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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 10:25:07 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/baf4c2h7mpmvevv1193074018.htm/, Retrieved Mon, 06 May 2024 01:40:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1416, Retrieved Mon, 06 May 2024 01:40:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWerkloosheid, mannen, central tendency
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-10-22 17:25:07] [9fe578921d87f9af8e79a90d6142ba02] [Current]
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Dataseries X:
7,6
7,9
7,7
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




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1416&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1416&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.216666666666670.0565069200635277145.409918952035
Geometric Mean8.20513120469308
Harmonic Mean8.19352227191762
Quadratic Mean8.22812250759552
Winsorized Mean ( 1 / 20 )8.218333333333330.0560715678007213146.568638182926
Winsorized Mean ( 2 / 20 )8.211666666666670.0542588307617376151.342492113881
Winsorized Mean ( 3 / 20 )8.196666666666670.0511432388994128160.268822293161
Winsorized Mean ( 4 / 20 )8.210.0479347484920318171.274498318579
Winsorized Mean ( 5 / 20 )8.210.0479347484920318171.274498318579
Winsorized Mean ( 6 / 20 )8.210.0479347484920318171.274498318579
Winsorized Mean ( 7 / 20 )8.221666666666670.0455407972971021180.534095901519
Winsorized Mean ( 8 / 20 )8.221666666666670.0455407972971021180.534095901519
Winsorized Mean ( 9 / 20 )8.206666666666670.0430389828988118190.679846825405
Winsorized Mean ( 10 / 20 )8.206666666666670.0430389828988118190.679846825405
Winsorized Mean ( 11 / 20 )8.206666666666670.0430389828988118190.679846825405
Winsorized Mean ( 12 / 20 )8.226666666666670.0391914514680594209.909721597612
Winsorized Mean ( 13 / 20 )8.248333333333330.0353746427317541233.170788349170
Winsorized Mean ( 14 / 20 )8.248333333333330.0353746427317541233.170788349170
Winsorized Mean ( 15 / 20 )8.248333333333330.0272560226762465302.624246806257
Winsorized Mean ( 16 / 20 )8.248333333333330.0272560226762465302.624246806257
Winsorized Mean ( 17 / 20 )8.248333333333330.0272560226762465302.624246806257
Winsorized Mean ( 18 / 20 )8.278333333333330.0229334170935273360.972518817085
Winsorized Mean ( 19 / 20 )8.246666666666670.0180186135189423457.674873707527
Winsorized Mean ( 20 / 20 )8.246666666666670.0180186135189423457.674873707527
Trimmed Mean ( 1 / 20 )8.215517241379310.0535944374668883153.290483671090
Trimmed Mean ( 2 / 20 )8.21250.0505208263600656162.556723468237
Trimmed Mean ( 3 / 20 )8.212962962962960.0479522165124585171.273896397034
Trimmed Mean ( 4 / 20 )8.219230769230770.0462825004260763177.588304295675
Trimmed Mean ( 5 / 20 )8.2220.0454716776619002180.815848958418
Trimmed Mean ( 6 / 20 )8.2250.0444130355920022185.193376006956
Trimmed Mean ( 7 / 20 )8.228260869565220.0430327415487392191.209311176371
Trimmed Mean ( 8 / 20 )8.229545454545460.041962878170352196.114895197057
Trimmed Mean ( 9 / 20 )8.230952380952380.0405376318531469203.044726706536
Trimmed Mean ( 10 / 20 )8.2350.0393130108299125209.472635805705
Trimmed Mean ( 11 / 20 )8.239473684210530.0376287687080483218.967400930348
Trimmed Mean ( 12 / 20 )8.244444444444440.0352866817909616233.641816855565
Trimmed Mean ( 13 / 20 )8.247058823529410.0333071093238195247.606561810861
Trimmed Mean ( 14 / 20 )8.2468750.0317450704199525259.784429232724
Trimmed Mean ( 15 / 20 )8.246666666666670.0294522146907762280.001580636629
Trimmed Mean ( 16 / 20 )8.246428571428570.0288593298977409285.745670486760
Trimmed Mean ( 17 / 20 )8.246153846153850.0278627235019613295.956489880588
Trimmed Mean ( 18 / 20 )8.245833333333330.0262230998583993314.449221406301
Trimmed Mean ( 19 / 20 )8.240909090909090.0251911230406115327.135438845804
Trimmed Mean ( 20 / 20 )8.240.0255466549463403322.54712083863
Median8.25
Midrange8.25
Midmean - Weighted Average at Xnp8.225
Midmean - Weighted Average at X(n+1)p8.24666666666667
Midmean - Empirical Distribution Function8.225
Midmean - Empirical Distribution Function - Averaging8.24666666666667
Midmean - Empirical Distribution Function - Interpolation8.24666666666667
Midmean - Closest Observation8.225
Midmean - True Basic - Statistics Graphics Toolkit8.24666666666667
Midmean - MS Excel (old versions)8.2842105263158
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.21666666666667 & 0.0565069200635277 & 145.409918952035 \tabularnewline
Geometric Mean & 8.20513120469308 &  &  \tabularnewline
Harmonic Mean & 8.19352227191762 &  &  \tabularnewline
Quadratic Mean & 8.22812250759552 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.21833333333333 & 0.0560715678007213 & 146.568638182926 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.21166666666667 & 0.0542588307617376 & 151.342492113881 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.19666666666667 & 0.0511432388994128 & 160.268822293161 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.21 & 0.0479347484920318 & 171.274498318579 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.21 & 0.0479347484920318 & 171.274498318579 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.21 & 0.0479347484920318 & 171.274498318579 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.22166666666667 & 0.0455407972971021 & 180.534095901519 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.22166666666667 & 0.0455407972971021 & 180.534095901519 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.20666666666667 & 0.0430389828988118 & 190.679846825405 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.20666666666667 & 0.0430389828988118 & 190.679846825405 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.20666666666667 & 0.0430389828988118 & 190.679846825405 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.22666666666667 & 0.0391914514680594 & 209.909721597612 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.24833333333333 & 0.0353746427317541 & 233.170788349170 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.24833333333333 & 0.0353746427317541 & 233.170788349170 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.24833333333333 & 0.0272560226762465 & 302.624246806257 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.24833333333333 & 0.0272560226762465 & 302.624246806257 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.24833333333333 & 0.0272560226762465 & 302.624246806257 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.27833333333333 & 0.0229334170935273 & 360.972518817085 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.24666666666667 & 0.0180186135189423 & 457.674873707527 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.24666666666667 & 0.0180186135189423 & 457.674873707527 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.21551724137931 & 0.0535944374668883 & 153.290483671090 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.2125 & 0.0505208263600656 & 162.556723468237 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.21296296296296 & 0.0479522165124585 & 171.273896397034 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.21923076923077 & 0.0462825004260763 & 177.588304295675 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.222 & 0.0454716776619002 & 180.815848958418 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.225 & 0.0444130355920022 & 185.193376006956 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.22826086956522 & 0.0430327415487392 & 191.209311176371 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.22954545454546 & 0.041962878170352 & 196.114895197057 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.23095238095238 & 0.0405376318531469 & 203.044726706536 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.235 & 0.0393130108299125 & 209.472635805705 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.23947368421053 & 0.0376287687080483 & 218.967400930348 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.24444444444444 & 0.0352866817909616 & 233.641816855565 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.24705882352941 & 0.0333071093238195 & 247.606561810861 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.246875 & 0.0317450704199525 & 259.784429232724 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.24666666666667 & 0.0294522146907762 & 280.001580636629 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.24642857142857 & 0.0288593298977409 & 285.745670486760 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.24615384615385 & 0.0278627235019613 & 295.956489880588 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.24583333333333 & 0.0262230998583993 & 314.449221406301 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.24090909090909 & 0.0251911230406115 & 327.135438845804 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.24 & 0.0255466549463403 & 322.54712083863 \tabularnewline
Median & 8.25 &  &  \tabularnewline
Midrange & 8.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.225 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.24666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.225 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.24666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.24666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 8.225 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.24666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.2842105263158 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1416&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]8.21666666666667[/C][C]0.0565069200635277[/C][C]145.409918952035[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.20513120469308[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.19352227191762[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.22812250759552[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.21833333333333[/C][C]0.0560715678007213[/C][C]146.568638182926[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.21166666666667[/C][C]0.0542588307617376[/C][C]151.342492113881[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.19666666666667[/C][C]0.0511432388994128[/C][C]160.268822293161[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.21[/C][C]0.0479347484920318[/C][C]171.274498318579[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.21[/C][C]0.0479347484920318[/C][C]171.274498318579[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.21[/C][C]0.0479347484920318[/C][C]171.274498318579[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.22166666666667[/C][C]0.0455407972971021[/C][C]180.534095901519[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.22166666666667[/C][C]0.0455407972971021[/C][C]180.534095901519[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.20666666666667[/C][C]0.0430389828988118[/C][C]190.679846825405[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.20666666666667[/C][C]0.0430389828988118[/C][C]190.679846825405[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.20666666666667[/C][C]0.0430389828988118[/C][C]190.679846825405[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.22666666666667[/C][C]0.0391914514680594[/C][C]209.909721597612[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.24833333333333[/C][C]0.0353746427317541[/C][C]233.170788349170[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.24833333333333[/C][C]0.0353746427317541[/C][C]233.170788349170[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.24833333333333[/C][C]0.0272560226762465[/C][C]302.624246806257[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.24833333333333[/C][C]0.0272560226762465[/C][C]302.624246806257[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.24833333333333[/C][C]0.0272560226762465[/C][C]302.624246806257[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.27833333333333[/C][C]0.0229334170935273[/C][C]360.972518817085[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.24666666666667[/C][C]0.0180186135189423[/C][C]457.674873707527[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.24666666666667[/C][C]0.0180186135189423[/C][C]457.674873707527[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.21551724137931[/C][C]0.0535944374668883[/C][C]153.290483671090[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.2125[/C][C]0.0505208263600656[/C][C]162.556723468237[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.21296296296296[/C][C]0.0479522165124585[/C][C]171.273896397034[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.21923076923077[/C][C]0.0462825004260763[/C][C]177.588304295675[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.222[/C][C]0.0454716776619002[/C][C]180.815848958418[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.225[/C][C]0.0444130355920022[/C][C]185.193376006956[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.22826086956522[/C][C]0.0430327415487392[/C][C]191.209311176371[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.22954545454546[/C][C]0.041962878170352[/C][C]196.114895197057[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.23095238095238[/C][C]0.0405376318531469[/C][C]203.044726706536[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.235[/C][C]0.0393130108299125[/C][C]209.472635805705[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.23947368421053[/C][C]0.0376287687080483[/C][C]218.967400930348[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.24444444444444[/C][C]0.0352866817909616[/C][C]233.641816855565[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.24705882352941[/C][C]0.0333071093238195[/C][C]247.606561810861[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.246875[/C][C]0.0317450704199525[/C][C]259.784429232724[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.24666666666667[/C][C]0.0294522146907762[/C][C]280.001580636629[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.24642857142857[/C][C]0.0288593298977409[/C][C]285.745670486760[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.24615384615385[/C][C]0.0278627235019613[/C][C]295.956489880588[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.24583333333333[/C][C]0.0262230998583993[/C][C]314.449221406301[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.24090909090909[/C][C]0.0251911230406115[/C][C]327.135438845804[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.24[/C][C]0.0255466549463403[/C][C]322.54712083863[/C][/ROW]
[ROW][C]Median[/C][C]8.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.24666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.24666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.24666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.24666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.2842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1416&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 Mean8.216666666666670.0565069200635277145.409918952035
Geometric Mean8.20513120469308
Harmonic Mean8.19352227191762
Quadratic Mean8.22812250759552
Winsorized Mean ( 1 / 20 )8.218333333333330.0560715678007213146.568638182926
Winsorized Mean ( 2 / 20 )8.211666666666670.0542588307617376151.342492113881
Winsorized Mean ( 3 / 20 )8.196666666666670.0511432388994128160.268822293161
Winsorized Mean ( 4 / 20 )8.210.0479347484920318171.274498318579
Winsorized Mean ( 5 / 20 )8.210.0479347484920318171.274498318579
Winsorized Mean ( 6 / 20 )8.210.0479347484920318171.274498318579
Winsorized Mean ( 7 / 20 )8.221666666666670.0455407972971021180.534095901519
Winsorized Mean ( 8 / 20 )8.221666666666670.0455407972971021180.534095901519
Winsorized Mean ( 9 / 20 )8.206666666666670.0430389828988118190.679846825405
Winsorized Mean ( 10 / 20 )8.206666666666670.0430389828988118190.679846825405
Winsorized Mean ( 11 / 20 )8.206666666666670.0430389828988118190.679846825405
Winsorized Mean ( 12 / 20 )8.226666666666670.0391914514680594209.909721597612
Winsorized Mean ( 13 / 20 )8.248333333333330.0353746427317541233.170788349170
Winsorized Mean ( 14 / 20 )8.248333333333330.0353746427317541233.170788349170
Winsorized Mean ( 15 / 20 )8.248333333333330.0272560226762465302.624246806257
Winsorized Mean ( 16 / 20 )8.248333333333330.0272560226762465302.624246806257
Winsorized Mean ( 17 / 20 )8.248333333333330.0272560226762465302.624246806257
Winsorized Mean ( 18 / 20 )8.278333333333330.0229334170935273360.972518817085
Winsorized Mean ( 19 / 20 )8.246666666666670.0180186135189423457.674873707527
Winsorized Mean ( 20 / 20 )8.246666666666670.0180186135189423457.674873707527
Trimmed Mean ( 1 / 20 )8.215517241379310.0535944374668883153.290483671090
Trimmed Mean ( 2 / 20 )8.21250.0505208263600656162.556723468237
Trimmed Mean ( 3 / 20 )8.212962962962960.0479522165124585171.273896397034
Trimmed Mean ( 4 / 20 )8.219230769230770.0462825004260763177.588304295675
Trimmed Mean ( 5 / 20 )8.2220.0454716776619002180.815848958418
Trimmed Mean ( 6 / 20 )8.2250.0444130355920022185.193376006956
Trimmed Mean ( 7 / 20 )8.228260869565220.0430327415487392191.209311176371
Trimmed Mean ( 8 / 20 )8.229545454545460.041962878170352196.114895197057
Trimmed Mean ( 9 / 20 )8.230952380952380.0405376318531469203.044726706536
Trimmed Mean ( 10 / 20 )8.2350.0393130108299125209.472635805705
Trimmed Mean ( 11 / 20 )8.239473684210530.0376287687080483218.967400930348
Trimmed Mean ( 12 / 20 )8.244444444444440.0352866817909616233.641816855565
Trimmed Mean ( 13 / 20 )8.247058823529410.0333071093238195247.606561810861
Trimmed Mean ( 14 / 20 )8.2468750.0317450704199525259.784429232724
Trimmed Mean ( 15 / 20 )8.246666666666670.0294522146907762280.001580636629
Trimmed Mean ( 16 / 20 )8.246428571428570.0288593298977409285.745670486760
Trimmed Mean ( 17 / 20 )8.246153846153850.0278627235019613295.956489880588
Trimmed Mean ( 18 / 20 )8.245833333333330.0262230998583993314.449221406301
Trimmed Mean ( 19 / 20 )8.240909090909090.0251911230406115327.135438845804
Trimmed Mean ( 20 / 20 )8.240.0255466549463403322.54712083863
Median8.25
Midrange8.25
Midmean - Weighted Average at Xnp8.225
Midmean - Weighted Average at X(n+1)p8.24666666666667
Midmean - Empirical Distribution Function8.225
Midmean - Empirical Distribution Function - Averaging8.24666666666667
Midmean - Empirical Distribution Function - Interpolation8.24666666666667
Midmean - Closest Observation8.225
Midmean - True Basic - Statistics Graphics Toolkit8.24666666666667
Midmean - MS Excel (old versions)8.2842105263158
Number of observations60



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')