Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 03 Apr 2011 08:16:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Apr/03/t1301818480frfd2s6pcltd5as.htm/, Retrieved Thu, 09 May 2024 17:32:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=119962, Retrieved Thu, 09 May 2024 17:32:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten werk...] [2011-04-03 08:16:49] [99f56e8d3669c8e32d9c5b2d6e7ae714] [Current]
Feedback Forum

Post a new message
Dataseries X:
8
8
8,2
8,5
8,7
8,7
8
8
8,3
8,5
8,7
8,6
8,3
7,9
7,9
8,1
8,3
8,1
7,4
7,3
7,7
8
8
7,7
6,9
6,6
6,9
7,5
7,9
7,7
6,5
6,1
6,4
6,8
7,1
7,3
7,2
7
7
7
7,3
7,5
7,2
7,7
8
7,9
8
8
7,9
7,9
8
8,1
8,1
8,2
8
8,3
8,5
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
7,9
8,1
8,2
8,5
8,6
8,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119962&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119962&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'Herman Ole Andreas Wold' @ www.yougetit.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.897222222222220.0748491498656544105.50850926693
Geometric Mean7.87072879143535
Harmonic Mean7.84285753473738
Quadratic Mean7.92236636926675
Winsorized Mean ( 1 / 24 )7.901388888888890.0735446447495949107.436631392966
Winsorized Mean ( 2 / 24 )7.904166666666670.0727677049857207108.621904019341
Winsorized Mean ( 3 / 24 )7.908333333333330.0716655748360984110.350518382361
Winsorized Mean ( 4 / 24 )7.919444444444440.0689639086193174114.83462296431
Winsorized Mean ( 5 / 24 )7.926388888888890.0674250599926028117.558499610657
Winsorized Mean ( 6 / 24 )7.926388888888890.0674250599926028117.558499610657
Winsorized Mean ( 7 / 24 )7.926388888888890.0638793198930472124.083802115614
Winsorized Mean ( 8 / 24 )7.926388888888890.0638793198930472124.083802115614
Winsorized Mean ( 9 / 24 )7.926388888888890.0638793198930472124.083802115614
Winsorized Mean ( 10 / 24 )7.940277777777780.0611144454204902129.924729303288
Winsorized Mean ( 11 / 24 )7.940277777777780.0559684869072857141.870509934121
Winsorized Mean ( 12 / 24 )7.940277777777780.0559684869072857141.870509934121
Winsorized Mean ( 13 / 24 )7.958333333333330.0526953478687726151.025349584028
Winsorized Mean ( 14 / 24 )7.958333333333330.0526953478687726151.025349584028
Winsorized Mean ( 15 / 24 )7.958333333333330.0526953478687726151.025349584028
Winsorized Mean ( 16 / 24 )7.980555555555560.0488778174261239163.275612042574
Winsorized Mean ( 17 / 24 )8.004166666666670.0450368263502162177.724926805999
Winsorized Mean ( 18 / 24 )7.979166666666670.0412982538934504193.20832999993
Winsorized Mean ( 19 / 24 )8.005555555555550.0292638480847891273.564690889601
Winsorized Mean ( 20 / 24 )8.005555555555550.0292638480847891273.564690889601
Winsorized Mean ( 21 / 24 )8.005555555555560.0292638480847891273.564690889601
Winsorized Mean ( 22 / 24 )8.005555555555560.0292638480847891273.564690889601
Winsorized Mean ( 23 / 24 )8.03750.015877748428183506.211572525827
Winsorized Mean ( 24 / 24 )8.03750.015877748428183506.211572525827
Trimmed Mean ( 1 / 24 )7.911428571428570.0715849220490861110.518086001458
Trimmed Mean ( 2 / 24 )7.922058823529410.0692315016904749114.428527911295
Trimmed Mean ( 3 / 24 )7.931818181818180.0669049038418287118.553614553725
Trimmed Mean ( 4 / 24 )7.9406250.0646157272829269122.889973291349
Trimmed Mean ( 5 / 24 )7.946774193548390.0628815268544148126.376928027638
Trimmed Mean ( 6 / 24 )7.951666666666670.061271446915805129.777687110822
Trimmed Mean ( 7 / 24 )7.956896551724140.0592916478922052134.19928159511
Trimmed Mean ( 8 / 24 )7.96250.057804108288814137.749724642684
Trimmed Mean ( 9 / 24 )7.968518518518520.0559414734892019142.443843923
Trimmed Mean ( 10 / 24 )7.9750.0535944071956636148.802840021809
Trimmed Mean ( 11 / 24 )7.980.0513491450160327155.406677122052
Trimmed Mean ( 12 / 24 )7.985416666666670.049732403008335160.567681906067
Trimmed Mean ( 13 / 24 )7.991304347826090.0476324582790509167.770143229007
Trimmed Mean ( 14 / 24 )7.995454545454550.0457443194701825174.785735979004
Trimmed Mean ( 15 / 24 )80.0432425565755193185.002937697005
Trimmed Mean ( 16 / 24 )8.0050.0398635493164189200.810016600878
Trimmed Mean ( 17 / 24 )8.00789473684210.0364462578978461219.717885970273
Trimmed Mean ( 18 / 24 )8.008333333333330.0329441566945864243.088126600895
Trimmed Mean ( 19 / 24 )8.011764705882350.0291791155146387274.571883505618
Trimmed Mean ( 20 / 24 )8.01250.0279508497187474286.663914715473
Trimmed Mean ( 21 / 24 )8.013333333333330.0261443092128011306.503922827295
Trimmed Mean ( 22 / 24 )8.014285714285710.0234093352440517342.354262978148
Trimmed Mean ( 23 / 24 )8.015384615384620.0189674277014429422.586802045638
Trimmed Mean ( 24 / 24 )8.01250.0183687076379873436.203796037877
Median8
Midrange7.4
Midmean - Weighted Average at Xnp7.9945945945946
Midmean - Weighted Average at X(n+1)p7.9945945945946
Midmean - Empirical Distribution Function7.9945945945946
Midmean - Empirical Distribution Function - Averaging7.9945945945946
Midmean - Empirical Distribution Function - Interpolation7.9945945945946
Midmean - Closest Observation7.9945945945946
Midmean - True Basic - Statistics Graphics Toolkit7.9945945945946
Midmean - MS Excel (old versions)8.075
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.89722222222222 & 0.0748491498656544 & 105.50850926693 \tabularnewline
Geometric Mean & 7.87072879143535 &  &  \tabularnewline
Harmonic Mean & 7.84285753473738 &  &  \tabularnewline
Quadratic Mean & 7.92236636926675 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.90138888888889 & 0.0735446447495949 & 107.436631392966 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.90416666666667 & 0.0727677049857207 & 108.621904019341 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.90833333333333 & 0.0716655748360984 & 110.350518382361 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.91944444444444 & 0.0689639086193174 & 114.83462296431 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.92638888888889 & 0.0674250599926028 & 117.558499610657 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.92638888888889 & 0.0674250599926028 & 117.558499610657 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.92638888888889 & 0.0638793198930472 & 124.083802115614 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.92638888888889 & 0.0638793198930472 & 124.083802115614 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.92638888888889 & 0.0638793198930472 & 124.083802115614 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.94027777777778 & 0.0611144454204902 & 129.924729303288 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.94027777777778 & 0.0559684869072857 & 141.870509934121 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.94027777777778 & 0.0559684869072857 & 141.870509934121 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.95833333333333 & 0.0526953478687726 & 151.025349584028 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.95833333333333 & 0.0526953478687726 & 151.025349584028 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.95833333333333 & 0.0526953478687726 & 151.025349584028 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.98055555555556 & 0.0488778174261239 & 163.275612042574 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.00416666666667 & 0.0450368263502162 & 177.724926805999 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.97916666666667 & 0.0412982538934504 & 193.20832999993 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.00555555555555 & 0.0292638480847891 & 273.564690889601 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.00555555555555 & 0.0292638480847891 & 273.564690889601 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.00555555555556 & 0.0292638480847891 & 273.564690889601 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.00555555555556 & 0.0292638480847891 & 273.564690889601 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.0375 & 0.015877748428183 & 506.211572525827 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.0375 & 0.015877748428183 & 506.211572525827 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.91142857142857 & 0.0715849220490861 & 110.518086001458 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.92205882352941 & 0.0692315016904749 & 114.428527911295 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.93181818181818 & 0.0669049038418287 & 118.553614553725 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.940625 & 0.0646157272829269 & 122.889973291349 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.94677419354839 & 0.0628815268544148 & 126.376928027638 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.95166666666667 & 0.061271446915805 & 129.777687110822 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.95689655172414 & 0.0592916478922052 & 134.19928159511 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.9625 & 0.057804108288814 & 137.749724642684 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.96851851851852 & 0.0559414734892019 & 142.443843923 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.975 & 0.0535944071956636 & 148.802840021809 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.98 & 0.0513491450160327 & 155.406677122052 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.98541666666667 & 0.049732403008335 & 160.567681906067 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.99130434782609 & 0.0476324582790509 & 167.770143229007 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.99545454545455 & 0.0457443194701825 & 174.785735979004 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8 & 0.0432425565755193 & 185.002937697005 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.005 & 0.0398635493164189 & 200.810016600878 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.0078947368421 & 0.0364462578978461 & 219.717885970273 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.00833333333333 & 0.0329441566945864 & 243.088126600895 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.01176470588235 & 0.0291791155146387 & 274.571883505618 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.0125 & 0.0279508497187474 & 286.663914715473 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.01333333333333 & 0.0261443092128011 & 306.503922827295 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.01428571428571 & 0.0234093352440517 & 342.354262978148 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.01538461538462 & 0.0189674277014429 & 422.586802045638 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.0125 & 0.0183687076379873 & 436.203796037877 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.9945945945946 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.9945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.9945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.9945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.9945945945946 &  &  \tabularnewline
Midmean - Closest Observation & 7.9945945945946 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.9945945945946 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.075 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119962&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]7.89722222222222[/C][C]0.0748491498656544[/C][C]105.50850926693[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.87072879143535[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.84285753473738[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.92236636926675[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.90138888888889[/C][C]0.0735446447495949[/C][C]107.436631392966[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.90416666666667[/C][C]0.0727677049857207[/C][C]108.621904019341[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.90833333333333[/C][C]0.0716655748360984[/C][C]110.350518382361[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.91944444444444[/C][C]0.0689639086193174[/C][C]114.83462296431[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.92638888888889[/C][C]0.0674250599926028[/C][C]117.558499610657[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.92638888888889[/C][C]0.0674250599926028[/C][C]117.558499610657[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.92638888888889[/C][C]0.0638793198930472[/C][C]124.083802115614[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.92638888888889[/C][C]0.0638793198930472[/C][C]124.083802115614[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.92638888888889[/C][C]0.0638793198930472[/C][C]124.083802115614[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.94027777777778[/C][C]0.0611144454204902[/C][C]129.924729303288[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.94027777777778[/C][C]0.0559684869072857[/C][C]141.870509934121[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.94027777777778[/C][C]0.0559684869072857[/C][C]141.870509934121[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.95833333333333[/C][C]0.0526953478687726[/C][C]151.025349584028[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.95833333333333[/C][C]0.0526953478687726[/C][C]151.025349584028[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.95833333333333[/C][C]0.0526953478687726[/C][C]151.025349584028[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.98055555555556[/C][C]0.0488778174261239[/C][C]163.275612042574[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.00416666666667[/C][C]0.0450368263502162[/C][C]177.724926805999[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.97916666666667[/C][C]0.0412982538934504[/C][C]193.20832999993[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.00555555555555[/C][C]0.0292638480847891[/C][C]273.564690889601[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.00555555555555[/C][C]0.0292638480847891[/C][C]273.564690889601[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.00555555555556[/C][C]0.0292638480847891[/C][C]273.564690889601[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.00555555555556[/C][C]0.0292638480847891[/C][C]273.564690889601[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.0375[/C][C]0.015877748428183[/C][C]506.211572525827[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.0375[/C][C]0.015877748428183[/C][C]506.211572525827[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.91142857142857[/C][C]0.0715849220490861[/C][C]110.518086001458[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.92205882352941[/C][C]0.0692315016904749[/C][C]114.428527911295[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.93181818181818[/C][C]0.0669049038418287[/C][C]118.553614553725[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.940625[/C][C]0.0646157272829269[/C][C]122.889973291349[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.94677419354839[/C][C]0.0628815268544148[/C][C]126.376928027638[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.95166666666667[/C][C]0.061271446915805[/C][C]129.777687110822[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.95689655172414[/C][C]0.0592916478922052[/C][C]134.19928159511[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.9625[/C][C]0.057804108288814[/C][C]137.749724642684[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.96851851851852[/C][C]0.0559414734892019[/C][C]142.443843923[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.975[/C][C]0.0535944071956636[/C][C]148.802840021809[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.98[/C][C]0.0513491450160327[/C][C]155.406677122052[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.98541666666667[/C][C]0.049732403008335[/C][C]160.567681906067[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.99130434782609[/C][C]0.0476324582790509[/C][C]167.770143229007[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.99545454545455[/C][C]0.0457443194701825[/C][C]174.785735979004[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8[/C][C]0.0432425565755193[/C][C]185.002937697005[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.005[/C][C]0.0398635493164189[/C][C]200.810016600878[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.0078947368421[/C][C]0.0364462578978461[/C][C]219.717885970273[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.00833333333333[/C][C]0.0329441566945864[/C][C]243.088126600895[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.01176470588235[/C][C]0.0291791155146387[/C][C]274.571883505618[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.0125[/C][C]0.0279508497187474[/C][C]286.663914715473[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.01333333333333[/C][C]0.0261443092128011[/C][C]306.503922827295[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.01428571428571[/C][C]0.0234093352440517[/C][C]342.354262978148[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.01538461538462[/C][C]0.0189674277014429[/C][C]422.586802045638[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.0125[/C][C]0.0183687076379873[/C][C]436.203796037877[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.075[/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=119962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119962&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 Mean7.897222222222220.0748491498656544105.50850926693
Geometric Mean7.87072879143535
Harmonic Mean7.84285753473738
Quadratic Mean7.92236636926675
Winsorized Mean ( 1 / 24 )7.901388888888890.0735446447495949107.436631392966
Winsorized Mean ( 2 / 24 )7.904166666666670.0727677049857207108.621904019341
Winsorized Mean ( 3 / 24 )7.908333333333330.0716655748360984110.350518382361
Winsorized Mean ( 4 / 24 )7.919444444444440.0689639086193174114.83462296431
Winsorized Mean ( 5 / 24 )7.926388888888890.0674250599926028117.558499610657
Winsorized Mean ( 6 / 24 )7.926388888888890.0674250599926028117.558499610657
Winsorized Mean ( 7 / 24 )7.926388888888890.0638793198930472124.083802115614
Winsorized Mean ( 8 / 24 )7.926388888888890.0638793198930472124.083802115614
Winsorized Mean ( 9 / 24 )7.926388888888890.0638793198930472124.083802115614
Winsorized Mean ( 10 / 24 )7.940277777777780.0611144454204902129.924729303288
Winsorized Mean ( 11 / 24 )7.940277777777780.0559684869072857141.870509934121
Winsorized Mean ( 12 / 24 )7.940277777777780.0559684869072857141.870509934121
Winsorized Mean ( 13 / 24 )7.958333333333330.0526953478687726151.025349584028
Winsorized Mean ( 14 / 24 )7.958333333333330.0526953478687726151.025349584028
Winsorized Mean ( 15 / 24 )7.958333333333330.0526953478687726151.025349584028
Winsorized Mean ( 16 / 24 )7.980555555555560.0488778174261239163.275612042574
Winsorized Mean ( 17 / 24 )8.004166666666670.0450368263502162177.724926805999
Winsorized Mean ( 18 / 24 )7.979166666666670.0412982538934504193.20832999993
Winsorized Mean ( 19 / 24 )8.005555555555550.0292638480847891273.564690889601
Winsorized Mean ( 20 / 24 )8.005555555555550.0292638480847891273.564690889601
Winsorized Mean ( 21 / 24 )8.005555555555560.0292638480847891273.564690889601
Winsorized Mean ( 22 / 24 )8.005555555555560.0292638480847891273.564690889601
Winsorized Mean ( 23 / 24 )8.03750.015877748428183506.211572525827
Winsorized Mean ( 24 / 24 )8.03750.015877748428183506.211572525827
Trimmed Mean ( 1 / 24 )7.911428571428570.0715849220490861110.518086001458
Trimmed Mean ( 2 / 24 )7.922058823529410.0692315016904749114.428527911295
Trimmed Mean ( 3 / 24 )7.931818181818180.0669049038418287118.553614553725
Trimmed Mean ( 4 / 24 )7.9406250.0646157272829269122.889973291349
Trimmed Mean ( 5 / 24 )7.946774193548390.0628815268544148126.376928027638
Trimmed Mean ( 6 / 24 )7.951666666666670.061271446915805129.777687110822
Trimmed Mean ( 7 / 24 )7.956896551724140.0592916478922052134.19928159511
Trimmed Mean ( 8 / 24 )7.96250.057804108288814137.749724642684
Trimmed Mean ( 9 / 24 )7.968518518518520.0559414734892019142.443843923
Trimmed Mean ( 10 / 24 )7.9750.0535944071956636148.802840021809
Trimmed Mean ( 11 / 24 )7.980.0513491450160327155.406677122052
Trimmed Mean ( 12 / 24 )7.985416666666670.049732403008335160.567681906067
Trimmed Mean ( 13 / 24 )7.991304347826090.0476324582790509167.770143229007
Trimmed Mean ( 14 / 24 )7.995454545454550.0457443194701825174.785735979004
Trimmed Mean ( 15 / 24 )80.0432425565755193185.002937697005
Trimmed Mean ( 16 / 24 )8.0050.0398635493164189200.810016600878
Trimmed Mean ( 17 / 24 )8.00789473684210.0364462578978461219.717885970273
Trimmed Mean ( 18 / 24 )8.008333333333330.0329441566945864243.088126600895
Trimmed Mean ( 19 / 24 )8.011764705882350.0291791155146387274.571883505618
Trimmed Mean ( 20 / 24 )8.01250.0279508497187474286.663914715473
Trimmed Mean ( 21 / 24 )8.013333333333330.0261443092128011306.503922827295
Trimmed Mean ( 22 / 24 )8.014285714285710.0234093352440517342.354262978148
Trimmed Mean ( 23 / 24 )8.015384615384620.0189674277014429422.586802045638
Trimmed Mean ( 24 / 24 )8.01250.0183687076379873436.203796037877
Median8
Midrange7.4
Midmean - Weighted Average at Xnp7.9945945945946
Midmean - Weighted Average at X(n+1)p7.9945945945946
Midmean - Empirical Distribution Function7.9945945945946
Midmean - Empirical Distribution Function - Averaging7.9945945945946
Midmean - Empirical Distribution Function - Interpolation7.9945945945946
Midmean - Closest Observation7.9945945945946
Midmean - True Basic - Statistics Graphics Toolkit7.9945945945946
Midmean - MS Excel (old versions)8.075
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')