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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, 20 Oct 2008 16:47:54 -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/21/t1224542936bs1rccrkorr5i4t.htm/, Retrieved Sun, 19 May 2024 19:19:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18281, Retrieved Sun, 19 May 2024 19:19:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Invoer België VS] [2008-10-13 18:50:00] [b8fbc01255310b0d45a84fea6711862e]
F RMPD    [Central Tendency] [Central Tendency ...] [2008-10-20 22:47:54] [21d7d81e7693ad6dde5aadefb1046611] [Current]
Feedback Forum
2008-10-23 14:47:11 [Thomas Beyers] [reply
Trimmed mean: op einde van datareeks zitten toch enkele outliers. trimmed mean buigt op laatst naar beneden (grafiek) , gaat van 87 naar 86,6 .
Winsorizd mean is tamelijk robuust
2008-10-25 13:57:15 [Astrid Sniekers] [reply
Q8:

De student heeft geen gebruik gemaakt van EDA-technieken en heeft de oefening bijgevolg niet opgelost. Hij had zes back-to-back histogrammen moeten maken voor zijn datareeksen te kunnen vergelijken.
Ook weet ik niet welke tijdreeksen de student heeft gekozen. Ik heb geen gegevens of grafieken van de tijdreeksen.

Q9:

Ik heb geen grafieken van de student zijn tijdreeksen, waardoor ik niet kan zien hoe de tijdreeks van invoer uit de VS naar België verloopt. Bijgevolg weet ik ook niet of de berekening die de student heeft gedaan juist is. Als de berekening klopt, gaat de tijdreeks volgens mij eerder stabiel verder lopen.
2008-10-26 22:31:02 [Elias Van Deun] [reply
Moeilijk om na te gaan of de berekening correct is aangezien er geen tijdreeksen zijn bijgevoegd. Het is wel goed dat zij opmerkt dat er invloedrijke externe factoren aanwezig kunnen zijn.
2008-10-27 22:01:42 [Steven Symons] [reply
door het feit dat de student geen tijdreeksen in bijlage heeft, kan deze oefn niet nagekeken worden.
wat we uit de grafiek kunnen afleiden is dat er toch sprake is van enkele outliers, dit zien we door de grote uitschieters aan het begin van de grafiek of door het feit dat er een verschil is tussen de midrange , het gemiddelde en de mediaan.

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Dataseries X:
882.5
789.6
773.3
804.3
817.8
836.7
721.8
760.8
841.4
1045.6
949.2
850.1
957.4
851.8
913.9
888.0
973.8
927.6
833.0
879.5
797.3
834.5
735.1
835.0
892.8
697.2
821.1
732.7
797.6
866.3
826.3
778.6
779.2
951.0
692.3
841.4
857.3
760.7
841.2
810.3
1007.4
931.3
931.2
855.8
858.4
925.9
930.7
1037.6
979.2
942.6
843.9
854.3
1029.8
944.0
856.4
1059.4
959.3
941.5
1026.4
921.3
968.0




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18281&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18281&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean872.9573770491811.391871672960776.6298464475507
Geometric Mean868.488552036185
Harmonic Mean864.011695432307
Quadratic Mean877.405873331936
Winsorized Mean ( 1 / 20 )872.81147540983611.311201976579577.1634594817635
Winsorized Mean ( 2 / 20 )873.35573770491811.048616985525579.0466117930487
Winsorized Mean ( 3 / 20 )873.50819672131110.835612781227980.6145636945068
Winsorized Mean ( 4 / 20 )873.4426229508210.748450252764681.2621915169736
Winsorized Mean ( 5 / 20 )873.9836065573779.964734862308687.7076629367431
Winsorized Mean ( 6 / 20 )871.2196721311479.3861395952191592.8198076848234
Winsorized Mean ( 7 / 20 )872.0344262295088.996283654460296.9327401984673
Winsorized Mean ( 8 / 20 )871.9688524590168.7292653754165399.8902903003346
Winsorized Mean ( 9 / 20 )870.7737704918038.48403737455774102.636720236890
Winsorized Mean ( 10 / 20 )872.1672131147548.13194897337208107.251928900519
Winsorized Mean ( 11 / 20 )872.4016393442627.70250101026496113.262125922688
Winsorized Mean ( 12 / 20 )872.106557377057.63298954132597114.254913183800
Winsorized Mean ( 13 / 20 )872.4262295081977.21957792903706120.841722062353
Winsorized Mean ( 14 / 20 )873.4819672131156.95379344057542125.612297040108
Winsorized Mean ( 15 / 20 )875.0557377049186.63642396816178131.856515180916
Winsorized Mean ( 16 / 20 )873.2459016393446.07556315218862143.730857496687
Winsorized Mean ( 17 / 20 )874.6672131147545.86784035141382149.061181070478
Winsorized Mean ( 18 / 20 )876.4967213114755.57962871985563157.088717783744
Winsorized Mean ( 19 / 20 )875.9983606557385.36355312651991163.324262851876
Winsorized Mean ( 20 / 20 )875.6049180327875.25326514454104166.678226577365
Trimmed Mean ( 1 / 20 )872.85932203389810.913520137526379.9796317810015
Trimmed Mean ( 2 / 20 )872.9105263157910.424591276617483.7357075354839
Trimmed Mean ( 3 / 20 )872.6636363636369.998669730925487.2779739553283
Trimmed Mean ( 4 / 20 )872.339622641519.5742792911535691.1128238600198
Trimmed Mean ( 5 / 20 )872.0098039215699.0761247906205796.0773263962522
Trimmed Mean ( 6 / 20 )871.5183673469398.7318006425636299.8096959633592
Trimmed Mean ( 7 / 20 )871.5829787234048.48006331418956102.780244254191
Trimmed Mean ( 8 / 20 )871.4955555555568.26836490105056105.401196728125
Trimmed Mean ( 9 / 20 )871.4116279069778.06333608423553108.070855388337
Trimmed Mean ( 10 / 20 )871.5170731707327.85515203190736110.948466640831
Trimmed Mean ( 11 / 20 )871.4153846153857.66658939566312113.664021854142
Trimmed Mean ( 12 / 20 )871.2675675675687.51771187281166115.895312604167
Trimmed Mean ( 13 / 20 )871.1457142857147.32088108631413118.994654333924
Trimmed Mean ( 14 / 20 )870.9636363636367.1510499575844121.79521070747
Trimmed Mean ( 15 / 20 )870.6096774193556.97040495705584124.900874882179
Trimmed Mean ( 16 / 20 )869.9862068965526.78304849606348128.25888056107
Trimmed Mean ( 17 / 20 )869.5259259259266.66719568967803130.418539727595
Trimmed Mean ( 18 / 20 )868.7886.52165193796786133.215941032068
Trimmed Mean ( 19 / 20 )867.6521739130436.34570867278746136.730540063055
Trimmed Mean ( 20 / 20 )866.376190476196.10398349542916141.936194802125
Median856.4
Midrange875.85
Midmean - Weighted Average at Xnp868.246666666667
Midmean - Weighted Average at X(n+1)p870.609677419355
Midmean - Empirical Distribution Function870.609677419355
Midmean - Empirical Distribution Function - Averaging870.609677419355
Midmean - Empirical Distribution Function - Interpolation870.609677419355
Midmean - Closest Observation868.725
Midmean - True Basic - Statistics Graphics Toolkit870.609677419355
Midmean - MS Excel (old versions)870.609677419355
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 872.95737704918 & 11.3918716729607 & 76.6298464475507 \tabularnewline
Geometric Mean & 868.488552036185 &  &  \tabularnewline
Harmonic Mean & 864.011695432307 &  &  \tabularnewline
Quadratic Mean & 877.405873331936 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 872.811475409836 & 11.3112019765795 & 77.1634594817635 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 873.355737704918 & 11.0486169855255 & 79.0466117930487 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 873.508196721311 & 10.8356127812279 & 80.6145636945068 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 873.44262295082 & 10.7484502527646 & 81.2621915169736 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 873.983606557377 & 9.9647348623086 & 87.7076629367431 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 871.219672131147 & 9.38613959521915 & 92.8198076848234 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 872.034426229508 & 8.9962836544602 & 96.9327401984673 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 871.968852459016 & 8.72926537541653 & 99.8902903003346 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 870.773770491803 & 8.48403737455774 & 102.636720236890 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 872.167213114754 & 8.13194897337208 & 107.251928900519 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 872.401639344262 & 7.70250101026496 & 113.262125922688 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 872.10655737705 & 7.63298954132597 & 114.254913183800 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 872.426229508197 & 7.21957792903706 & 120.841722062353 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 873.481967213115 & 6.95379344057542 & 125.612297040108 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 875.055737704918 & 6.63642396816178 & 131.856515180916 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 873.245901639344 & 6.07556315218862 & 143.730857496687 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 874.667213114754 & 5.86784035141382 & 149.061181070478 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 876.496721311475 & 5.57962871985563 & 157.088717783744 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 875.998360655738 & 5.36355312651991 & 163.324262851876 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 875.604918032787 & 5.25326514454104 & 166.678226577365 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 872.859322033898 & 10.9135201375263 & 79.9796317810015 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 872.91052631579 & 10.4245912766174 & 83.7357075354839 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 872.663636363636 & 9.9986697309254 & 87.2779739553283 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 872.33962264151 & 9.57427929115356 & 91.1128238600198 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 872.009803921569 & 9.07612479062057 & 96.0773263962522 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 871.518367346939 & 8.73180064256362 & 99.8096959633592 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 871.582978723404 & 8.48006331418956 & 102.780244254191 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 871.495555555556 & 8.26836490105056 & 105.401196728125 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 871.411627906977 & 8.06333608423553 & 108.070855388337 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 871.517073170732 & 7.85515203190736 & 110.948466640831 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 871.415384615385 & 7.66658939566312 & 113.664021854142 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 871.267567567568 & 7.51771187281166 & 115.895312604167 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 871.145714285714 & 7.32088108631413 & 118.994654333924 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 870.963636363636 & 7.1510499575844 & 121.79521070747 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 870.609677419355 & 6.97040495705584 & 124.900874882179 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 869.986206896552 & 6.78304849606348 & 128.25888056107 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 869.525925925926 & 6.66719568967803 & 130.418539727595 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 868.788 & 6.52165193796786 & 133.215941032068 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 867.652173913043 & 6.34570867278746 & 136.730540063055 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 866.37619047619 & 6.10398349542916 & 141.936194802125 \tabularnewline
Median & 856.4 &  &  \tabularnewline
Midrange & 875.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 868.246666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 870.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 870.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 870.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 870.609677419355 &  &  \tabularnewline
Midmean - Closest Observation & 868.725 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 870.609677419355 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 870.609677419355 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18281&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]872.95737704918[/C][C]11.3918716729607[/C][C]76.6298464475507[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]868.488552036185[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]864.011695432307[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]877.405873331936[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]872.811475409836[/C][C]11.3112019765795[/C][C]77.1634594817635[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]873.355737704918[/C][C]11.0486169855255[/C][C]79.0466117930487[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]873.508196721311[/C][C]10.8356127812279[/C][C]80.6145636945068[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]873.44262295082[/C][C]10.7484502527646[/C][C]81.2621915169736[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]873.983606557377[/C][C]9.9647348623086[/C][C]87.7076629367431[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]871.219672131147[/C][C]9.38613959521915[/C][C]92.8198076848234[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]872.034426229508[/C][C]8.9962836544602[/C][C]96.9327401984673[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]871.968852459016[/C][C]8.72926537541653[/C][C]99.8902903003346[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]870.773770491803[/C][C]8.48403737455774[/C][C]102.636720236890[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]872.167213114754[/C][C]8.13194897337208[/C][C]107.251928900519[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]872.401639344262[/C][C]7.70250101026496[/C][C]113.262125922688[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]872.10655737705[/C][C]7.63298954132597[/C][C]114.254913183800[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]872.426229508197[/C][C]7.21957792903706[/C][C]120.841722062353[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]873.481967213115[/C][C]6.95379344057542[/C][C]125.612297040108[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]875.055737704918[/C][C]6.63642396816178[/C][C]131.856515180916[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]873.245901639344[/C][C]6.07556315218862[/C][C]143.730857496687[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]874.667213114754[/C][C]5.86784035141382[/C][C]149.061181070478[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]876.496721311475[/C][C]5.57962871985563[/C][C]157.088717783744[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]875.998360655738[/C][C]5.36355312651991[/C][C]163.324262851876[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]875.604918032787[/C][C]5.25326514454104[/C][C]166.678226577365[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]872.859322033898[/C][C]10.9135201375263[/C][C]79.9796317810015[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]872.91052631579[/C][C]10.4245912766174[/C][C]83.7357075354839[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]872.663636363636[/C][C]9.9986697309254[/C][C]87.2779739553283[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]872.33962264151[/C][C]9.57427929115356[/C][C]91.1128238600198[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]872.009803921569[/C][C]9.07612479062057[/C][C]96.0773263962522[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]871.518367346939[/C][C]8.73180064256362[/C][C]99.8096959633592[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]871.582978723404[/C][C]8.48006331418956[/C][C]102.780244254191[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]871.495555555556[/C][C]8.26836490105056[/C][C]105.401196728125[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]871.411627906977[/C][C]8.06333608423553[/C][C]108.070855388337[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]871.517073170732[/C][C]7.85515203190736[/C][C]110.948466640831[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]871.415384615385[/C][C]7.66658939566312[/C][C]113.664021854142[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]871.267567567568[/C][C]7.51771187281166[/C][C]115.895312604167[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]871.145714285714[/C][C]7.32088108631413[/C][C]118.994654333924[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]870.963636363636[/C][C]7.1510499575844[/C][C]121.79521070747[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]870.609677419355[/C][C]6.97040495705584[/C][C]124.900874882179[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]869.986206896552[/C][C]6.78304849606348[/C][C]128.25888056107[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]869.525925925926[/C][C]6.66719568967803[/C][C]130.418539727595[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]868.788[/C][C]6.52165193796786[/C][C]133.215941032068[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]867.652173913043[/C][C]6.34570867278746[/C][C]136.730540063055[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]866.37619047619[/C][C]6.10398349542916[/C][C]141.936194802125[/C][/ROW]
[ROW][C]Median[/C][C]856.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]875.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]868.246666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]870.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]870.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]870.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]870.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]868.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]870.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]870.609677419355[/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=18281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18281&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 Mean872.9573770491811.391871672960776.6298464475507
Geometric Mean868.488552036185
Harmonic Mean864.011695432307
Quadratic Mean877.405873331936
Winsorized Mean ( 1 / 20 )872.81147540983611.311201976579577.1634594817635
Winsorized Mean ( 2 / 20 )873.35573770491811.048616985525579.0466117930487
Winsorized Mean ( 3 / 20 )873.50819672131110.835612781227980.6145636945068
Winsorized Mean ( 4 / 20 )873.4426229508210.748450252764681.2621915169736
Winsorized Mean ( 5 / 20 )873.9836065573779.964734862308687.7076629367431
Winsorized Mean ( 6 / 20 )871.2196721311479.3861395952191592.8198076848234
Winsorized Mean ( 7 / 20 )872.0344262295088.996283654460296.9327401984673
Winsorized Mean ( 8 / 20 )871.9688524590168.7292653754165399.8902903003346
Winsorized Mean ( 9 / 20 )870.7737704918038.48403737455774102.636720236890
Winsorized Mean ( 10 / 20 )872.1672131147548.13194897337208107.251928900519
Winsorized Mean ( 11 / 20 )872.4016393442627.70250101026496113.262125922688
Winsorized Mean ( 12 / 20 )872.106557377057.63298954132597114.254913183800
Winsorized Mean ( 13 / 20 )872.4262295081977.21957792903706120.841722062353
Winsorized Mean ( 14 / 20 )873.4819672131156.95379344057542125.612297040108
Winsorized Mean ( 15 / 20 )875.0557377049186.63642396816178131.856515180916
Winsorized Mean ( 16 / 20 )873.2459016393446.07556315218862143.730857496687
Winsorized Mean ( 17 / 20 )874.6672131147545.86784035141382149.061181070478
Winsorized Mean ( 18 / 20 )876.4967213114755.57962871985563157.088717783744
Winsorized Mean ( 19 / 20 )875.9983606557385.36355312651991163.324262851876
Winsorized Mean ( 20 / 20 )875.6049180327875.25326514454104166.678226577365
Trimmed Mean ( 1 / 20 )872.85932203389810.913520137526379.9796317810015
Trimmed Mean ( 2 / 20 )872.9105263157910.424591276617483.7357075354839
Trimmed Mean ( 3 / 20 )872.6636363636369.998669730925487.2779739553283
Trimmed Mean ( 4 / 20 )872.339622641519.5742792911535691.1128238600198
Trimmed Mean ( 5 / 20 )872.0098039215699.0761247906205796.0773263962522
Trimmed Mean ( 6 / 20 )871.5183673469398.7318006425636299.8096959633592
Trimmed Mean ( 7 / 20 )871.5829787234048.48006331418956102.780244254191
Trimmed Mean ( 8 / 20 )871.4955555555568.26836490105056105.401196728125
Trimmed Mean ( 9 / 20 )871.4116279069778.06333608423553108.070855388337
Trimmed Mean ( 10 / 20 )871.5170731707327.85515203190736110.948466640831
Trimmed Mean ( 11 / 20 )871.4153846153857.66658939566312113.664021854142
Trimmed Mean ( 12 / 20 )871.2675675675687.51771187281166115.895312604167
Trimmed Mean ( 13 / 20 )871.1457142857147.32088108631413118.994654333924
Trimmed Mean ( 14 / 20 )870.9636363636367.1510499575844121.79521070747
Trimmed Mean ( 15 / 20 )870.6096774193556.97040495705584124.900874882179
Trimmed Mean ( 16 / 20 )869.9862068965526.78304849606348128.25888056107
Trimmed Mean ( 17 / 20 )869.5259259259266.66719568967803130.418539727595
Trimmed Mean ( 18 / 20 )868.7886.52165193796786133.215941032068
Trimmed Mean ( 19 / 20 )867.6521739130436.34570867278746136.730540063055
Trimmed Mean ( 20 / 20 )866.376190476196.10398349542916141.936194802125
Median856.4
Midrange875.85
Midmean - Weighted Average at Xnp868.246666666667
Midmean - Weighted Average at X(n+1)p870.609677419355
Midmean - Empirical Distribution Function870.609677419355
Midmean - Empirical Distribution Function - Averaging870.609677419355
Midmean - Empirical Distribution Function - Interpolation870.609677419355
Midmean - Closest Observation868.725
Midmean - True Basic - Statistics Graphics Toolkit870.609677419355
Midmean - MS Excel (old versions)870.609677419355
Number of observations61



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;
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')