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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, 27 Oct 2008 04:35:54 -0600
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/Oct/27/t1225103799jn4xsnmmps9m2v6.htm/, Retrieved Sun, 19 May 2024 13:37:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19199, Retrieved Sun, 19 May 2024 13:37:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q6 Distributions] [2007-10-22 19:20:42] [b731da8b544846036771bbf9bf2f34ce]
F    D  [Central Tendency] [Q6] [2008-10-23 11:15:50] [28075c6928548bea087cb2be962cfe7e]
F   P     [Central Tendency] [q6 central tendency] [2008-10-23 12:36:56] [7173087adebe3e3a714c80ea2417b3eb]
F   P         [Central Tendency] [q6] [2008-10-27 10:35:54] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
Feedback Forum
2008-11-03 16:33:21 [Lindsay Heyndrickx] [reply
Als je hier de central tendancy berekent en je trekt het gemiddelde af van de tijdreeks ligt dit zeer dicht bij nul. Als je de extreme waarden eruit haalt verandert dit een beetje maar niet spectaculair. Als je een horizontale lijn door nul trekt valt dit niet buiten het betrouwbaarheidsinterval. Het resultaat is hier robuust zelfs als we rekening houden met de outliers.
2008-11-03 20:02:12 [Jeroen Aerts] [reply
We stellen vast dat de standaard errors niet gelijk zijn aan 0, maar dat de waarden wel bijna 0 zijn. We kunnen dus stellen dat het bekomen resultaat robuust is en dus niet gevoelig of onderhevig is aan of voor outliers.
2008-11-03 22:18:16 [Nick Wuyts] [reply
We bekomen hier inderdaad een robuust resultaat.
We verminderen eerst de central tendency met een random component ( - gemiddelde). Dit kunnen we makkelijk doen mbv een toevoeging aan de R code te doen (x <- x-gemiddelde).
Bij de winsorized mean zien we dat het gemiddelde nabij 0 is (0.0114291533021248). De stippellijnen geven het bereik van 95% aan. Als we een horizontale lijn trekken, valt deze binnen het betrouwbaarheidsinterval. Dit geeft aan dat het resultaat robuust is. De robuustheid heeft trouwens betrekking op outliers.

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Dataseries X:
0.135240492
0.065197194
0.071527133
0.07172211
0.212776724
-0.002781178
0.176803126
0.135141136
0.059111035
-0.061166679
0.124280535
0.133623064
0.055544019
0.029718204
-0.026438963
-0.028675043
0.169365871
-0.038471919
0.17230276
0.060852508
-0.04661364
-0.114759508
0.135843117
0.118275005
0
0.002974711
-0.078150901
-0.064416259
0.077460171
-0.114179153
0.031355959
-0.011454849
-0.035431525
-0.126335763
0.069348753
0.068790469
0.029872258
-0.035619778
-0.082842715
-0.02803716
0.070595183
-0.098724654
0.020781398
-0.037933461
-0.054082436
-0.141291518
-0.02090897
0.05643331
0.015260009
-0.074707064
-0.103635101
-0.095329803
0.067000045
-0.109898302
-0.037635526
-0.084295986
-0.06988259
-0.170605486
-0.003384892
0.046805191
0.014508325




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19199&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19199&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.00821014742622950.01142915330212480.718351325701718
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.0889097251877916
Winsorized Mean ( 1 / 20 )0.008100973163934430.01115024802788860.726528517004518
Winsorized Mean ( 2 / 20 )0.008443772803278690.01100853228013760.767020760661579
Winsorized Mean ( 3 / 20 )0.00886865965573770.01086070913641450.816582006234041
Winsorized Mean ( 4 / 20 )0.00670850234426230.01035319782500520.647964277091262
Winsorized Mean ( 5 / 20 )0.007009996278688520.01027551259896960.682204046870759
Winsorized Mean ( 6 / 20 )0.00761627611475410.01015883176761670.749719681256315
Winsorized Mean ( 7 / 20 )0.008005565049180330.01002096286858340.798881819458535
Winsorized Mean ( 8 / 20 )0.007225541704918030.009690775647841270.74561025530785
Winsorized Mean ( 9 / 20 )0.00796742011475410.009234046950154020.862830799730903
Winsorized Mean ( 10 / 20 )0.001514704868852460.007987248163897060.189640391505429
Winsorized Mean ( 11 / 20 )0.001326037377049180.007678681731993790.172690759082272
Winsorized Mean ( 12 / 20 )0.001965157377049180.007557086751949550.260041659114501
Winsorized Mean ( 13 / 20 )0.002794711672131150.007354970598045040.379975913550761
Winsorized Mean ( 14 / 20 )0.003763213540983610.007107348299777940.529482077176545
Winsorized Mean ( 15 / 20 )0.004425007639344260.006959562332100630.635816941955407
Winsorized Mean ( 16 / 20 )0.005813550327868850.006600495433486550.8807748428057
Winsorized Mean ( 17 / 20 )0.007392584180327870.006214396536380941.18959003292588
Winsorized Mean ( 18 / 20 )0.008513020737704920.005676392244900881.49972383345287
Winsorized Mean ( 19 / 20 )0.008138311147540980.005570217477508421.46104010847011
Winsorized Mean ( 20 / 20 )0.007358052131147540.005423571064442441.35668032071854
Trimmed Mean ( 1 / 20 )0.007773690762711870.01086896263237860.715219200363616
Trimmed Mean ( 2 / 20 )0.00742344117543860.01052293953130020.705453181913456
Trimmed Mean ( 3 / 20 )0.006857620909090910.01018950142173290.673008484445025
Trimmed Mean ( 4 / 20 )0.006086090320754720.009845169911784670.618180323477167
Trimmed Mean ( 5 / 20 )0.005899976921568630.009616763388501950.613509627222688
Trimmed Mean ( 6 / 20 )0.005623604755102040.009351586389587320.601353024056297
Trimmed Mean ( 7 / 20 )0.005192565914893620.009047273090705380.573937125897984
Trimmed Mean ( 8 / 20 )0.00464782640.008694012113661020.53460086542746
Trimmed Mean ( 9 / 20 )0.004190731534883720.008330901552688040.503034576555708
Trimmed Mean ( 10 / 20 )0.003566400902439020.00798177721738570.446817895978202
Trimmed Mean ( 11 / 20 )0.003887307205128210.007859749782044190.494584091469281
Trimmed Mean ( 12 / 20 )0.004271183027027030.007760213532218180.550395038653808
Trimmed Mean ( 13 / 20 )0.00460610580.007639426985910830.602938650830083
Trimmed Mean ( 14 / 20 )0.004863670.007509091197822980.64770421238326
Trimmed Mean ( 15 / 20 )0.00501834245161290.007375148311207050.680439530143033
Trimmed Mean ( 16 / 20 )0.005101545724137930.007203735841453350.70818056580885
Trimmed Mean ( 17 / 20 )0.005001008037037040.007041121883846090.710257274271941
Trimmed Mean ( 18 / 20 )0.004657746520.006893563973590140.675665959994604
Trimmed Mean ( 19 / 20 )0.004089698869565220.006813044581281530.600274784756501
Trimmed Mean ( 20 / 20 )0.00347073809523810.00667011011114570.520341948993993
Median0
Midrange0.021085619
Midmean - Weighted Average at Xnp0.00289260490000000
Midmean - Weighted Average at X(n+1)p0.00501834245161291
Midmean - Empirical Distribution Function0.00501834245161291
Midmean - Empirical Distribution Function - Averaging0.00501834245161291
Midmean - Empirical Distribution Function - Interpolation0.00501834245161291
Midmean - Closest Observation0.00284851115625
Midmean - True Basic - Statistics Graphics Toolkit0.00501834245161291
Midmean - MS Excel (old versions)0.00501834245161291
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0082101474262295 & 0.0114291533021248 & 0.718351325701718 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 0.0889097251877916 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.00810097316393443 & 0.0111502480278886 & 0.726528517004518 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.00844377280327869 & 0.0110085322801376 & 0.767020760661579 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.0088686596557377 & 0.0108607091364145 & 0.816582006234041 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.0067085023442623 & 0.0103531978250052 & 0.647964277091262 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.00700999627868852 & 0.0102755125989696 & 0.682204046870759 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.0076162761147541 & 0.0101588317676167 & 0.749719681256315 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.00800556504918033 & 0.0100209628685834 & 0.798881819458535 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.00722554170491803 & 0.00969077564784127 & 0.74561025530785 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.0079674201147541 & 0.00923404695015402 & 0.862830799730903 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.00151470486885246 & 0.00798724816389706 & 0.189640391505429 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.00132603737704918 & 0.00767868173199379 & 0.172690759082272 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.00196515737704918 & 0.00755708675194955 & 0.260041659114501 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.00279471167213115 & 0.00735497059804504 & 0.379975913550761 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.00376321354098361 & 0.00710734829977794 & 0.529482077176545 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.00442500763934426 & 0.00695956233210063 & 0.635816941955407 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.00581355032786885 & 0.00660049543348655 & 0.8807748428057 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.00739258418032787 & 0.00621439653638094 & 1.18959003292588 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.00851302073770492 & 0.00567639224490088 & 1.49972383345287 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.00813831114754098 & 0.00557021747750842 & 1.46104010847011 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.00735805213114754 & 0.00542357106444244 & 1.35668032071854 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.00777369076271187 & 0.0108689626323786 & 0.715219200363616 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.0074234411754386 & 0.0105229395313002 & 0.705453181913456 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.00685762090909091 & 0.0101895014217329 & 0.673008484445025 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.00608609032075472 & 0.00984516991178467 & 0.618180323477167 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.00589997692156863 & 0.00961676338850195 & 0.613509627222688 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.00562360475510204 & 0.00935158638958732 & 0.601353024056297 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.00519256591489362 & 0.00904727309070538 & 0.573937125897984 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.0046478264 & 0.00869401211366102 & 0.53460086542746 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.00419073153488372 & 0.00833090155268804 & 0.503034576555708 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.00356640090243902 & 0.0079817772173857 & 0.446817895978202 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.00388730720512821 & 0.00785974978204419 & 0.494584091469281 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.00427118302702703 & 0.00776021353221818 & 0.550395038653808 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.0046061058 & 0.00763942698591083 & 0.602938650830083 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.00486367 & 0.00750909119782298 & 0.64770421238326 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.0050183424516129 & 0.00737514831120705 & 0.680439530143033 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.00510154572413793 & 0.00720373584145335 & 0.70818056580885 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.00500100803703704 & 0.00704112188384609 & 0.710257274271941 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.00465774652 & 0.00689356397359014 & 0.675665959994604 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.00408969886956522 & 0.00681304458128153 & 0.600274784756501 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.0034707380952381 & 0.0066701101111457 & 0.520341948993993 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 0.021085619 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.00289260490000000 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.00501834245161291 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.00501834245161291 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.00501834245161291 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.00501834245161291 &  &  \tabularnewline
Midmean - Closest Observation & 0.00284851115625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.00501834245161291 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.00501834245161291 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19199&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]0.0082101474262295[/C][C]0.0114291533021248[/C][C]0.718351325701718[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.0889097251877916[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.00810097316393443[/C][C]0.0111502480278886[/C][C]0.726528517004518[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.00844377280327869[/C][C]0.0110085322801376[/C][C]0.767020760661579[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.0088686596557377[/C][C]0.0108607091364145[/C][C]0.816582006234041[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.0067085023442623[/C][C]0.0103531978250052[/C][C]0.647964277091262[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.00700999627868852[/C][C]0.0102755125989696[/C][C]0.682204046870759[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.0076162761147541[/C][C]0.0101588317676167[/C][C]0.749719681256315[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.00800556504918033[/C][C]0.0100209628685834[/C][C]0.798881819458535[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.00722554170491803[/C][C]0.00969077564784127[/C][C]0.74561025530785[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.0079674201147541[/C][C]0.00923404695015402[/C][C]0.862830799730903[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.00151470486885246[/C][C]0.00798724816389706[/C][C]0.189640391505429[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.00132603737704918[/C][C]0.00767868173199379[/C][C]0.172690759082272[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.00196515737704918[/C][C]0.00755708675194955[/C][C]0.260041659114501[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.00279471167213115[/C][C]0.00735497059804504[/C][C]0.379975913550761[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.00376321354098361[/C][C]0.00710734829977794[/C][C]0.529482077176545[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.00442500763934426[/C][C]0.00695956233210063[/C][C]0.635816941955407[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.00581355032786885[/C][C]0.00660049543348655[/C][C]0.8807748428057[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.00739258418032787[/C][C]0.00621439653638094[/C][C]1.18959003292588[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.00851302073770492[/C][C]0.00567639224490088[/C][C]1.49972383345287[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.00813831114754098[/C][C]0.00557021747750842[/C][C]1.46104010847011[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.00735805213114754[/C][C]0.00542357106444244[/C][C]1.35668032071854[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.00777369076271187[/C][C]0.0108689626323786[/C][C]0.715219200363616[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.0074234411754386[/C][C]0.0105229395313002[/C][C]0.705453181913456[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.00685762090909091[/C][C]0.0101895014217329[/C][C]0.673008484445025[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.00608609032075472[/C][C]0.00984516991178467[/C][C]0.618180323477167[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.00589997692156863[/C][C]0.00961676338850195[/C][C]0.613509627222688[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.00562360475510204[/C][C]0.00935158638958732[/C][C]0.601353024056297[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.00519256591489362[/C][C]0.00904727309070538[/C][C]0.573937125897984[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.0046478264[/C][C]0.00869401211366102[/C][C]0.53460086542746[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.00419073153488372[/C][C]0.00833090155268804[/C][C]0.503034576555708[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.00356640090243902[/C][C]0.0079817772173857[/C][C]0.446817895978202[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.00388730720512821[/C][C]0.00785974978204419[/C][C]0.494584091469281[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.00427118302702703[/C][C]0.00776021353221818[/C][C]0.550395038653808[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.0046061058[/C][C]0.00763942698591083[/C][C]0.602938650830083[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.00486367[/C][C]0.00750909119782298[/C][C]0.64770421238326[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.0050183424516129[/C][C]0.00737514831120705[/C][C]0.680439530143033[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.00510154572413793[/C][C]0.00720373584145335[/C][C]0.70818056580885[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.00500100803703704[/C][C]0.00704112188384609[/C][C]0.710257274271941[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.00465774652[/C][C]0.00689356397359014[/C][C]0.675665959994604[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.00408969886956522[/C][C]0.00681304458128153[/C][C]0.600274784756501[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.0034707380952381[/C][C]0.0066701101111457[/C][C]0.520341948993993[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.021085619[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.00289260490000000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.00501834245161291[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.00501834245161291[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.00501834245161291[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.00501834245161291[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.00284851115625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.00501834245161291[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.00501834245161291[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19199&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 Mean0.00821014742622950.01142915330212480.718351325701718
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.0889097251877916
Winsorized Mean ( 1 / 20 )0.008100973163934430.01115024802788860.726528517004518
Winsorized Mean ( 2 / 20 )0.008443772803278690.01100853228013760.767020760661579
Winsorized Mean ( 3 / 20 )0.00886865965573770.01086070913641450.816582006234041
Winsorized Mean ( 4 / 20 )0.00670850234426230.01035319782500520.647964277091262
Winsorized Mean ( 5 / 20 )0.007009996278688520.01027551259896960.682204046870759
Winsorized Mean ( 6 / 20 )0.00761627611475410.01015883176761670.749719681256315
Winsorized Mean ( 7 / 20 )0.008005565049180330.01002096286858340.798881819458535
Winsorized Mean ( 8 / 20 )0.007225541704918030.009690775647841270.74561025530785
Winsorized Mean ( 9 / 20 )0.00796742011475410.009234046950154020.862830799730903
Winsorized Mean ( 10 / 20 )0.001514704868852460.007987248163897060.189640391505429
Winsorized Mean ( 11 / 20 )0.001326037377049180.007678681731993790.172690759082272
Winsorized Mean ( 12 / 20 )0.001965157377049180.007557086751949550.260041659114501
Winsorized Mean ( 13 / 20 )0.002794711672131150.007354970598045040.379975913550761
Winsorized Mean ( 14 / 20 )0.003763213540983610.007107348299777940.529482077176545
Winsorized Mean ( 15 / 20 )0.004425007639344260.006959562332100630.635816941955407
Winsorized Mean ( 16 / 20 )0.005813550327868850.006600495433486550.8807748428057
Winsorized Mean ( 17 / 20 )0.007392584180327870.006214396536380941.18959003292588
Winsorized Mean ( 18 / 20 )0.008513020737704920.005676392244900881.49972383345287
Winsorized Mean ( 19 / 20 )0.008138311147540980.005570217477508421.46104010847011
Winsorized Mean ( 20 / 20 )0.007358052131147540.005423571064442441.35668032071854
Trimmed Mean ( 1 / 20 )0.007773690762711870.01086896263237860.715219200363616
Trimmed Mean ( 2 / 20 )0.00742344117543860.01052293953130020.705453181913456
Trimmed Mean ( 3 / 20 )0.006857620909090910.01018950142173290.673008484445025
Trimmed Mean ( 4 / 20 )0.006086090320754720.009845169911784670.618180323477167
Trimmed Mean ( 5 / 20 )0.005899976921568630.009616763388501950.613509627222688
Trimmed Mean ( 6 / 20 )0.005623604755102040.009351586389587320.601353024056297
Trimmed Mean ( 7 / 20 )0.005192565914893620.009047273090705380.573937125897984
Trimmed Mean ( 8 / 20 )0.00464782640.008694012113661020.53460086542746
Trimmed Mean ( 9 / 20 )0.004190731534883720.008330901552688040.503034576555708
Trimmed Mean ( 10 / 20 )0.003566400902439020.00798177721738570.446817895978202
Trimmed Mean ( 11 / 20 )0.003887307205128210.007859749782044190.494584091469281
Trimmed Mean ( 12 / 20 )0.004271183027027030.007760213532218180.550395038653808
Trimmed Mean ( 13 / 20 )0.00460610580.007639426985910830.602938650830083
Trimmed Mean ( 14 / 20 )0.004863670.007509091197822980.64770421238326
Trimmed Mean ( 15 / 20 )0.00501834245161290.007375148311207050.680439530143033
Trimmed Mean ( 16 / 20 )0.005101545724137930.007203735841453350.70818056580885
Trimmed Mean ( 17 / 20 )0.005001008037037040.007041121883846090.710257274271941
Trimmed Mean ( 18 / 20 )0.004657746520.006893563973590140.675665959994604
Trimmed Mean ( 19 / 20 )0.004089698869565220.006813044581281530.600274784756501
Trimmed Mean ( 20 / 20 )0.00347073809523810.00667011011114570.520341948993993
Median0
Midrange0.021085619
Midmean - Weighted Average at Xnp0.00289260490000000
Midmean - Weighted Average at X(n+1)p0.00501834245161291
Midmean - Empirical Distribution Function0.00501834245161291
Midmean - Empirical Distribution Function - Averaging0.00501834245161291
Midmean - Empirical Distribution Function - Interpolation0.00501834245161291
Midmean - Closest Observation0.00284851115625
Midmean - True Basic - Statistics Graphics Toolkit0.00501834245161291
Midmean - MS Excel (old versions)0.00501834245161291
Number of observations61



Parameters (Session):
par1 = 0 ; par2 = 0 ;
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')