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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, 24 Apr 2008 08:50:24 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/24/t12090487190pl4x0nqsv0x53w.htm/, Retrieved Sun, 12 May 2024 08:29:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10695, Retrieved Sun, 12 May 2024 08:29:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact262
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten eige...] [2008-04-24 14:50:24] [9ed44c8445a965e8d6beecda46dd06a5] [Current]
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Dataseries X:
7,1
7,1
7,3
7,1
7,4
7,3
7,4
7,6
7,8
7,7
8
8,1
7,7
7,9
8,1
8,1
8,2
8,1
8,3
8,3
8,3
8,5
8,7
8,7
8,4
8,4
8,6
8,7
8,7
8,6
8
8,1
8,1
8,5
8,6
8,6
8,3
8,3
8,5
9,2
9,2
9
7,4
7,3
7,4
8,6
8,7
8,7
8,5
8,4
8,6
8,4
8,4
8,2
7,7
7,6
7,7
8,1
8,2
8,3
8,1
8
8,2
7,6
7,7
7,6
6,9
6,9
7
7,4
7,4
7,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10695&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10695&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10695&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.043055555555560.06604245294121.786142057181
Geometric Mean8.0235241236409
Harmonic Mean8.00372313398643
Quadratic Mean8.06228358882684
Winsorized Mean ( 1 / 24 )8.043055555555560.06604245294121.786142057181
Winsorized Mean ( 2 / 24 )8.040277777777780.0641136669791564125.406612296746
Winsorized Mean ( 3 / 24 )8.031944444444440.0608953278839538131.897548195334
Winsorized Mean ( 4 / 24 )8.031944444444440.0608953278839538131.897548195334
Winsorized Mean ( 5 / 24 )8.031944444444440.0608953278839538131.897548195334
Winsorized Mean ( 6 / 24 )8.048611111111110.0575651313627347139.817471454976
Winsorized Mean ( 7 / 24 )8.048611111111110.0575651313627347139.817471454976
Winsorized Mean ( 8 / 24 )8.048611111111110.0575651313627347139.817471454976
Winsorized Mean ( 9 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 10 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 11 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 12 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 13 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 14 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 15 / 24 )8.048611111111110.0470155076951465171.190560427405
Winsorized Mean ( 16 / 24 )8.070833333333330.0434900335748812185.578917050891
Winsorized Mean ( 17 / 24 )8.070833333333330.0434900335748812185.578917050891
Winsorized Mean ( 18 / 24 )8.070833333333330.0434900335748812185.578917050891
Winsorized Mean ( 19 / 24 )8.044444444444440.0399965221927509201.128598273538
Winsorized Mean ( 20 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 21 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 22 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 23 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 24 / 24 )8.038888888888890.0316818320219066253.738132420195
Trimmed Mean ( 1 / 24 )8.042857142857140.063785725298444126.091803537951
Trimmed Mean ( 2 / 24 )8.042647058823530.0610960820347246131.639325975967
Trimmed Mean ( 3 / 24 )8.04393939393940.0591363163055902136.023680480399
Trimmed Mean ( 4 / 24 )8.04843750.0582479046007406138.175571381801
Trimmed Mean ( 5 / 24 )8.053225806451610.0571543477859567140.903117932707
Trimmed Mean ( 6 / 24 )8.058333333333330.0558089794258723144.391340179168
Trimmed Mean ( 7 / 24 )8.06034482758620.0551047868959955146.273042354728
Trimmed Mean ( 8 / 24 )8.06250.0542099394250495148.727338298306
Trimmed Mean ( 9 / 24 )8.064814814814810.0530783611346149151.941669682702
Trimmed Mean ( 10 / 24 )8.067307692307690.052589158211879153.402487634522
Trimmed Mean ( 11 / 24 )8.070.0519222338439607155.424745866142
Trimmed Mean ( 12 / 24 )8.072916666666670.0510301314943531158.199017526733
Trimmed Mean ( 13 / 24 )8.076086956521740.0498485418708919162.012501337328
Trimmed Mean ( 14 / 24 )8.079545454545460.0482877589938972167.320779072944
Trimmed Mean ( 15 / 24 )8.083333333333330.0462177679589405174.896661831755
Trimmed Mean ( 16 / 24 )8.08750.0450338192006282179.587255612715
Trimmed Mean ( 17 / 24 )8.089473684210530.0442721239923165182.721607971970
Trimmed Mean ( 18 / 24 )8.091666666666670.0431635869465831187.465112125192
Trimmed Mean ( 19 / 24 )8.094117647058820.041569300098819194.713830346371
Trimmed Mean ( 20 / 24 )8.10.0401609664451250201.688373487417
Trimmed Mean ( 21 / 24 )8.103333333333330.0393870663564651205.735894620728
Trimmed Mean ( 22 / 24 )8.107142857142860.0381200316143582212.674085351210
Trimmed Mean ( 23 / 24 )8.111538461538460.0360883203253536224.769077319450
Trimmed Mean ( 24 / 24 )8.116666666666670.0327853507996047247.569919757105
Median8.1
Midrange8.05
Midmean - Weighted Average at Xnp8.09756097560975
Midmean - Weighted Average at X(n+1)p8.09756097560975
Midmean - Empirical Distribution Function8.09756097560975
Midmean - Empirical Distribution Function - Averaging8.09756097560975
Midmean - Empirical Distribution Function - Interpolation8.09756097560975
Midmean - Closest Observation8.09756097560975
Midmean - True Basic - Statistics Graphics Toolkit8.09756097560975
Midmean - MS Excel (old versions)8.09756097560975
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.04305555555556 & 0.06604245294 & 121.786142057181 \tabularnewline
Geometric Mean & 8.0235241236409 &  &  \tabularnewline
Harmonic Mean & 8.00372313398643 &  &  \tabularnewline
Quadratic Mean & 8.06228358882684 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.04305555555556 & 0.06604245294 & 121.786142057181 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.04027777777778 & 0.0641136669791564 & 125.406612296746 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.03194444444444 & 0.0608953278839538 & 131.897548195334 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.03194444444444 & 0.0608953278839538 & 131.897548195334 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.03194444444444 & 0.0608953278839538 & 131.897548195334 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.04861111111111 & 0.0575651313627347 & 139.817471454976 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.04861111111111 & 0.0575651313627347 & 139.817471454976 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.04861111111111 & 0.0575651313627347 & 139.817471454976 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.04861111111111 & 0.0534415369346322 & 150.605906431095 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.04861111111111 & 0.0534415369346322 & 150.605906431095 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.04861111111111 & 0.0534415369346322 & 150.605906431095 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 8.04861111111111 & 0.0534415369346322 & 150.605906431095 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 8.04861111111111 & 0.0534415369346322 & 150.605906431095 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.04861111111111 & 0.0534415369346322 & 150.605906431095 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.04861111111111 & 0.0470155076951465 & 171.190560427405 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.07083333333333 & 0.0434900335748812 & 185.578917050891 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.07083333333333 & 0.0434900335748812 & 185.578917050891 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.07083333333333 & 0.0434900335748812 & 185.578917050891 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.04444444444444 & 0.0399965221927509 & 201.128598273538 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.07222222222222 & 0.0357800522221482 & 225.606775867852 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.07222222222222 & 0.0357800522221482 & 225.606775867852 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.07222222222222 & 0.0357800522221482 & 225.606775867852 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.07222222222222 & 0.0357800522221482 & 225.606775867852 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.03888888888889 & 0.0316818320219066 & 253.738132420195 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.04285714285714 & 0.063785725298444 & 126.091803537951 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.04264705882353 & 0.0610960820347246 & 131.639325975967 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.0439393939394 & 0.0591363163055902 & 136.023680480399 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.0484375 & 0.0582479046007406 & 138.175571381801 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.05322580645161 & 0.0571543477859567 & 140.903117932707 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.05833333333333 & 0.0558089794258723 & 144.391340179168 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.0603448275862 & 0.0551047868959955 & 146.273042354728 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.0625 & 0.0542099394250495 & 148.727338298306 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.06481481481481 & 0.0530783611346149 & 151.941669682702 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.06730769230769 & 0.052589158211879 & 153.402487634522 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.07 & 0.0519222338439607 & 155.424745866142 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.07291666666667 & 0.0510301314943531 & 158.199017526733 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.07608695652174 & 0.0498485418708919 & 162.012501337328 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.07954545454546 & 0.0482877589938972 & 167.320779072944 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.08333333333333 & 0.0462177679589405 & 174.896661831755 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.0875 & 0.0450338192006282 & 179.587255612715 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.08947368421053 & 0.0442721239923165 & 182.721607971970 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.09166666666667 & 0.0431635869465831 & 187.465112125192 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.09411764705882 & 0.041569300098819 & 194.713830346371 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.1 & 0.0401609664451250 & 201.688373487417 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.10333333333333 & 0.0393870663564651 & 205.735894620728 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.10714285714286 & 0.0381200316143582 & 212.674085351210 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.11153846153846 & 0.0360883203253536 & 224.769077319450 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.11666666666667 & 0.0327853507996047 & 247.569919757105 \tabularnewline
Median & 8.1 &  &  \tabularnewline
Midrange & 8.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.09756097560975 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.09756097560975 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.09756097560975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.09756097560975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.09756097560975 &  &  \tabularnewline
Midmean - Closest Observation & 8.09756097560975 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.09756097560975 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.09756097560975 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10695&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]8.04305555555556[/C][C]0.06604245294[/C][C]121.786142057181[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.0235241236409[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.00372313398643[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.06228358882684[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.04305555555556[/C][C]0.06604245294[/C][C]121.786142057181[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.04027777777778[/C][C]0.0641136669791564[/C][C]125.406612296746[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.03194444444444[/C][C]0.0608953278839538[/C][C]131.897548195334[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.03194444444444[/C][C]0.0608953278839538[/C][C]131.897548195334[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.03194444444444[/C][C]0.0608953278839538[/C][C]131.897548195334[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.04861111111111[/C][C]0.0575651313627347[/C][C]139.817471454976[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.04861111111111[/C][C]0.0575651313627347[/C][C]139.817471454976[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.04861111111111[/C][C]0.0575651313627347[/C][C]139.817471454976[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.04861111111111[/C][C]0.0534415369346322[/C][C]150.605906431095[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.04861111111111[/C][C]0.0534415369346322[/C][C]150.605906431095[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.04861111111111[/C][C]0.0534415369346322[/C][C]150.605906431095[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]8.04861111111111[/C][C]0.0534415369346322[/C][C]150.605906431095[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]8.04861111111111[/C][C]0.0534415369346322[/C][C]150.605906431095[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.04861111111111[/C][C]0.0534415369346322[/C][C]150.605906431095[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.04861111111111[/C][C]0.0470155076951465[/C][C]171.190560427405[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.07083333333333[/C][C]0.0434900335748812[/C][C]185.578917050891[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.07083333333333[/C][C]0.0434900335748812[/C][C]185.578917050891[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.07083333333333[/C][C]0.0434900335748812[/C][C]185.578917050891[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.04444444444444[/C][C]0.0399965221927509[/C][C]201.128598273538[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.07222222222222[/C][C]0.0357800522221482[/C][C]225.606775867852[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.07222222222222[/C][C]0.0357800522221482[/C][C]225.606775867852[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.07222222222222[/C][C]0.0357800522221482[/C][C]225.606775867852[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.07222222222222[/C][C]0.0357800522221482[/C][C]225.606775867852[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.03888888888889[/C][C]0.0316818320219066[/C][C]253.738132420195[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.04285714285714[/C][C]0.063785725298444[/C][C]126.091803537951[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.04264705882353[/C][C]0.0610960820347246[/C][C]131.639325975967[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.0439393939394[/C][C]0.0591363163055902[/C][C]136.023680480399[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.0484375[/C][C]0.0582479046007406[/C][C]138.175571381801[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.05322580645161[/C][C]0.0571543477859567[/C][C]140.903117932707[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.05833333333333[/C][C]0.0558089794258723[/C][C]144.391340179168[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.0603448275862[/C][C]0.0551047868959955[/C][C]146.273042354728[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.0625[/C][C]0.0542099394250495[/C][C]148.727338298306[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.06481481481481[/C][C]0.0530783611346149[/C][C]151.941669682702[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.06730769230769[/C][C]0.052589158211879[/C][C]153.402487634522[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.07[/C][C]0.0519222338439607[/C][C]155.424745866142[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.07291666666667[/C][C]0.0510301314943531[/C][C]158.199017526733[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.07608695652174[/C][C]0.0498485418708919[/C][C]162.012501337328[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.07954545454546[/C][C]0.0482877589938972[/C][C]167.320779072944[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.08333333333333[/C][C]0.0462177679589405[/C][C]174.896661831755[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.0875[/C][C]0.0450338192006282[/C][C]179.587255612715[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.08947368421053[/C][C]0.0442721239923165[/C][C]182.721607971970[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.09166666666667[/C][C]0.0431635869465831[/C][C]187.465112125192[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.09411764705882[/C][C]0.041569300098819[/C][C]194.713830346371[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.1[/C][C]0.0401609664451250[/C][C]201.688373487417[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.10333333333333[/C][C]0.0393870663564651[/C][C]205.735894620728[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.10714285714286[/C][C]0.0381200316143582[/C][C]212.674085351210[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.11153846153846[/C][C]0.0360883203253536[/C][C]224.769077319450[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.11666666666667[/C][C]0.0327853507996047[/C][C]247.569919757105[/C][/ROW]
[ROW][C]Median[/C][C]8.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.09756097560975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.09756097560975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.09756097560975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.09756097560975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.09756097560975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.09756097560975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.09756097560975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.09756097560975[/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=10695&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10695&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 Mean8.043055555555560.06604245294121.786142057181
Geometric Mean8.0235241236409
Harmonic Mean8.00372313398643
Quadratic Mean8.06228358882684
Winsorized Mean ( 1 / 24 )8.043055555555560.06604245294121.786142057181
Winsorized Mean ( 2 / 24 )8.040277777777780.0641136669791564125.406612296746
Winsorized Mean ( 3 / 24 )8.031944444444440.0608953278839538131.897548195334
Winsorized Mean ( 4 / 24 )8.031944444444440.0608953278839538131.897548195334
Winsorized Mean ( 5 / 24 )8.031944444444440.0608953278839538131.897548195334
Winsorized Mean ( 6 / 24 )8.048611111111110.0575651313627347139.817471454976
Winsorized Mean ( 7 / 24 )8.048611111111110.0575651313627347139.817471454976
Winsorized Mean ( 8 / 24 )8.048611111111110.0575651313627347139.817471454976
Winsorized Mean ( 9 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 10 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 11 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 12 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 13 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 14 / 24 )8.048611111111110.0534415369346322150.605906431095
Winsorized Mean ( 15 / 24 )8.048611111111110.0470155076951465171.190560427405
Winsorized Mean ( 16 / 24 )8.070833333333330.0434900335748812185.578917050891
Winsorized Mean ( 17 / 24 )8.070833333333330.0434900335748812185.578917050891
Winsorized Mean ( 18 / 24 )8.070833333333330.0434900335748812185.578917050891
Winsorized Mean ( 19 / 24 )8.044444444444440.0399965221927509201.128598273538
Winsorized Mean ( 20 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 21 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 22 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 23 / 24 )8.072222222222220.0357800522221482225.606775867852
Winsorized Mean ( 24 / 24 )8.038888888888890.0316818320219066253.738132420195
Trimmed Mean ( 1 / 24 )8.042857142857140.063785725298444126.091803537951
Trimmed Mean ( 2 / 24 )8.042647058823530.0610960820347246131.639325975967
Trimmed Mean ( 3 / 24 )8.04393939393940.0591363163055902136.023680480399
Trimmed Mean ( 4 / 24 )8.04843750.0582479046007406138.175571381801
Trimmed Mean ( 5 / 24 )8.053225806451610.0571543477859567140.903117932707
Trimmed Mean ( 6 / 24 )8.058333333333330.0558089794258723144.391340179168
Trimmed Mean ( 7 / 24 )8.06034482758620.0551047868959955146.273042354728
Trimmed Mean ( 8 / 24 )8.06250.0542099394250495148.727338298306
Trimmed Mean ( 9 / 24 )8.064814814814810.0530783611346149151.941669682702
Trimmed Mean ( 10 / 24 )8.067307692307690.052589158211879153.402487634522
Trimmed Mean ( 11 / 24 )8.070.0519222338439607155.424745866142
Trimmed Mean ( 12 / 24 )8.072916666666670.0510301314943531158.199017526733
Trimmed Mean ( 13 / 24 )8.076086956521740.0498485418708919162.012501337328
Trimmed Mean ( 14 / 24 )8.079545454545460.0482877589938972167.320779072944
Trimmed Mean ( 15 / 24 )8.083333333333330.0462177679589405174.896661831755
Trimmed Mean ( 16 / 24 )8.08750.0450338192006282179.587255612715
Trimmed Mean ( 17 / 24 )8.089473684210530.0442721239923165182.721607971970
Trimmed Mean ( 18 / 24 )8.091666666666670.0431635869465831187.465112125192
Trimmed Mean ( 19 / 24 )8.094117647058820.041569300098819194.713830346371
Trimmed Mean ( 20 / 24 )8.10.0401609664451250201.688373487417
Trimmed Mean ( 21 / 24 )8.103333333333330.0393870663564651205.735894620728
Trimmed Mean ( 22 / 24 )8.107142857142860.0381200316143582212.674085351210
Trimmed Mean ( 23 / 24 )8.111538461538460.0360883203253536224.769077319450
Trimmed Mean ( 24 / 24 )8.116666666666670.0327853507996047247.569919757105
Median8.1
Midrange8.05
Midmean - Weighted Average at Xnp8.09756097560975
Midmean - Weighted Average at X(n+1)p8.09756097560975
Midmean - Empirical Distribution Function8.09756097560975
Midmean - Empirical Distribution Function - Averaging8.09756097560975
Midmean - Empirical Distribution Function - Interpolation8.09756097560975
Midmean - Closest Observation8.09756097560975
Midmean - True Basic - Statistics Graphics Toolkit8.09756097560975
Midmean - MS Excel (old versions)8.09756097560975
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')