Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 23 Oct 2008 05:15:50 -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/23/t12247606038e019zrdlbhp18g.htm/, Retrieved Sun, 19 May 2024 21:23:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18465, Retrieved Sun, 19 May 2024 21:23:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact231
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] [75a00449045803b2332dacf227dc78d5] [Current]
F   P       [Central Tendency] [q6 central tendency] [2008-10-23 12:36:56] [7173087adebe3e3a714c80ea2417b3eb]
-   P         [Central Tendency] [Q6 Central Tendency] [2008-10-24 14:09:17] [7d3039e6253bb5fb3b26df1537d500b4]
F   P         [Central Tendency] [q6] [2008-10-27 10:35:54] [e43247bc0ab243a5af99ac7f55ba0b41]
-   P         [Central Tendency] [Q6 central tendency] [2008-10-27 19:48:51] [c993f605b206b366f754f7f8c1fcc291]
-               [Central Tendency] [Q6 central tendency] [2008-11-02 13:16:52] [c993f605b206b366f754f7f8c1fcc291]
F           [Central Tendency] [] [2008-10-27 17:28:56] [29747f79f5beb5b2516e1271770ecb47]
F           [Central Tendency] [] [2008-10-27 17:30:01] [af90f76a5211a482a7c35f2c76d2fd61]
F           [Central Tendency] [Investigation Dis...] [2008-10-27 19:51:22] [79c17183721a40a589db5f9f561947d8]
F RMPD      [Maximum-likelihood Fitting - Weibull Distribution] [Investigation Dis...] [2008-10-27 20:09:55] [79c17183721a40a589db5f9f561947d8]
F RM D      [Box-Cox Normality Plot] [Investigation Dis...] [2008-10-27 20:20:18] [79c17183721a40a589db5f9f561947d8]
-           [Central Tendency] [investigating dis...] [2008-10-27 20:38:53] [4ad596f10399a71ad29b7d76e6ab90ac]
F RMPD      [Univariate Explorative Data Analysis] [Investigation Dis...] [2008-10-27 20:38:46] [79c17183721a40a589db5f9f561947d8]
-   PD        [Univariate Explorative Data Analysis] [Q7] [2008-10-31 16:10:18] [57850c80fd59ccfb28f882be994e814e]
-   PD        [Univariate Explorative Data Analysis] [verbetering] [2008-11-02 20:06:37] [79c17183721a40a589db5f9f561947d8]
-           [Central Tendency] [Q6 reproductie] [2008-10-29 19:29:49] [ed2ba3b6182103c15c0ab511ae4e6284]
Feedback Forum
2008-10-29 14:18:40 [Tom Ardies] [reply
Ik Tom ardies zal in het vervolg zelf ook bloggen zodat ik geen plagiaat pleeg, maar heb dit samen met Nauwelaerts Toon opgelost.

Het bekomen resultaat klopt en de robuustheid kan men aflezen van de grafieken. Indien men een horizontale lijn trekt en deze tussen de stippelijnen valt dan is dit correct.
2008-11-01 12:41:01 [Matthieu Blondeau] [reply
Het gemiddelde is zo goed als 0.
2008-11-01 19:59:58 [Steffi Van Isveldt] [reply
Je hebt met deze berekening inderdaad aangetoont dat de mean zo goed als 0 is.
2008-11-02 18:50:34 [Annelies Michiels] [reply
Het klopt inderdaad dat als we in plaats van het gemiddelde, de mediaan van het resultaat aftrekken dat men een juister resultaat bekomt.

Goed gevonden!
2008-11-03 09:04:26 [Jeroen Michel] [reply
Dit is inderdaad een correcte uitvoering. Let er in het vervolg wel op dat je inderdaad zorgt voor je eigen blogs. Misschien is het ook handig te kijken naar onderstaande link:

http://www.freestatistics.org/blog/date/2008/Oct/26/t12250256167dp9ltadv8ubjpf.htm
2008-11-03 09:36:46 [Dorien Peeters] [reply
Je hebt aangetoond dat de mean of error gelijk is aan 0.De mean of the error component is niet 0 maar 0.011429. Dwz dat het resultaat redelijk robust is.
2008-11-03 10:01:37 [Dorien Peeters] [reply
Je kan in excel werken maar ook op een andere manier: De oorspronkelijke reeks plakken in central tendency. In de R-code: x<-x-...
Reproduce, descriptive statistics of central tendency aanklikken, en edit underlying code nemen. x<-0.86... (gemiddelde of mediaan) Random component.
Hulp van stippellijn (95% betrouwbaarheid)Ik neem 0 trek horizontale lijn en kijk of deze lijn binnen betrouiwbaarheidsinterval valt.
Antwoord: Het resultaat is robuust, zelfs als we rekening houden met outliers.
2008-11-03 11:19:29 [Astrid Sniekers] [reply
De student de oefening niet correct uitgevoerd. Hieronder vindt u hoe het wel moet.

7. Kopieer het gemiddelde van de oorspronkelijke datareeks
8. Central tendency
9. Voeg in de R-code volgende lijn toe: x <- x - 0.86210009042623

http://www.freestatistics.org/blog/date/2008/Nov/03/t1225707290pyy8qhbkhx639xl.htm

Het gemidddelde van de error component ligt heel dicht bij nul, namelijk 0.0114291533021248 (tweede kolom, arithmetic mean). We kunnen besluiten dat dit een heel robuust resultaat is en dus ongevoelig aan outliers.

Het besluit van de student is wel correct.
2008-11-03 19:31:15 [Joris Deboel] [reply
Je hebt aangetoond dat de mean of error gelijk is aan 0.De mean of the error component is niet 0 maar 0.01142 met andere woorden het resultaat is robuust. Als je de juiste werkwijze duidelijker wil zien moet je naar de uitleg van astrid kijken.
2008-11-03 21:47:39 [Bart Haemels] [reply
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/03/t1225744548etxgp8wm0x8w30z.htm/
In deze link moet je maar eens in de R-code zien, nl. de 1ste lijn.
Je moet x <- x - Arthimetic Mean invoegen. ZO bekom je de robuuste central tendency.

Niet met de mediaan zoals jij zegt in je oplossing.

Post a new message
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=18465&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=18465&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18465&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=18465&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=18465&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18465&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):
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')