 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 0.0546666640902074 & 0.0221267038721315 & 2.47061941110262 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 0.0595075115343431 & 0.0209485401206592 & 2.84065195911468 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 0.0580188676271414 & 0.0205591877493055 & 2.82204084784922 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 0.0569873067147107 & 0.0198339363104589 & 2.87322222995442 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 0.0583747801610923 & 0.0195521982169389 & 2.98558655724551 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 0.057600921198497 & 0.0193344667653701 & 2.97918333603416 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 0.0616747090629815 & 0.0178602203337518 & 3.45318858952878 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 0.0605223558034763 & 0.0169975889031459 & 3.56064358000062 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 0.0665467029061983 & 0.015810261712389 & 4.20908294351964 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 0.0668233517027402 & 0.0155828263054073 & 4.28826904651771 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 0.0716856233108066 & 0.0134444796210209 & 5.33197455993192 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 0.0700526217433758 & 0.0128501209152649 & 5.45151459704623 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 0.0696536985030394 & 0.0122577578972667 & 5.68241754216498 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 0.0697153265370628 & 0.0122363502555353 & 5.69739547178504 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 0.0669033697548614 & 0.0115574405077412 & 5.78877042110227 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 0.0678429366351759 & 0.0112550863002692 & 6.02775801315298 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 0.0668270552412017 & 0.010911914547662 & 6.12422824146107 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 0.0661407438928451 & 0.0100604974683777 & 6.57430152939651 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 0.067846655965636 & 0.00958933133706072 & 7.07522282637405 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 0.069427683606109 & 0.00879310131881599 & 7.89569926341501 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 0.057622879900763 & 0.0244468414195408 & 2.35706850271071 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 0.0562949779583132 & 0.0228690364489271 & 2.46162439261644 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 0.0579175061063314 & 0.0219542411846388 & 2.6381010219955 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 0.0591392608192315 & 0.0211455518926622 & 2.79677074022143 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 0.0591392608192315 & 0.0203934679011067 & 2.89991192797681 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 0.0626020011417435 & 0.019639108202709 & 3.18761934073504 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 0.0642184586892786 & 0.0188874990681729 & 3.40005092561421 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 0.0650679737500047 & 0.0182971618356912 & 3.55617851196355 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 0.0662179338590312 & 0.0176723792079975 & 3.74697334635422 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 0.0662179338590312 & 0.017076942405212 & 3.87762236867539 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 0.0688954382436596 & 0.0164068662702738 & 4.19918326319788 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 0.0703871669100019 & 0.0156183185984417 & 4.50670579335119 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 0.0714833421619963 & 0.0149796118072239 & 4.77204236544526 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 0.0728082965569822 & 0.0143651198591435 & 5.06840856678543 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 0.0735410362395207 & 0.0138595575558899 & 5.30616045591355 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 0.0743073498829757 & 0.0132571118038161 & 5.60509340062941 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 0.0746007698627097 & 0.0129653389728343 & 5.75386189431818 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 0.075103219511474 & 0.0126996416893676 & 5.91380618040209 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 0.0757009589953052 & 0.0124633168760518 & 6.07390149413307 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 0.0757009589953052 & 0.0121317854489661 & 6.23988606736829 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 0.0773964207053614 & 0.0118243617606951 & 6.54550514198844 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 0.078457918935382 & 0.0114577152791379 & 6.84760591653361 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 0.0797710809653701 & 0.0110099059395483 & 7.24539168666532 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 0.08134459813866 & 0.010597201188238 & 7.6760454665092 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 0.0829485202795904 & 0.0101211951780386 & 8.19552620223901 \tabularnewline
Median & 0.0957444165846209 &  &  \tabularnewline
Midrange & 0.115355059857958 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.0725964939184126 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0757009589953052 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.0757009589953052 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0757009589953052 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.0757009589953052 &  &  \tabularnewline
Midmean - Closest Observation & 0.0721345545041572 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0757009589953052 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0757009589953052 &  &  \tabularnewline
Number of observations & 77 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200946&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]0.0591224170425084[/C][C]0.0261070782847707[/C][C]2.26461254674357[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.410728483454046[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.235149962738784[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]0.0588817999241245[/C][C]0.0257650948927374[/C][C]2.28533215845915[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]0.053302783191838[/C][C]0.0242963868425844[/C][C]2.19385637614289[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]0.0546330486313922[/C][C]0.0236997211077608[/C][C]2.30521905228252[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]0.0529930438083201[/C][C]0.0231259402021381[/C][C]2.29149791727909[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]0.0537431239353858[/C][C]0.0226686535581409[/C][C]2.37081235537632[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]0.0546666640902074[/C][C]0.0221267038721315[/C][C]2.47061941110262[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]0.0595075115343431[/C][C]0.0209485401206592[/C][C]2.84065195911468[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]0.0580188676271414[/C][C]0.0205591877493055[/C][C]2.82204084784922[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]0.0569873067147107[/C][C]0.0198339363104589[/C][C]2.87322222995442[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]0.0583747801610923[/C][C]0.0195521982169389[/C][C]2.98558655724551[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]0.057600921198497[/C][C]0.0193344667653701[/C][C]2.97918333603416[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]0.0616747090629815[/C][C]0.0178602203337518[/C][C]3.45318858952878[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]0.0605223558034763[/C][C]0.0169975889031459[/C][C]3.56064358000062[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]0.0665467029061983[/C][C]0.015810261712389[/C][C]4.20908294351964[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]0.0668233517027402[/C][C]0.0155828263054073[/C][C]4.28826904651771[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]0.0716856233108066[/C][C]0.0134444796210209[/C][C]5.33197455993192[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]0.0700526217433758[/C][C]0.0128501209152649[/C][C]5.45151459704623[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]0.0696536985030394[/C][C]0.0122577578972667[/C][C]5.68241754216498[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]0.0697153265370628[/C][C]0.0122363502555353[/C][C]5.69739547178504[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]0.0669033697548614[/C][C]0.0115574405077412[/C][C]5.78877042110227[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]0.0678429366351759[/C][C]0.0112550863002692[/C][C]6.02775801315298[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]0.0668270552412017[/C][C]0.010911914547662[/C][C]6.12422824146107[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]0.0661407438928451[/C][C]0.0100604974683777[/C][C]6.57430152939651[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]0.067846655965636[/C][C]0.00958933133706072[/C][C]7.07522282637405[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]0.069427683606109[/C][C]0.00879310131881599[/C][C]7.89569926341501[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]0.057622879900763[/C][C]0.0244468414195408[/C][C]2.35706850271071[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]0.0562949779583132[/C][C]0.0228690364489271[/C][C]2.46162439261644[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]0.0579175061063314[/C][C]0.0219542411846388[/C][C]2.6381010219955[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]0.0591392608192315[/C][C]0.0211455518926622[/C][C]2.79677074022143[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]0.0591392608192315[/C][C]0.0203934679011067[/C][C]2.89991192797681[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]0.0626020011417435[/C][C]0.019639108202709[/C][C]3.18761934073504[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]0.0642184586892786[/C][C]0.0188874990681729[/C][C]3.40005092561421[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]0.0650679737500047[/C][C]0.0182971618356912[/C][C]3.55617851196355[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]0.0662179338590312[/C][C]0.0176723792079975[/C][C]3.74697334635422[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]0.0662179338590312[/C][C]0.017076942405212[/C][C]3.87762236867539[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]0.0688954382436596[/C][C]0.0164068662702738[/C][C]4.19918326319788[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]0.0703871669100019[/C][C]0.0156183185984417[/C][C]4.50670579335119[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]0.0714833421619963[/C][C]0.0149796118072239[/C][C]4.77204236544526[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]0.0728082965569822[/C][C]0.0143651198591435[/C][C]5.06840856678543[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]0.0735410362395207[/C][C]0.0138595575558899[/C][C]5.30616045591355[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]0.0743073498829757[/C][C]0.0132571118038161[/C][C]5.60509340062941[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]0.0746007698627097[/C][C]0.0129653389728343[/C][C]5.75386189431818[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]0.075103219511474[/C][C]0.0126996416893676[/C][C]5.91380618040209[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]0.0757009589953052[/C][C]0.0124633168760518[/C][C]6.07390149413307[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]0.0757009589953052[/C][C]0.0121317854489661[/C][C]6.23988606736829[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]0.0773964207053614[/C][C]0.0118243617606951[/C][C]6.54550514198844[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]0.078457918935382[/C][C]0.0114577152791379[/C][C]6.84760591653361[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]0.0797710809653701[/C][C]0.0110099059395483[/C][C]7.24539168666532[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]0.08134459813866[/C][C]0.010597201188238[/C][C]7.6760454665092[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]0.0829485202795904[/C][C]0.0101211951780386[/C][C]8.19552620223901[/C][/ROW]
[ROW][C]Median[/C][C]0.0957444165846209[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.115355059857958[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.0725964939184126[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0757009589953052[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.0757009589953052[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0757009589953052[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.0757009589953052[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.0721345545041572[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0757009589953052[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0757009589953052[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]77[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200946&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200946&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 Mean0.05912241704250840.02610707828477072.26461254674357
Geometric MeanNaN
Harmonic Mean-0.410728483454046
Quadratic Mean0.235149962738784
Winsorized Mean ( 1 / 25 )0.05888179992412450.02576509489273742.28533215845915
Winsorized Mean ( 2 / 25 )0.0533027831918380.02429638684258442.19385637614289
Winsorized Mean ( 3 / 25 )0.05463304863139220.02369972110776082.30521905228252
Winsorized Mean ( 4 / 25 )0.05299304380832010.02312594020213812.29149791727909
Winsorized Mean ( 5 / 25 )0.05374312393538580.02266865355814092.37081235537632
Winsorized Mean ( 6 / 25 )0.05466666409020740.02212670387213152.47061941110262
Winsorized Mean ( 7 / 25 )0.05950751153434310.02094854012065922.84065195911468
Winsorized Mean ( 8 / 25 )0.05801886762714140.02055918774930552.82204084784922
Winsorized Mean ( 9 / 25 )0.05698730671471070.01983393631045892.87322222995442
Winsorized Mean ( 10 / 25 )0.05837478016109230.01955219821693892.98558655724551
Winsorized Mean ( 11 / 25 )0.0576009211984970.01933446676537012.97918333603416
Winsorized Mean ( 12 / 25 )0.06167470906298150.01786022033375183.45318858952878
Winsorized Mean ( 13 / 25 )0.06052235580347630.01699758890314593.56064358000062
Winsorized Mean ( 14 / 25 )0.06654670290619830.0158102617123894.20908294351964
Winsorized Mean ( 15 / 25 )0.06682335170274020.01558282630540734.28826904651771
Winsorized Mean ( 16 / 25 )0.07168562331080660.01344447962102095.33197455993192
Winsorized Mean ( 17 / 25 )0.07005262174337580.01285012091526495.45151459704623
Winsorized Mean ( 18 / 25 )0.06965369850303940.01225775789726675.68241754216498
Winsorized Mean ( 19 / 25 )0.06971532653706280.01223635025553535.69739547178504
Winsorized Mean ( 20 / 25 )0.06690336975486140.01155744050774125.78877042110227
Winsorized Mean ( 21 / 25 )0.06784293663517590.01125508630026926.02775801315298
Winsorized Mean ( 22 / 25 )0.06682705524120170.0109119145476626.12422824146107
Winsorized Mean ( 23 / 25 )0.06614074389284510.01006049746837776.57430152939651
Winsorized Mean ( 24 / 25 )0.0678466559656360.009589331337060727.07522282637405
Winsorized Mean ( 25 / 25 )0.0694276836061090.008793101318815997.89569926341501
Trimmed Mean ( 1 / 25 )0.0576228799007630.02444684141954082.35706850271071
Trimmed Mean ( 2 / 25 )0.05629497795831320.02286903644892712.46162439261644
Trimmed Mean ( 3 / 25 )0.05791750610633140.02195424118463882.6381010219955
Trimmed Mean ( 4 / 25 )0.05913926081923150.02114555189266222.79677074022143
Trimmed Mean ( 5 / 25 )0.05913926081923150.02039346790110672.89991192797681
Trimmed Mean ( 6 / 25 )0.06260200114174350.0196391082027093.18761934073504
Trimmed Mean ( 7 / 25 )0.06421845868927860.01888749906817293.40005092561421
Trimmed Mean ( 8 / 25 )0.06506797375000470.01829716183569123.55617851196355
Trimmed Mean ( 9 / 25 )0.06621793385903120.01767237920799753.74697334635422
Trimmed Mean ( 10 / 25 )0.06621793385903120.0170769424052123.87762236867539
Trimmed Mean ( 11 / 25 )0.06889543824365960.01640686627027384.19918326319788
Trimmed Mean ( 12 / 25 )0.07038716691000190.01561831859844174.50670579335119
Trimmed Mean ( 13 / 25 )0.07148334216199630.01497961180722394.77204236544526
Trimmed Mean ( 14 / 25 )0.07280829655698220.01436511985914355.06840856678543
Trimmed Mean ( 15 / 25 )0.07354103623952070.01385955755588995.30616045591355
Trimmed Mean ( 16 / 25 )0.07430734988297570.01325711180381615.60509340062941
Trimmed Mean ( 17 / 25 )0.07460076986270970.01296533897283435.75386189431818
Trimmed Mean ( 18 / 25 )0.0751032195114740.01269964168936765.91380618040209
Trimmed Mean ( 19 / 25 )0.07570095899530520.01246331687605186.07390149413307
Trimmed Mean ( 20 / 25 )0.07570095899530520.01213178544896616.23988606736829
Trimmed Mean ( 21 / 25 )0.07739642070536140.01182436176069516.54550514198844
Trimmed Mean ( 22 / 25 )0.0784579189353820.01145771527913796.84760591653361
Trimmed Mean ( 23 / 25 )0.07977108096537010.01100990593954837.24539168666532
Trimmed Mean ( 24 / 25 )0.081344598138660.0105972011882387.6760454665092
Trimmed Mean ( 25 / 25 )0.08294852027959040.01012119517803868.19552620223901
Median0.0957444165846209
Midrange0.115355059857958
Midmean - Weighted Average at Xnp0.0725964939184126
Midmean - Weighted Average at X(n+1)p0.0757009589953052
Midmean - Empirical Distribution Function0.0757009589953052
Midmean - Empirical Distribution Function - Averaging0.0757009589953052
Midmean - Empirical Distribution Function - Interpolation0.0757009589953052
Midmean - Closest Observation0.0721345545041572
Midmean - True Basic - Statistics Graphics Toolkit0.0757009589953052
Midmean - MS Excel (old versions)0.0757009589953052
Number of observations77



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')