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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 computationTue, 05 Mar 2013 14:39:18 -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/Mar/05/t1362512406rwvo4ip3h53c1xz.htm/, Retrieved Sat, 04 May 2024 12:57:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207483, Retrieved Sat, 04 May 2024 12:57:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opdracht 5, oefen...] [2013-03-05 19:39:18] [1d769b43b3426eacfc1d7d5ec9e3993f] [Current]
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Dataseries X:
7,14
7,11
7,21
7,25
7,25
7,45
7,45
7,49
7,47
7,49
7,47
7,51
7,52
7,5
7,54
7,54
7,57
7,53
7,54
7,63
7,61
7,64
7,68
7,7
7,72
7,71
7,77
7,83
7,85
7,89
8,01
8,18
8,25
8,31
8,34
8,38
8,36
8,34
8,34
8,3
8,35
8,36
8,34
8,39
8,23
8,14
8,04
8,05
7,99
8,17
8,22
8,12
8,11
8,12
8,11
8,03
8,03
7,96
7,96
7,87
7,9
7,87
7,94
7,82
7,83
7,86
7,81
7,76
7,75
7,75
7,74
7,72




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=207483&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=207483&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207483&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 Mean7.850138888888890.0398758308745101196.864584805603
Geometric Mean7.84290845037711
Harmonic Mean7.83564003245978
Quadratic Mean7.85732628754138
Winsorized Mean ( 1 / 24 )7.850416666666670.0397426371858378197.531347252018
Winsorized Mean ( 2 / 24 )7.851805555555550.0391704505158991200.452265729457
Winsorized Mean ( 3 / 24 )7.853472222222220.0387955193405207202.432454977334
Winsorized Mean ( 4 / 24 )7.852916666666670.0386941770659442202.94827961539
Winsorized Mean ( 5 / 24 )7.866111111111110.035894317336321219.14641912277
Winsorized Mean ( 6 / 24 )7.866111111111110.035894317336321219.14641912277
Winsorized Mean ( 7 / 24 )7.868055555555560.0355823665297785221.122323299403
Winsorized Mean ( 8 / 24 )7.868055555555560.0355823665297785221.122323299403
Winsorized Mean ( 9 / 24 )7.866805555555550.034503422517911228.000730984639
Winsorized Mean ( 10 / 24 )7.865416666666670.0342536894166767229.622466969568
Winsorized Mean ( 11 / 24 )7.859305555555560.0326911894090748240.410511138328
Winsorized Mean ( 12 / 24 )7.857638888888890.0318793776677556246.480309960269
Winsorized Mean ( 13 / 24 )7.857638888888890.0313078841407765250.979556892343
Winsorized Mean ( 14 / 24 )7.851805555555560.0297737467125908263.715736932603
Winsorized Mean ( 15 / 24 )7.851805555555550.0291361855406555269.486393289178
Winsorized Mean ( 16 / 24 )7.845138888888890.0281310043533715278.878734308278
Winsorized Mean ( 17 / 24 )7.840416666666670.0274435239545189285.692780550351
Winsorized Mean ( 18 / 24 )7.847916666666670.0263069469484104298.321073975515
Winsorized Mean ( 19 / 24 )7.855833333333330.0243850421711782322.157873592628
Winsorized Mean ( 20 / 24 )7.861388888888890.023606968245581333.011372197718
Winsorized Mean ( 21 / 24 )7.846805555555560.0206864080981566379.321800011032
Winsorized Mean ( 22 / 24 )7.855972222222220.0185841356720857422.724648637938
Winsorized Mean ( 23 / 24 )7.859166666666670.0172987534264624454.319827152647
Winsorized Mean ( 24 / 24 )7.86250.0168705255471746466.049500237221
Trimmed Mean ( 1 / 24 )7.8530.0388463821721855202.155247435702
Trimmed Mean ( 2 / 24 )7.855735294117650.0377775454488982207.9472131069
Trimmed Mean ( 3 / 24 )7.857878787878790.0368658597547277213.147851159801
Trimmed Mean ( 4 / 24 )7.859531250.0359421311284482218.671820597171
Trimmed Mean ( 5 / 24 )7.861451612903230.0348615504283032225.504933553406
Trimmed Mean ( 6 / 24 )7.860333333333330.0344365187406555228.255747699999
Trimmed Mean ( 7 / 24 )7.859137931034480.0339007523403434231.827832377684
Trimmed Mean ( 8 / 24 )7.85750.0333061848318289235.917143908089
Trimmed Mean ( 9 / 24 )7.855740740740740.0325565699699412241.295097978497
Trimmed Mean ( 10 / 24 )7.854038461538460.0318677740638511246.45707747902
Trimmed Mean ( 11 / 24 )7.85240.0310477709607735252.913486443871
Trimmed Mean ( 12 / 24 )7.851458333333330.030359824352138258.613430771724
Trimmed Mean ( 13 / 24 )7.850652173913040.0296475303431928264.799532474906
Trimmed Mean ( 14 / 24 )7.849772727272730.0288403211921348272.18048907907
Trimmed Mean ( 15 / 24 )7.849523809523810.0281277002956185279.067386491833
Trimmed Mean ( 16 / 24 )7.849250.0273143793726458287.366953973726
Trimmed Mean ( 17 / 24 )7.849736842105260.0264507563132995296.767954349887
Trimmed Mean ( 18 / 24 )7.850833333333330.0254276908176393308.751328999453
Trimmed Mean ( 19 / 24 )7.851176470588240.0243150911007443322.89315462807
Trimmed Mean ( 20 / 24 )7.8506250.0232922244917525337.049172902306
Trimmed Mean ( 21 / 24 )7.849333333333330.0220288908175455356.319952663323
Trimmed Mean ( 22 / 24 )7.849642857142860.0211475175401359371.185073720592
Trimmed Mean ( 23 / 24 )7.848846153846150.0204963555715638382.938621768226
Trimmed Mean ( 24 / 24 )7.84750.0198750626651095394.841522375485
Median7.84
Midrange7.75
Midmean - Weighted Average at Xnp7.83425
Midmean - Weighted Average at X(n+1)p7.85810810810811
Midmean - Empirical Distribution Function7.83425
Midmean - Empirical Distribution Function - Averaging7.85810810810811
Midmean - Empirical Distribution Function - Interpolation7.85810810810811
Midmean - Closest Observation7.83425
Midmean - True Basic - Statistics Graphics Toolkit7.85810810810811
Midmean - MS Excel (old versions)7.83425
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.85013888888889 & 0.0398758308745101 & 196.864584805603 \tabularnewline
Geometric Mean & 7.84290845037711 &  &  \tabularnewline
Harmonic Mean & 7.83564003245978 &  &  \tabularnewline
Quadratic Mean & 7.85732628754138 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 7.85041666666667 & 0.0397426371858378 & 197.531347252018 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 7.85180555555555 & 0.0391704505158991 & 200.452265729457 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 7.85347222222222 & 0.0387955193405207 & 202.432454977334 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 7.85291666666667 & 0.0386941770659442 & 202.94827961539 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 7.86611111111111 & 0.035894317336321 & 219.14641912277 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 7.86611111111111 & 0.035894317336321 & 219.14641912277 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 7.86805555555556 & 0.0355823665297785 & 221.122323299403 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 7.86805555555556 & 0.0355823665297785 & 221.122323299403 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 7.86680555555555 & 0.034503422517911 & 228.000730984639 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.86541666666667 & 0.0342536894166767 & 229.622466969568 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 7.85930555555556 & 0.0326911894090748 & 240.410511138328 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.85763888888889 & 0.0318793776677556 & 246.480309960269 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 7.85763888888889 & 0.0313078841407765 & 250.979556892343 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 7.85180555555556 & 0.0297737467125908 & 263.715736932603 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 7.85180555555555 & 0.0291361855406555 & 269.486393289178 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 7.84513888888889 & 0.0281310043533715 & 278.878734308278 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 7.84041666666667 & 0.0274435239545189 & 285.692780550351 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 7.84791666666667 & 0.0263069469484104 & 298.321073975515 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 7.85583333333333 & 0.0243850421711782 & 322.157873592628 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 7.86138888888889 & 0.023606968245581 & 333.011372197718 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7.84680555555556 & 0.0206864080981566 & 379.321800011032 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7.85597222222222 & 0.0185841356720857 & 422.724648637938 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7.85916666666667 & 0.0172987534264624 & 454.319827152647 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7.8625 & 0.0168705255471746 & 466.049500237221 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 7.853 & 0.0388463821721855 & 202.155247435702 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 7.85573529411765 & 0.0377775454488982 & 207.9472131069 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 7.85787878787879 & 0.0368658597547277 & 213.147851159801 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 7.85953125 & 0.0359421311284482 & 218.671820597171 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 7.86145161290323 & 0.0348615504283032 & 225.504933553406 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 7.86033333333333 & 0.0344365187406555 & 228.255747699999 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 7.85913793103448 & 0.0339007523403434 & 231.827832377684 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 7.8575 & 0.0333061848318289 & 235.917143908089 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 7.85574074074074 & 0.0325565699699412 & 241.295097978497 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 7.85403846153846 & 0.0318677740638511 & 246.45707747902 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 7.8524 & 0.0310477709607735 & 252.913486443871 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7.85145833333333 & 0.030359824352138 & 258.613430771724 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7.85065217391304 & 0.0296475303431928 & 264.799532474906 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7.84977272727273 & 0.0288403211921348 & 272.18048907907 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7.84952380952381 & 0.0281277002956185 & 279.067386491833 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7.84925 & 0.0273143793726458 & 287.366953973726 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7.84973684210526 & 0.0264507563132995 & 296.767954349887 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7.85083333333333 & 0.0254276908176393 & 308.751328999453 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7.85117647058824 & 0.0243150911007443 & 322.89315462807 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7.850625 & 0.0232922244917525 & 337.049172902306 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7.84933333333333 & 0.0220288908175455 & 356.319952663323 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7.84964285714286 & 0.0211475175401359 & 371.185073720592 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7.84884615384615 & 0.0204963555715638 & 382.938621768226 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7.8475 & 0.0198750626651095 & 394.841522375485 \tabularnewline
Median & 7.84 &  &  \tabularnewline
Midrange & 7.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.83425 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.85810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.83425 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.85810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.85810810810811 &  &  \tabularnewline
Midmean - Closest Observation & 7.83425 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.85810810810811 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.83425 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207483&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]7.85013888888889[/C][C]0.0398758308745101[/C][C]196.864584805603[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.84290845037711[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.83564003245978[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.85732628754138[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]7.85041666666667[/C][C]0.0397426371858378[/C][C]197.531347252018[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]7.85180555555555[/C][C]0.0391704505158991[/C][C]200.452265729457[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]7.85347222222222[/C][C]0.0387955193405207[/C][C]202.432454977334[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]7.85291666666667[/C][C]0.0386941770659442[/C][C]202.94827961539[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]7.86611111111111[/C][C]0.035894317336321[/C][C]219.14641912277[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]7.86611111111111[/C][C]0.035894317336321[/C][C]219.14641912277[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]7.86805555555556[/C][C]0.0355823665297785[/C][C]221.122323299403[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]7.86805555555556[/C][C]0.0355823665297785[/C][C]221.122323299403[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]7.86680555555555[/C][C]0.034503422517911[/C][C]228.000730984639[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.86541666666667[/C][C]0.0342536894166767[/C][C]229.622466969568[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]7.85930555555556[/C][C]0.0326911894090748[/C][C]240.410511138328[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.85763888888889[/C][C]0.0318793776677556[/C][C]246.480309960269[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]7.85763888888889[/C][C]0.0313078841407765[/C][C]250.979556892343[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]7.85180555555556[/C][C]0.0297737467125908[/C][C]263.715736932603[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]7.85180555555555[/C][C]0.0291361855406555[/C][C]269.486393289178[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]7.84513888888889[/C][C]0.0281310043533715[/C][C]278.878734308278[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]7.84041666666667[/C][C]0.0274435239545189[/C][C]285.692780550351[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]7.84791666666667[/C][C]0.0263069469484104[/C][C]298.321073975515[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]7.85583333333333[/C][C]0.0243850421711782[/C][C]322.157873592628[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]7.86138888888889[/C][C]0.023606968245581[/C][C]333.011372197718[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7.84680555555556[/C][C]0.0206864080981566[/C][C]379.321800011032[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7.85597222222222[/C][C]0.0185841356720857[/C][C]422.724648637938[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7.85916666666667[/C][C]0.0172987534264624[/C][C]454.319827152647[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7.8625[/C][C]0.0168705255471746[/C][C]466.049500237221[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]7.853[/C][C]0.0388463821721855[/C][C]202.155247435702[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]7.85573529411765[/C][C]0.0377775454488982[/C][C]207.9472131069[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]7.85787878787879[/C][C]0.0368658597547277[/C][C]213.147851159801[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]7.85953125[/C][C]0.0359421311284482[/C][C]218.671820597171[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]7.86145161290323[/C][C]0.0348615504283032[/C][C]225.504933553406[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]7.86033333333333[/C][C]0.0344365187406555[/C][C]228.255747699999[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]7.85913793103448[/C][C]0.0339007523403434[/C][C]231.827832377684[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]7.8575[/C][C]0.0333061848318289[/C][C]235.917143908089[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]7.85574074074074[/C][C]0.0325565699699412[/C][C]241.295097978497[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]7.85403846153846[/C][C]0.0318677740638511[/C][C]246.45707747902[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]7.8524[/C][C]0.0310477709607735[/C][C]252.913486443871[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7.85145833333333[/C][C]0.030359824352138[/C][C]258.613430771724[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7.85065217391304[/C][C]0.0296475303431928[/C][C]264.799532474906[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7.84977272727273[/C][C]0.0288403211921348[/C][C]272.18048907907[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7.84952380952381[/C][C]0.0281277002956185[/C][C]279.067386491833[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7.84925[/C][C]0.0273143793726458[/C][C]287.366953973726[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7.84973684210526[/C][C]0.0264507563132995[/C][C]296.767954349887[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7.85083333333333[/C][C]0.0254276908176393[/C][C]308.751328999453[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7.85117647058824[/C][C]0.0243150911007443[/C][C]322.89315462807[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7.850625[/C][C]0.0232922244917525[/C][C]337.049172902306[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7.84933333333333[/C][C]0.0220288908175455[/C][C]356.319952663323[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7.84964285714286[/C][C]0.0211475175401359[/C][C]371.185073720592[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7.84884615384615[/C][C]0.0204963555715638[/C][C]382.938621768226[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7.8475[/C][C]0.0198750626651095[/C][C]394.841522375485[/C][/ROW]
[ROW][C]Median[/C][C]7.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.83425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.85810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.83425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.85810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.85810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.83425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.85810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.83425[/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=207483&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207483&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 Mean7.850138888888890.0398758308745101196.864584805603
Geometric Mean7.84290845037711
Harmonic Mean7.83564003245978
Quadratic Mean7.85732628754138
Winsorized Mean ( 1 / 24 )7.850416666666670.0397426371858378197.531347252018
Winsorized Mean ( 2 / 24 )7.851805555555550.0391704505158991200.452265729457
Winsorized Mean ( 3 / 24 )7.853472222222220.0387955193405207202.432454977334
Winsorized Mean ( 4 / 24 )7.852916666666670.0386941770659442202.94827961539
Winsorized Mean ( 5 / 24 )7.866111111111110.035894317336321219.14641912277
Winsorized Mean ( 6 / 24 )7.866111111111110.035894317336321219.14641912277
Winsorized Mean ( 7 / 24 )7.868055555555560.0355823665297785221.122323299403
Winsorized Mean ( 8 / 24 )7.868055555555560.0355823665297785221.122323299403
Winsorized Mean ( 9 / 24 )7.866805555555550.034503422517911228.000730984639
Winsorized Mean ( 10 / 24 )7.865416666666670.0342536894166767229.622466969568
Winsorized Mean ( 11 / 24 )7.859305555555560.0326911894090748240.410511138328
Winsorized Mean ( 12 / 24 )7.857638888888890.0318793776677556246.480309960269
Winsorized Mean ( 13 / 24 )7.857638888888890.0313078841407765250.979556892343
Winsorized Mean ( 14 / 24 )7.851805555555560.0297737467125908263.715736932603
Winsorized Mean ( 15 / 24 )7.851805555555550.0291361855406555269.486393289178
Winsorized Mean ( 16 / 24 )7.845138888888890.0281310043533715278.878734308278
Winsorized Mean ( 17 / 24 )7.840416666666670.0274435239545189285.692780550351
Winsorized Mean ( 18 / 24 )7.847916666666670.0263069469484104298.321073975515
Winsorized Mean ( 19 / 24 )7.855833333333330.0243850421711782322.157873592628
Winsorized Mean ( 20 / 24 )7.861388888888890.023606968245581333.011372197718
Winsorized Mean ( 21 / 24 )7.846805555555560.0206864080981566379.321800011032
Winsorized Mean ( 22 / 24 )7.855972222222220.0185841356720857422.724648637938
Winsorized Mean ( 23 / 24 )7.859166666666670.0172987534264624454.319827152647
Winsorized Mean ( 24 / 24 )7.86250.0168705255471746466.049500237221
Trimmed Mean ( 1 / 24 )7.8530.0388463821721855202.155247435702
Trimmed Mean ( 2 / 24 )7.855735294117650.0377775454488982207.9472131069
Trimmed Mean ( 3 / 24 )7.857878787878790.0368658597547277213.147851159801
Trimmed Mean ( 4 / 24 )7.859531250.0359421311284482218.671820597171
Trimmed Mean ( 5 / 24 )7.861451612903230.0348615504283032225.504933553406
Trimmed Mean ( 6 / 24 )7.860333333333330.0344365187406555228.255747699999
Trimmed Mean ( 7 / 24 )7.859137931034480.0339007523403434231.827832377684
Trimmed Mean ( 8 / 24 )7.85750.0333061848318289235.917143908089
Trimmed Mean ( 9 / 24 )7.855740740740740.0325565699699412241.295097978497
Trimmed Mean ( 10 / 24 )7.854038461538460.0318677740638511246.45707747902
Trimmed Mean ( 11 / 24 )7.85240.0310477709607735252.913486443871
Trimmed Mean ( 12 / 24 )7.851458333333330.030359824352138258.613430771724
Trimmed Mean ( 13 / 24 )7.850652173913040.0296475303431928264.799532474906
Trimmed Mean ( 14 / 24 )7.849772727272730.0288403211921348272.18048907907
Trimmed Mean ( 15 / 24 )7.849523809523810.0281277002956185279.067386491833
Trimmed Mean ( 16 / 24 )7.849250.0273143793726458287.366953973726
Trimmed Mean ( 17 / 24 )7.849736842105260.0264507563132995296.767954349887
Trimmed Mean ( 18 / 24 )7.850833333333330.0254276908176393308.751328999453
Trimmed Mean ( 19 / 24 )7.851176470588240.0243150911007443322.89315462807
Trimmed Mean ( 20 / 24 )7.8506250.0232922244917525337.049172902306
Trimmed Mean ( 21 / 24 )7.849333333333330.0220288908175455356.319952663323
Trimmed Mean ( 22 / 24 )7.849642857142860.0211475175401359371.185073720592
Trimmed Mean ( 23 / 24 )7.848846153846150.0204963555715638382.938621768226
Trimmed Mean ( 24 / 24 )7.84750.0198750626651095394.841522375485
Median7.84
Midrange7.75
Midmean - Weighted Average at Xnp7.83425
Midmean - Weighted Average at X(n+1)p7.85810810810811
Midmean - Empirical Distribution Function7.83425
Midmean - Empirical Distribution Function - Averaging7.85810810810811
Midmean - Empirical Distribution Function - Interpolation7.85810810810811
Midmean - Closest Observation7.83425
Midmean - True Basic - Statistics Graphics Toolkit7.85810810810811
Midmean - MS Excel (old versions)7.83425
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')