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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 computationThu, 26 Feb 2015 14:47:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Feb/26/t1424962077grmtycs7rk12ljy.htm/, Retrieved Sat, 18 May 2024 05:29:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277600, Retrieved Sat, 18 May 2024 05:29:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsraf Meutermans
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde en med...] [2015-02-26 14:47:07] [567f06ca3de45fa0ce67a0a89b883c29] [Current]
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Dataseries X:
94,67
94,6
93,9
93,41
93,37
93,35
93,08
93,05
92,61
92,37
92,24
91,95
92,63
92,7
92,47
92,58
92,55
92,56
89,92
89,96
90,03
90,31
90,8
90,36
90,31
93,8
93,95
93,99
94,44
94,15
91,91
91,86
93,12
93,47
93,57
94,57
95,85
96,62
95,69
95,39
95,14
95,07
94,21
95,4
95,1
94,89
95,43
94,88
96,03
96,37
96,04
95,72
95,74
95,78
93,66
95,29
94,33
95,66
95,2
94,61
96,21
96,27
95,12
95,55
93,51
92,86
92,45
93,34
92,01
91,77
92,19
91,97




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

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277600&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277600&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277600&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.69388888888890.207195064657179452.201354525085
Geometric Mean93.6775399523636
Harmonic Mean93.6611082530816
Quadratic Mean93.7101532949101
Winsorized Mean ( 1 / 24 )93.69097222222220.2063902967819453.950469974026
Winsorized Mean ( 2 / 24 )93.69013888888890.205399101283624456.137043947031
Winsorized Mean ( 3 / 24 )93.69930555555560.202116764466579463.589973859142
Winsorized Mean ( 4 / 24 )93.68986111111110.200510839494807467.255841864537
Winsorized Mean ( 5 / 24 )93.69263888888890.199575742605664469.459051814796
Winsorized Mean ( 6 / 24 )93.71430555555560.188836817796302496.271366194303
Winsorized Mean ( 7 / 24 )93.80180555555560.169397039695115553.739343523255
Winsorized Mean ( 8 / 24 )93.80736111111110.167003297721176561.709633229693
Winsorized Mean ( 9 / 24 )93.81111111111110.165577964789782566.567605962628
Winsorized Mean ( 10 / 24 )93.81250.164010256511602571.991666834346
Winsorized Mean ( 11 / 24 )93.81097222222220.162786422635468576.282534522525
Winsorized Mean ( 12 / 24 )93.79930555555550.158836527610867590.539890077139
Winsorized Mean ( 13 / 24 )93.81013888888890.150465305045774623.466910596766
Winsorized Mean ( 14 / 24 )93.81402777777780.148118304306084633.372277770024
Winsorized Mean ( 15 / 24 )93.83902777777780.143826964117601652.443916573597
Winsorized Mean ( 16 / 24 )93.83458333333330.137951837990117680.198137991145
Winsorized Mean ( 17 / 24 )93.81805555555550.13416315116394699.283333326861
Winsorized Mean ( 18 / 24 )93.82305555555560.129194512959148726.215482427049
Winsorized Mean ( 19 / 24 )93.82041666666670.128072480075082732.557194267379
Winsorized Mean ( 20 / 24 )93.82041666666670.12651112229739741.598169101075
Winsorized Mean ( 21 / 24 )93.82041666666670.124061805849258756.239327844895
Winsorized Mean ( 22 / 24 )93.77152777777780.115561610860291811.441854087198
Winsorized Mean ( 23 / 24 )93.79069444444450.112036268438281837.145825649415
Winsorized Mean ( 24 / 24 )93.77402777777780.0953357996747154983.61820111368
Trimmed Mean ( 1 / 24 )93.7060.201773954658345464.410781652509
Trimmed Mean ( 2 / 24 )93.72191176470590.196264417481846477.528800009687
Trimmed Mean ( 3 / 24 )93.73924242424240.190296702528682492.595200960532
Trimmed Mean ( 4 / 24 )93.754218750.184650544665358507.738652598674
Trimmed Mean ( 5 / 24 )93.77290322580640.178397945397622525.638919309306
Trimmed Mean ( 6 / 24 )93.79216666666670.1710722402776548.260585788024
Trimmed Mean ( 7 / 24 )93.8082758620690.165358899104551567.301042581064
Trimmed Mean ( 8 / 24 )93.80946428571430.163520009427906573.687982369362
Trimmed Mean ( 9 / 24 )93.80981481481480.161695353036575580.163950621359
Trimmed Mean ( 10 / 24 )93.80961538461540.159621054252465587.702016027543
Trimmed Mean ( 11 / 24 )93.80920.157241485931542596.593191957254
Trimmed Mean ( 12 / 24 )93.80895833333330.154380264025258607.6486455418
Trimmed Mean ( 13 / 24 )93.81021739130430.151482684755448619.280134510097
Trimmed Mean ( 14 / 24 )93.81022727272730.149437807860729627.754305390742
Trimmed Mean ( 15 / 24 )93.80976190476190.147094385342251637.752159516426
Trimmed Mean ( 16 / 24 )93.806250.144754295583045648.03776373036
Trimmed Mean ( 17 / 24 )93.80289473684210.142739358951362657.162084977591
Trimmed Mean ( 18 / 24 )93.80111111111110.140627718472646667.017229105915
Trimmed Mean ( 19 / 24 )93.79852941176470.138620098159376676.658945255699
Trimmed Mean ( 20 / 24 )93.79593750.135745298866349690.970061455673
Trimmed Mean ( 21 / 24 )93.7930.131743524781444711.936318354907
Trimmed Mean ( 22 / 24 )93.78964285714290.126352452947441742.285888950307
Trimmed Mean ( 23 / 24 )93.79192307692310.120981904852648775.255797064518
Trimmed Mean ( 24 / 24 )93.79208333333330.113712036453049824.821067838845
Median93.73
Midrange93.27
Midmean - Weighted Average at Xnp93.7651351351351
Midmean - Weighted Average at X(n+1)p93.8011111111111
Midmean - Empirical Distribution Function93.7651351351351
Midmean - Empirical Distribution Function - Averaging93.8011111111111
Midmean - Empirical Distribution Function - Interpolation93.8011111111111
Midmean - Closest Observation93.7651351351351
Midmean - True Basic - Statistics Graphics Toolkit93.8011111111111
Midmean - MS Excel (old versions)93.8028947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93.6938888888889 & 0.207195064657179 & 452.201354525085 \tabularnewline
Geometric Mean & 93.6775399523636 &  &  \tabularnewline
Harmonic Mean & 93.6611082530816 &  &  \tabularnewline
Quadratic Mean & 93.7101532949101 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 93.6909722222222 & 0.2063902967819 & 453.950469974026 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 93.6901388888889 & 0.205399101283624 & 456.137043947031 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 93.6993055555556 & 0.202116764466579 & 463.589973859142 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 93.6898611111111 & 0.200510839494807 & 467.255841864537 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 93.6926388888889 & 0.199575742605664 & 469.459051814796 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 93.7143055555556 & 0.188836817796302 & 496.271366194303 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 93.8018055555556 & 0.169397039695115 & 553.739343523255 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 93.8073611111111 & 0.167003297721176 & 561.709633229693 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 93.8111111111111 & 0.165577964789782 & 566.567605962628 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 93.8125 & 0.164010256511602 & 571.991666834346 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 93.8109722222222 & 0.162786422635468 & 576.282534522525 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 93.7993055555555 & 0.158836527610867 & 590.539890077139 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 93.8101388888889 & 0.150465305045774 & 623.466910596766 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 93.8140277777778 & 0.148118304306084 & 633.372277770024 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 93.8390277777778 & 0.143826964117601 & 652.443916573597 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 93.8345833333333 & 0.137951837990117 & 680.198137991145 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 93.8180555555555 & 0.13416315116394 & 699.283333326861 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 93.8230555555556 & 0.129194512959148 & 726.215482427049 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 93.8204166666667 & 0.128072480075082 & 732.557194267379 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 93.8204166666667 & 0.12651112229739 & 741.598169101075 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 93.8204166666667 & 0.124061805849258 & 756.239327844895 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 93.7715277777778 & 0.115561610860291 & 811.441854087198 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 93.7906944444445 & 0.112036268438281 & 837.145825649415 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 93.7740277777778 & 0.0953357996747154 & 983.61820111368 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 93.706 & 0.201773954658345 & 464.410781652509 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.7219117647059 & 0.196264417481846 & 477.528800009687 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.7392424242424 & 0.190296702528682 & 492.595200960532 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.75421875 & 0.184650544665358 & 507.738652598674 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 93.7729032258064 & 0.178397945397622 & 525.638919309306 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 93.7921666666667 & 0.1710722402776 & 548.260585788024 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 93.808275862069 & 0.165358899104551 & 567.301042581064 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 93.8094642857143 & 0.163520009427906 & 573.687982369362 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 93.8098148148148 & 0.161695353036575 & 580.163950621359 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 93.8096153846154 & 0.159621054252465 & 587.702016027543 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 93.8092 & 0.157241485931542 & 596.593191957254 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 93.8089583333333 & 0.154380264025258 & 607.6486455418 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 93.8102173913043 & 0.151482684755448 & 619.280134510097 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 93.8102272727273 & 0.149437807860729 & 627.754305390742 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 93.8097619047619 & 0.147094385342251 & 637.752159516426 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 93.80625 & 0.144754295583045 & 648.03776373036 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 93.8028947368421 & 0.142739358951362 & 657.162084977591 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 93.8011111111111 & 0.140627718472646 & 667.017229105915 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 93.7985294117647 & 0.138620098159376 & 676.658945255699 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 93.7959375 & 0.135745298866349 & 690.970061455673 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 93.793 & 0.131743524781444 & 711.936318354907 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 93.7896428571429 & 0.126352452947441 & 742.285888950307 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 93.7919230769231 & 0.120981904852648 & 775.255797064518 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 93.7920833333333 & 0.113712036453049 & 824.821067838845 \tabularnewline
Median & 93.73 &  &  \tabularnewline
Midrange & 93.27 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 93.7651351351351 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93.8011111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 93.7651351351351 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93.8011111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93.8011111111111 &  &  \tabularnewline
Midmean - Closest Observation & 93.7651351351351 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93.8011111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93.8028947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277600&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]93.6938888888889[/C][C]0.207195064657179[/C][C]452.201354525085[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.6775399523636[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]93.6611082530816[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]93.7101532949101[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]93.6909722222222[/C][C]0.2063902967819[/C][C]453.950469974026[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]93.6901388888889[/C][C]0.205399101283624[/C][C]456.137043947031[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]93.6993055555556[/C][C]0.202116764466579[/C][C]463.589973859142[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]93.6898611111111[/C][C]0.200510839494807[/C][C]467.255841864537[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]93.6926388888889[/C][C]0.199575742605664[/C][C]469.459051814796[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]93.7143055555556[/C][C]0.188836817796302[/C][C]496.271366194303[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]93.8018055555556[/C][C]0.169397039695115[/C][C]553.739343523255[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]93.8073611111111[/C][C]0.167003297721176[/C][C]561.709633229693[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]93.8111111111111[/C][C]0.165577964789782[/C][C]566.567605962628[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]93.8125[/C][C]0.164010256511602[/C][C]571.991666834346[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]93.8109722222222[/C][C]0.162786422635468[/C][C]576.282534522525[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]93.7993055555555[/C][C]0.158836527610867[/C][C]590.539890077139[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]93.8101388888889[/C][C]0.150465305045774[/C][C]623.466910596766[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]93.8140277777778[/C][C]0.148118304306084[/C][C]633.372277770024[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]93.8390277777778[/C][C]0.143826964117601[/C][C]652.443916573597[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]93.8345833333333[/C][C]0.137951837990117[/C][C]680.198137991145[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]93.8180555555555[/C][C]0.13416315116394[/C][C]699.283333326861[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]93.8230555555556[/C][C]0.129194512959148[/C][C]726.215482427049[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]93.8204166666667[/C][C]0.128072480075082[/C][C]732.557194267379[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]93.8204166666667[/C][C]0.12651112229739[/C][C]741.598169101075[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]93.8204166666667[/C][C]0.124061805849258[/C][C]756.239327844895[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]93.7715277777778[/C][C]0.115561610860291[/C][C]811.441854087198[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]93.7906944444445[/C][C]0.112036268438281[/C][C]837.145825649415[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]93.7740277777778[/C][C]0.0953357996747154[/C][C]983.61820111368[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]93.706[/C][C]0.201773954658345[/C][C]464.410781652509[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.7219117647059[/C][C]0.196264417481846[/C][C]477.528800009687[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.7392424242424[/C][C]0.190296702528682[/C][C]492.595200960532[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.75421875[/C][C]0.184650544665358[/C][C]507.738652598674[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]93.7729032258064[/C][C]0.178397945397622[/C][C]525.638919309306[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]93.7921666666667[/C][C]0.1710722402776[/C][C]548.260585788024[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]93.808275862069[/C][C]0.165358899104551[/C][C]567.301042581064[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]93.8094642857143[/C][C]0.163520009427906[/C][C]573.687982369362[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]93.8098148148148[/C][C]0.161695353036575[/C][C]580.163950621359[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]93.8096153846154[/C][C]0.159621054252465[/C][C]587.702016027543[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]93.8092[/C][C]0.157241485931542[/C][C]596.593191957254[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]93.8089583333333[/C][C]0.154380264025258[/C][C]607.6486455418[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]93.8102173913043[/C][C]0.151482684755448[/C][C]619.280134510097[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]93.8102272727273[/C][C]0.149437807860729[/C][C]627.754305390742[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]93.8097619047619[/C][C]0.147094385342251[/C][C]637.752159516426[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]93.80625[/C][C]0.144754295583045[/C][C]648.03776373036[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]93.8028947368421[/C][C]0.142739358951362[/C][C]657.162084977591[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]93.8011111111111[/C][C]0.140627718472646[/C][C]667.017229105915[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]93.7985294117647[/C][C]0.138620098159376[/C][C]676.658945255699[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]93.7959375[/C][C]0.135745298866349[/C][C]690.970061455673[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]93.793[/C][C]0.131743524781444[/C][C]711.936318354907[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]93.7896428571429[/C][C]0.126352452947441[/C][C]742.285888950307[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]93.7919230769231[/C][C]0.120981904852648[/C][C]775.255797064518[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]93.7920833333333[/C][C]0.113712036453049[/C][C]824.821067838845[/C][/ROW]
[ROW][C]Median[/C][C]93.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]93.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]93.7651351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93.8011111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]93.7651351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93.8011111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93.8011111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]93.7651351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93.8011111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93.8028947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277600&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277600&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 Mean93.69388888888890.207195064657179452.201354525085
Geometric Mean93.6775399523636
Harmonic Mean93.6611082530816
Quadratic Mean93.7101532949101
Winsorized Mean ( 1 / 24 )93.69097222222220.2063902967819453.950469974026
Winsorized Mean ( 2 / 24 )93.69013888888890.205399101283624456.137043947031
Winsorized Mean ( 3 / 24 )93.69930555555560.202116764466579463.589973859142
Winsorized Mean ( 4 / 24 )93.68986111111110.200510839494807467.255841864537
Winsorized Mean ( 5 / 24 )93.69263888888890.199575742605664469.459051814796
Winsorized Mean ( 6 / 24 )93.71430555555560.188836817796302496.271366194303
Winsorized Mean ( 7 / 24 )93.80180555555560.169397039695115553.739343523255
Winsorized Mean ( 8 / 24 )93.80736111111110.167003297721176561.709633229693
Winsorized Mean ( 9 / 24 )93.81111111111110.165577964789782566.567605962628
Winsorized Mean ( 10 / 24 )93.81250.164010256511602571.991666834346
Winsorized Mean ( 11 / 24 )93.81097222222220.162786422635468576.282534522525
Winsorized Mean ( 12 / 24 )93.79930555555550.158836527610867590.539890077139
Winsorized Mean ( 13 / 24 )93.81013888888890.150465305045774623.466910596766
Winsorized Mean ( 14 / 24 )93.81402777777780.148118304306084633.372277770024
Winsorized Mean ( 15 / 24 )93.83902777777780.143826964117601652.443916573597
Winsorized Mean ( 16 / 24 )93.83458333333330.137951837990117680.198137991145
Winsorized Mean ( 17 / 24 )93.81805555555550.13416315116394699.283333326861
Winsorized Mean ( 18 / 24 )93.82305555555560.129194512959148726.215482427049
Winsorized Mean ( 19 / 24 )93.82041666666670.128072480075082732.557194267379
Winsorized Mean ( 20 / 24 )93.82041666666670.12651112229739741.598169101075
Winsorized Mean ( 21 / 24 )93.82041666666670.124061805849258756.239327844895
Winsorized Mean ( 22 / 24 )93.77152777777780.115561610860291811.441854087198
Winsorized Mean ( 23 / 24 )93.79069444444450.112036268438281837.145825649415
Winsorized Mean ( 24 / 24 )93.77402777777780.0953357996747154983.61820111368
Trimmed Mean ( 1 / 24 )93.7060.201773954658345464.410781652509
Trimmed Mean ( 2 / 24 )93.72191176470590.196264417481846477.528800009687
Trimmed Mean ( 3 / 24 )93.73924242424240.190296702528682492.595200960532
Trimmed Mean ( 4 / 24 )93.754218750.184650544665358507.738652598674
Trimmed Mean ( 5 / 24 )93.77290322580640.178397945397622525.638919309306
Trimmed Mean ( 6 / 24 )93.79216666666670.1710722402776548.260585788024
Trimmed Mean ( 7 / 24 )93.8082758620690.165358899104551567.301042581064
Trimmed Mean ( 8 / 24 )93.80946428571430.163520009427906573.687982369362
Trimmed Mean ( 9 / 24 )93.80981481481480.161695353036575580.163950621359
Trimmed Mean ( 10 / 24 )93.80961538461540.159621054252465587.702016027543
Trimmed Mean ( 11 / 24 )93.80920.157241485931542596.593191957254
Trimmed Mean ( 12 / 24 )93.80895833333330.154380264025258607.6486455418
Trimmed Mean ( 13 / 24 )93.81021739130430.151482684755448619.280134510097
Trimmed Mean ( 14 / 24 )93.81022727272730.149437807860729627.754305390742
Trimmed Mean ( 15 / 24 )93.80976190476190.147094385342251637.752159516426
Trimmed Mean ( 16 / 24 )93.806250.144754295583045648.03776373036
Trimmed Mean ( 17 / 24 )93.80289473684210.142739358951362657.162084977591
Trimmed Mean ( 18 / 24 )93.80111111111110.140627718472646667.017229105915
Trimmed Mean ( 19 / 24 )93.79852941176470.138620098159376676.658945255699
Trimmed Mean ( 20 / 24 )93.79593750.135745298866349690.970061455673
Trimmed Mean ( 21 / 24 )93.7930.131743524781444711.936318354907
Trimmed Mean ( 22 / 24 )93.78964285714290.126352452947441742.285888950307
Trimmed Mean ( 23 / 24 )93.79192307692310.120981904852648775.255797064518
Trimmed Mean ( 24 / 24 )93.79208333333330.113712036453049824.821067838845
Median93.73
Midrange93.27
Midmean - Weighted Average at Xnp93.7651351351351
Midmean - Weighted Average at X(n+1)p93.8011111111111
Midmean - Empirical Distribution Function93.7651351351351
Midmean - Empirical Distribution Function - Averaging93.8011111111111
Midmean - Empirical Distribution Function - Interpolation93.8011111111111
Midmean - Closest Observation93.7651351351351
Midmean - True Basic - Statistics Graphics Toolkit93.8011111111111
Midmean - MS Excel (old versions)93.8028947368421
Number of observations72



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')