Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 17:50:46 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331160797i028jvyv3wjcrg1.htm/, Retrieved Mon, 29 Apr 2024 03:20:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163736, Retrieved Mon, 29 Apr 2024 03:20:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 22:50:46] [bc260e3c602952c552b9bde15a0b19a6] [Current]
Feedback Forum

Post a new message
Dataseries X:
7.72
7.67
7.84
7.79
7.83
7.94
8.02
8.06
8.12
8.13
7.97
8.01
8
7.9
7.99
8.02
8.08
8.02
8.07
8.11
8.19
8.16
8.08
8.22
8.15
8.19
8.31
8.3
8.34
8.31
8.38
8.34
8.44
8.64
8.6
8.61
8.54
8.69
8.73
8.91
9.01
9.08
8.94
9.03
9.02
8.96
9.03
8.94
8.95
8.95
8.99
8.93
8.98
8.95
9.02
8.92
9.1
9.06
8.97
8.89
8.99
8.79
8.83
8.61
8.71
8.91
8.91
8.89
8.98
9




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=163736&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=163736&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163736&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 Mean8.510857142857140.0528103536405649161.158874276497
Geometric Mean8.49945348625133
Harmonic Mean8.48796602429952
Quadratic Mean8.52215499238812
Winsorized Mean ( 1 / 23 )8.511285714285720.0526045922266896161.79738980977
Winsorized Mean ( 2 / 23 )8.512714285714290.052097186386027163.400653206821
Winsorized Mean ( 3 / 23 )8.513142857142860.0515689824669512165.082622341805
Winsorized Mean ( 4 / 23 )8.513714285714290.0514599168335954165.443607560519
Winsorized Mean ( 5 / 23 )8.517285714285710.0505706243868169168.423582219128
Winsorized Mean ( 6 / 23 )8.520714285714290.0499785964244892170.48726645591
Winsorized Mean ( 7 / 23 )8.522714285714290.049338448098926172.739812744532
Winsorized Mean ( 8 / 23 )8.523857142857140.048809127908307174.636538453834
Winsorized Mean ( 9 / 23 )8.523857142857140.0484258596869909176.018705665787
Winsorized Mean ( 10 / 23 )8.525285714285710.0482032109050399176.861365751765
Winsorized Mean ( 11 / 23 )8.525285714285710.0477427203554508178.56723812162
Winsorized Mean ( 12 / 23 )8.525285714285710.0477427203554508178.56723812162
Winsorized Mean ( 13 / 23 )8.523428571428570.0474879894216201179.485985303645
Winsorized Mean ( 14 / 23 )8.529428571428570.0460096693925329185.383391883552
Winsorized Mean ( 15 / 23 )8.529428571428570.0454049575983128187.852362882628
Winsorized Mean ( 16 / 23 )8.531714285714290.0450713588473505189.293478251007
Winsorized Mean ( 17 / 23 )8.531714285714290.0450713588473505189.293478251007
Winsorized Mean ( 18 / 23 )8.536857142857140.0436186859767843195.715596462507
Winsorized Mean ( 19 / 23 )8.539571428571430.043235325884261197.513751866505
Winsorized Mean ( 20 / 23 )8.539571428571430.042452475298581201.156030797028
Winsorized Mean ( 21 / 23 )8.542571428571430.041219849745164207.244118583272
Winsorized Mean ( 22 / 23 )8.542571428571430.0403713024135035211.600095064411
Winsorized Mean ( 23 / 23 )8.552428571428570.0390309298779056219.119262548492
Trimmed Mean ( 1 / 23 )8.514558823529410.0522023456492858163.106824370179
Trimmed Mean ( 2 / 23 )8.51803030303030.0516931143814222164.780752813213
Trimmed Mean ( 3 / 23 )8.52093750.0513685324734143165.878546450787
Trimmed Mean ( 4 / 23 )8.523870967741940.0511689659831396166.582826210531
Trimmed Mean ( 5 / 23 )8.526833333333330.050917842136468167.462582378885
Trimmed Mean ( 6 / 23 )8.529137931034480.0508293495504957167.799470315105
Trimmed Mean ( 7 / 23 )8.530892857142860.0508156055292675167.879389968687
Trimmed Mean ( 8 / 23 )8.532407407407410.0508797071252165167.697651765347
Trimmed Mean ( 9 / 23 )8.533846153846150.0509932668241527167.352411118798
Trimmed Mean ( 10 / 23 )8.53540.0511214719854503166.963110968895
Trimmed Mean ( 11 / 23 )8.5368750.0512262367066688166.650442211552
Trimmed Mean ( 12 / 23 )8.538478260869570.051341395368522166.307873005427
Trimmed Mean ( 13 / 23 )8.540227272727270.051368675967476166.253599336189
Trimmed Mean ( 14 / 23 )8.542380952380950.0513293769578993166.422845135788
Trimmed Mean ( 15 / 23 )8.5440.0514517448808303166.058508215594
Trimmed Mean ( 16 / 23 )8.545789473684210.0515763345928652165.6920667423
Trimmed Mean ( 17 / 23 )8.54750.0516372804295378165.529631477467
Trimmed Mean ( 18 / 23 )8.549411764705880.0515273687318315165.919820381288
Trimmed Mean ( 19 / 23 )8.55093750.0515219170694188165.966990096249
Trimmed Mean ( 20 / 23 )8.552333333333330.0513735101768676166.473602911102
Trimmed Mean ( 21 / 23 )8.553928571428570.0511128518139942167.353772443716
Trimmed Mean ( 22 / 23 )8.555384615384620.050806513117394168.39149334292
Trimmed Mean ( 23 / 23 )8.557083333333330.0502835408526123170.176626153184
Median8.605
Midrange8.385
Midmean - Weighted Average at Xnp8.52333333333333
Midmean - Weighted Average at X(n+1)p8.55615384615384
Midmean - Empirical Distribution Function8.55615384615384
Midmean - Empirical Distribution Function - Averaging8.55615384615384
Midmean - Empirical Distribution Function - Interpolation8.54941176470588
Midmean - Closest Observation8.55615384615384
Midmean - True Basic - Statistics Graphics Toolkit8.55615384615384
Midmean - MS Excel (old versions)8.55615384615384
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.51085714285714 & 0.0528103536405649 & 161.158874276497 \tabularnewline
Geometric Mean & 8.49945348625133 &  &  \tabularnewline
Harmonic Mean & 8.48796602429952 &  &  \tabularnewline
Quadratic Mean & 8.52215499238812 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 8.51128571428572 & 0.0526045922266896 & 161.79738980977 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 8.51271428571429 & 0.052097186386027 & 163.400653206821 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 8.51314285714286 & 0.0515689824669512 & 165.082622341805 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 8.51371428571429 & 0.0514599168335954 & 165.443607560519 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 8.51728571428571 & 0.0505706243868169 & 168.423582219128 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 8.52071428571429 & 0.0499785964244892 & 170.48726645591 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 8.52271428571429 & 0.049338448098926 & 172.739812744532 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 8.52385714285714 & 0.048809127908307 & 174.636538453834 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 8.52385714285714 & 0.0484258596869909 & 176.018705665787 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 8.52528571428571 & 0.0482032109050399 & 176.861365751765 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 8.52528571428571 & 0.0477427203554508 & 178.56723812162 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 8.52528571428571 & 0.0477427203554508 & 178.56723812162 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 8.52342857142857 & 0.0474879894216201 & 179.485985303645 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 8.52942857142857 & 0.0460096693925329 & 185.383391883552 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 8.52942857142857 & 0.0454049575983128 & 187.852362882628 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 8.53171428571429 & 0.0450713588473505 & 189.293478251007 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 8.53171428571429 & 0.0450713588473505 & 189.293478251007 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 8.53685714285714 & 0.0436186859767843 & 195.715596462507 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 8.53957142857143 & 0.043235325884261 & 197.513751866505 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 8.53957142857143 & 0.042452475298581 & 201.156030797028 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 8.54257142857143 & 0.041219849745164 & 207.244118583272 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 8.54257142857143 & 0.0403713024135035 & 211.600095064411 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 8.55242857142857 & 0.0390309298779056 & 219.119262548492 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 8.51455882352941 & 0.0522023456492858 & 163.106824370179 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 8.5180303030303 & 0.0516931143814222 & 164.780752813213 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 8.5209375 & 0.0513685324734143 & 165.878546450787 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 8.52387096774194 & 0.0511689659831396 & 166.582826210531 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 8.52683333333333 & 0.050917842136468 & 167.462582378885 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 8.52913793103448 & 0.0508293495504957 & 167.799470315105 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 8.53089285714286 & 0.0508156055292675 & 167.879389968687 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 8.53240740740741 & 0.0508797071252165 & 167.697651765347 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 8.53384615384615 & 0.0509932668241527 & 167.352411118798 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 8.5354 & 0.0511214719854503 & 166.963110968895 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 8.536875 & 0.0512262367066688 & 166.650442211552 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 8.53847826086957 & 0.051341395368522 & 166.307873005427 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 8.54022727272727 & 0.051368675967476 & 166.253599336189 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 8.54238095238095 & 0.0513293769578993 & 166.422845135788 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 8.544 & 0.0514517448808303 & 166.058508215594 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 8.54578947368421 & 0.0515763345928652 & 165.6920667423 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 8.5475 & 0.0516372804295378 & 165.529631477467 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 8.54941176470588 & 0.0515273687318315 & 165.919820381288 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 8.5509375 & 0.0515219170694188 & 165.966990096249 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 8.55233333333333 & 0.0513735101768676 & 166.473602911102 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 8.55392857142857 & 0.0511128518139942 & 167.353772443716 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 8.55538461538462 & 0.050806513117394 & 168.39149334292 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 8.55708333333333 & 0.0502835408526123 & 170.176626153184 \tabularnewline
Median & 8.605 &  &  \tabularnewline
Midrange & 8.385 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.52333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.55615384615384 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.55615384615384 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.55615384615384 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.54941176470588 &  &  \tabularnewline
Midmean - Closest Observation & 8.55615384615384 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.55615384615384 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.55615384615384 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163736&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]8.51085714285714[/C][C]0.0528103536405649[/C][C]161.158874276497[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.49945348625133[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.48796602429952[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.52215499238812[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]8.51128571428572[/C][C]0.0526045922266896[/C][C]161.79738980977[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]8.51271428571429[/C][C]0.052097186386027[/C][C]163.400653206821[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]8.51314285714286[/C][C]0.0515689824669512[/C][C]165.082622341805[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]8.51371428571429[/C][C]0.0514599168335954[/C][C]165.443607560519[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]8.51728571428571[/C][C]0.0505706243868169[/C][C]168.423582219128[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]8.52071428571429[/C][C]0.0499785964244892[/C][C]170.48726645591[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]8.52271428571429[/C][C]0.049338448098926[/C][C]172.739812744532[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]8.52385714285714[/C][C]0.048809127908307[/C][C]174.636538453834[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]8.52385714285714[/C][C]0.0484258596869909[/C][C]176.018705665787[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]8.52528571428571[/C][C]0.0482032109050399[/C][C]176.861365751765[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]8.52528571428571[/C][C]0.0477427203554508[/C][C]178.56723812162[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]8.52528571428571[/C][C]0.0477427203554508[/C][C]178.56723812162[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]8.52342857142857[/C][C]0.0474879894216201[/C][C]179.485985303645[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]8.52942857142857[/C][C]0.0460096693925329[/C][C]185.383391883552[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]8.52942857142857[/C][C]0.0454049575983128[/C][C]187.852362882628[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]8.53171428571429[/C][C]0.0450713588473505[/C][C]189.293478251007[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]8.53171428571429[/C][C]0.0450713588473505[/C][C]189.293478251007[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]8.53685714285714[/C][C]0.0436186859767843[/C][C]195.715596462507[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]8.53957142857143[/C][C]0.043235325884261[/C][C]197.513751866505[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]8.53957142857143[/C][C]0.042452475298581[/C][C]201.156030797028[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]8.54257142857143[/C][C]0.041219849745164[/C][C]207.244118583272[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]8.54257142857143[/C][C]0.0403713024135035[/C][C]211.600095064411[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]8.55242857142857[/C][C]0.0390309298779056[/C][C]219.119262548492[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]8.51455882352941[/C][C]0.0522023456492858[/C][C]163.106824370179[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]8.5180303030303[/C][C]0.0516931143814222[/C][C]164.780752813213[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]8.5209375[/C][C]0.0513685324734143[/C][C]165.878546450787[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]8.52387096774194[/C][C]0.0511689659831396[/C][C]166.582826210531[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]8.52683333333333[/C][C]0.050917842136468[/C][C]167.462582378885[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]8.52913793103448[/C][C]0.0508293495504957[/C][C]167.799470315105[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]8.53089285714286[/C][C]0.0508156055292675[/C][C]167.879389968687[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]8.53240740740741[/C][C]0.0508797071252165[/C][C]167.697651765347[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]8.53384615384615[/C][C]0.0509932668241527[/C][C]167.352411118798[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]8.5354[/C][C]0.0511214719854503[/C][C]166.963110968895[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]8.536875[/C][C]0.0512262367066688[/C][C]166.650442211552[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]8.53847826086957[/C][C]0.051341395368522[/C][C]166.307873005427[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]8.54022727272727[/C][C]0.051368675967476[/C][C]166.253599336189[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]8.54238095238095[/C][C]0.0513293769578993[/C][C]166.422845135788[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]8.544[/C][C]0.0514517448808303[/C][C]166.058508215594[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]8.54578947368421[/C][C]0.0515763345928652[/C][C]165.6920667423[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]8.5475[/C][C]0.0516372804295378[/C][C]165.529631477467[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]8.54941176470588[/C][C]0.0515273687318315[/C][C]165.919820381288[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]8.5509375[/C][C]0.0515219170694188[/C][C]165.966990096249[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]8.55233333333333[/C][C]0.0513735101768676[/C][C]166.473602911102[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]8.55392857142857[/C][C]0.0511128518139942[/C][C]167.353772443716[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]8.55538461538462[/C][C]0.050806513117394[/C][C]168.39149334292[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]8.55708333333333[/C][C]0.0502835408526123[/C][C]170.176626153184[/C][/ROW]
[ROW][C]Median[/C][C]8.605[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.52333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.55615384615384[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.55615384615384[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.55615384615384[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.54941176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.55615384615384[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.55615384615384[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.55615384615384[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163736&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163736&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 Mean8.510857142857140.0528103536405649161.158874276497
Geometric Mean8.49945348625133
Harmonic Mean8.48796602429952
Quadratic Mean8.52215499238812
Winsorized Mean ( 1 / 23 )8.511285714285720.0526045922266896161.79738980977
Winsorized Mean ( 2 / 23 )8.512714285714290.052097186386027163.400653206821
Winsorized Mean ( 3 / 23 )8.513142857142860.0515689824669512165.082622341805
Winsorized Mean ( 4 / 23 )8.513714285714290.0514599168335954165.443607560519
Winsorized Mean ( 5 / 23 )8.517285714285710.0505706243868169168.423582219128
Winsorized Mean ( 6 / 23 )8.520714285714290.0499785964244892170.48726645591
Winsorized Mean ( 7 / 23 )8.522714285714290.049338448098926172.739812744532
Winsorized Mean ( 8 / 23 )8.523857142857140.048809127908307174.636538453834
Winsorized Mean ( 9 / 23 )8.523857142857140.0484258596869909176.018705665787
Winsorized Mean ( 10 / 23 )8.525285714285710.0482032109050399176.861365751765
Winsorized Mean ( 11 / 23 )8.525285714285710.0477427203554508178.56723812162
Winsorized Mean ( 12 / 23 )8.525285714285710.0477427203554508178.56723812162
Winsorized Mean ( 13 / 23 )8.523428571428570.0474879894216201179.485985303645
Winsorized Mean ( 14 / 23 )8.529428571428570.0460096693925329185.383391883552
Winsorized Mean ( 15 / 23 )8.529428571428570.0454049575983128187.852362882628
Winsorized Mean ( 16 / 23 )8.531714285714290.0450713588473505189.293478251007
Winsorized Mean ( 17 / 23 )8.531714285714290.0450713588473505189.293478251007
Winsorized Mean ( 18 / 23 )8.536857142857140.0436186859767843195.715596462507
Winsorized Mean ( 19 / 23 )8.539571428571430.043235325884261197.513751866505
Winsorized Mean ( 20 / 23 )8.539571428571430.042452475298581201.156030797028
Winsorized Mean ( 21 / 23 )8.542571428571430.041219849745164207.244118583272
Winsorized Mean ( 22 / 23 )8.542571428571430.0403713024135035211.600095064411
Winsorized Mean ( 23 / 23 )8.552428571428570.0390309298779056219.119262548492
Trimmed Mean ( 1 / 23 )8.514558823529410.0522023456492858163.106824370179
Trimmed Mean ( 2 / 23 )8.51803030303030.0516931143814222164.780752813213
Trimmed Mean ( 3 / 23 )8.52093750.0513685324734143165.878546450787
Trimmed Mean ( 4 / 23 )8.523870967741940.0511689659831396166.582826210531
Trimmed Mean ( 5 / 23 )8.526833333333330.050917842136468167.462582378885
Trimmed Mean ( 6 / 23 )8.529137931034480.0508293495504957167.799470315105
Trimmed Mean ( 7 / 23 )8.530892857142860.0508156055292675167.879389968687
Trimmed Mean ( 8 / 23 )8.532407407407410.0508797071252165167.697651765347
Trimmed Mean ( 9 / 23 )8.533846153846150.0509932668241527167.352411118798
Trimmed Mean ( 10 / 23 )8.53540.0511214719854503166.963110968895
Trimmed Mean ( 11 / 23 )8.5368750.0512262367066688166.650442211552
Trimmed Mean ( 12 / 23 )8.538478260869570.051341395368522166.307873005427
Trimmed Mean ( 13 / 23 )8.540227272727270.051368675967476166.253599336189
Trimmed Mean ( 14 / 23 )8.542380952380950.0513293769578993166.422845135788
Trimmed Mean ( 15 / 23 )8.5440.0514517448808303166.058508215594
Trimmed Mean ( 16 / 23 )8.545789473684210.0515763345928652165.6920667423
Trimmed Mean ( 17 / 23 )8.54750.0516372804295378165.529631477467
Trimmed Mean ( 18 / 23 )8.549411764705880.0515273687318315165.919820381288
Trimmed Mean ( 19 / 23 )8.55093750.0515219170694188165.966990096249
Trimmed Mean ( 20 / 23 )8.552333333333330.0513735101768676166.473602911102
Trimmed Mean ( 21 / 23 )8.553928571428570.0511128518139942167.353772443716
Trimmed Mean ( 22 / 23 )8.555384615384620.050806513117394168.39149334292
Trimmed Mean ( 23 / 23 )8.557083333333330.0502835408526123170.176626153184
Median8.605
Midrange8.385
Midmean - Weighted Average at Xnp8.52333333333333
Midmean - Weighted Average at X(n+1)p8.55615384615384
Midmean - Empirical Distribution Function8.55615384615384
Midmean - Empirical Distribution Function - Averaging8.55615384615384
Midmean - Empirical Distribution Function - Interpolation8.54941176470588
Midmean - Closest Observation8.55615384615384
Midmean - True Basic - Statistics Graphics Toolkit8.55615384615384
Midmean - MS Excel (old versions)8.55615384615384
Number of observations70



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')