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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 computationWed, 07 Mar 2012 12:15:25 -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/2012/Mar/07/t1331140643558jjw8bx7qsxch.htm/, Retrieved Mon, 29 Apr 2024 02:10:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163668, Retrieved Mon, 29 Apr 2024 02:10:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid gemid...] [2012-03-07 17:15:25] [3b1daca0bbde728cac84422b4a85488f] [Current]
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Dataseries X:
62,02
62,02
62,02
62,07
62,11
62,15
62,2
62,22
62,31
62,47
62,47
62,47
62,55
62,6
62,71
62,72
62,77
62,82
62,82
62,82
63,13
64,09
64,2
64,23
64,23
64,24
64,29
64,29
64,29
64,31
64,35
64,42
65,35
65,83
66,15
66,19
66,19
66,4
66,4
66,4
66,48
66,49
66,56
66,59
66,65
67,69
67,91
67,94
68
68,1
68,12
68,12
68,14
68,14
68,16
68,24
68,42
68,97
69,13
69,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163668&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163668&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean65.07283333333330.306255136395683212.479157408348
Geometric Mean65.0304843442439
Harmonic Mean64.9883313384202
Quadratic Mean65.1153390403009
Winsorized Mean ( 1 / 20 )65.07166666666670.305990765218898212.658923285205
Winsorized Mean ( 2 / 20 )65.06633333333330.304812433449962213.463514584666
Winsorized Mean ( 3 / 20 )65.04133333333330.298766339804832217.699669165614
Winsorized Mean ( 4 / 20 )65.0320.29606637673844219.653446353526
Winsorized Mean ( 5 / 20 )65.02866666666670.294297926093952220.962028274391
Winsorized Mean ( 6 / 20 )65.03166666666670.293114019837393221.864742951373
Winsorized Mean ( 7 / 20 )65.0340.292732905004402222.161563965698
Winsorized Mean ( 8 / 20 )65.04333333333330.290318514608818224.041285899297
Winsorized Mean ( 9 / 20 )65.06733333333330.286559650238846227.063835676447
Winsorized Mean ( 10 / 20 )65.0640.285958809407869227.529272956224
Winsorized Mean ( 11 / 20 )65.04566666666670.282685404053311230.099133998443
Winsorized Mean ( 12 / 20 )65.04966666666670.278111363162584233.897910272147
Winsorized Mean ( 13 / 20 )65.0540.275323969417109236.281643540613
Winsorized Mean ( 14 / 20 )65.02833333333330.262538581148251247.690579605185
Winsorized Mean ( 15 / 20 )64.77083333333330.220750810719112293.411530958086
Winsorized Mean ( 16 / 20 )64.76816666666670.216361343977172299.351841119549
Winsorized Mean ( 17 / 20 )64.77383333333330.212940151225095304.187974699342
Winsorized Mean ( 18 / 20 )64.75283333333330.209974856130814308.383749018941
Winsorized Mean ( 19 / 20 )64.74966666666670.209531218318642309.021572948617
Winsorized Mean ( 20 / 20 )64.82633333333330.189893066350076341.383361590587
Trimmed Mean ( 1 / 20 )65.05431034482760.304061647209291213.951055458334
Trimmed Mean ( 2 / 20 )65.03571428571430.301410952276346215.770906115206
Trimmed Mean ( 3 / 20 )65.01870370370370.298625320763325217.726693562044
Trimmed Mean ( 4 / 20 )65.010.297651187232531218.410014098862
Trimmed Mean ( 5 / 20 )65.00340.297000049474331218.866630207811
Trimmed Mean ( 6 / 20 )64.99708333333330.296256334033692219.394746597861
Trimmed Mean ( 7 / 20 )64.98956521739130.295129539481503220.206914331815
Trimmed Mean ( 8 / 20 )64.98090909090910.293247620325947221.590575973583
Trimmed Mean ( 9 / 20 )64.96976190476190.290887641517876223.350024654689
Trimmed Mean ( 10 / 20 )64.95350.288146942125732225.417974318317
Trimmed Mean ( 11 / 20 )64.93605263157890.284053302621627228.605166819964
Trimmed Mean ( 12 / 20 )64.91944444444450.278837992573273232.821373605983
Trimmed Mean ( 13 / 20 )64.90029411764710.272336063394065238.30958452145
Trimmed Mean ( 14 / 20 )64.8781250.263448531080031246.264895590901
Trimmed Mean ( 15 / 20 )64.85666666666670.254225591436024255.114625952155
Trimmed Mean ( 16 / 20 )64.86892857142860.253136587806204256.260579055806
Trimmed Mean ( 17 / 20 )64.88346153846150.251365466270003258.124007650149
Trimmed Mean ( 18 / 20 )64.89958333333330.248163894510558261.519039509481
Trimmed Mean ( 19 / 20 )64.92181818181820.242328742011833267.908039479065
Trimmed Mean ( 20 / 20 )64.9490.230957845322019281.215820616283
Median64.33
Midrange65.61
Midmean - Weighted Average at Xnp64.7874193548387
Midmean - Weighted Average at X(n+1)p64.8566666666667
Midmean - Empirical Distribution Function64.7874193548387
Midmean - Empirical Distribution Function - Averaging64.8566666666667
Midmean - Empirical Distribution Function - Interpolation64.8566666666667
Midmean - Closest Observation64.7874193548387
Midmean - True Basic - Statistics Graphics Toolkit64.8566666666667
Midmean - MS Excel (old versions)64.878125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 65.0728333333333 & 0.306255136395683 & 212.479157408348 \tabularnewline
Geometric Mean & 65.0304843442439 &  &  \tabularnewline
Harmonic Mean & 64.9883313384202 &  &  \tabularnewline
Quadratic Mean & 65.1153390403009 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 65.0716666666667 & 0.305990765218898 & 212.658923285205 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 65.0663333333333 & 0.304812433449962 & 213.463514584666 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 65.0413333333333 & 0.298766339804832 & 217.699669165614 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 65.032 & 0.29606637673844 & 219.653446353526 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 65.0286666666667 & 0.294297926093952 & 220.962028274391 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 65.0316666666667 & 0.293114019837393 & 221.864742951373 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 65.034 & 0.292732905004402 & 222.161563965698 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 65.0433333333333 & 0.290318514608818 & 224.041285899297 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 65.0673333333333 & 0.286559650238846 & 227.063835676447 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 65.064 & 0.285958809407869 & 227.529272956224 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 65.0456666666667 & 0.282685404053311 & 230.099133998443 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 65.0496666666667 & 0.278111363162584 & 233.897910272147 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 65.054 & 0.275323969417109 & 236.281643540613 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 65.0283333333333 & 0.262538581148251 & 247.690579605185 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 64.7708333333333 & 0.220750810719112 & 293.411530958086 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 64.7681666666667 & 0.216361343977172 & 299.351841119549 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 64.7738333333333 & 0.212940151225095 & 304.187974699342 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 64.7528333333333 & 0.209974856130814 & 308.383749018941 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 64.7496666666667 & 0.209531218318642 & 309.021572948617 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 64.8263333333333 & 0.189893066350076 & 341.383361590587 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 65.0543103448276 & 0.304061647209291 & 213.951055458334 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 65.0357142857143 & 0.301410952276346 & 215.770906115206 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 65.0187037037037 & 0.298625320763325 & 217.726693562044 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 65.01 & 0.297651187232531 & 218.410014098862 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 65.0034 & 0.297000049474331 & 218.866630207811 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 64.9970833333333 & 0.296256334033692 & 219.394746597861 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 64.9895652173913 & 0.295129539481503 & 220.206914331815 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 64.9809090909091 & 0.293247620325947 & 221.590575973583 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 64.9697619047619 & 0.290887641517876 & 223.350024654689 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 64.9535 & 0.288146942125732 & 225.417974318317 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 64.9360526315789 & 0.284053302621627 & 228.605166819964 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 64.9194444444445 & 0.278837992573273 & 232.821373605983 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 64.9002941176471 & 0.272336063394065 & 238.30958452145 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 64.878125 & 0.263448531080031 & 246.264895590901 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 64.8566666666667 & 0.254225591436024 & 255.114625952155 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 64.8689285714286 & 0.253136587806204 & 256.260579055806 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 64.8834615384615 & 0.251365466270003 & 258.124007650149 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 64.8995833333333 & 0.248163894510558 & 261.519039509481 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 64.9218181818182 & 0.242328742011833 & 267.908039479065 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 64.949 & 0.230957845322019 & 281.215820616283 \tabularnewline
Median & 64.33 &  &  \tabularnewline
Midrange & 65.61 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 64.7874193548387 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 64.8566666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 64.7874193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 64.8566666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 64.8566666666667 &  &  \tabularnewline
Midmean - Closest Observation & 64.7874193548387 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 64.8566666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 64.878125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163668&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]65.0728333333333[/C][C]0.306255136395683[/C][C]212.479157408348[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]65.0304843442439[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]64.9883313384202[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]65.1153390403009[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]65.0716666666667[/C][C]0.305990765218898[/C][C]212.658923285205[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]65.0663333333333[/C][C]0.304812433449962[/C][C]213.463514584666[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]65.0413333333333[/C][C]0.298766339804832[/C][C]217.699669165614[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]65.032[/C][C]0.29606637673844[/C][C]219.653446353526[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]65.0286666666667[/C][C]0.294297926093952[/C][C]220.962028274391[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]65.0316666666667[/C][C]0.293114019837393[/C][C]221.864742951373[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]65.034[/C][C]0.292732905004402[/C][C]222.161563965698[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]65.0433333333333[/C][C]0.290318514608818[/C][C]224.041285899297[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]65.0673333333333[/C][C]0.286559650238846[/C][C]227.063835676447[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]65.064[/C][C]0.285958809407869[/C][C]227.529272956224[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]65.0456666666667[/C][C]0.282685404053311[/C][C]230.099133998443[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]65.0496666666667[/C][C]0.278111363162584[/C][C]233.897910272147[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]65.054[/C][C]0.275323969417109[/C][C]236.281643540613[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]65.0283333333333[/C][C]0.262538581148251[/C][C]247.690579605185[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]64.7708333333333[/C][C]0.220750810719112[/C][C]293.411530958086[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]64.7681666666667[/C][C]0.216361343977172[/C][C]299.351841119549[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]64.7738333333333[/C][C]0.212940151225095[/C][C]304.187974699342[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]64.7528333333333[/C][C]0.209974856130814[/C][C]308.383749018941[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]64.7496666666667[/C][C]0.209531218318642[/C][C]309.021572948617[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]64.8263333333333[/C][C]0.189893066350076[/C][C]341.383361590587[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]65.0543103448276[/C][C]0.304061647209291[/C][C]213.951055458334[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]65.0357142857143[/C][C]0.301410952276346[/C][C]215.770906115206[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]65.0187037037037[/C][C]0.298625320763325[/C][C]217.726693562044[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]65.01[/C][C]0.297651187232531[/C][C]218.410014098862[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]65.0034[/C][C]0.297000049474331[/C][C]218.866630207811[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]64.9970833333333[/C][C]0.296256334033692[/C][C]219.394746597861[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]64.9895652173913[/C][C]0.295129539481503[/C][C]220.206914331815[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]64.9809090909091[/C][C]0.293247620325947[/C][C]221.590575973583[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]64.9697619047619[/C][C]0.290887641517876[/C][C]223.350024654689[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]64.9535[/C][C]0.288146942125732[/C][C]225.417974318317[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]64.9360526315789[/C][C]0.284053302621627[/C][C]228.605166819964[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]64.9194444444445[/C][C]0.278837992573273[/C][C]232.821373605983[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]64.9002941176471[/C][C]0.272336063394065[/C][C]238.30958452145[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]64.878125[/C][C]0.263448531080031[/C][C]246.264895590901[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]64.8566666666667[/C][C]0.254225591436024[/C][C]255.114625952155[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]64.8689285714286[/C][C]0.253136587806204[/C][C]256.260579055806[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]64.8834615384615[/C][C]0.251365466270003[/C][C]258.124007650149[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]64.8995833333333[/C][C]0.248163894510558[/C][C]261.519039509481[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]64.9218181818182[/C][C]0.242328742011833[/C][C]267.908039479065[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]64.949[/C][C]0.230957845322019[/C][C]281.215820616283[/C][/ROW]
[ROW][C]Median[/C][C]64.33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]65.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]64.7874193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]64.8566666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]64.7874193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]64.8566666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]64.8566666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]64.7874193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]64.8566666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]64.878125[/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=163668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163668&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 Mean65.07283333333330.306255136395683212.479157408348
Geometric Mean65.0304843442439
Harmonic Mean64.9883313384202
Quadratic Mean65.1153390403009
Winsorized Mean ( 1 / 20 )65.07166666666670.305990765218898212.658923285205
Winsorized Mean ( 2 / 20 )65.06633333333330.304812433449962213.463514584666
Winsorized Mean ( 3 / 20 )65.04133333333330.298766339804832217.699669165614
Winsorized Mean ( 4 / 20 )65.0320.29606637673844219.653446353526
Winsorized Mean ( 5 / 20 )65.02866666666670.294297926093952220.962028274391
Winsorized Mean ( 6 / 20 )65.03166666666670.293114019837393221.864742951373
Winsorized Mean ( 7 / 20 )65.0340.292732905004402222.161563965698
Winsorized Mean ( 8 / 20 )65.04333333333330.290318514608818224.041285899297
Winsorized Mean ( 9 / 20 )65.06733333333330.286559650238846227.063835676447
Winsorized Mean ( 10 / 20 )65.0640.285958809407869227.529272956224
Winsorized Mean ( 11 / 20 )65.04566666666670.282685404053311230.099133998443
Winsorized Mean ( 12 / 20 )65.04966666666670.278111363162584233.897910272147
Winsorized Mean ( 13 / 20 )65.0540.275323969417109236.281643540613
Winsorized Mean ( 14 / 20 )65.02833333333330.262538581148251247.690579605185
Winsorized Mean ( 15 / 20 )64.77083333333330.220750810719112293.411530958086
Winsorized Mean ( 16 / 20 )64.76816666666670.216361343977172299.351841119549
Winsorized Mean ( 17 / 20 )64.77383333333330.212940151225095304.187974699342
Winsorized Mean ( 18 / 20 )64.75283333333330.209974856130814308.383749018941
Winsorized Mean ( 19 / 20 )64.74966666666670.209531218318642309.021572948617
Winsorized Mean ( 20 / 20 )64.82633333333330.189893066350076341.383361590587
Trimmed Mean ( 1 / 20 )65.05431034482760.304061647209291213.951055458334
Trimmed Mean ( 2 / 20 )65.03571428571430.301410952276346215.770906115206
Trimmed Mean ( 3 / 20 )65.01870370370370.298625320763325217.726693562044
Trimmed Mean ( 4 / 20 )65.010.297651187232531218.410014098862
Trimmed Mean ( 5 / 20 )65.00340.297000049474331218.866630207811
Trimmed Mean ( 6 / 20 )64.99708333333330.296256334033692219.394746597861
Trimmed Mean ( 7 / 20 )64.98956521739130.295129539481503220.206914331815
Trimmed Mean ( 8 / 20 )64.98090909090910.293247620325947221.590575973583
Trimmed Mean ( 9 / 20 )64.96976190476190.290887641517876223.350024654689
Trimmed Mean ( 10 / 20 )64.95350.288146942125732225.417974318317
Trimmed Mean ( 11 / 20 )64.93605263157890.284053302621627228.605166819964
Trimmed Mean ( 12 / 20 )64.91944444444450.278837992573273232.821373605983
Trimmed Mean ( 13 / 20 )64.90029411764710.272336063394065238.30958452145
Trimmed Mean ( 14 / 20 )64.8781250.263448531080031246.264895590901
Trimmed Mean ( 15 / 20 )64.85666666666670.254225591436024255.114625952155
Trimmed Mean ( 16 / 20 )64.86892857142860.253136587806204256.260579055806
Trimmed Mean ( 17 / 20 )64.88346153846150.251365466270003258.124007650149
Trimmed Mean ( 18 / 20 )64.89958333333330.248163894510558261.519039509481
Trimmed Mean ( 19 / 20 )64.92181818181820.242328742011833267.908039479065
Trimmed Mean ( 20 / 20 )64.9490.230957845322019281.215820616283
Median64.33
Midrange65.61
Midmean - Weighted Average at Xnp64.7874193548387
Midmean - Weighted Average at X(n+1)p64.8566666666667
Midmean - Empirical Distribution Function64.7874193548387
Midmean - Empirical Distribution Function - Averaging64.8566666666667
Midmean - Empirical Distribution Function - Interpolation64.8566666666667
Midmean - Closest Observation64.7874193548387
Midmean - True Basic - Statistics Graphics Toolkit64.8566666666667
Midmean - MS Excel (old versions)64.878125
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')