Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 20 Nov 2009 07:39:41 -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/2009/Nov/20/t1258728072zqb2zdqe58n4j73.htm/, Retrieved Fri, 29 Mar 2024 15:25:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58221, Retrieved Fri, 29 Mar 2024 15:25:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsETSHWP(4)
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [invoer-textiel] [2008-12-19 19:19:44] [5e74953d94072114d25d7276793b561e]
-   PD  [Multiple Regression] [invoer-textiel] [2008-12-19 19:31:41] [5e74953d94072114d25d7276793b561e]
-   PD    [Multiple Regression] [werkloosheid/invoer] [2008-12-19 20:08:51] [5e74953d94072114d25d7276793b561e]
- RM D        [Central Tendency] [Paper statistiek:...] [2009-11-20 14:39:41] [af31b947d6acaef3c71f428c4bb503e9] [Current]
Feedback Forum

Post a new message
Dataseries X:
0,51
0,51
0,51
0,51
0,52
0,52
0,52
0,53
0,53
0,52
0,52
0,52
0,52
0,52
0,52
0,52
0,52
0,52
0,52
0,53
0,53
0,53
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,54
0,53
0,53
0,53
0,53
0,53
0,54
0,55
0,55
0,55
0,55
0,55
0,55
0,55
0,55
0,56
0,56
0,56
0,56
0,56
0,55
0,56
0,55
0,55
0,56
0,55
0,55
0,55
0,55




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58221&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58221&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5368333333333330.00195271311570365274.916642396744
Geometric Mean0.536623283882939
Harmonic Mean0.536412774524785
Quadratic Mean0.537042828832115
Winsorized Mean ( 1 / 20 )0.5368333333333330.00195271311570365274.916642396744
Winsorized Mean ( 2 / 20 )0.5368333333333330.00195271311570365274.916642396744
Winsorized Mean ( 3 / 20 )0.5368333333333330.00195271311570365274.916642396744
Winsorized Mean ( 4 / 20 )0.53750.00181993046368683295.340954352249
Winsorized Mean ( 5 / 20 )0.53750.00181993046368683295.340954352249
Winsorized Mean ( 6 / 20 )0.53750.00181993046368683295.340954352249
Winsorized Mean ( 7 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 8 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 9 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 10 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 11 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 12 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 13 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 14 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 15 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 16 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 17 / 20 )0.5391666666666670.00117149927278653460.236450155198
Winsorized Mean ( 18 / 20 )0.5391666666666670.00117149927278653460.236450155198
Winsorized Mean ( 19 / 20 )0.5391666666666670.00117149927278653460.236450155198
Winsorized Mean ( 20 / 20 )0.5391666666666670.00117149927278653460.236450155198
Trimmed Mean ( 1 / 20 )0.5368965517241380.00192426000345662279.014556639795
Trimmed Mean ( 2 / 20 )0.5369642857142860.00188844130836496284.342586309552
Trimmed Mean ( 3 / 20 )0.5370370370370370.00184344703455955291.322195305356
Trimmed Mean ( 4 / 20 )0.5371153846153850.00178684100830338300.594950596852
Trimmed Mean ( 5 / 20 )0.5370.00176704526812186303.897138170525
Trimmed Mean ( 6 / 20 )0.5368750.00174012538270026308.526618447975
Trimmed Mean ( 7 / 20 )0.5367391304347830.00170405449511665314.977679395190
Trimmed Mean ( 8 / 20 )0.5368181818181820.00171341946575145313.302254671625
Trimmed Mean ( 9 / 20 )0.5369047619047620.0017205492747898312.054278114386
Trimmed Mean ( 10 / 20 )0.5370.00172463299700515311.370593588611
Trimmed Mean ( 11 / 20 )0.5371052631578950.00172455674874333311.445398099703
Trimmed Mean ( 12 / 20 )0.5372222222222220.00171876252600855312.563378647662
Trimmed Mean ( 13 / 20 )0.5373529411764710.00170502160348318315.159022078498
Trimmed Mean ( 14 / 20 )0.53750.00168005376258062319.930237931423
Trimmed Mean ( 15 / 20 )0.5376666666666670.0016388483013352328.075921504522
Trimmed Mean ( 16 / 20 )0.5378571428571430.00157335139695230341.854428641314
Trimmed Mean ( 17 / 20 )0.5380769230769230.00146961332111868366.135033851854
Trimmed Mean ( 18 / 20 )0.5379166666666670.00147185757948910365.467878253128
Trimmed Mean ( 19 / 20 )0.5377272727272730.00146115920621106368.014156459828
Trimmed Mean ( 20 / 20 )0.53750.0014281014264437376.373827549839
Median0.54
Midrange0.535
Midmean - Weighted Average at Xnp0.535714285714286
Midmean - Weighted Average at X(n+1)p0.535714285714286
Midmean - Empirical Distribution Function0.535714285714286
Midmean - Empirical Distribution Function - Averaging0.535714285714286
Midmean - Empirical Distribution Function - Interpolation0.535714285714286
Midmean - Closest Observation0.535714285714286
Midmean - True Basic - Statistics Graphics Toolkit0.535714285714286
Midmean - MS Excel (old versions)0.535714285714286
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.536833333333333 & 0.00195271311570365 & 274.916642396744 \tabularnewline
Geometric Mean & 0.536623283882939 &  &  \tabularnewline
Harmonic Mean & 0.536412774524785 &  &  \tabularnewline
Quadratic Mean & 0.537042828832115 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.536833333333333 & 0.00195271311570365 & 274.916642396744 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.536833333333333 & 0.00195271311570365 & 274.916642396744 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.536833333333333 & 0.00195271311570365 & 274.916642396744 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.5375 & 0.00181993046368683 & 295.340954352249 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.5375 & 0.00181993046368683 & 295.340954352249 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.5375 & 0.00181993046368683 & 295.340954352249 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.536333333333333 & 0.00161151693051169 & 332.812720225681 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.539166666666667 & 0.00117149927278653 & 460.236450155198 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.539166666666667 & 0.00117149927278653 & 460.236450155198 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.539166666666667 & 0.00117149927278653 & 460.236450155198 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.539166666666667 & 0.00117149927278653 & 460.236450155198 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.536896551724138 & 0.00192426000345662 & 279.014556639795 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.536964285714286 & 0.00188844130836496 & 284.342586309552 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.537037037037037 & 0.00184344703455955 & 291.322195305356 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.537115384615385 & 0.00178684100830338 & 300.594950596852 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.537 & 0.00176704526812186 & 303.897138170525 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.536875 & 0.00174012538270026 & 308.526618447975 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.536739130434783 & 0.00170405449511665 & 314.977679395190 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.536818181818182 & 0.00171341946575145 & 313.302254671625 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.536904761904762 & 0.0017205492747898 & 312.054278114386 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.537 & 0.00172463299700515 & 311.370593588611 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.537105263157895 & 0.00172455674874333 & 311.445398099703 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.537222222222222 & 0.00171876252600855 & 312.563378647662 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.537352941176471 & 0.00170502160348318 & 315.159022078498 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.5375 & 0.00168005376258062 & 319.930237931423 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.537666666666667 & 0.0016388483013352 & 328.075921504522 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.537857142857143 & 0.00157335139695230 & 341.854428641314 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.538076923076923 & 0.00146961332111868 & 366.135033851854 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.537916666666667 & 0.00147185757948910 & 365.467878253128 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.537727272727273 & 0.00146115920621106 & 368.014156459828 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.5375 & 0.0014281014264437 & 376.373827549839 \tabularnewline
Median & 0.54 &  &  \tabularnewline
Midrange & 0.535 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.535714285714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.535714285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.535714285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.535714285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.535714285714286 &  &  \tabularnewline
Midmean - Closest Observation & 0.535714285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.535714285714286 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.535714285714286 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58221&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.536833333333333[/C][C]0.00195271311570365[/C][C]274.916642396744[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.536623283882939[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.536412774524785[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.537042828832115[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.536833333333333[/C][C]0.00195271311570365[/C][C]274.916642396744[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.536833333333333[/C][C]0.00195271311570365[/C][C]274.916642396744[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.536833333333333[/C][C]0.00195271311570365[/C][C]274.916642396744[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.5375[/C][C]0.00181993046368683[/C][C]295.340954352249[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.5375[/C][C]0.00181993046368683[/C][C]295.340954352249[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.5375[/C][C]0.00181993046368683[/C][C]295.340954352249[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.536333333333333[/C][C]0.00161151693051169[/C][C]332.812720225681[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.539166666666667[/C][C]0.00117149927278653[/C][C]460.236450155198[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.539166666666667[/C][C]0.00117149927278653[/C][C]460.236450155198[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.539166666666667[/C][C]0.00117149927278653[/C][C]460.236450155198[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.539166666666667[/C][C]0.00117149927278653[/C][C]460.236450155198[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.536896551724138[/C][C]0.00192426000345662[/C][C]279.014556639795[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.536964285714286[/C][C]0.00188844130836496[/C][C]284.342586309552[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.537037037037037[/C][C]0.00184344703455955[/C][C]291.322195305356[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.537115384615385[/C][C]0.00178684100830338[/C][C]300.594950596852[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.537[/C][C]0.00176704526812186[/C][C]303.897138170525[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.536875[/C][C]0.00174012538270026[/C][C]308.526618447975[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.536739130434783[/C][C]0.00170405449511665[/C][C]314.977679395190[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.536818181818182[/C][C]0.00171341946575145[/C][C]313.302254671625[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.536904761904762[/C][C]0.0017205492747898[/C][C]312.054278114386[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.537[/C][C]0.00172463299700515[/C][C]311.370593588611[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.537105263157895[/C][C]0.00172455674874333[/C][C]311.445398099703[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.537222222222222[/C][C]0.00171876252600855[/C][C]312.563378647662[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.537352941176471[/C][C]0.00170502160348318[/C][C]315.159022078498[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.5375[/C][C]0.00168005376258062[/C][C]319.930237931423[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.537666666666667[/C][C]0.0016388483013352[/C][C]328.075921504522[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.537857142857143[/C][C]0.00157335139695230[/C][C]341.854428641314[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.538076923076923[/C][C]0.00146961332111868[/C][C]366.135033851854[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.537916666666667[/C][C]0.00147185757948910[/C][C]365.467878253128[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.537727272727273[/C][C]0.00146115920621106[/C][C]368.014156459828[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.5375[/C][C]0.0014281014264437[/C][C]376.373827549839[/C][/ROW]
[ROW][C]Median[/C][C]0.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.535[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.535714285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58221&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5368333333333330.00195271311570365274.916642396744
Geometric Mean0.536623283882939
Harmonic Mean0.536412774524785
Quadratic Mean0.537042828832115
Winsorized Mean ( 1 / 20 )0.5368333333333330.00195271311570365274.916642396744
Winsorized Mean ( 2 / 20 )0.5368333333333330.00195271311570365274.916642396744
Winsorized Mean ( 3 / 20 )0.5368333333333330.00195271311570365274.916642396744
Winsorized Mean ( 4 / 20 )0.53750.00181993046368683295.340954352249
Winsorized Mean ( 5 / 20 )0.53750.00181993046368683295.340954352249
Winsorized Mean ( 6 / 20 )0.53750.00181993046368683295.340954352249
Winsorized Mean ( 7 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 8 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 9 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 10 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 11 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 12 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 13 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 14 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 15 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 16 / 20 )0.5363333333333330.00161151693051169332.812720225681
Winsorized Mean ( 17 / 20 )0.5391666666666670.00117149927278653460.236450155198
Winsorized Mean ( 18 / 20 )0.5391666666666670.00117149927278653460.236450155198
Winsorized Mean ( 19 / 20 )0.5391666666666670.00117149927278653460.236450155198
Winsorized Mean ( 20 / 20 )0.5391666666666670.00117149927278653460.236450155198
Trimmed Mean ( 1 / 20 )0.5368965517241380.00192426000345662279.014556639795
Trimmed Mean ( 2 / 20 )0.5369642857142860.00188844130836496284.342586309552
Trimmed Mean ( 3 / 20 )0.5370370370370370.00184344703455955291.322195305356
Trimmed Mean ( 4 / 20 )0.5371153846153850.00178684100830338300.594950596852
Trimmed Mean ( 5 / 20 )0.5370.00176704526812186303.897138170525
Trimmed Mean ( 6 / 20 )0.5368750.00174012538270026308.526618447975
Trimmed Mean ( 7 / 20 )0.5367391304347830.00170405449511665314.977679395190
Trimmed Mean ( 8 / 20 )0.5368181818181820.00171341946575145313.302254671625
Trimmed Mean ( 9 / 20 )0.5369047619047620.0017205492747898312.054278114386
Trimmed Mean ( 10 / 20 )0.5370.00172463299700515311.370593588611
Trimmed Mean ( 11 / 20 )0.5371052631578950.00172455674874333311.445398099703
Trimmed Mean ( 12 / 20 )0.5372222222222220.00171876252600855312.563378647662
Trimmed Mean ( 13 / 20 )0.5373529411764710.00170502160348318315.159022078498
Trimmed Mean ( 14 / 20 )0.53750.00168005376258062319.930237931423
Trimmed Mean ( 15 / 20 )0.5376666666666670.0016388483013352328.075921504522
Trimmed Mean ( 16 / 20 )0.5378571428571430.00157335139695230341.854428641314
Trimmed Mean ( 17 / 20 )0.5380769230769230.00146961332111868366.135033851854
Trimmed Mean ( 18 / 20 )0.5379166666666670.00147185757948910365.467878253128
Trimmed Mean ( 19 / 20 )0.5377272727272730.00146115920621106368.014156459828
Trimmed Mean ( 20 / 20 )0.53750.0014281014264437376.373827549839
Median0.54
Midrange0.535
Midmean - Weighted Average at Xnp0.535714285714286
Midmean - Weighted Average at X(n+1)p0.535714285714286
Midmean - Empirical Distribution Function0.535714285714286
Midmean - Empirical Distribution Function - Averaging0.535714285714286
Midmean - Empirical Distribution Function - Interpolation0.535714285714286
Midmean - Closest Observation0.535714285714286
Midmean - True Basic - Statistics Graphics Toolkit0.535714285714286
Midmean - MS Excel (old versions)0.535714285714286
Number of observations60



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')