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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 14:52:16 -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/20/t1256072154akh0j8rimlhujzw.htm/, Retrieved Thu, 02 May 2024 14:05:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49165, Retrieved Thu, 02 May 2024 14:05:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTotale buitenlandse handel min uitvoer=invoer
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Y[t]-X[t]=c+e[t]] [2009-10-20 20:52:16] [fe64bd97bfa4d92f47365386639c265d] [Current]
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Dataseries X:
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6
18.6
18.1
20.4
18.1
19.6
19.9
19.2
17.8
19.2
22
21.1
19.5
22.2
20.9
22.2
23.5
21.5
24.3
22.8
20.3
23.7
23.3
19.6
18
17.3





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49165&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49165&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49165&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.49508196721310.32069278005224957.6722742688494
Geometric Mean18.3312847093118
Harmonic Mean18.1704907636299
Quadratic Mean18.6611545335381
Winsorized Mean ( 1 / 20 )18.48688524590160.31749941189942658.2265180754342
Winsorized Mean ( 2 / 20 )18.48360655737700.31501739329088858.6748762164673
Winsorized Mean ( 3 / 20 )18.47868852459020.31138782202497259.3430032183733
Winsorized Mean ( 4 / 20 )18.45245901639340.30182148812841361.1369956818405
Winsorized Mean ( 5 / 20 )18.44426229508200.28202550547530465.399270409949
Winsorized Mean ( 6 / 20 )18.47377049180330.27637289333666666.843641099416
Winsorized Mean ( 7 / 20 )18.48524590163930.26504805282001669.7429983165807
Winsorized Mean ( 8 / 20 )18.41967213114750.25108311462303573.3608556624846
Winsorized Mean ( 9 / 20 )18.52295081967210.23389542105923179.1933024416985
Winsorized Mean ( 10 / 20 )18.45737704918030.22037547462537183.7542248317653
Winsorized Mean ( 11 / 20 )18.43934426229510.21046758623437987.6113257732754
Winsorized Mean ( 12 / 20 )18.36065573770490.18896147999235097.1661300411503
Winsorized Mean ( 13 / 20 )18.33934426229510.18516391628386299.043834405513
Winsorized Mean ( 14 / 20 )18.27049180327870.165911034529538110.122222160129
Winsorized Mean ( 15 / 20 )18.22131147540980.150338684202539121.201749051241
Winsorized Mean ( 16 / 20 )18.24754098360660.146257624291052124.763006865844
Winsorized Mean ( 17 / 20 )18.21967213114750.142015539674056128.293510505710
Winsorized Mean ( 18 / 20 )18.19016393442620.137636269643908132.161122802062
Winsorized Mean ( 19 / 20 )18.22131147540980.123498960286289147.542225725384
Winsorized Mean ( 20 / 20 )18.22131147540980.113828428894460160.076982985545
Trimmed Mean ( 1 / 20 )18.46949152542370.30781041017269860.0028163929263
Trimmed Mean ( 2 / 20 )18.45087719298250.29589000453008262.3572169066179
Trimmed Mean ( 3 / 20 )18.43272727272730.28280764715483965.1776126217521
Trimmed Mean ( 4 / 20 )18.41509433962260.26828483101833468.6400877370669
Trimmed Mean ( 5 / 20 )18.40392156862740.25404894980412472.4424233314768
Trimmed Mean ( 6 / 20 )18.39387755102040.24331903141385175.595720746295
Trimmed Mean ( 7 / 20 )18.37659574468090.23141787885274879.4087122212969
Trimmed Mean ( 8 / 20 )18.35555555555560.21958536582477383.5918891343746
Trimmed Mean ( 9 / 20 )18.34418604651160.20852013310226387.9732128192878
Trimmed Mean ( 10 / 20 )18.31463414634150.19870191474183292.171402425272
Trimmed Mean ( 11 / 20 )18.29230769230770.18965785713152696.448984339321
Trimmed Mean ( 12 / 20 )18.27027027027030.18025111216414101.360097315977
Trimmed Mean ( 13 / 20 )18.25714285714290.173800122534586105.046777820940
Trimmed Mean ( 14 / 20 )18.24545454545450.165779318279290110.058689677540
Trimmed Mean ( 15 / 20 )18.24193548387100.16029369506771113.803200282864
Trimmed Mean ( 16 / 20 )18.24482758620690.156830224707129116.334894120556
Trimmed Mean ( 17 / 20 )18.24444444444440.152503639051750119.632846520163
Trimmed Mean ( 18 / 20 )18.2480.146869556636720124.246306844489
Trimmed Mean ( 19 / 20 )18.25652173913040.139142786013028131.207102159224
Trimmed Mean ( 20 / 20 )18.26190476190480.132463146802312137.864041454177
Median18.1
Midrange19.25
Midmean - Weighted Average at Xnp18.2419354838710
Midmean - Weighted Average at X(n+1)p18.2419354838710
Midmean - Empirical Distribution Function18.2419354838710
Midmean - Empirical Distribution Function - Averaging18.2419354838710
Midmean - Empirical Distribution Function - Interpolation18.2419354838710
Midmean - Closest Observation18.19375
Midmean - True Basic - Statistics Graphics Toolkit18.2419354838710
Midmean - MS Excel (old versions)18.2419354838710
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.4950819672131 & 0.320692780052249 & 57.6722742688494 \tabularnewline
Geometric Mean & 18.3312847093118 &  &  \tabularnewline
Harmonic Mean & 18.1704907636299 &  &  \tabularnewline
Quadratic Mean & 18.6611545335381 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18.4868852459016 & 0.317499411899426 & 58.2265180754342 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18.4836065573770 & 0.315017393290888 & 58.6748762164673 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18.4786885245902 & 0.311387822024972 & 59.3430032183733 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18.4524590163934 & 0.301821488128413 & 61.1369956818405 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18.4442622950820 & 0.282025505475304 & 65.399270409949 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18.4737704918033 & 0.276372893336666 & 66.843641099416 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18.4852459016393 & 0.265048052820016 & 69.7429983165807 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18.4196721311475 & 0.251083114623035 & 73.3608556624846 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18.5229508196721 & 0.233895421059231 & 79.1933024416985 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18.4573770491803 & 0.220375474625371 & 83.7542248317653 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18.4393442622951 & 0.210467586234379 & 87.6113257732754 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18.3606557377049 & 0.188961479992350 & 97.1661300411503 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18.3393442622951 & 0.185163916283862 & 99.043834405513 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18.2704918032787 & 0.165911034529538 & 110.122222160129 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18.2213114754098 & 0.150338684202539 & 121.201749051241 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18.2475409836066 & 0.146257624291052 & 124.763006865844 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18.2196721311475 & 0.142015539674056 & 128.293510505710 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18.1901639344262 & 0.137636269643908 & 132.161122802062 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18.2213114754098 & 0.123498960286289 & 147.542225725384 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18.2213114754098 & 0.113828428894460 & 160.076982985545 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18.4694915254237 & 0.307810410172698 & 60.0028163929263 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18.4508771929825 & 0.295890004530082 & 62.3572169066179 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18.4327272727273 & 0.282807647154839 & 65.1776126217521 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18.4150943396226 & 0.268284831018334 & 68.6400877370669 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18.4039215686274 & 0.254048949804124 & 72.4424233314768 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18.3938775510204 & 0.243319031413851 & 75.595720746295 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18.3765957446809 & 0.231417878852748 & 79.4087122212969 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18.3555555555556 & 0.219585365824773 & 83.5918891343746 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18.3441860465116 & 0.208520133102263 & 87.9732128192878 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18.3146341463415 & 0.198701914741832 & 92.171402425272 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18.2923076923077 & 0.189657857131526 & 96.448984339321 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18.2702702702703 & 0.18025111216414 & 101.360097315977 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18.2571428571429 & 0.173800122534586 & 105.046777820940 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18.2454545454545 & 0.165779318279290 & 110.058689677540 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18.2419354838710 & 0.16029369506771 & 113.803200282864 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18.2448275862069 & 0.156830224707129 & 116.334894120556 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18.2444444444444 & 0.152503639051750 & 119.632846520163 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18.248 & 0.146869556636720 & 124.246306844489 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18.2565217391304 & 0.139142786013028 & 131.207102159224 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18.2619047619048 & 0.132463146802312 & 137.864041454177 \tabularnewline
Median & 18.1 &  &  \tabularnewline
Midrange & 19.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.2419354838710 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18.2419354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.2419354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18.2419354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18.2419354838710 &  &  \tabularnewline
Midmean - Closest Observation & 18.19375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18.2419354838710 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18.2419354838710 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49165&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]18.4950819672131[/C][C]0.320692780052249[/C][C]57.6722742688494[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18.3312847093118[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18.1704907636299[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18.6611545335381[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18.4868852459016[/C][C]0.317499411899426[/C][C]58.2265180754342[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18.4836065573770[/C][C]0.315017393290888[/C][C]58.6748762164673[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18.4786885245902[/C][C]0.311387822024972[/C][C]59.3430032183733[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18.4524590163934[/C][C]0.301821488128413[/C][C]61.1369956818405[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18.4442622950820[/C][C]0.282025505475304[/C][C]65.399270409949[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18.4737704918033[/C][C]0.276372893336666[/C][C]66.843641099416[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18.4852459016393[/C][C]0.265048052820016[/C][C]69.7429983165807[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18.4196721311475[/C][C]0.251083114623035[/C][C]73.3608556624846[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18.5229508196721[/C][C]0.233895421059231[/C][C]79.1933024416985[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18.4573770491803[/C][C]0.220375474625371[/C][C]83.7542248317653[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18.4393442622951[/C][C]0.210467586234379[/C][C]87.6113257732754[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18.3606557377049[/C][C]0.188961479992350[/C][C]97.1661300411503[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18.3393442622951[/C][C]0.185163916283862[/C][C]99.043834405513[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18.2704918032787[/C][C]0.165911034529538[/C][C]110.122222160129[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18.2213114754098[/C][C]0.150338684202539[/C][C]121.201749051241[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18.2475409836066[/C][C]0.146257624291052[/C][C]124.763006865844[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18.2196721311475[/C][C]0.142015539674056[/C][C]128.293510505710[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18.1901639344262[/C][C]0.137636269643908[/C][C]132.161122802062[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18.2213114754098[/C][C]0.123498960286289[/C][C]147.542225725384[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18.2213114754098[/C][C]0.113828428894460[/C][C]160.076982985545[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18.4694915254237[/C][C]0.307810410172698[/C][C]60.0028163929263[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18.4508771929825[/C][C]0.295890004530082[/C][C]62.3572169066179[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18.4327272727273[/C][C]0.282807647154839[/C][C]65.1776126217521[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18.4150943396226[/C][C]0.268284831018334[/C][C]68.6400877370669[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18.4039215686274[/C][C]0.254048949804124[/C][C]72.4424233314768[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18.3938775510204[/C][C]0.243319031413851[/C][C]75.595720746295[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18.3765957446809[/C][C]0.231417878852748[/C][C]79.4087122212969[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18.3555555555556[/C][C]0.219585365824773[/C][C]83.5918891343746[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18.3441860465116[/C][C]0.208520133102263[/C][C]87.9732128192878[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18.3146341463415[/C][C]0.198701914741832[/C][C]92.171402425272[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18.2923076923077[/C][C]0.189657857131526[/C][C]96.448984339321[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18.2702702702703[/C][C]0.18025111216414[/C][C]101.360097315977[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18.2571428571429[/C][C]0.173800122534586[/C][C]105.046777820940[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18.2454545454545[/C][C]0.165779318279290[/C][C]110.058689677540[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18.2419354838710[/C][C]0.16029369506771[/C][C]113.803200282864[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18.2448275862069[/C][C]0.156830224707129[/C][C]116.334894120556[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18.2444444444444[/C][C]0.152503639051750[/C][C]119.632846520163[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18.248[/C][C]0.146869556636720[/C][C]124.246306844489[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18.2565217391304[/C][C]0.139142786013028[/C][C]131.207102159224[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18.2619047619048[/C][C]0.132463146802312[/C][C]137.864041454177[/C][/ROW]
[ROW][C]Median[/C][C]18.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.2419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18.2419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.2419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18.2419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18.2419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.19375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18.2419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18.2419354838710[/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=49165&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49165&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 Mean18.49508196721310.32069278005224957.6722742688494
Geometric Mean18.3312847093118
Harmonic Mean18.1704907636299
Quadratic Mean18.6611545335381
Winsorized Mean ( 1 / 20 )18.48688524590160.31749941189942658.2265180754342
Winsorized Mean ( 2 / 20 )18.48360655737700.31501739329088858.6748762164673
Winsorized Mean ( 3 / 20 )18.47868852459020.31138782202497259.3430032183733
Winsorized Mean ( 4 / 20 )18.45245901639340.30182148812841361.1369956818405
Winsorized Mean ( 5 / 20 )18.44426229508200.28202550547530465.399270409949
Winsorized Mean ( 6 / 20 )18.47377049180330.27637289333666666.843641099416
Winsorized Mean ( 7 / 20 )18.48524590163930.26504805282001669.7429983165807
Winsorized Mean ( 8 / 20 )18.41967213114750.25108311462303573.3608556624846
Winsorized Mean ( 9 / 20 )18.52295081967210.23389542105923179.1933024416985
Winsorized Mean ( 10 / 20 )18.45737704918030.22037547462537183.7542248317653
Winsorized Mean ( 11 / 20 )18.43934426229510.21046758623437987.6113257732754
Winsorized Mean ( 12 / 20 )18.36065573770490.18896147999235097.1661300411503
Winsorized Mean ( 13 / 20 )18.33934426229510.18516391628386299.043834405513
Winsorized Mean ( 14 / 20 )18.27049180327870.165911034529538110.122222160129
Winsorized Mean ( 15 / 20 )18.22131147540980.150338684202539121.201749051241
Winsorized Mean ( 16 / 20 )18.24754098360660.146257624291052124.763006865844
Winsorized Mean ( 17 / 20 )18.21967213114750.142015539674056128.293510505710
Winsorized Mean ( 18 / 20 )18.19016393442620.137636269643908132.161122802062
Winsorized Mean ( 19 / 20 )18.22131147540980.123498960286289147.542225725384
Winsorized Mean ( 20 / 20 )18.22131147540980.113828428894460160.076982985545
Trimmed Mean ( 1 / 20 )18.46949152542370.30781041017269860.0028163929263
Trimmed Mean ( 2 / 20 )18.45087719298250.29589000453008262.3572169066179
Trimmed Mean ( 3 / 20 )18.43272727272730.28280764715483965.1776126217521
Trimmed Mean ( 4 / 20 )18.41509433962260.26828483101833468.6400877370669
Trimmed Mean ( 5 / 20 )18.40392156862740.25404894980412472.4424233314768
Trimmed Mean ( 6 / 20 )18.39387755102040.24331903141385175.595720746295
Trimmed Mean ( 7 / 20 )18.37659574468090.23141787885274879.4087122212969
Trimmed Mean ( 8 / 20 )18.35555555555560.21958536582477383.5918891343746
Trimmed Mean ( 9 / 20 )18.34418604651160.20852013310226387.9732128192878
Trimmed Mean ( 10 / 20 )18.31463414634150.19870191474183292.171402425272
Trimmed Mean ( 11 / 20 )18.29230769230770.18965785713152696.448984339321
Trimmed Mean ( 12 / 20 )18.27027027027030.18025111216414101.360097315977
Trimmed Mean ( 13 / 20 )18.25714285714290.173800122534586105.046777820940
Trimmed Mean ( 14 / 20 )18.24545454545450.165779318279290110.058689677540
Trimmed Mean ( 15 / 20 )18.24193548387100.16029369506771113.803200282864
Trimmed Mean ( 16 / 20 )18.24482758620690.156830224707129116.334894120556
Trimmed Mean ( 17 / 20 )18.24444444444440.152503639051750119.632846520163
Trimmed Mean ( 18 / 20 )18.2480.146869556636720124.246306844489
Trimmed Mean ( 19 / 20 )18.25652173913040.139142786013028131.207102159224
Trimmed Mean ( 20 / 20 )18.26190476190480.132463146802312137.864041454177
Median18.1
Midrange19.25
Midmean - Weighted Average at Xnp18.2419354838710
Midmean - Weighted Average at X(n+1)p18.2419354838710
Midmean - Empirical Distribution Function18.2419354838710
Midmean - Empirical Distribution Function - Averaging18.2419354838710
Midmean - Empirical Distribution Function - Interpolation18.2419354838710
Midmean - Closest Observation18.19375
Midmean - True Basic - Statistics Graphics Toolkit18.2419354838710
Midmean - MS Excel (old versions)18.2419354838710
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')