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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 computationWed, 21 Oct 2009 09:09:05 -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/21/t1256137830tb5914fmjybk77r.htm/, Retrieved Thu, 02 May 2024 11:26:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49401, Retrieved Thu, 02 May 2024 11:26:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsworkshop 3 deel 2.1 central tendency
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3 deel 2...] [2009-10-21 15:09:05] [6198946fb53eb5eb18db46bb758f7fde] [Current]
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Dataseries X:
0,6089
0,6086
0,6267
0,6229
0,6239
0,6184
0,6201
0,6166
0,6116
0,6157
0,6141
0,6282
0,6441
0,6387
0,6363
0,6306
0,6299
0,6371
0,6422
0,6571
0,6698
0,6826
0,689
0,7132
0,7022
0,7005
0,6992
0,6969
0,6976
0,6928
0,702
0,6922
0,6769
0,6712
0,6653
0,6716
0,6643
0,6658
0,6694
0,6813
0,6914
0,6986
0,695
0,6987
0,6897
0,6923
0,6829
0,684
0,669
0,6876
0,6853
0,6776
0,6814
0,6793
0,6792
0,686
0,683
0,6894
0,6946
0,6833
0,6867
0,6878
0,6767
0,6751
0,6725
0,674
0,6729
0,6634
0,668
0,6802
0,6793
0,6814
0,6756
0,6744
0,6777
0,6889
0,6961
0,709
0,7206
0,7473




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=49401&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=49401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49401&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.67089250.00329391065289277203.676593173773
Geometric Mean0.670241915316317
Harmonic Mean0.669579362296661
Quadratic Mean0.671531000401322
Winsorized Mean ( 1 / 26 )0.67056250.00321088357599705208.840490204250
Winsorized Mean ( 2 / 26 )0.6704450.00316061848017365212.124621875642
Winsorized Mean ( 3 / 26 )0.670381250.00311298174745185215.350202598761
Winsorized Mean ( 4 / 26 )0.670121250.00304537088726168220.045858060512
Winsorized Mean ( 5 / 26 )0.6701650.00303105294609403221.099733959979
Winsorized Mean ( 6 / 26 )0.67018750.00298642730066411224.411121560189
Winsorized Mean ( 7 / 26 )0.67022250.00293964120722499227.994660828927
Winsorized Mean ( 8 / 26 )0.67045250.00287386189636299233.293221517878
Winsorized Mean ( 9 / 26 )0.670553750.00284901934258066235.363003675717
Winsorized Mean ( 10 / 26 )0.670778750.00276190443706186242.868196668520
Winsorized Mean ( 11 / 26 )0.670888750.00270873002247398247.676492095456
Winsorized Mean ( 12 / 26 )0.671023750.00264368739639197253.821140470614
Winsorized Mean ( 13 / 26 )0.670958750.00260011969889387258.049177614952
Winsorized Mean ( 14 / 26 )0.671886250.00240005586943805279.94608732059
Winsorized Mean ( 15 / 26 )0.671698750.00233234242399206287.993196492269
Winsorized Mean ( 16 / 26 )0.671918750.00226110766917764297.163535889636
Winsorized Mean ( 17 / 26 )0.672641250.00212191749155829316.996892045047
Winsorized Mean ( 18 / 26 )0.672888750.00202367865449958332.507707438558
Winsorized Mean ( 19 / 26 )0.67557250.00144270203486111468.268903540457
Winsorized Mean ( 20 / 26 )0.67707250.00118970927067674569.107526257119
Winsorized Mean ( 21 / 26 )0.677203750.00114187061126896593.065224130277
Winsorized Mean ( 22 / 26 )0.677451250.00109934530826478616.231537904405
Winsorized Mean ( 23 / 26 )0.677278750.00103808138163877652.43319259884
Winsorized Mean ( 24 / 26 )0.677878750.000940111247372727721.062269911595
Winsorized Mean ( 25 / 26 )0.677910.000862313270926051786.152808795326
Winsorized Mean ( 26 / 26 )0.67781250.000816203342047571830.445631721629
Trimmed Mean ( 1 / 26 )0.6707115384615380.00313026166070819214.266924353473
Trimmed Mean ( 2 / 26 )0.6708684210526320.00303600106934678220.971075348460
Trimmed Mean ( 3 / 26 )0.6710972972972970.00295686750315628226.962248589408
Trimmed Mean ( 4 / 26 )0.67136250.00288470647477662232.731650817953
Trimmed Mean ( 5 / 26 )0.6717171428571430.00282262375293554237.976153271776
Trimmed Mean ( 6 / 26 )0.6720823529411760.00275250619392039244.171059242534
Trimmed Mean ( 7 / 26 )0.6724651515151520.00268026326197502250.895186698798
Trimmed Mean ( 8 / 26 )0.6728656250.00260453208745703258.344148739961
Trimmed Mean ( 9 / 26 )0.6732548387096770.0025284240073551266.274500143648
Trimmed Mean ( 10 / 26 )0.6736550.00244083484027783275.993684162309
Trimmed Mean ( 11 / 26 )0.6740517241379310.00235292771943156286.473621170469
Trimmed Mean ( 12 / 26 )0.67446250.00225551497632837299.028163004229
Trimmed Mean ( 13 / 26 )0.6748870370370370.00214802502418300314.189559916197
Trimmed Mean ( 14 / 26 )0.6753519230769230.00202065034851527334.225029863855
Trimmed Mean ( 15 / 26 )0.6757480.00190860615879436354.053138142896
Trimmed Mean ( 16 / 26 )0.6761979166666670.0017778495496326380.345972923527
Trimmed Mean ( 17 / 26 )0.6766630434782610.00162339882823462416.818733455723
Trimmed Mean ( 18 / 26 )0.6770931818181820.00145730063286124464.62148341265
Trimmed Mean ( 19 / 26 )0.6775380952380950.00125600509877195539.438968759404
Trimmed Mean ( 20 / 26 )0.6777450.00117375110933565577.417984621636
Trimmed Mean ( 21 / 26 )0.6778157894736840.00113379187502461597.830875670167
Trimmed Mean ( 22 / 26 )0.6778805555555560.00109089899903808621.396257722564
Trimmed Mean ( 23 / 26 )0.6779264705882350.00104263231952453650.206652808718
Trimmed Mean ( 24 / 26 )0.6779968750.000991399348825087683.878676946377
Trimmed Mean ( 25 / 26 )0.678010.000948590606073577714.75512793283
Trimmed Mean ( 26 / 26 )0.6780214285714290.00091007525043331745.016885415361
Median0.67845
Midrange0.67795
Midmean - Weighted Average at Xnp0.677241463414634
Midmean - Weighted Average at X(n+1)p0.677745
Midmean - Empirical Distribution Function0.677241463414634
Midmean - Empirical Distribution Function - Averaging0.677745
Midmean - Empirical Distribution Function - Interpolation0.677745
Midmean - Closest Observation0.677241463414634
Midmean - True Basic - Statistics Graphics Toolkit0.677745
Midmean - MS Excel (old versions)0.677538095238095
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.6708925 & 0.00329391065289277 & 203.676593173773 \tabularnewline
Geometric Mean & 0.670241915316317 &  &  \tabularnewline
Harmonic Mean & 0.669579362296661 &  &  \tabularnewline
Quadratic Mean & 0.671531000401322 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 0.6705625 & 0.00321088357599705 & 208.840490204250 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 0.670445 & 0.00316061848017365 & 212.124621875642 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 0.67038125 & 0.00311298174745185 & 215.350202598761 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 0.67012125 & 0.00304537088726168 & 220.045858060512 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 0.670165 & 0.00303105294609403 & 221.099733959979 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 0.6701875 & 0.00298642730066411 & 224.411121560189 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 0.6702225 & 0.00293964120722499 & 227.994660828927 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 0.6704525 & 0.00287386189636299 & 233.293221517878 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 0.67055375 & 0.00284901934258066 & 235.363003675717 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 0.67077875 & 0.00276190443706186 & 242.868196668520 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 0.67088875 & 0.00270873002247398 & 247.676492095456 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 0.67102375 & 0.00264368739639197 & 253.821140470614 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 0.67095875 & 0.00260011969889387 & 258.049177614952 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 0.67188625 & 0.00240005586943805 & 279.94608732059 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 0.67169875 & 0.00233234242399206 & 287.993196492269 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 0.67191875 & 0.00226110766917764 & 297.163535889636 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 0.67264125 & 0.00212191749155829 & 316.996892045047 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 0.67288875 & 0.00202367865449958 & 332.507707438558 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 0.6755725 & 0.00144270203486111 & 468.268903540457 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 0.6770725 & 0.00118970927067674 & 569.107526257119 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 0.67720375 & 0.00114187061126896 & 593.065224130277 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 0.67745125 & 0.00109934530826478 & 616.231537904405 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 0.67727875 & 0.00103808138163877 & 652.43319259884 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 0.67787875 & 0.000940111247372727 & 721.062269911595 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 0.67791 & 0.000862313270926051 & 786.152808795326 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 0.6778125 & 0.000816203342047571 & 830.445631721629 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 0.670711538461538 & 0.00313026166070819 & 214.266924353473 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 0.670868421052632 & 0.00303600106934678 & 220.971075348460 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 0.671097297297297 & 0.00295686750315628 & 226.962248589408 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 0.6713625 & 0.00288470647477662 & 232.731650817953 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 0.671717142857143 & 0.00282262375293554 & 237.976153271776 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 0.672082352941176 & 0.00275250619392039 & 244.171059242534 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 0.672465151515152 & 0.00268026326197502 & 250.895186698798 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 0.672865625 & 0.00260453208745703 & 258.344148739961 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 0.673254838709677 & 0.0025284240073551 & 266.274500143648 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 0.673655 & 0.00244083484027783 & 275.993684162309 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 0.674051724137931 & 0.00235292771943156 & 286.473621170469 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 0.6744625 & 0.00225551497632837 & 299.028163004229 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 0.674887037037037 & 0.00214802502418300 & 314.189559916197 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 0.675351923076923 & 0.00202065034851527 & 334.225029863855 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 0.675748 & 0.00190860615879436 & 354.053138142896 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 0.676197916666667 & 0.0017778495496326 & 380.345972923527 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 0.676663043478261 & 0.00162339882823462 & 416.818733455723 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 0.677093181818182 & 0.00145730063286124 & 464.62148341265 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 0.677538095238095 & 0.00125600509877195 & 539.438968759404 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 0.677745 & 0.00117375110933565 & 577.417984621636 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 0.677815789473684 & 0.00113379187502461 & 597.830875670167 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 0.677880555555556 & 0.00109089899903808 & 621.396257722564 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 0.677926470588235 & 0.00104263231952453 & 650.206652808718 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 0.677996875 & 0.000991399348825087 & 683.878676946377 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 0.67801 & 0.000948590606073577 & 714.75512793283 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 0.678021428571429 & 0.00091007525043331 & 745.016885415361 \tabularnewline
Median & 0.67845 &  &  \tabularnewline
Midrange & 0.67795 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.677241463414634 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.677745 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.677241463414634 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.677745 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.677745 &  &  \tabularnewline
Midmean - Closest Observation & 0.677241463414634 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.677745 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.677538095238095 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49401&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.6708925[/C][C]0.00329391065289277[/C][C]203.676593173773[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.670241915316317[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.669579362296661[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.671531000401322[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]0.6705625[/C][C]0.00321088357599705[/C][C]208.840490204250[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]0.670445[/C][C]0.00316061848017365[/C][C]212.124621875642[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]0.67038125[/C][C]0.00311298174745185[/C][C]215.350202598761[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]0.67012125[/C][C]0.00304537088726168[/C][C]220.045858060512[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]0.670165[/C][C]0.00303105294609403[/C][C]221.099733959979[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]0.6701875[/C][C]0.00298642730066411[/C][C]224.411121560189[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]0.6702225[/C][C]0.00293964120722499[/C][C]227.994660828927[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]0.6704525[/C][C]0.00287386189636299[/C][C]233.293221517878[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]0.67055375[/C][C]0.00284901934258066[/C][C]235.363003675717[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]0.67077875[/C][C]0.00276190443706186[/C][C]242.868196668520[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]0.67088875[/C][C]0.00270873002247398[/C][C]247.676492095456[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]0.67102375[/C][C]0.00264368739639197[/C][C]253.821140470614[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]0.67095875[/C][C]0.00260011969889387[/C][C]258.049177614952[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]0.67188625[/C][C]0.00240005586943805[/C][C]279.94608732059[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]0.67169875[/C][C]0.00233234242399206[/C][C]287.993196492269[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]0.67191875[/C][C]0.00226110766917764[/C][C]297.163535889636[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]0.67264125[/C][C]0.00212191749155829[/C][C]316.996892045047[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]0.67288875[/C][C]0.00202367865449958[/C][C]332.507707438558[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]0.6755725[/C][C]0.00144270203486111[/C][C]468.268903540457[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]0.6770725[/C][C]0.00118970927067674[/C][C]569.107526257119[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]0.67720375[/C][C]0.00114187061126896[/C][C]593.065224130277[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]0.67745125[/C][C]0.00109934530826478[/C][C]616.231537904405[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]0.67727875[/C][C]0.00103808138163877[/C][C]652.43319259884[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]0.67787875[/C][C]0.000940111247372727[/C][C]721.062269911595[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]0.67791[/C][C]0.000862313270926051[/C][C]786.152808795326[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]0.6778125[/C][C]0.000816203342047571[/C][C]830.445631721629[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]0.670711538461538[/C][C]0.00313026166070819[/C][C]214.266924353473[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]0.670868421052632[/C][C]0.00303600106934678[/C][C]220.971075348460[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]0.671097297297297[/C][C]0.00295686750315628[/C][C]226.962248589408[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]0.6713625[/C][C]0.00288470647477662[/C][C]232.731650817953[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]0.671717142857143[/C][C]0.00282262375293554[/C][C]237.976153271776[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]0.672082352941176[/C][C]0.00275250619392039[/C][C]244.171059242534[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]0.672465151515152[/C][C]0.00268026326197502[/C][C]250.895186698798[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]0.672865625[/C][C]0.00260453208745703[/C][C]258.344148739961[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]0.673254838709677[/C][C]0.0025284240073551[/C][C]266.274500143648[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]0.673655[/C][C]0.00244083484027783[/C][C]275.993684162309[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]0.674051724137931[/C][C]0.00235292771943156[/C][C]286.473621170469[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]0.6744625[/C][C]0.00225551497632837[/C][C]299.028163004229[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]0.674887037037037[/C][C]0.00214802502418300[/C][C]314.189559916197[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]0.675351923076923[/C][C]0.00202065034851527[/C][C]334.225029863855[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]0.675748[/C][C]0.00190860615879436[/C][C]354.053138142896[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]0.676197916666667[/C][C]0.0017778495496326[/C][C]380.345972923527[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]0.676663043478261[/C][C]0.00162339882823462[/C][C]416.818733455723[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]0.677093181818182[/C][C]0.00145730063286124[/C][C]464.62148341265[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]0.677538095238095[/C][C]0.00125600509877195[/C][C]539.438968759404[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]0.677745[/C][C]0.00117375110933565[/C][C]577.417984621636[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]0.677815789473684[/C][C]0.00113379187502461[/C][C]597.830875670167[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]0.677880555555556[/C][C]0.00109089899903808[/C][C]621.396257722564[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]0.677926470588235[/C][C]0.00104263231952453[/C][C]650.206652808718[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]0.677996875[/C][C]0.000991399348825087[/C][C]683.878676946377[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]0.67801[/C][C]0.000948590606073577[/C][C]714.75512793283[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]0.678021428571429[/C][C]0.00091007525043331[/C][C]745.016885415361[/C][/ROW]
[ROW][C]Median[/C][C]0.67845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.67795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.677241463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.677745[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.677241463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.677745[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.677745[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.677241463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.677745[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.677538095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49401&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.67089250.00329391065289277203.676593173773
Geometric Mean0.670241915316317
Harmonic Mean0.669579362296661
Quadratic Mean0.671531000401322
Winsorized Mean ( 1 / 26 )0.67056250.00321088357599705208.840490204250
Winsorized Mean ( 2 / 26 )0.6704450.00316061848017365212.124621875642
Winsorized Mean ( 3 / 26 )0.670381250.00311298174745185215.350202598761
Winsorized Mean ( 4 / 26 )0.670121250.00304537088726168220.045858060512
Winsorized Mean ( 5 / 26 )0.6701650.00303105294609403221.099733959979
Winsorized Mean ( 6 / 26 )0.67018750.00298642730066411224.411121560189
Winsorized Mean ( 7 / 26 )0.67022250.00293964120722499227.994660828927
Winsorized Mean ( 8 / 26 )0.67045250.00287386189636299233.293221517878
Winsorized Mean ( 9 / 26 )0.670553750.00284901934258066235.363003675717
Winsorized Mean ( 10 / 26 )0.670778750.00276190443706186242.868196668520
Winsorized Mean ( 11 / 26 )0.670888750.00270873002247398247.676492095456
Winsorized Mean ( 12 / 26 )0.671023750.00264368739639197253.821140470614
Winsorized Mean ( 13 / 26 )0.670958750.00260011969889387258.049177614952
Winsorized Mean ( 14 / 26 )0.671886250.00240005586943805279.94608732059
Winsorized Mean ( 15 / 26 )0.671698750.00233234242399206287.993196492269
Winsorized Mean ( 16 / 26 )0.671918750.00226110766917764297.163535889636
Winsorized Mean ( 17 / 26 )0.672641250.00212191749155829316.996892045047
Winsorized Mean ( 18 / 26 )0.672888750.00202367865449958332.507707438558
Winsorized Mean ( 19 / 26 )0.67557250.00144270203486111468.268903540457
Winsorized Mean ( 20 / 26 )0.67707250.00118970927067674569.107526257119
Winsorized Mean ( 21 / 26 )0.677203750.00114187061126896593.065224130277
Winsorized Mean ( 22 / 26 )0.677451250.00109934530826478616.231537904405
Winsorized Mean ( 23 / 26 )0.677278750.00103808138163877652.43319259884
Winsorized Mean ( 24 / 26 )0.677878750.000940111247372727721.062269911595
Winsorized Mean ( 25 / 26 )0.677910.000862313270926051786.152808795326
Winsorized Mean ( 26 / 26 )0.67781250.000816203342047571830.445631721629
Trimmed Mean ( 1 / 26 )0.6707115384615380.00313026166070819214.266924353473
Trimmed Mean ( 2 / 26 )0.6708684210526320.00303600106934678220.971075348460
Trimmed Mean ( 3 / 26 )0.6710972972972970.00295686750315628226.962248589408
Trimmed Mean ( 4 / 26 )0.67136250.00288470647477662232.731650817953
Trimmed Mean ( 5 / 26 )0.6717171428571430.00282262375293554237.976153271776
Trimmed Mean ( 6 / 26 )0.6720823529411760.00275250619392039244.171059242534
Trimmed Mean ( 7 / 26 )0.6724651515151520.00268026326197502250.895186698798
Trimmed Mean ( 8 / 26 )0.6728656250.00260453208745703258.344148739961
Trimmed Mean ( 9 / 26 )0.6732548387096770.0025284240073551266.274500143648
Trimmed Mean ( 10 / 26 )0.6736550.00244083484027783275.993684162309
Trimmed Mean ( 11 / 26 )0.6740517241379310.00235292771943156286.473621170469
Trimmed Mean ( 12 / 26 )0.67446250.00225551497632837299.028163004229
Trimmed Mean ( 13 / 26 )0.6748870370370370.00214802502418300314.189559916197
Trimmed Mean ( 14 / 26 )0.6753519230769230.00202065034851527334.225029863855
Trimmed Mean ( 15 / 26 )0.6757480.00190860615879436354.053138142896
Trimmed Mean ( 16 / 26 )0.6761979166666670.0017778495496326380.345972923527
Trimmed Mean ( 17 / 26 )0.6766630434782610.00162339882823462416.818733455723
Trimmed Mean ( 18 / 26 )0.6770931818181820.00145730063286124464.62148341265
Trimmed Mean ( 19 / 26 )0.6775380952380950.00125600509877195539.438968759404
Trimmed Mean ( 20 / 26 )0.6777450.00117375110933565577.417984621636
Trimmed Mean ( 21 / 26 )0.6778157894736840.00113379187502461597.830875670167
Trimmed Mean ( 22 / 26 )0.6778805555555560.00109089899903808621.396257722564
Trimmed Mean ( 23 / 26 )0.6779264705882350.00104263231952453650.206652808718
Trimmed Mean ( 24 / 26 )0.6779968750.000991399348825087683.878676946377
Trimmed Mean ( 25 / 26 )0.678010.000948590606073577714.75512793283
Trimmed Mean ( 26 / 26 )0.6780214285714290.00091007525043331745.016885415361
Median0.67845
Midrange0.67795
Midmean - Weighted Average at Xnp0.677241463414634
Midmean - Weighted Average at X(n+1)p0.677745
Midmean - Empirical Distribution Function0.677241463414634
Midmean - Empirical Distribution Function - Averaging0.677745
Midmean - Empirical Distribution Function - Interpolation0.677745
Midmean - Closest Observation0.677241463414634
Midmean - True Basic - Statistics Graphics Toolkit0.677745
Midmean - MS Excel (old versions)0.677538095238095
Number of observations80



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')