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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 11:56:35 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t1255888899nb7879d7oeir03c.htm/, Retrieved Mon, 29 Apr 2024 11:46:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47426, Retrieved Mon, 29 Apr 2024 11:46:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop3,deel2,gemiddeldes
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2009-10-12 17:11:03] [0750c128064677e728c9436fc3f45ae7]
- RMPD    [Central Tendency] [] [2009-10-18 17:56:35] [30f5b608e5a1bbbae86b1702c0071566] [Current]
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Dataseries X:
0,65
0,57
0,52
0,56
0,55
0,65
0,48
0,59
0,68
0,69
0,78
0,76
0,79
0,89
0,89
0,73
1,60
1,63
1,55
1,07
1,00
0,83
0,75
0,63
0,53
0,47
0,50
0,50
0,49
0,50
0,47
0,46
0,43
0,44
0,45
0,38
0,36
0,32
0,32
0,29
0,29
0,31
0,27
0,29
0,32
0,32
0,34
0,38
0,44
0,50
0,60
0,59
0,81
0,85
1,13
1,28
1,47
1,50
1,80
2,22




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47426&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47426&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47426&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.7076666666666670.055134333467725212.8353173450609
Geometric Mean0.612652145281306
Harmonic Mean0.5430890291452
Quadratic Mean0.824706008223537
Winsorized Mean ( 1 / 20 )0.7010.052203264179172313.4282790745426
Winsorized Mean ( 2 / 20 )0.6953333333333330.050297682588991913.8243612338019
Winsorized Mean ( 3 / 20 )0.6938333333333330.04983027218835313.9239322376309
Winsorized Mean ( 4 / 20 )0.6918333333333330.04863765000610914.2242343790548
Winsorized Mean ( 5 / 20 )0.68850.047298084073904614.5566149978549
Winsorized Mean ( 6 / 20 )0.68550.046432275570870614.7634375350333
Winsorized Mean ( 7 / 20 )0.6633333333333330.040367427341944416.4323905933953
Winsorized Mean ( 8 / 20 )0.6433333333333330.035433287891079618.1561850910057
Winsorized Mean ( 9 / 20 )0.6373333333333330.032919922244784219.3601105310725
Winsorized Mean ( 10 / 20 )0.6290.029879891392113921.0509466632804
Winsorized Mean ( 11 / 20 )0.61250.025297802544081224.2115890869463
Winsorized Mean ( 12 / 20 )0.61250.025297802544081224.2115890869463
Winsorized Mean ( 13 / 20 )0.6146666666666670.022091830259588227.8232568077918
Winsorized Mean ( 14 / 20 )0.6123333333333330.020930833993801629.2550852734615
Winsorized Mean ( 15 / 20 )0.6073333333333330.020061862893299030.2730278121974
Winsorized Mean ( 16 / 20 )0.6046666666666670.018784334539862232.1899434543983
Winsorized Mean ( 17 / 20 )0.6046666666666670.017920834490927733.7409882878375
Winsorized Mean ( 18 / 20 )0.6016666666666670.016527953835964336.4029735705977
Winsorized Mean ( 19 / 20 )0.59850.016016984276409037.3665847247858
Winsorized Mean ( 20 / 20 )0.5951666666666670.014505973183615341.0290753424883
Trimmed Mean ( 1 / 20 )0.6891379310344830.049991701962822413.7850463972396
Trimmed Mean ( 2 / 20 )0.6764285714285710.047193597251336314.3330581016351
Trimmed Mean ( 3 / 20 )0.6659259259259260.044999043796439614.7986683658957
Trimmed Mean ( 4 / 20 )0.6551923076923080.042434840818367615.4399614811024
Trimmed Mean ( 5 / 20 )0.64420.039639281692044116.2515558431346
Trimmed Mean ( 6 / 20 )0.6331250.036504099947036917.3439422124799
Trimmed Mean ( 7 / 20 )0.6217391304347830.03261442783756319.0633155832557
Trimmed Mean ( 8 / 20 )0.6136363636363640.029750710029530320.6259401213374
Trimmed Mean ( 9 / 20 )0.6083333333333330.02769276577078621.9672292167756
Trimmed Mean ( 10 / 20 )0.60350.025751649187914923.4353922576431
Trimmed Mean ( 11 / 20 )0.5994736842105260.024111368467827224.8626984822711
Trimmed Mean ( 12 / 20 )0.59750.02331078842816925.6319086692913
Trimmed Mean ( 13 / 20 )0.5952941176470590.022173498715747726.8470991104475
Trimmed Mean ( 14 / 20 )0.59250.021515185934740427.5386883384212
Trimmed Mean ( 15 / 20 )0.5896666666666670.020879970787255228.2407802517900
Trimmed Mean ( 16 / 20 )0.5871428571428570.020189952074658929.0809435788508
Trimmed Mean ( 17 / 20 )0.5846153846153850.019534827039306529.9268267612027
Trimmed Mean ( 18 / 20 )0.5816666666666670.018753421587967331.0165621744396
Trimmed Mean ( 19 / 20 )0.5786363636363640.017998261755240532.1495693031514
Trimmed Mean ( 20 / 20 )0.57550.01688155330842734.0904648692913
Median0.565
Midrange1.245
Midmean - Weighted Average at Xnp0.58483870967742
Midmean - Weighted Average at X(n+1)p0.58483870967742
Midmean - Empirical Distribution Function0.58483870967742
Midmean - Empirical Distribution Function - Averaging0.58483870967742
Midmean - Empirical Distribution Function - Interpolation0.58483870967742
Midmean - Closest Observation0.58483870967742
Midmean - True Basic - Statistics Graphics Toolkit0.58483870967742
Midmean - MS Excel (old versions)0.5925
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.707666666666667 & 0.0551343334677252 & 12.8353173450609 \tabularnewline
Geometric Mean & 0.612652145281306 &  &  \tabularnewline
Harmonic Mean & 0.5430890291452 &  &  \tabularnewline
Quadratic Mean & 0.824706008223537 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.701 & 0.0522032641791723 & 13.4282790745426 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.695333333333333 & 0.0502976825889919 & 13.8243612338019 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.693833333333333 & 0.049830272188353 & 13.9239322376309 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.691833333333333 & 0.048637650006109 & 14.2242343790548 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.6885 & 0.0472980840739046 & 14.5566149978549 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.6855 & 0.0464322755708706 & 14.7634375350333 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.663333333333333 & 0.0403674273419444 & 16.4323905933953 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.643333333333333 & 0.0354332878910796 & 18.1561850910057 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.637333333333333 & 0.0329199222447842 & 19.3601105310725 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.629 & 0.0298798913921139 & 21.0509466632804 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.6125 & 0.0252978025440812 & 24.2115890869463 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.6125 & 0.0252978025440812 & 24.2115890869463 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.614666666666667 & 0.0220918302595882 & 27.8232568077918 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.612333333333333 & 0.0209308339938016 & 29.2550852734615 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.607333333333333 & 0.0200618628932990 & 30.2730278121974 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.604666666666667 & 0.0187843345398622 & 32.1899434543983 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.604666666666667 & 0.0179208344909277 & 33.7409882878375 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.601666666666667 & 0.0165279538359643 & 36.4029735705977 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.5985 & 0.0160169842764090 & 37.3665847247858 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.595166666666667 & 0.0145059731836153 & 41.0290753424883 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.689137931034483 & 0.0499917019628224 & 13.7850463972396 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.676428571428571 & 0.0471935972513363 & 14.3330581016351 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.665925925925926 & 0.0449990437964396 & 14.7986683658957 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.655192307692308 & 0.0424348408183676 & 15.4399614811024 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.6442 & 0.0396392816920441 & 16.2515558431346 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.633125 & 0.0365040999470369 & 17.3439422124799 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.621739130434783 & 0.032614427837563 & 19.0633155832557 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.613636363636364 & 0.0297507100295303 & 20.6259401213374 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.608333333333333 & 0.027692765770786 & 21.9672292167756 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.6035 & 0.0257516491879149 & 23.4353922576431 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.599473684210526 & 0.0241113684678272 & 24.8626984822711 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.5975 & 0.023310788428169 & 25.6319086692913 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.595294117647059 & 0.0221734987157477 & 26.8470991104475 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.5925 & 0.0215151859347404 & 27.5386883384212 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.589666666666667 & 0.0208799707872552 & 28.2407802517900 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.587142857142857 & 0.0201899520746589 & 29.0809435788508 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.584615384615385 & 0.0195348270393065 & 29.9268267612027 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.581666666666667 & 0.0187534215879673 & 31.0165621744396 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.578636363636364 & 0.0179982617552405 & 32.1495693031514 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.5755 & 0.016881553308427 & 34.0904648692913 \tabularnewline
Median & 0.565 &  &  \tabularnewline
Midrange & 1.245 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.58483870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.58483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.58483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.58483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.58483870967742 &  &  \tabularnewline
Midmean - Closest Observation & 0.58483870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.58483870967742 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.5925 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47426&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]0.707666666666667[/C][C]0.0551343334677252[/C][C]12.8353173450609[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.612652145281306[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.5430890291452[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.824706008223537[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.701[/C][C]0.0522032641791723[/C][C]13.4282790745426[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.695333333333333[/C][C]0.0502976825889919[/C][C]13.8243612338019[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.693833333333333[/C][C]0.049830272188353[/C][C]13.9239322376309[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.691833333333333[/C][C]0.048637650006109[/C][C]14.2242343790548[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.6885[/C][C]0.0472980840739046[/C][C]14.5566149978549[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.6855[/C][C]0.0464322755708706[/C][C]14.7634375350333[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.663333333333333[/C][C]0.0403674273419444[/C][C]16.4323905933953[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.643333333333333[/C][C]0.0354332878910796[/C][C]18.1561850910057[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.637333333333333[/C][C]0.0329199222447842[/C][C]19.3601105310725[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.629[/C][C]0.0298798913921139[/C][C]21.0509466632804[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.6125[/C][C]0.0252978025440812[/C][C]24.2115890869463[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.6125[/C][C]0.0252978025440812[/C][C]24.2115890869463[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.614666666666667[/C][C]0.0220918302595882[/C][C]27.8232568077918[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.612333333333333[/C][C]0.0209308339938016[/C][C]29.2550852734615[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.607333333333333[/C][C]0.0200618628932990[/C][C]30.2730278121974[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.604666666666667[/C][C]0.0187843345398622[/C][C]32.1899434543983[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.604666666666667[/C][C]0.0179208344909277[/C][C]33.7409882878375[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.601666666666667[/C][C]0.0165279538359643[/C][C]36.4029735705977[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.5985[/C][C]0.0160169842764090[/C][C]37.3665847247858[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.595166666666667[/C][C]0.0145059731836153[/C][C]41.0290753424883[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.689137931034483[/C][C]0.0499917019628224[/C][C]13.7850463972396[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.676428571428571[/C][C]0.0471935972513363[/C][C]14.3330581016351[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.665925925925926[/C][C]0.0449990437964396[/C][C]14.7986683658957[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.655192307692308[/C][C]0.0424348408183676[/C][C]15.4399614811024[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.6442[/C][C]0.0396392816920441[/C][C]16.2515558431346[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.633125[/C][C]0.0365040999470369[/C][C]17.3439422124799[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.621739130434783[/C][C]0.032614427837563[/C][C]19.0633155832557[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.613636363636364[/C][C]0.0297507100295303[/C][C]20.6259401213374[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.608333333333333[/C][C]0.027692765770786[/C][C]21.9672292167756[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.6035[/C][C]0.0257516491879149[/C][C]23.4353922576431[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.599473684210526[/C][C]0.0241113684678272[/C][C]24.8626984822711[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.5975[/C][C]0.023310788428169[/C][C]25.6319086692913[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.595294117647059[/C][C]0.0221734987157477[/C][C]26.8470991104475[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.5925[/C][C]0.0215151859347404[/C][C]27.5386883384212[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.589666666666667[/C][C]0.0208799707872552[/C][C]28.2407802517900[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.587142857142857[/C][C]0.0201899520746589[/C][C]29.0809435788508[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.584615384615385[/C][C]0.0195348270393065[/C][C]29.9268267612027[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.581666666666667[/C][C]0.0187534215879673[/C][C]31.0165621744396[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.578636363636364[/C][C]0.0179982617552405[/C][C]32.1495693031514[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.5755[/C][C]0.016881553308427[/C][C]34.0904648692913[/C][/ROW]
[ROW][C]Median[/C][C]0.565[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.58483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.58483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.58483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.58483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.58483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.58483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.58483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.5925[/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=47426&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47426&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 Mean0.7076666666666670.055134333467725212.8353173450609
Geometric Mean0.612652145281306
Harmonic Mean0.5430890291452
Quadratic Mean0.824706008223537
Winsorized Mean ( 1 / 20 )0.7010.052203264179172313.4282790745426
Winsorized Mean ( 2 / 20 )0.6953333333333330.050297682588991913.8243612338019
Winsorized Mean ( 3 / 20 )0.6938333333333330.04983027218835313.9239322376309
Winsorized Mean ( 4 / 20 )0.6918333333333330.04863765000610914.2242343790548
Winsorized Mean ( 5 / 20 )0.68850.047298084073904614.5566149978549
Winsorized Mean ( 6 / 20 )0.68550.046432275570870614.7634375350333
Winsorized Mean ( 7 / 20 )0.6633333333333330.040367427341944416.4323905933953
Winsorized Mean ( 8 / 20 )0.6433333333333330.035433287891079618.1561850910057
Winsorized Mean ( 9 / 20 )0.6373333333333330.032919922244784219.3601105310725
Winsorized Mean ( 10 / 20 )0.6290.029879891392113921.0509466632804
Winsorized Mean ( 11 / 20 )0.61250.025297802544081224.2115890869463
Winsorized Mean ( 12 / 20 )0.61250.025297802544081224.2115890869463
Winsorized Mean ( 13 / 20 )0.6146666666666670.022091830259588227.8232568077918
Winsorized Mean ( 14 / 20 )0.6123333333333330.020930833993801629.2550852734615
Winsorized Mean ( 15 / 20 )0.6073333333333330.020061862893299030.2730278121974
Winsorized Mean ( 16 / 20 )0.6046666666666670.018784334539862232.1899434543983
Winsorized Mean ( 17 / 20 )0.6046666666666670.017920834490927733.7409882878375
Winsorized Mean ( 18 / 20 )0.6016666666666670.016527953835964336.4029735705977
Winsorized Mean ( 19 / 20 )0.59850.016016984276409037.3665847247858
Winsorized Mean ( 20 / 20 )0.5951666666666670.014505973183615341.0290753424883
Trimmed Mean ( 1 / 20 )0.6891379310344830.049991701962822413.7850463972396
Trimmed Mean ( 2 / 20 )0.6764285714285710.047193597251336314.3330581016351
Trimmed Mean ( 3 / 20 )0.6659259259259260.044999043796439614.7986683658957
Trimmed Mean ( 4 / 20 )0.6551923076923080.042434840818367615.4399614811024
Trimmed Mean ( 5 / 20 )0.64420.039639281692044116.2515558431346
Trimmed Mean ( 6 / 20 )0.6331250.036504099947036917.3439422124799
Trimmed Mean ( 7 / 20 )0.6217391304347830.03261442783756319.0633155832557
Trimmed Mean ( 8 / 20 )0.6136363636363640.029750710029530320.6259401213374
Trimmed Mean ( 9 / 20 )0.6083333333333330.02769276577078621.9672292167756
Trimmed Mean ( 10 / 20 )0.60350.025751649187914923.4353922576431
Trimmed Mean ( 11 / 20 )0.5994736842105260.024111368467827224.8626984822711
Trimmed Mean ( 12 / 20 )0.59750.02331078842816925.6319086692913
Trimmed Mean ( 13 / 20 )0.5952941176470590.022173498715747726.8470991104475
Trimmed Mean ( 14 / 20 )0.59250.021515185934740427.5386883384212
Trimmed Mean ( 15 / 20 )0.5896666666666670.020879970787255228.2407802517900
Trimmed Mean ( 16 / 20 )0.5871428571428570.020189952074658929.0809435788508
Trimmed Mean ( 17 / 20 )0.5846153846153850.019534827039306529.9268267612027
Trimmed Mean ( 18 / 20 )0.5816666666666670.018753421587967331.0165621744396
Trimmed Mean ( 19 / 20 )0.5786363636363640.017998261755240532.1495693031514
Trimmed Mean ( 20 / 20 )0.57550.01688155330842734.0904648692913
Median0.565
Midrange1.245
Midmean - Weighted Average at Xnp0.58483870967742
Midmean - Weighted Average at X(n+1)p0.58483870967742
Midmean - Empirical Distribution Function0.58483870967742
Midmean - Empirical Distribution Function - Averaging0.58483870967742
Midmean - Empirical Distribution Function - Interpolation0.58483870967742
Midmean - Closest Observation0.58483870967742
Midmean - True Basic - Statistics Graphics Toolkit0.58483870967742
Midmean - MS Excel (old versions)0.5925
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')