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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 computationTue, 27 Oct 2009 06:02:12 -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/2009/Oct/27/t1256645126ec6cn2j10eslj21.htm/, Retrieved Tue, 07 May 2024 11:44:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50918, Retrieved Tue, 07 May 2024 11:44:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmediaan, getrimd gemiddelde
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [median werklooshe...] [2009-10-27 12:02:12] [a54ad7d84632b3d861404e40e79a6400] [Current]
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Dataseries X:
9.3
8.7
8.2
8.3
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.0
8.2
8.1
8.1
8.0
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3




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=50918&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=50918&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50918&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 Mean7.852459016393440.087297198465837889.9508707540754
Geometric Mean7.82220630738301
Harmonic Mean7.79077334126053
Quadratic Mean7.88152019953877
Winsorized Mean ( 1 / 20 )7.847540983606560.083555111140425193.9205379120106
Winsorized Mean ( 2 / 20 )7.850819672131150.082634984811891895.0060036920507
Winsorized Mean ( 3 / 20 )7.855737704918030.081331964631632896.5885644161935
Winsorized Mean ( 4 / 20 )7.86885245901640.0781458977245983100.694376648507
Winsorized Mean ( 5 / 20 )7.877049180327870.0763366659719306103.188278922534
Winsorized Mean ( 6 / 20 )7.86721311475410.0746474889309129105.391530611770
Winsorized Mean ( 7 / 20 )7.878688524590160.0722440745428192109.056536116612
Winsorized Mean ( 8 / 20 )7.878688524590160.0722440745428192109.056536116612
Winsorized Mean ( 9 / 20 )7.86393442622950.0698958157899792112.509373234284
Winsorized Mean ( 10 / 20 )7.880327868852460.0666046024817723118.315064953793
Winsorized Mean ( 11 / 20 )7.89836065573770.0631803647335284125.012900591032
Winsorized Mean ( 12 / 20 )7.89836065573770.0631803647335284125.012900591031
Winsorized Mean ( 13 / 20 )7.919672131147540.0593599592801745133.417748717907
Winsorized Mean ( 14 / 20 )7.896721311475410.0557593979000759141.621351895277
Winsorized Mean ( 15 / 20 )7.872131147540980.0522254019564577150.733758911119
Winsorized Mean ( 16 / 20 )7.89836065573770.0475343880859238166.160983106809
Winsorized Mean ( 17 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 18 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 19 / 20 )7.957377049180330.0282899716145710281.279075058591
Winsorized Mean ( 20 / 20 )7.957377049180330.0282899716145710281.279075058591
Trimmed Mean ( 1 / 20 )7.857627118644070.081489759401895296.424718594289
Trimmed Mean ( 2 / 20 )7.868421052631580.078924390975365499.6956828604169
Trimmed Mean ( 3 / 20 )7.878181818181820.0763516104046705103.182916200807
Trimmed Mean ( 4 / 20 )7.886792452830190.0737763131504186106.901417488161
Trimmed Mean ( 5 / 20 )7.89215686274510.0718300356235851109.872656949564
Trimmed Mean ( 6 / 20 )7.895918367346940.0699829415362552112.826328731215
Trimmed Mean ( 7 / 20 )7.902127659574470.0681111189901064116.018174077015
Trimmed Mean ( 8 / 20 )7.906666666666670.0663933792488438119.088179516098
Trimmed Mean ( 9 / 20 )7.911627906976740.0641158715685458123.395778820826
Trimmed Mean ( 10 / 20 )7.919512195121950.0617053889605258128.343931195187
Trimmed Mean ( 11 / 20 )7.925641025641030.0594302626870287133.360356614592
Trimmed Mean ( 12 / 20 )7.929729729729730.0573259036754344138.327164882144
Trimmed Mean ( 13 / 20 )7.934285714285710.0543785142232081145.908468218123
Trimmed Mean ( 14 / 20 )7.936363636363640.0514594172658839154.225680313430
Trimmed Mean ( 15 / 20 )7.941935483870970.0483655866167518164.206330149632
Trimmed Mean ( 16 / 20 )7.951724137931030.0448370584914623177.347141080746
Trimmed Mean ( 17 / 20 )7.959259259259260.0414341406702771192.094227863856
Trimmed Mean ( 18 / 20 )7.9640.0382448253580359208.237321662305
Trimmed Mean ( 19 / 20 )7.96956521739130.032929906760223242.016027419124
Trimmed Mean ( 20 / 20 )7.971428571428570.0317301547599193251.225644241038
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.9030303030303
Midmean - Weighted Average at X(n+1)p7.9030303030303
Midmean - Empirical Distribution Function7.9030303030303
Midmean - Empirical Distribution Function - Averaging7.9030303030303
Midmean - Empirical Distribution Function - Interpolation7.9030303030303
Midmean - Closest Observation7.9030303030303
Midmean - True Basic - Statistics Graphics Toolkit7.9030303030303
Midmean - MS Excel (old versions)7.9030303030303
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.85245901639344 & 0.0872971984658378 & 89.9508707540754 \tabularnewline
Geometric Mean & 7.82220630738301 &  &  \tabularnewline
Harmonic Mean & 7.79077334126053 &  &  \tabularnewline
Quadratic Mean & 7.88152019953877 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.84754098360656 & 0.0835551111404251 & 93.9205379120106 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.85081967213115 & 0.0826349848118918 & 95.0060036920507 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.85573770491803 & 0.0813319646316328 & 96.5885644161935 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.8688524590164 & 0.0781458977245983 & 100.694376648507 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.87704918032787 & 0.0763366659719306 & 103.188278922534 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.8672131147541 & 0.0746474889309129 & 105.391530611770 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.87868852459016 & 0.0722440745428192 & 109.056536116612 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.87868852459016 & 0.0722440745428192 & 109.056536116612 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.8639344262295 & 0.0698958157899792 & 112.509373234284 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.88032786885246 & 0.0666046024817723 & 118.315064953793 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.8983606557377 & 0.0631803647335284 & 125.012900591032 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.8983606557377 & 0.0631803647335284 & 125.012900591031 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.91967213114754 & 0.0593599592801745 & 133.417748717907 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.89672131147541 & 0.0557593979000759 & 141.621351895277 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.87213114754098 & 0.0522254019564577 & 150.733758911119 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.8983606557377 & 0.0475343880859238 & 166.160983106809 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.92622950819672 & 0.0427792426648031 & 185.282137187484 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.92622950819672 & 0.0427792426648031 & 185.282137187484 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.95737704918033 & 0.0282899716145710 & 281.279075058591 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.95737704918033 & 0.0282899716145710 & 281.279075058591 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.85762711864407 & 0.0814897594018952 & 96.424718594289 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.86842105263158 & 0.0789243909753654 & 99.6956828604169 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.87818181818182 & 0.0763516104046705 & 103.182916200807 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.88679245283019 & 0.0737763131504186 & 106.901417488161 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.8921568627451 & 0.0718300356235851 & 109.872656949564 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.89591836734694 & 0.0699829415362552 & 112.826328731215 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.90212765957447 & 0.0681111189901064 & 116.018174077015 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.90666666666667 & 0.0663933792488438 & 119.088179516098 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.91162790697674 & 0.0641158715685458 & 123.395778820826 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.91951219512195 & 0.0617053889605258 & 128.343931195187 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.92564102564103 & 0.0594302626870287 & 133.360356614592 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.92972972972973 & 0.0573259036754344 & 138.327164882144 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.93428571428571 & 0.0543785142232081 & 145.908468218123 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.93636363636364 & 0.0514594172658839 & 154.225680313430 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.94193548387097 & 0.0483655866167518 & 164.206330149632 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.95172413793103 & 0.0448370584914623 & 177.347141080746 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.95925925925926 & 0.0414341406702771 & 192.094227863856 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.964 & 0.0382448253580359 & 208.237321662305 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.9695652173913 & 0.032929906760223 & 242.016027419124 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.97142857142857 & 0.0317301547599193 & 251.225644241038 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.9030303030303 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.9030303030303 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.9030303030303 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.9030303030303 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.9030303030303 &  &  \tabularnewline
Midmean - Closest Observation & 7.9030303030303 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.9030303030303 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.9030303030303 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50918&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]7.85245901639344[/C][C]0.0872971984658378[/C][C]89.9508707540754[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.82220630738301[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.79077334126053[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.88152019953877[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.84754098360656[/C][C]0.0835551111404251[/C][C]93.9205379120106[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.85081967213115[/C][C]0.0826349848118918[/C][C]95.0060036920507[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.85573770491803[/C][C]0.0813319646316328[/C][C]96.5885644161935[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.8688524590164[/C][C]0.0781458977245983[/C][C]100.694376648507[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.87704918032787[/C][C]0.0763366659719306[/C][C]103.188278922534[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.8672131147541[/C][C]0.0746474889309129[/C][C]105.391530611770[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.87868852459016[/C][C]0.0722440745428192[/C][C]109.056536116612[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.87868852459016[/C][C]0.0722440745428192[/C][C]109.056536116612[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.8639344262295[/C][C]0.0698958157899792[/C][C]112.509373234284[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.88032786885246[/C][C]0.0666046024817723[/C][C]118.315064953793[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.8983606557377[/C][C]0.0631803647335284[/C][C]125.012900591032[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.8983606557377[/C][C]0.0631803647335284[/C][C]125.012900591031[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.91967213114754[/C][C]0.0593599592801745[/C][C]133.417748717907[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.89672131147541[/C][C]0.0557593979000759[/C][C]141.621351895277[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.87213114754098[/C][C]0.0522254019564577[/C][C]150.733758911119[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.8983606557377[/C][C]0.0475343880859238[/C][C]166.160983106809[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.92622950819672[/C][C]0.0427792426648031[/C][C]185.282137187484[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.92622950819672[/C][C]0.0427792426648031[/C][C]185.282137187484[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.95737704918033[/C][C]0.0282899716145710[/C][C]281.279075058591[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.95737704918033[/C][C]0.0282899716145710[/C][C]281.279075058591[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.85762711864407[/C][C]0.0814897594018952[/C][C]96.424718594289[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.86842105263158[/C][C]0.0789243909753654[/C][C]99.6956828604169[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.87818181818182[/C][C]0.0763516104046705[/C][C]103.182916200807[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.88679245283019[/C][C]0.0737763131504186[/C][C]106.901417488161[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.8921568627451[/C][C]0.0718300356235851[/C][C]109.872656949564[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.89591836734694[/C][C]0.0699829415362552[/C][C]112.826328731215[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.90212765957447[/C][C]0.0681111189901064[/C][C]116.018174077015[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.90666666666667[/C][C]0.0663933792488438[/C][C]119.088179516098[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.91162790697674[/C][C]0.0641158715685458[/C][C]123.395778820826[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.91951219512195[/C][C]0.0617053889605258[/C][C]128.343931195187[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.92564102564103[/C][C]0.0594302626870287[/C][C]133.360356614592[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.92972972972973[/C][C]0.0573259036754344[/C][C]138.327164882144[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.93428571428571[/C][C]0.0543785142232081[/C][C]145.908468218123[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.93636363636364[/C][C]0.0514594172658839[/C][C]154.225680313430[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.94193548387097[/C][C]0.0483655866167518[/C][C]164.206330149632[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.95172413793103[/C][C]0.0448370584914623[/C][C]177.347141080746[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.95925925925926[/C][C]0.0414341406702771[/C][C]192.094227863856[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.964[/C][C]0.0382448253580359[/C][C]208.237321662305[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.9695652173913[/C][C]0.032929906760223[/C][C]242.016027419124[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.97142857142857[/C][C]0.0317301547599193[/C][C]251.225644241038[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.9030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.9030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.9030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.9030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.9030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.9030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.9030303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.9030303030303[/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=50918&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50918&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 Mean7.852459016393440.087297198465837889.9508707540754
Geometric Mean7.82220630738301
Harmonic Mean7.79077334126053
Quadratic Mean7.88152019953877
Winsorized Mean ( 1 / 20 )7.847540983606560.083555111140425193.9205379120106
Winsorized Mean ( 2 / 20 )7.850819672131150.082634984811891895.0060036920507
Winsorized Mean ( 3 / 20 )7.855737704918030.081331964631632896.5885644161935
Winsorized Mean ( 4 / 20 )7.86885245901640.0781458977245983100.694376648507
Winsorized Mean ( 5 / 20 )7.877049180327870.0763366659719306103.188278922534
Winsorized Mean ( 6 / 20 )7.86721311475410.0746474889309129105.391530611770
Winsorized Mean ( 7 / 20 )7.878688524590160.0722440745428192109.056536116612
Winsorized Mean ( 8 / 20 )7.878688524590160.0722440745428192109.056536116612
Winsorized Mean ( 9 / 20 )7.86393442622950.0698958157899792112.509373234284
Winsorized Mean ( 10 / 20 )7.880327868852460.0666046024817723118.315064953793
Winsorized Mean ( 11 / 20 )7.89836065573770.0631803647335284125.012900591032
Winsorized Mean ( 12 / 20 )7.89836065573770.0631803647335284125.012900591031
Winsorized Mean ( 13 / 20 )7.919672131147540.0593599592801745133.417748717907
Winsorized Mean ( 14 / 20 )7.896721311475410.0557593979000759141.621351895277
Winsorized Mean ( 15 / 20 )7.872131147540980.0522254019564577150.733758911119
Winsorized Mean ( 16 / 20 )7.89836065573770.0475343880859238166.160983106809
Winsorized Mean ( 17 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 18 / 20 )7.926229508196720.0427792426648031185.282137187484
Winsorized Mean ( 19 / 20 )7.957377049180330.0282899716145710281.279075058591
Winsorized Mean ( 20 / 20 )7.957377049180330.0282899716145710281.279075058591
Trimmed Mean ( 1 / 20 )7.857627118644070.081489759401895296.424718594289
Trimmed Mean ( 2 / 20 )7.868421052631580.078924390975365499.6956828604169
Trimmed Mean ( 3 / 20 )7.878181818181820.0763516104046705103.182916200807
Trimmed Mean ( 4 / 20 )7.886792452830190.0737763131504186106.901417488161
Trimmed Mean ( 5 / 20 )7.89215686274510.0718300356235851109.872656949564
Trimmed Mean ( 6 / 20 )7.895918367346940.0699829415362552112.826328731215
Trimmed Mean ( 7 / 20 )7.902127659574470.0681111189901064116.018174077015
Trimmed Mean ( 8 / 20 )7.906666666666670.0663933792488438119.088179516098
Trimmed Mean ( 9 / 20 )7.911627906976740.0641158715685458123.395778820826
Trimmed Mean ( 10 / 20 )7.919512195121950.0617053889605258128.343931195187
Trimmed Mean ( 11 / 20 )7.925641025641030.0594302626870287133.360356614592
Trimmed Mean ( 12 / 20 )7.929729729729730.0573259036754344138.327164882144
Trimmed Mean ( 13 / 20 )7.934285714285710.0543785142232081145.908468218123
Trimmed Mean ( 14 / 20 )7.936363636363640.0514594172658839154.225680313430
Trimmed Mean ( 15 / 20 )7.941935483870970.0483655866167518164.206330149632
Trimmed Mean ( 16 / 20 )7.951724137931030.0448370584914623177.347141080746
Trimmed Mean ( 17 / 20 )7.959259259259260.0414341406702771192.094227863856
Trimmed Mean ( 18 / 20 )7.9640.0382448253580359208.237321662305
Trimmed Mean ( 19 / 20 )7.96956521739130.032929906760223242.016027419124
Trimmed Mean ( 20 / 20 )7.971428571428570.0317301547599193251.225644241038
Median8
Midrange7.7
Midmean - Weighted Average at Xnp7.9030303030303
Midmean - Weighted Average at X(n+1)p7.9030303030303
Midmean - Empirical Distribution Function7.9030303030303
Midmean - Empirical Distribution Function - Averaging7.9030303030303
Midmean - Empirical Distribution Function - Interpolation7.9030303030303
Midmean - Closest Observation7.9030303030303
Midmean - True Basic - Statistics Graphics Toolkit7.9030303030303
Midmean - MS Excel (old versions)7.9030303030303
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')