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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 28 Feb 2013 15:02:31 -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/2013/Feb/28/t1362081796f4tgjos0klo3zmk.htm/, Retrieved Wed, 01 May 2024 23:07:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207206, Retrieved Wed, 01 May 2024 23:07:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Werkloosheidsinde...] [2013-02-28 20:02:31] [66913edeccd589e3e35c84ad0be9abda] [Current]
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Dataseries X:
8,5
8,5
8,5
8,6
8,6
8,4
8,2
8
8
8
8
7,9
7,9
7,9
7,9
8
7,9
7,4
7,2
7
6,9
7,1
7,2
7,2
7,1
6,9
6,8
6,8
6,8
6,9
7,1
7,2
7,2
7,1
7,1
7,2
7,5
7,7
7,8
7,7
7,7
7,8
8
8,1
8,1
8
8,1
8,2
8,4
8,5
8,5
8,5
8,5
8,5
8,4
8,3
8,2
8,1
7,9
7,6
7,3
7,1
7
7,1
7,1
7,1
7,3
7,3
7,3
7,2
7,2
7,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207206&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207206&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.683333333333330.0664020570226466115.70926681854
Geometric Mean7.66297447741549
Harmonic Mean7.64267737628506
Quadratic Mean7.70367877488844
Winsorized Mean ( 1 / 24 )7.683333333333330.0664020570226466115.70926681854
Winsorized Mean ( 2 / 24 )7.680555555555560.0658886197072039116.568773024635
Winsorized Mean ( 3 / 24 )7.684722222222220.0651427865369768117.967354955873
Winsorized Mean ( 4 / 24 )7.684722222222220.0651427865369768117.967354955873
Winsorized Mean ( 5 / 24 )7.684722222222220.0651427865369768117.967354955873
Winsorized Mean ( 6 / 24 )7.693055555555560.0637976060821941120.585332710512
Winsorized Mean ( 7 / 24 )7.693055555555560.0637976060821941120.585332710512
Winsorized Mean ( 8 / 24 )7.704166666666670.0621862233081177123.888640551371
Winsorized Mean ( 9 / 24 )7.704166666666670.0621862233081177123.888640551371
Winsorized Mean ( 10 / 24 )7.690277777777780.0597713340302978128.661638602204
Winsorized Mean ( 11 / 24 )7.690277777777780.0597713340302978128.661638602204
Winsorized Mean ( 12 / 24 )7.690277777777780.0597713340302978128.661638602204
Winsorized Mean ( 13 / 24 )7.672222222222220.0568549145421808134.943870446418
Winsorized Mean ( 14 / 24 )7.652777777777780.0539508057892916141.84733046743
Winsorized Mean ( 15 / 24 )7.652777777777780.0539508057892916141.84733046743
Winsorized Mean ( 16 / 24 )7.652777777777780.0539508057892916141.84733046743
Winsorized Mean ( 17 / 24 )7.629166666666670.0507162123393813150.428557551065
Winsorized Mean ( 18 / 24 )7.654166666666670.0471793393616084162.235562647474
Winsorized Mean ( 19 / 24 )7.654166666666670.0471793393616084162.235562647474
Winsorized Mean ( 20 / 24 )7.654166666666670.0471793393616084162.235562647474
Winsorized Mean ( 21 / 24 )7.6250.043459098825626175.452326579397
Winsorized Mean ( 22 / 24 )7.6250.043459098825626175.452326579397
Winsorized Mean ( 23 / 24 )7.6250.043459098825626175.452326579397
Winsorized Mean ( 24 / 24 )7.6250.043459098825626175.452326579397
Trimmed Mean ( 1 / 24 )7.682857142857140.0658114323789245116.740463854689
Trimmed Mean ( 2 / 24 )7.682352941176470.0650838985949975118.037688384066
Trimmed Mean ( 3 / 24 )7.683333333333330.0645075783240052119.107452689386
Trimmed Mean ( 4 / 24 )7.68281250.0641084571896261119.840857771308
Trimmed Mean ( 5 / 24 )7.682258064516130.0635842938123144120.820057972057
Trimmed Mean ( 6 / 24 )7.681666666666670.0629093000888166122.107012092354
Trimmed Mean ( 7 / 24 )7.679310344827590.0624058211511477123.054391452172
Trimmed Mean ( 8 / 24 )7.676785714285710.0617384024246802124.343770048978
Trimmed Mean ( 9 / 24 )7.672222222222220.0612253553817853125.311191325559
Trimmed Mean ( 10 / 24 )7.667307692307690.0605231811694489126.683818400775
Trimmed Mean ( 11 / 24 )7.6640.0601196086725353127.479206355865
Trimmed Mean ( 12 / 24 )7.660416666666670.059529745777953128.682166647245
Trimmed Mean ( 13 / 24 )7.656521739130430.0587019141408312130.430529416157
Trimmed Mean ( 14 / 24 )7.654545454545450.0582019653278001131.51695842974
Trimmed Mean ( 15 / 24 )7.654761904761910.0580562406001083131.850802353669
Trimmed Mean ( 16 / 24 )7.6550.0577294752071444132.601240051679
Trimmed Mean ( 17 / 24 )7.655263157894740.0571610696759732133.924420961501
Trimmed Mean ( 18 / 24 )7.658333333333330.056956541494789134.459240893937
Trimmed Mean ( 19 / 24 )7.658823529411770.0572883451761975133.68903405843
Trimmed Mean ( 20 / 24 )7.6593750.0574770948417856133.259605780069
Trimmed Mean ( 21 / 24 )7.660.0574556300573526133.320268046034
Trimmed Mean ( 22 / 24 )7.664285714285710.0580125615192841132.114244114837
Trimmed Mean ( 23 / 24 )7.669230769230770.0583805106492624131.366284466161
Trimmed Mean ( 24 / 24 )7.6750.0584367613105293131.338558603813
Median7.75
Midrange7.7
Midmean - Weighted Average at Xnp7.54893617021277
Midmean - Weighted Average at X(n+1)p7.67027027027027
Midmean - Empirical Distribution Function7.54893617021277
Midmean - Empirical Distribution Function - Averaging7.67027027027027
Midmean - Empirical Distribution Function - Interpolation7.67027027027027
Midmean - Closest Observation7.54893617021277
Midmean - True Basic - Statistics Graphics Toolkit7.67027027027027
Midmean - MS Excel (old versions)7.54893617021277
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.68333333333333 & 0.0664020570226466 & 115.70926681854 \tabularnewline
Geometric Mean & 7.66297447741549 &  &  \tabularnewline
Harmonic Mean & 7.64267737628506 &  &  \tabularnewline
Quadratic Mean & 7.70367877488844 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.68333333333333 & 0.0664020570226466 & 115.70926681854 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.68055555555556 & 0.0658886197072039 & 116.568773024635 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.68472222222222 & 0.0651427865369768 & 117.967354955873 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.68472222222222 & 0.0651427865369768 & 117.967354955873 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.68472222222222 & 0.0651427865369768 & 117.967354955873 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.69305555555556 & 0.0637976060821941 & 120.585332710512 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.69305555555556 & 0.0637976060821941 & 120.585332710512 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.70416666666667 & 0.0621862233081177 & 123.888640551371 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.70416666666667 & 0.0621862233081177 & 123.888640551371 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.69027777777778 & 0.0597713340302978 & 128.661638602204 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.69027777777778 & 0.0597713340302978 & 128.661638602204 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.69027777777778 & 0.0597713340302978 & 128.661638602204 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.67222222222222 & 0.0568549145421808 & 134.943870446418 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.65277777777778 & 0.0539508057892916 & 141.84733046743 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.65277777777778 & 0.0539508057892916 & 141.84733046743 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.65277777777778 & 0.0539508057892916 & 141.84733046743 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.62916666666667 & 0.0507162123393813 & 150.428557551065 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.65416666666667 & 0.0471793393616084 & 162.235562647474 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.65416666666667 & 0.0471793393616084 & 162.235562647474 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.65416666666667 & 0.0471793393616084 & 162.235562647474 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.625 & 0.043459098825626 & 175.452326579397 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7.625 & 0.043459098825626 & 175.452326579397 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7.625 & 0.043459098825626 & 175.452326579397 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7.625 & 0.043459098825626 & 175.452326579397 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.68285714285714 & 0.0658114323789245 & 116.740463854689 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.68235294117647 & 0.0650838985949975 & 118.037688384066 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.68333333333333 & 0.0645075783240052 & 119.107452689386 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.6828125 & 0.0641084571896261 & 119.840857771308 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.68225806451613 & 0.0635842938123144 & 120.820057972057 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.68166666666667 & 0.0629093000888166 & 122.107012092354 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.67931034482759 & 0.0624058211511477 & 123.054391452172 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.67678571428571 & 0.0617384024246802 & 124.343770048978 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.67222222222222 & 0.0612253553817853 & 125.311191325559 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.66730769230769 & 0.0605231811694489 & 126.683818400775 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.664 & 0.0601196086725353 & 127.479206355865 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.66041666666667 & 0.059529745777953 & 128.682166647245 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.65652173913043 & 0.0587019141408312 & 130.430529416157 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.65454545454545 & 0.0582019653278001 & 131.51695842974 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7.65476190476191 & 0.0580562406001083 & 131.850802353669 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7.655 & 0.0577294752071444 & 132.601240051679 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7.65526315789474 & 0.0571610696759732 & 133.924420961501 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7.65833333333333 & 0.056956541494789 & 134.459240893937 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7.65882352941177 & 0.0572883451761975 & 133.68903405843 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7.659375 & 0.0574770948417856 & 133.259605780069 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7.66 & 0.0574556300573526 & 133.320268046034 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7.66428571428571 & 0.0580125615192841 & 132.114244114837 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7.66923076923077 & 0.0583805106492624 & 131.366284466161 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7.675 & 0.0584367613105293 & 131.338558603813 \tabularnewline
Median & 7.75 &  &  \tabularnewline
Midrange & 7.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.54893617021277 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.67027027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.54893617021277 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.67027027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.67027027027027 &  &  \tabularnewline
Midmean - Closest Observation & 7.54893617021277 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.67027027027027 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.54893617021277 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207206&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]7.68333333333333[/C][C]0.0664020570226466[/C][C]115.70926681854[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.66297447741549[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.64267737628506[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.70367877488844[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.68333333333333[/C][C]0.0664020570226466[/C][C]115.70926681854[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.68055555555556[/C][C]0.0658886197072039[/C][C]116.568773024635[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.68472222222222[/C][C]0.0651427865369768[/C][C]117.967354955873[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.68472222222222[/C][C]0.0651427865369768[/C][C]117.967354955873[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.68472222222222[/C][C]0.0651427865369768[/C][C]117.967354955873[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.69305555555556[/C][C]0.0637976060821941[/C][C]120.585332710512[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.69305555555556[/C][C]0.0637976060821941[/C][C]120.585332710512[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.70416666666667[/C][C]0.0621862233081177[/C][C]123.888640551371[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.70416666666667[/C][C]0.0621862233081177[/C][C]123.888640551371[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.69027777777778[/C][C]0.0597713340302978[/C][C]128.661638602204[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.69027777777778[/C][C]0.0597713340302978[/C][C]128.661638602204[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.69027777777778[/C][C]0.0597713340302978[/C][C]128.661638602204[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.67222222222222[/C][C]0.0568549145421808[/C][C]134.943870446418[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.65277777777778[/C][C]0.0539508057892916[/C][C]141.84733046743[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.65277777777778[/C][C]0.0539508057892916[/C][C]141.84733046743[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.65277777777778[/C][C]0.0539508057892916[/C][C]141.84733046743[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.62916666666667[/C][C]0.0507162123393813[/C][C]150.428557551065[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.65416666666667[/C][C]0.0471793393616084[/C][C]162.235562647474[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.65416666666667[/C][C]0.0471793393616084[/C][C]162.235562647474[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.65416666666667[/C][C]0.0471793393616084[/C][C]162.235562647474[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.625[/C][C]0.043459098825626[/C][C]175.452326579397[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7.625[/C][C]0.043459098825626[/C][C]175.452326579397[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7.625[/C][C]0.043459098825626[/C][C]175.452326579397[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7.625[/C][C]0.043459098825626[/C][C]175.452326579397[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.68285714285714[/C][C]0.0658114323789245[/C][C]116.740463854689[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.68235294117647[/C][C]0.0650838985949975[/C][C]118.037688384066[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.68333333333333[/C][C]0.0645075783240052[/C][C]119.107452689386[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.6828125[/C][C]0.0641084571896261[/C][C]119.840857771308[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.68225806451613[/C][C]0.0635842938123144[/C][C]120.820057972057[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.68166666666667[/C][C]0.0629093000888166[/C][C]122.107012092354[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.67931034482759[/C][C]0.0624058211511477[/C][C]123.054391452172[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.67678571428571[/C][C]0.0617384024246802[/C][C]124.343770048978[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.67222222222222[/C][C]0.0612253553817853[/C][C]125.311191325559[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.66730769230769[/C][C]0.0605231811694489[/C][C]126.683818400775[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.664[/C][C]0.0601196086725353[/C][C]127.479206355865[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.66041666666667[/C][C]0.059529745777953[/C][C]128.682166647245[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.65652173913043[/C][C]0.0587019141408312[/C][C]130.430529416157[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.65454545454545[/C][C]0.0582019653278001[/C][C]131.51695842974[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7.65476190476191[/C][C]0.0580562406001083[/C][C]131.850802353669[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7.655[/C][C]0.0577294752071444[/C][C]132.601240051679[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7.65526315789474[/C][C]0.0571610696759732[/C][C]133.924420961501[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7.65833333333333[/C][C]0.056956541494789[/C][C]134.459240893937[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7.65882352941177[/C][C]0.0572883451761975[/C][C]133.68903405843[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7.659375[/C][C]0.0574770948417856[/C][C]133.259605780069[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7.66[/C][C]0.0574556300573526[/C][C]133.320268046034[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7.66428571428571[/C][C]0.0580125615192841[/C][C]132.114244114837[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7.66923076923077[/C][C]0.0583805106492624[/C][C]131.366284466161[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7.675[/C][C]0.0584367613105293[/C][C]131.338558603813[/C][/ROW]
[ROW][C]Median[/C][C]7.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.54893617021277[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.67027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.54893617021277[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.67027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.67027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.54893617021277[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.67027027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.54893617021277[/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=207206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207206&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 Mean7.683333333333330.0664020570226466115.70926681854
Geometric Mean7.66297447741549
Harmonic Mean7.64267737628506
Quadratic Mean7.70367877488844
Winsorized Mean ( 1 / 24 )7.683333333333330.0664020570226466115.70926681854
Winsorized Mean ( 2 / 24 )7.680555555555560.0658886197072039116.568773024635
Winsorized Mean ( 3 / 24 )7.684722222222220.0651427865369768117.967354955873
Winsorized Mean ( 4 / 24 )7.684722222222220.0651427865369768117.967354955873
Winsorized Mean ( 5 / 24 )7.684722222222220.0651427865369768117.967354955873
Winsorized Mean ( 6 / 24 )7.693055555555560.0637976060821941120.585332710512
Winsorized Mean ( 7 / 24 )7.693055555555560.0637976060821941120.585332710512
Winsorized Mean ( 8 / 24 )7.704166666666670.0621862233081177123.888640551371
Winsorized Mean ( 9 / 24 )7.704166666666670.0621862233081177123.888640551371
Winsorized Mean ( 10 / 24 )7.690277777777780.0597713340302978128.661638602204
Winsorized Mean ( 11 / 24 )7.690277777777780.0597713340302978128.661638602204
Winsorized Mean ( 12 / 24 )7.690277777777780.0597713340302978128.661638602204
Winsorized Mean ( 13 / 24 )7.672222222222220.0568549145421808134.943870446418
Winsorized Mean ( 14 / 24 )7.652777777777780.0539508057892916141.84733046743
Winsorized Mean ( 15 / 24 )7.652777777777780.0539508057892916141.84733046743
Winsorized Mean ( 16 / 24 )7.652777777777780.0539508057892916141.84733046743
Winsorized Mean ( 17 / 24 )7.629166666666670.0507162123393813150.428557551065
Winsorized Mean ( 18 / 24 )7.654166666666670.0471793393616084162.235562647474
Winsorized Mean ( 19 / 24 )7.654166666666670.0471793393616084162.235562647474
Winsorized Mean ( 20 / 24 )7.654166666666670.0471793393616084162.235562647474
Winsorized Mean ( 21 / 24 )7.6250.043459098825626175.452326579397
Winsorized Mean ( 22 / 24 )7.6250.043459098825626175.452326579397
Winsorized Mean ( 23 / 24 )7.6250.043459098825626175.452326579397
Winsorized Mean ( 24 / 24 )7.6250.043459098825626175.452326579397
Trimmed Mean ( 1 / 24 )7.682857142857140.0658114323789245116.740463854689
Trimmed Mean ( 2 / 24 )7.682352941176470.0650838985949975118.037688384066
Trimmed Mean ( 3 / 24 )7.683333333333330.0645075783240052119.107452689386
Trimmed Mean ( 4 / 24 )7.68281250.0641084571896261119.840857771308
Trimmed Mean ( 5 / 24 )7.682258064516130.0635842938123144120.820057972057
Trimmed Mean ( 6 / 24 )7.681666666666670.0629093000888166122.107012092354
Trimmed Mean ( 7 / 24 )7.679310344827590.0624058211511477123.054391452172
Trimmed Mean ( 8 / 24 )7.676785714285710.0617384024246802124.343770048978
Trimmed Mean ( 9 / 24 )7.672222222222220.0612253553817853125.311191325559
Trimmed Mean ( 10 / 24 )7.667307692307690.0605231811694489126.683818400775
Trimmed Mean ( 11 / 24 )7.6640.0601196086725353127.479206355865
Trimmed Mean ( 12 / 24 )7.660416666666670.059529745777953128.682166647245
Trimmed Mean ( 13 / 24 )7.656521739130430.0587019141408312130.430529416157
Trimmed Mean ( 14 / 24 )7.654545454545450.0582019653278001131.51695842974
Trimmed Mean ( 15 / 24 )7.654761904761910.0580562406001083131.850802353669
Trimmed Mean ( 16 / 24 )7.6550.0577294752071444132.601240051679
Trimmed Mean ( 17 / 24 )7.655263157894740.0571610696759732133.924420961501
Trimmed Mean ( 18 / 24 )7.658333333333330.056956541494789134.459240893937
Trimmed Mean ( 19 / 24 )7.658823529411770.0572883451761975133.68903405843
Trimmed Mean ( 20 / 24 )7.6593750.0574770948417856133.259605780069
Trimmed Mean ( 21 / 24 )7.660.0574556300573526133.320268046034
Trimmed Mean ( 22 / 24 )7.664285714285710.0580125615192841132.114244114837
Trimmed Mean ( 23 / 24 )7.669230769230770.0583805106492624131.366284466161
Trimmed Mean ( 24 / 24 )7.6750.0584367613105293131.338558603813
Median7.75
Midrange7.7
Midmean - Weighted Average at Xnp7.54893617021277
Midmean - Weighted Average at X(n+1)p7.67027027027027
Midmean - Empirical Distribution Function7.54893617021277
Midmean - Empirical Distribution Function - Averaging7.67027027027027
Midmean - Empirical Distribution Function - Interpolation7.67027027027027
Midmean - Closest Observation7.54893617021277
Midmean - True Basic - Statistics Graphics Toolkit7.67027027027027
Midmean - MS Excel (old versions)7.54893617021277
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')