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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 computationMon, 22 Oct 2007 01:59:32 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/qjmm6utp6lsu0iz1193043313.htm/, Retrieved Mon, 06 May 2024 07:17:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1569, Retrieved Mon, 06 May 2024 07:17:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgroep 1, ws1, deel1
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [vraag 8, deel 1, ...] [2007-10-22 08:59:32] [234bcf6fb77cd83fa17f2489a043102b] [Current]
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Dataseries X:
4,5
5,6
5,4
5,4
5,2
5,3
5,3
5,3
5,2
5,2
5,0
5,0
5,0
6,5
6,5
6,6
6,2
6,2
6,2
6,1
6,1
6,1
5,9
5,9
5,9
6,2
6,1
6,2
6,6
6,6
6,7
5,8
5,7
5,7
6,1
6,2
6,2
6,2
6,1
6,2
6,5
6,5
6,5
6,0
6,3
6,0
6,1
6,1
6,1
6,2
6,1
6,2
6,8
6,8
6,8
6,7
6,7
6,7
5,7
5,6
5,6
5,8
5,7
5,7
6,1
6,1
5,9
5,9
5,8
5,6
5,5
5,5
5,4




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1569&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1569&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.961643835616440.0588974722818897101.220707861338
Geometric Mean5.94001142157706
Harmonic Mean5.91764401898883
Quadratic Mean5.98255454668903
Winsorized Mean ( 1 / 24 )5.968493150684930.0569010968805784104.892409424222
Winsorized Mean ( 2 / 24 )5.968493150684930.0569010968805784104.892409424222
Winsorized Mean ( 3 / 24 )5.964383561643840.0561095994458704106.298808413304
Winsorized Mean ( 4 / 24 )5.975342465753430.0536981253664966111.276556210686
Winsorized Mean ( 5 / 24 )5.975342465753420.0536981253664966111.276556210686
Winsorized Mean ( 6 / 24 )5.975342465753420.0536981253664966111.276556210686
Winsorized Mean ( 7 / 24 )5.975342465753420.0501057034093616119.254736670098
Winsorized Mean ( 8 / 24 )5.975342465753420.0501057034093616119.254736670098
Winsorized Mean ( 9 / 24 )5.975342465753420.0501057034093616119.254736670098
Winsorized Mean ( 10 / 24 )5.975342465753420.0453206410985182131.845938647783
Winsorized Mean ( 11 / 24 )5.975342465753430.0453206410985182131.845938647783
Winsorized Mean ( 12 / 24 )5.975342465753420.0453206410985182131.845938647783
Winsorized Mean ( 13 / 24 )5.993150684931510.0423046484955872141.666481061925
Winsorized Mean ( 14 / 24 )5.993150684931510.0423046484955872141.666481061925
Winsorized Mean ( 15 / 24 )5.972602739726030.0326563837354673182.892349260317
Winsorized Mean ( 16 / 24 )5.950684931506850.0298476144787684199.368861981910
Winsorized Mean ( 17 / 24 )5.950684931506850.0298476144787684199.368861981910
Winsorized Mean ( 18 / 24 )5.950684931506850.0298476144787684199.368861981910
Winsorized Mean ( 19 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 20 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 21 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 22 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 23 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 24 / 24 )6.009589041095890.0210244099236920285.838654350238
Trimmed Mean ( 1 / 24 )5.970422535211270.0556430983243703107.298527849884
Trimmed Mean ( 2 / 24 )5.972463768115940.0541493962094765110.296036266250
Trimmed Mean ( 3 / 24 )5.974626865671640.0523678705423311114.089551547491
Trimmed Mean ( 4 / 24 )5.978461538461540.0505970273000068118.158355490200
Trimmed Mean ( 5 / 24 )5.979365079365080.0493770061475157121.096144660968
Trimmed Mean ( 6 / 24 )5.980327868852460.0478967281661562124.858797204402
Trimmed Mean ( 7 / 24 )5.981355932203390.0460905631694171129.773982370696
Trimmed Mean ( 8 / 24 )5.982456140350880.0448558542780894133.370687876367
Trimmed Mean ( 9 / 24 )5.983636363636360.0433266223524167138.105304285336
Trimmed Mean ( 10 / 24 )5.984905660377360.0414186234532216144.497937434757
Trimmed Mean ( 11 / 24 )5.986274509803920.0401975131259983148.921513901621
Trimmed Mean ( 12 / 24 )5.987755102040820.0386455035029537154.940537948565
Trimmed Mean ( 13 / 24 )5.989361702127660.0366539991991504163.402680007329
Trimmed Mean ( 14 / 24 )5.988888888888890.034847752883544171.858682219851
Trimmed Mean ( 15 / 24 )5.988372093023260.032471011405231184.422099400900
Trimmed Mean ( 16 / 24 )5.990243902439020.0317775956604765188.505259064939
Trimmed Mean ( 17 / 24 )5.99487179487180.0313761554402721191.064574698569
Trimmed Mean ( 18 / 24 )60.0307562342614623195.082400172704
Trimmed Mean ( 19 / 24 )6.005714285714290.0298294471683158201.335085153486
Trimmed Mean ( 20 / 24 )6.009090909090910.0296327382054666202.785543051245
Trimmed Mean ( 21 / 24 )6.012903225806450.0292346588696197205.677215274607
Trimmed Mean ( 22 / 24 )6.017241379310350.0285395609607704210.838610572232
Trimmed Mean ( 23 / 24 )6.022222222222220.0273904621520719219.865666697657
Trimmed Mean ( 24 / 24 )6.0280.0255081686262786236.31645565452
Median6.1
Midrange5.65
Midmean - Weighted Average at Xnp5.98095238095238
Midmean - Weighted Average at X(n+1)p5.98095238095238
Midmean - Empirical Distribution Function5.98095238095238
Midmean - Empirical Distribution Function - Averaging5.98095238095238
Midmean - Empirical Distribution Function - Interpolation5.98095238095238
Midmean - Closest Observation5.98095238095238
Midmean - True Basic - Statistics Graphics Toolkit5.98095238095238
Midmean - MS Excel (old versions)5.98095238095238
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.96164383561644 & 0.0588974722818897 & 101.220707861338 \tabularnewline
Geometric Mean & 5.94001142157706 &  &  \tabularnewline
Harmonic Mean & 5.91764401898883 &  &  \tabularnewline
Quadratic Mean & 5.98255454668903 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 5.96849315068493 & 0.0569010968805784 & 104.892409424222 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 5.96849315068493 & 0.0569010968805784 & 104.892409424222 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 5.96438356164384 & 0.0561095994458704 & 106.298808413304 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 5.97534246575343 & 0.0536981253664966 & 111.276556210686 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 5.97534246575342 & 0.0536981253664966 & 111.276556210686 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 5.97534246575342 & 0.0536981253664966 & 111.276556210686 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 5.97534246575342 & 0.0501057034093616 & 119.254736670098 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 5.97534246575342 & 0.0501057034093616 & 119.254736670098 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 5.97534246575342 & 0.0501057034093616 & 119.254736670098 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 5.97534246575342 & 0.0453206410985182 & 131.845938647783 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 5.97534246575343 & 0.0453206410985182 & 131.845938647783 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 5.97534246575342 & 0.0453206410985182 & 131.845938647783 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 5.99315068493151 & 0.0423046484955872 & 141.666481061925 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 5.99315068493151 & 0.0423046484955872 & 141.666481061925 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 5.97260273972603 & 0.0326563837354673 & 182.892349260317 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 5.95068493150685 & 0.0298476144787684 & 199.368861981910 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 5.95068493150685 & 0.0298476144787684 & 199.368861981910 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 5.95068493150685 & 0.0298476144787684 & 199.368861981910 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 5.97671232876712 & 0.0257697736246986 & 231.927234434021 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 5.97671232876712 & 0.0257697736246986 & 231.927234434021 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 5.97671232876712 & 0.0257697736246986 & 231.927234434021 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 5.97671232876712 & 0.0257697736246986 & 231.927234434021 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 5.97671232876712 & 0.0257697736246986 & 231.927234434021 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6.00958904109589 & 0.0210244099236920 & 285.838654350238 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 5.97042253521127 & 0.0556430983243703 & 107.298527849884 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 5.97246376811594 & 0.0541493962094765 & 110.296036266250 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 5.97462686567164 & 0.0523678705423311 & 114.089551547491 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 5.97846153846154 & 0.0505970273000068 & 118.158355490200 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 5.97936507936508 & 0.0493770061475157 & 121.096144660968 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 5.98032786885246 & 0.0478967281661562 & 124.858797204402 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 5.98135593220339 & 0.0460905631694171 & 129.773982370696 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 5.98245614035088 & 0.0448558542780894 & 133.370687876367 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 5.98363636363636 & 0.0433266223524167 & 138.105304285336 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 5.98490566037736 & 0.0414186234532216 & 144.497937434757 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 5.98627450980392 & 0.0401975131259983 & 148.921513901621 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 5.98775510204082 & 0.0386455035029537 & 154.940537948565 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 5.98936170212766 & 0.0366539991991504 & 163.402680007329 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 5.98888888888889 & 0.034847752883544 & 171.858682219851 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 5.98837209302326 & 0.032471011405231 & 184.422099400900 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 5.99024390243902 & 0.0317775956604765 & 188.505259064939 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 5.9948717948718 & 0.0313761554402721 & 191.064574698569 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6 & 0.0307562342614623 & 195.082400172704 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6.00571428571429 & 0.0298294471683158 & 201.335085153486 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6.00909090909091 & 0.0296327382054666 & 202.785543051245 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6.01290322580645 & 0.0292346588696197 & 205.677215274607 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6.01724137931035 & 0.0285395609607704 & 210.838610572232 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6.02222222222222 & 0.0273904621520719 & 219.865666697657 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6.028 & 0.0255081686262786 & 236.31645565452 \tabularnewline
Median & 6.1 &  &  \tabularnewline
Midrange & 5.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.98095238095238 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.98095238095238 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.98095238095238 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.98095238095238 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.98095238095238 &  &  \tabularnewline
Midmean - Closest Observation & 5.98095238095238 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.98095238095238 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.98095238095238 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1569&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]5.96164383561644[/C][C]0.0588974722818897[/C][C]101.220707861338[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.94001142157706[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5.91764401898883[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.98255454668903[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]5.96849315068493[/C][C]0.0569010968805784[/C][C]104.892409424222[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]5.96849315068493[/C][C]0.0569010968805784[/C][C]104.892409424222[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]5.96438356164384[/C][C]0.0561095994458704[/C][C]106.298808413304[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]5.97534246575343[/C][C]0.0536981253664966[/C][C]111.276556210686[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]5.97534246575342[/C][C]0.0536981253664966[/C][C]111.276556210686[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]5.97534246575342[/C][C]0.0536981253664966[/C][C]111.276556210686[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]5.97534246575342[/C][C]0.0501057034093616[/C][C]119.254736670098[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]5.97534246575342[/C][C]0.0501057034093616[/C][C]119.254736670098[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]5.97534246575342[/C][C]0.0501057034093616[/C][C]119.254736670098[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]5.97534246575342[/C][C]0.0453206410985182[/C][C]131.845938647783[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]5.97534246575343[/C][C]0.0453206410985182[/C][C]131.845938647783[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]5.97534246575342[/C][C]0.0453206410985182[/C][C]131.845938647783[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]5.99315068493151[/C][C]0.0423046484955872[/C][C]141.666481061925[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]5.99315068493151[/C][C]0.0423046484955872[/C][C]141.666481061925[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]5.97260273972603[/C][C]0.0326563837354673[/C][C]182.892349260317[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]5.95068493150685[/C][C]0.0298476144787684[/C][C]199.368861981910[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]5.95068493150685[/C][C]0.0298476144787684[/C][C]199.368861981910[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]5.95068493150685[/C][C]0.0298476144787684[/C][C]199.368861981910[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]5.97671232876712[/C][C]0.0257697736246986[/C][C]231.927234434021[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]5.97671232876712[/C][C]0.0257697736246986[/C][C]231.927234434021[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]5.97671232876712[/C][C]0.0257697736246986[/C][C]231.927234434021[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]5.97671232876712[/C][C]0.0257697736246986[/C][C]231.927234434021[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]5.97671232876712[/C][C]0.0257697736246986[/C][C]231.927234434021[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6.00958904109589[/C][C]0.0210244099236920[/C][C]285.838654350238[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]5.97042253521127[/C][C]0.0556430983243703[/C][C]107.298527849884[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]5.97246376811594[/C][C]0.0541493962094765[/C][C]110.296036266250[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]5.97462686567164[/C][C]0.0523678705423311[/C][C]114.089551547491[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]5.97846153846154[/C][C]0.0505970273000068[/C][C]118.158355490200[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]5.97936507936508[/C][C]0.0493770061475157[/C][C]121.096144660968[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]5.98032786885246[/C][C]0.0478967281661562[/C][C]124.858797204402[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]5.98135593220339[/C][C]0.0460905631694171[/C][C]129.773982370696[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]5.98245614035088[/C][C]0.0448558542780894[/C][C]133.370687876367[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]5.98363636363636[/C][C]0.0433266223524167[/C][C]138.105304285336[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]5.98490566037736[/C][C]0.0414186234532216[/C][C]144.497937434757[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]5.98627450980392[/C][C]0.0401975131259983[/C][C]148.921513901621[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]5.98775510204082[/C][C]0.0386455035029537[/C][C]154.940537948565[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]5.98936170212766[/C][C]0.0366539991991504[/C][C]163.402680007329[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]5.98888888888889[/C][C]0.034847752883544[/C][C]171.858682219851[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]5.98837209302326[/C][C]0.032471011405231[/C][C]184.422099400900[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]5.99024390243902[/C][C]0.0317775956604765[/C][C]188.505259064939[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]5.9948717948718[/C][C]0.0313761554402721[/C][C]191.064574698569[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6[/C][C]0.0307562342614623[/C][C]195.082400172704[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6.00571428571429[/C][C]0.0298294471683158[/C][C]201.335085153486[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6.00909090909091[/C][C]0.0296327382054666[/C][C]202.785543051245[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6.01290322580645[/C][C]0.0292346588696197[/C][C]205.677215274607[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6.01724137931035[/C][C]0.0285395609607704[/C][C]210.838610572232[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6.02222222222222[/C][C]0.0273904621520719[/C][C]219.865666697657[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6.028[/C][C]0.0255081686262786[/C][C]236.31645565452[/C][/ROW]
[ROW][C]Median[/C][C]6.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.98095238095238[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1569&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 Mean5.961643835616440.0588974722818897101.220707861338
Geometric Mean5.94001142157706
Harmonic Mean5.91764401898883
Quadratic Mean5.98255454668903
Winsorized Mean ( 1 / 24 )5.968493150684930.0569010968805784104.892409424222
Winsorized Mean ( 2 / 24 )5.968493150684930.0569010968805784104.892409424222
Winsorized Mean ( 3 / 24 )5.964383561643840.0561095994458704106.298808413304
Winsorized Mean ( 4 / 24 )5.975342465753430.0536981253664966111.276556210686
Winsorized Mean ( 5 / 24 )5.975342465753420.0536981253664966111.276556210686
Winsorized Mean ( 6 / 24 )5.975342465753420.0536981253664966111.276556210686
Winsorized Mean ( 7 / 24 )5.975342465753420.0501057034093616119.254736670098
Winsorized Mean ( 8 / 24 )5.975342465753420.0501057034093616119.254736670098
Winsorized Mean ( 9 / 24 )5.975342465753420.0501057034093616119.254736670098
Winsorized Mean ( 10 / 24 )5.975342465753420.0453206410985182131.845938647783
Winsorized Mean ( 11 / 24 )5.975342465753430.0453206410985182131.845938647783
Winsorized Mean ( 12 / 24 )5.975342465753420.0453206410985182131.845938647783
Winsorized Mean ( 13 / 24 )5.993150684931510.0423046484955872141.666481061925
Winsorized Mean ( 14 / 24 )5.993150684931510.0423046484955872141.666481061925
Winsorized Mean ( 15 / 24 )5.972602739726030.0326563837354673182.892349260317
Winsorized Mean ( 16 / 24 )5.950684931506850.0298476144787684199.368861981910
Winsorized Mean ( 17 / 24 )5.950684931506850.0298476144787684199.368861981910
Winsorized Mean ( 18 / 24 )5.950684931506850.0298476144787684199.368861981910
Winsorized Mean ( 19 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 20 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 21 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 22 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 23 / 24 )5.976712328767120.0257697736246986231.927234434021
Winsorized Mean ( 24 / 24 )6.009589041095890.0210244099236920285.838654350238
Trimmed Mean ( 1 / 24 )5.970422535211270.0556430983243703107.298527849884
Trimmed Mean ( 2 / 24 )5.972463768115940.0541493962094765110.296036266250
Trimmed Mean ( 3 / 24 )5.974626865671640.0523678705423311114.089551547491
Trimmed Mean ( 4 / 24 )5.978461538461540.0505970273000068118.158355490200
Trimmed Mean ( 5 / 24 )5.979365079365080.0493770061475157121.096144660968
Trimmed Mean ( 6 / 24 )5.980327868852460.0478967281661562124.858797204402
Trimmed Mean ( 7 / 24 )5.981355932203390.0460905631694171129.773982370696
Trimmed Mean ( 8 / 24 )5.982456140350880.0448558542780894133.370687876367
Trimmed Mean ( 9 / 24 )5.983636363636360.0433266223524167138.105304285336
Trimmed Mean ( 10 / 24 )5.984905660377360.0414186234532216144.497937434757
Trimmed Mean ( 11 / 24 )5.986274509803920.0401975131259983148.921513901621
Trimmed Mean ( 12 / 24 )5.987755102040820.0386455035029537154.940537948565
Trimmed Mean ( 13 / 24 )5.989361702127660.0366539991991504163.402680007329
Trimmed Mean ( 14 / 24 )5.988888888888890.034847752883544171.858682219851
Trimmed Mean ( 15 / 24 )5.988372093023260.032471011405231184.422099400900
Trimmed Mean ( 16 / 24 )5.990243902439020.0317775956604765188.505259064939
Trimmed Mean ( 17 / 24 )5.99487179487180.0313761554402721191.064574698569
Trimmed Mean ( 18 / 24 )60.0307562342614623195.082400172704
Trimmed Mean ( 19 / 24 )6.005714285714290.0298294471683158201.335085153486
Trimmed Mean ( 20 / 24 )6.009090909090910.0296327382054666202.785543051245
Trimmed Mean ( 21 / 24 )6.012903225806450.0292346588696197205.677215274607
Trimmed Mean ( 22 / 24 )6.017241379310350.0285395609607704210.838610572232
Trimmed Mean ( 23 / 24 )6.022222222222220.0273904621520719219.865666697657
Trimmed Mean ( 24 / 24 )6.0280.0255081686262786236.31645565452
Median6.1
Midrange5.65
Midmean - Weighted Average at Xnp5.98095238095238
Midmean - Weighted Average at X(n+1)p5.98095238095238
Midmean - Empirical Distribution Function5.98095238095238
Midmean - Empirical Distribution Function - Averaging5.98095238095238
Midmean - Empirical Distribution Function - Interpolation5.98095238095238
Midmean - Closest Observation5.98095238095238
Midmean - True Basic - Statistics Graphics Toolkit5.98095238095238
Midmean - MS Excel (old versions)5.98095238095238
Number of observations73



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')