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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, 07 Oct 2013 06:24:36 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/07/t1381141497jp9n81ppuncyll2.htm/, Retrieved Fri, 03 May 2024 11:29:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=213616, Retrieved Fri, 03 May 2024 11:29:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2013-10-03 21:38:39] [636b129f405b59a1fda23d46ce07447c]
- RMPD    [Central Tendency] [] [2013-10-07 10:24:36] [f3e37d24265d1c1b6ba14664c97da4c0] [Current]
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Dataseries X:
1,31
1,32
1,32
1,33
1,33
1,33
1,34
1,33
1,32
1,31
1,31
1,33
1,34
1,33
1,33
1,34
1,34
1,34
1,35
1,35
1,35
1,34
1,35
1,36
1,35
1,36
1,36
1,36
1,37
1,39
1,39
1,38
1,37
1,39
1,38
1,4
1,41
1,4
1,42
1,43
1,44
1,44
1,44
1,46
1,46
1,49
1,49
1,48
1,49
1,5
1,5
1,5
1,47
1,49
1,49
1,5
1,52
1,52
1,52
1,52
1,53
1,54
1,51
1,49
1,49
1,49
1,48
1,49
1,49
1,47
1,49
1,49




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=213616&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=213616&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213616&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.414444444444440.00868481507387045162.864083162808
Geometric Mean1.41255600727745
Harmonic Mean1.410674901551
Quadratic Mean1.41633623597412
Winsorized Mean ( 1 / 24 )1.414305555555560.00865760267466319163.359951790647
Winsorized Mean ( 2 / 24 )1.414027777777780.00860737146824852164.281021563197
Winsorized Mean ( 3 / 24 )1.414444444444440.00853944380532246165.636600777541
Winsorized Mean ( 4 / 24 )1.414444444444440.00853944380532246165.636600777541
Winsorized Mean ( 5 / 24 )1.414444444444440.00853944380532246165.636600777541
Winsorized Mean ( 6 / 24 )1.414444444444440.00827417709549091170.946841978432
Winsorized Mean ( 7 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 8 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 9 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 10 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 11 / 24 )1.411944444444440.00790108768311348178.702540849168
Winsorized Mean ( 12 / 24 )1.411944444444440.00790108768311348178.702540849168
Winsorized Mean ( 13 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 14 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 15 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 16 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 17 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 18 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 19 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 20 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 21 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 22 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 23 / 24 )1.413194444444440.00685139142879166206.263860287673
Winsorized Mean ( 24 / 24 )1.416527777777780.00642812592470331220.364036792443
Trimmed Mean ( 1 / 24 )1.414142857142860.00862009990945462164.05179429438
Trimmed Mean ( 2 / 24 )1.413970588235290.00857016617591557164.987534571841
Trimmed Mean ( 3 / 24 )1.413939393939390.00853589374069236165.646320923473
Trimmed Mean ( 4 / 24 )1.413750.00851731429836558165.985421046549
Trimmed Mean ( 5 / 24 )1.413548387096770.00848707847347923166.553000719139
Trimmed Mean ( 6 / 24 )1.413333333333330.00844278405720144167.401336307755
Trimmed Mean ( 7 / 24 )1.413103448275860.00844972640855398167.236592044604
Trimmed Mean ( 8 / 24 )1.413035714285710.00848191216364343166.594004632882
Trimmed Mean ( 9 / 24 )1.412962962962960.00850711721445421166.091864887231
Trimmed Mean ( 10 / 24 )1.412884615384620.00852348604525256165.763703710358
Trimmed Mean ( 11 / 24 )1.41280.008528655180254165.653314636403
Trimmed Mean ( 12 / 24 )1.412916666666670.00856223738186763165.017226649056
Trimmed Mean ( 13 / 24 )1.413043478260870.00858528999911069164.588904790315
Trimmed Mean ( 14 / 24 )1.412954545454550.00864241192461269163.490765978256
Trimmed Mean ( 15 / 24 )1.412857142857140.00869061540308207162.572738215533
Trimmed Mean ( 16 / 24 )1.412750.00872652528729181161.891469226285
Trimmed Mean ( 17 / 24 )1.412631578947370.00874552688367945161.52618335478
Trimmed Mean ( 18 / 24 )1.41250.0087412087355657161.590924405329
Trimmed Mean ( 19 / 24 )1.412352941176470.00870448512177424162.255770607669
Trimmed Mean ( 20 / 24 )1.4118750.00870017496116248162.28121920566
Trimmed Mean ( 21 / 24 )1.411333333333330.00865339390376052163.095930802365
Trimmed Mean ( 22 / 24 )1.410714285714290.00854382681053432165.115037675496
Trimmed Mean ( 23 / 24 )1.410.00833897245099547169.0855807818
Trimmed Mean ( 24 / 24 )1.409583333333330.00815340167888213172.882851704001
Median1.4
Midrange1.425
Midmean - Weighted Average at Xnp1.41625
Midmean - Weighted Average at X(n+1)p1.41625
Midmean - Empirical Distribution Function1.41625
Midmean - Empirical Distribution Function - Averaging1.41625
Midmean - Empirical Distribution Function - Interpolation1.41625
Midmean - Closest Observation1.41625
Midmean - True Basic - Statistics Graphics Toolkit1.41625
Midmean - MS Excel (old versions)1.41625
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.41444444444444 & 0.00868481507387045 & 162.864083162808 \tabularnewline
Geometric Mean & 1.41255600727745 &  &  \tabularnewline
Harmonic Mean & 1.410674901551 &  &  \tabularnewline
Quadratic Mean & 1.41633623597412 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.41430555555556 & 0.00865760267466319 & 163.359951790647 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.41402777777778 & 0.00860737146824852 & 164.281021563197 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.41444444444444 & 0.00853944380532246 & 165.636600777541 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.41444444444444 & 0.00853944380532246 & 165.636600777541 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.41444444444444 & 0.00853944380532246 & 165.636600777541 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.41444444444444 & 0.00827417709549091 & 170.946841978432 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.41347222222222 & 0.00812211119277411 & 174.027686727526 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.41347222222222 & 0.00812211119277411 & 174.027686727526 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.41347222222222 & 0.00812211119277411 & 174.027686727526 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.41347222222222 & 0.00812211119277411 & 174.027686727526 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.41194444444444 & 0.00790108768311348 & 178.702540849168 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.41194444444444 & 0.00790108768311348 & 178.702540849168 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.41375 & 0.00764642536181263 & 184.890315814822 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.41375 & 0.00764642536181263 & 184.890315814822 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.41375 & 0.00764642536181263 & 184.890315814822 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.41375 & 0.00764642536181263 & 184.890315814822 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.41375 & 0.00764642536181263 & 184.890315814822 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.41375 & 0.00764642536181263 & 184.890315814822 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.41638888888889 & 0.00729789118777188 & 194.081941268479 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.41638888888889 & 0.00729789118777188 & 194.081941268479 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.41638888888889 & 0.00729789118777188 & 194.081941268479 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.41638888888889 & 0.00729789118777188 & 194.081941268479 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.41319444444444 & 0.00685139142879166 & 206.263860287673 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.41652777777778 & 0.00642812592470331 & 220.364036792443 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.41414285714286 & 0.00862009990945462 & 164.05179429438 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.41397058823529 & 0.00857016617591557 & 164.987534571841 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.41393939393939 & 0.00853589374069236 & 165.646320923473 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.41375 & 0.00851731429836558 & 165.985421046549 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.41354838709677 & 0.00848707847347923 & 166.553000719139 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.41333333333333 & 0.00844278405720144 & 167.401336307755 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.41310344827586 & 0.00844972640855398 & 167.236592044604 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.41303571428571 & 0.00848191216364343 & 166.594004632882 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.41296296296296 & 0.00850711721445421 & 166.091864887231 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.41288461538462 & 0.00852348604525256 & 165.763703710358 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.4128 & 0.008528655180254 & 165.653314636403 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.41291666666667 & 0.00856223738186763 & 165.017226649056 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.41304347826087 & 0.00858528999911069 & 164.588904790315 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.41295454545455 & 0.00864241192461269 & 163.490765978256 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.41285714285714 & 0.00869061540308207 & 162.572738215533 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.41275 & 0.00872652528729181 & 161.891469226285 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.41263157894737 & 0.00874552688367945 & 161.52618335478 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.4125 & 0.0087412087355657 & 161.590924405329 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.41235294117647 & 0.00870448512177424 & 162.255770607669 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.411875 & 0.00870017496116248 & 162.28121920566 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.41133333333333 & 0.00865339390376052 & 163.095930802365 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.41071428571429 & 0.00854382681053432 & 165.115037675496 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.41 & 0.00833897245099547 & 169.0855807818 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.40958333333333 & 0.00815340167888213 & 172.882851704001 \tabularnewline
Median & 1.4 &  &  \tabularnewline
Midrange & 1.425 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.41625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.41625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.41625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.41625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.41625 &  &  \tabularnewline
Midmean - Closest Observation & 1.41625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.41625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.41625 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=213616&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]1.41444444444444[/C][C]0.00868481507387045[/C][C]162.864083162808[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.41255600727745[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.410674901551[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.41633623597412[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.41430555555556[/C][C]0.00865760267466319[/C][C]163.359951790647[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.41402777777778[/C][C]0.00860737146824852[/C][C]164.281021563197[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.41444444444444[/C][C]0.00853944380532246[/C][C]165.636600777541[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.41444444444444[/C][C]0.00853944380532246[/C][C]165.636600777541[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.41444444444444[/C][C]0.00853944380532246[/C][C]165.636600777541[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.41444444444444[/C][C]0.00827417709549091[/C][C]170.946841978432[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.41347222222222[/C][C]0.00812211119277411[/C][C]174.027686727526[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.41347222222222[/C][C]0.00812211119277411[/C][C]174.027686727526[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.41347222222222[/C][C]0.00812211119277411[/C][C]174.027686727526[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.41347222222222[/C][C]0.00812211119277411[/C][C]174.027686727526[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.41194444444444[/C][C]0.00790108768311348[/C][C]178.702540849168[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.41194444444444[/C][C]0.00790108768311348[/C][C]178.702540849168[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.41375[/C][C]0.00764642536181263[/C][C]184.890315814822[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.41375[/C][C]0.00764642536181263[/C][C]184.890315814822[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.41375[/C][C]0.00764642536181263[/C][C]184.890315814822[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.41375[/C][C]0.00764642536181263[/C][C]184.890315814822[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.41375[/C][C]0.00764642536181263[/C][C]184.890315814822[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.41375[/C][C]0.00764642536181263[/C][C]184.890315814822[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.41638888888889[/C][C]0.00729789118777188[/C][C]194.081941268479[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.41638888888889[/C][C]0.00729789118777188[/C][C]194.081941268479[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.41638888888889[/C][C]0.00729789118777188[/C][C]194.081941268479[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.41638888888889[/C][C]0.00729789118777188[/C][C]194.081941268479[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.41319444444444[/C][C]0.00685139142879166[/C][C]206.263860287673[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.41652777777778[/C][C]0.00642812592470331[/C][C]220.364036792443[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.41414285714286[/C][C]0.00862009990945462[/C][C]164.05179429438[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.41397058823529[/C][C]0.00857016617591557[/C][C]164.987534571841[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.41393939393939[/C][C]0.00853589374069236[/C][C]165.646320923473[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.41375[/C][C]0.00851731429836558[/C][C]165.985421046549[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.41354838709677[/C][C]0.00848707847347923[/C][C]166.553000719139[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.41333333333333[/C][C]0.00844278405720144[/C][C]167.401336307755[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.41310344827586[/C][C]0.00844972640855398[/C][C]167.236592044604[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.41303571428571[/C][C]0.00848191216364343[/C][C]166.594004632882[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.41296296296296[/C][C]0.00850711721445421[/C][C]166.091864887231[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.41288461538462[/C][C]0.00852348604525256[/C][C]165.763703710358[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.4128[/C][C]0.008528655180254[/C][C]165.653314636403[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.41291666666667[/C][C]0.00856223738186763[/C][C]165.017226649056[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.41304347826087[/C][C]0.00858528999911069[/C][C]164.588904790315[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.41295454545455[/C][C]0.00864241192461269[/C][C]163.490765978256[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.41285714285714[/C][C]0.00869061540308207[/C][C]162.572738215533[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.41275[/C][C]0.00872652528729181[/C][C]161.891469226285[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.41263157894737[/C][C]0.00874552688367945[/C][C]161.52618335478[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.4125[/C][C]0.0087412087355657[/C][C]161.590924405329[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.41235294117647[/C][C]0.00870448512177424[/C][C]162.255770607669[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.411875[/C][C]0.00870017496116248[/C][C]162.28121920566[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.41133333333333[/C][C]0.00865339390376052[/C][C]163.095930802365[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.41071428571429[/C][C]0.00854382681053432[/C][C]165.115037675496[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.41[/C][C]0.00833897245099547[/C][C]169.0855807818[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.40958333333333[/C][C]0.00815340167888213[/C][C]172.882851704001[/C][/ROW]
[ROW][C]Median[/C][C]1.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.41625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.41625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.41625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.41625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.41625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.41625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.41625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.41625[/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=213616&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=213616&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 Mean1.414444444444440.00868481507387045162.864083162808
Geometric Mean1.41255600727745
Harmonic Mean1.410674901551
Quadratic Mean1.41633623597412
Winsorized Mean ( 1 / 24 )1.414305555555560.00865760267466319163.359951790647
Winsorized Mean ( 2 / 24 )1.414027777777780.00860737146824852164.281021563197
Winsorized Mean ( 3 / 24 )1.414444444444440.00853944380532246165.636600777541
Winsorized Mean ( 4 / 24 )1.414444444444440.00853944380532246165.636600777541
Winsorized Mean ( 5 / 24 )1.414444444444440.00853944380532246165.636600777541
Winsorized Mean ( 6 / 24 )1.414444444444440.00827417709549091170.946841978432
Winsorized Mean ( 7 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 8 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 9 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 10 / 24 )1.413472222222220.00812211119277411174.027686727526
Winsorized Mean ( 11 / 24 )1.411944444444440.00790108768311348178.702540849168
Winsorized Mean ( 12 / 24 )1.411944444444440.00790108768311348178.702540849168
Winsorized Mean ( 13 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 14 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 15 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 16 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 17 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 18 / 24 )1.413750.00764642536181263184.890315814822
Winsorized Mean ( 19 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 20 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 21 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 22 / 24 )1.416388888888890.00729789118777188194.081941268479
Winsorized Mean ( 23 / 24 )1.413194444444440.00685139142879166206.263860287673
Winsorized Mean ( 24 / 24 )1.416527777777780.00642812592470331220.364036792443
Trimmed Mean ( 1 / 24 )1.414142857142860.00862009990945462164.05179429438
Trimmed Mean ( 2 / 24 )1.413970588235290.00857016617591557164.987534571841
Trimmed Mean ( 3 / 24 )1.413939393939390.00853589374069236165.646320923473
Trimmed Mean ( 4 / 24 )1.413750.00851731429836558165.985421046549
Trimmed Mean ( 5 / 24 )1.413548387096770.00848707847347923166.553000719139
Trimmed Mean ( 6 / 24 )1.413333333333330.00844278405720144167.401336307755
Trimmed Mean ( 7 / 24 )1.413103448275860.00844972640855398167.236592044604
Trimmed Mean ( 8 / 24 )1.413035714285710.00848191216364343166.594004632882
Trimmed Mean ( 9 / 24 )1.412962962962960.00850711721445421166.091864887231
Trimmed Mean ( 10 / 24 )1.412884615384620.00852348604525256165.763703710358
Trimmed Mean ( 11 / 24 )1.41280.008528655180254165.653314636403
Trimmed Mean ( 12 / 24 )1.412916666666670.00856223738186763165.017226649056
Trimmed Mean ( 13 / 24 )1.413043478260870.00858528999911069164.588904790315
Trimmed Mean ( 14 / 24 )1.412954545454550.00864241192461269163.490765978256
Trimmed Mean ( 15 / 24 )1.412857142857140.00869061540308207162.572738215533
Trimmed Mean ( 16 / 24 )1.412750.00872652528729181161.891469226285
Trimmed Mean ( 17 / 24 )1.412631578947370.00874552688367945161.52618335478
Trimmed Mean ( 18 / 24 )1.41250.0087412087355657161.590924405329
Trimmed Mean ( 19 / 24 )1.412352941176470.00870448512177424162.255770607669
Trimmed Mean ( 20 / 24 )1.4118750.00870017496116248162.28121920566
Trimmed Mean ( 21 / 24 )1.411333333333330.00865339390376052163.095930802365
Trimmed Mean ( 22 / 24 )1.410714285714290.00854382681053432165.115037675496
Trimmed Mean ( 23 / 24 )1.410.00833897245099547169.0855807818
Trimmed Mean ( 24 / 24 )1.409583333333330.00815340167888213172.882851704001
Median1.4
Midrange1.425
Midmean - Weighted Average at Xnp1.41625
Midmean - Weighted Average at X(n+1)p1.41625
Midmean - Empirical Distribution Function1.41625
Midmean - Empirical Distribution Function - Averaging1.41625
Midmean - Empirical Distribution Function - Interpolation1.41625
Midmean - Closest Observation1.41625
Midmean - True Basic - Statistics Graphics Toolkit1.41625
Midmean - MS Excel (old versions)1.41625
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')