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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 29 Oct 2008 07:39:13 -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/2008/Oct/29/t1225287588nlt1zjdjgghpynx.htm/, Retrieved Fri, 17 May 2024 04:46:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19845, Retrieved Fri, 17 May 2024 04:46:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Explorative Data Analysis] [Investigation Dis...] [2007-10-21 17:06:37] [b9964c45117f7aac638ab9056d451faa]
-    D  [Univariate Explorative Data Analysis] [investigation dis...] [2008-10-27 17:49:03] [4ad596f10399a71ad29b7d76e6ab90ac]
F   PD    [Univariate Explorative Data Analysis] [investigating dis...] [2008-10-27 19:06:15] [4ad596f10399a71ad29b7d76e6ab90ac]
- RMP         [Central Tendency] [feedback taak 3 t...] [2008-10-29 13:39:13] [b23db733701c4d62df5e228d507c1c6a] [Current]
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Dataseries X:
58.44
58.96
59.43
60.03
60.47
60.48
60.68
60.77
60.91
60.95
60.95
60.95
60.93
60.93
60.93
60.93
61.8
62.74
62.86
62.86
62.92
62.92
62.92
62.92
62.95
64.17
65.33
65.68
65.97
66.58
66.78
66.83
66.85
66.86
66.86
66.86
66.96
67.66
68.44
68.56
68.65
68.68
68.69
68.71
68.71
68.82
69.75
70.43
70.91
71.47
71.87
72.31
72.56
73.23
73.57
73.72
73.68
73.76
73.76
73.78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19845&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19845&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean65.98466666666670.602623945413462109.495593676409
Geometric Mean65.8233791336607
Harmonic Mean65.6634452815308
Quadratic Mean66.1468246907338
Winsorized Mean ( 1 / 20 )65.9930.600771457904558109.847095982519
Winsorized Mean ( 2 / 20 )66.00866666666670.5977557588759110.427487626047
Winsorized Mean ( 3 / 20 )66.03666666666670.59193700357036111.560294876577
Winsorized Mean ( 4 / 20 )66.06333333333330.586456016367562112.648402419881
Winsorized Mean ( 5 / 20 )66.0550.584313228630451113.047243778519
Winsorized Mean ( 6 / 20 )66.0410.573795555039468115.095001033003
Winsorized Mean ( 7 / 20 )65.97333333333330.55597700774853118.661981365915
Winsorized Mean ( 8 / 20 )65.95866666666670.546403933005397120.714114014284
Winsorized Mean ( 9 / 20 )65.89566666666670.533160408053365123.594448633686
Winsorized Mean ( 10 / 20 )65.8290.520706587515931126.422445151005
Winsorized Mean ( 11 / 20 )65.72633333333330.50229394497277130.852330574872
Winsorized Mean ( 12 / 20 )65.63033333333330.48585506003303135.082123728158
Winsorized Mean ( 13 / 20 )65.48733333333330.461244439690073141.979669993066
Winsorized Mean ( 14 / 20 )65.27033333333330.428967290093158152.156900632584
Winsorized Mean ( 15 / 20 )65.24283333333330.425138069408355153.462693717664
Winsorized Mean ( 16 / 20 )65.46950.387495319818647168.95558901367
Winsorized Mean ( 17 / 20 )65.73016666666670.345679833880701190.147530241383
Winsorized Mean ( 18 / 20 )65.76316666666670.339999708513224193.421244254122
Winsorized Mean ( 19 / 20 )65.75366666666670.338620412006565194.181048558266
Winsorized Mean ( 20 / 20 )65.74366666666670.331392454000899198.386130622299
Trimmed Mean ( 1 / 20 )65.98034482758620.594357567003364111.011196778812
Trimmed Mean ( 2 / 20 )65.96678571428570.586111448731341112.549901314969
Trimmed Mean ( 3 / 20 )65.94351851851850.577522429307052114.183476125147
Trimmed Mean ( 4 / 20 )65.90769230769230.569147348255256115.800754426310
Trimmed Mean ( 5 / 20 )65.8610.560237795721694117.559008876148
Trimmed Mean ( 6 / 20 )65.81250.549207964525163119.831656223159
Trimmed Mean ( 7 / 20 )65.76282608695650.537933302534074122.250892029112
Trimmed Mean ( 8 / 20 )65.72181818181820.528168809175598124.433357366182
Trimmed Mean ( 9 / 20 )65.67952380952380.517500801211424126.916757724382
Trimmed Mean ( 10 / 20 )65.64350.506516452513308129.597962068715
Trimmed Mean ( 11 / 20 )65.61421052631580.494661490584496132.644670699523
Trimmed Mean ( 12 / 20 )65.59722222222220.483075893855185135.790717476552
Trimmed Mean ( 13 / 20 )65.59235294117650.470991872348994139.264299008060
Trimmed Mean ( 14 / 20 )65.60750.460158852305200142.575764154779
Trimmed Mean ( 15 / 20 )65.65566666666670.452286828770115145.163782118532
Trimmed Mean ( 16 / 20 )65.71464285714290.440058462368744149.331619493043
Trimmed Mean ( 17 / 20 )65.750.433361458653344151.720921847356
Trimmed Mean ( 18 / 20 )65.75291666666670.434823585402983151.217456628367
Trimmed Mean ( 19 / 20 )65.75136363636360.435021667099609151.145031636569
Trimmed Mean ( 20 / 20 )65.7510.431242330214023152.468798615776
Median66.68
Midrange66.11
Midmean - Weighted Average at Xnp65.3615625
Midmean - Weighted Average at X(n+1)p65.3615625
Midmean - Empirical Distribution Function65.3615625
Midmean - Empirical Distribution Function - Averaging65.3615625
Midmean - Empirical Distribution Function - Interpolation65.3615625
Midmean - Closest Observation65.3615625
Midmean - True Basic - Statistics Graphics Toolkit65.3615625
Midmean - MS Excel (old versions)65.4663636363636
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 65.9846666666667 & 0.602623945413462 & 109.495593676409 \tabularnewline
Geometric Mean & 65.8233791336607 &  &  \tabularnewline
Harmonic Mean & 65.6634452815308 &  &  \tabularnewline
Quadratic Mean & 66.1468246907338 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 65.993 & 0.600771457904558 & 109.847095982519 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 66.0086666666667 & 0.5977557588759 & 110.427487626047 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 66.0366666666667 & 0.59193700357036 & 111.560294876577 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 66.0633333333333 & 0.586456016367562 & 112.648402419881 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 66.055 & 0.584313228630451 & 113.047243778519 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 66.041 & 0.573795555039468 & 115.095001033003 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 65.9733333333333 & 0.55597700774853 & 118.661981365915 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 65.9586666666667 & 0.546403933005397 & 120.714114014284 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 65.8956666666667 & 0.533160408053365 & 123.594448633686 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 65.829 & 0.520706587515931 & 126.422445151005 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 65.7263333333333 & 0.50229394497277 & 130.852330574872 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 65.6303333333333 & 0.48585506003303 & 135.082123728158 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 65.4873333333333 & 0.461244439690073 & 141.979669993066 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 65.2703333333333 & 0.428967290093158 & 152.156900632584 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 65.2428333333333 & 0.425138069408355 & 153.462693717664 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 65.4695 & 0.387495319818647 & 168.95558901367 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 65.7301666666667 & 0.345679833880701 & 190.147530241383 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 65.7631666666667 & 0.339999708513224 & 193.421244254122 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 65.7536666666667 & 0.338620412006565 & 194.181048558266 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 65.7436666666667 & 0.331392454000899 & 198.386130622299 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 65.9803448275862 & 0.594357567003364 & 111.011196778812 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 65.9667857142857 & 0.586111448731341 & 112.549901314969 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 65.9435185185185 & 0.577522429307052 & 114.183476125147 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 65.9076923076923 & 0.569147348255256 & 115.800754426310 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 65.861 & 0.560237795721694 & 117.559008876148 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 65.8125 & 0.549207964525163 & 119.831656223159 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 65.7628260869565 & 0.537933302534074 & 122.250892029112 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 65.7218181818182 & 0.528168809175598 & 124.433357366182 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 65.6795238095238 & 0.517500801211424 & 126.916757724382 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 65.6435 & 0.506516452513308 & 129.597962068715 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 65.6142105263158 & 0.494661490584496 & 132.644670699523 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 65.5972222222222 & 0.483075893855185 & 135.790717476552 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 65.5923529411765 & 0.470991872348994 & 139.264299008060 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 65.6075 & 0.460158852305200 & 142.575764154779 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 65.6556666666667 & 0.452286828770115 & 145.163782118532 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 65.7146428571429 & 0.440058462368744 & 149.331619493043 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 65.75 & 0.433361458653344 & 151.720921847356 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 65.7529166666667 & 0.434823585402983 & 151.217456628367 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 65.7513636363636 & 0.435021667099609 & 151.145031636569 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 65.751 & 0.431242330214023 & 152.468798615776 \tabularnewline
Median & 66.68 &  &  \tabularnewline
Midrange & 66.11 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 65.3615625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 65.3615625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 65.3615625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 65.3615625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 65.3615625 &  &  \tabularnewline
Midmean - Closest Observation & 65.3615625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 65.3615625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 65.4663636363636 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19845&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]65.9846666666667[/C][C]0.602623945413462[/C][C]109.495593676409[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]65.8233791336607[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]65.6634452815308[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]66.1468246907338[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]65.993[/C][C]0.600771457904558[/C][C]109.847095982519[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]66.0086666666667[/C][C]0.5977557588759[/C][C]110.427487626047[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]66.0366666666667[/C][C]0.59193700357036[/C][C]111.560294876577[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]66.0633333333333[/C][C]0.586456016367562[/C][C]112.648402419881[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]66.055[/C][C]0.584313228630451[/C][C]113.047243778519[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]66.041[/C][C]0.573795555039468[/C][C]115.095001033003[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]65.9733333333333[/C][C]0.55597700774853[/C][C]118.661981365915[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]65.9586666666667[/C][C]0.546403933005397[/C][C]120.714114014284[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]65.8956666666667[/C][C]0.533160408053365[/C][C]123.594448633686[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]65.829[/C][C]0.520706587515931[/C][C]126.422445151005[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]65.7263333333333[/C][C]0.50229394497277[/C][C]130.852330574872[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]65.6303333333333[/C][C]0.48585506003303[/C][C]135.082123728158[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]65.4873333333333[/C][C]0.461244439690073[/C][C]141.979669993066[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]65.2703333333333[/C][C]0.428967290093158[/C][C]152.156900632584[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]65.2428333333333[/C][C]0.425138069408355[/C][C]153.462693717664[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]65.4695[/C][C]0.387495319818647[/C][C]168.95558901367[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]65.7301666666667[/C][C]0.345679833880701[/C][C]190.147530241383[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]65.7631666666667[/C][C]0.339999708513224[/C][C]193.421244254122[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]65.7536666666667[/C][C]0.338620412006565[/C][C]194.181048558266[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]65.7436666666667[/C][C]0.331392454000899[/C][C]198.386130622299[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]65.9803448275862[/C][C]0.594357567003364[/C][C]111.011196778812[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]65.9667857142857[/C][C]0.586111448731341[/C][C]112.549901314969[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]65.9435185185185[/C][C]0.577522429307052[/C][C]114.183476125147[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]65.9076923076923[/C][C]0.569147348255256[/C][C]115.800754426310[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]65.861[/C][C]0.560237795721694[/C][C]117.559008876148[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]65.8125[/C][C]0.549207964525163[/C][C]119.831656223159[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]65.7628260869565[/C][C]0.537933302534074[/C][C]122.250892029112[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]65.7218181818182[/C][C]0.528168809175598[/C][C]124.433357366182[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]65.6795238095238[/C][C]0.517500801211424[/C][C]126.916757724382[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]65.6435[/C][C]0.506516452513308[/C][C]129.597962068715[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]65.6142105263158[/C][C]0.494661490584496[/C][C]132.644670699523[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]65.5972222222222[/C][C]0.483075893855185[/C][C]135.790717476552[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]65.5923529411765[/C][C]0.470991872348994[/C][C]139.264299008060[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]65.6075[/C][C]0.460158852305200[/C][C]142.575764154779[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]65.6556666666667[/C][C]0.452286828770115[/C][C]145.163782118532[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]65.7146428571429[/C][C]0.440058462368744[/C][C]149.331619493043[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]65.75[/C][C]0.433361458653344[/C][C]151.720921847356[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]65.7529166666667[/C][C]0.434823585402983[/C][C]151.217456628367[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]65.7513636363636[/C][C]0.435021667099609[/C][C]151.145031636569[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]65.751[/C][C]0.431242330214023[/C][C]152.468798615776[/C][/ROW]
[ROW][C]Median[/C][C]66.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]66.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]65.3615625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]65.3615625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]65.3615625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]65.3615625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]65.3615625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]65.3615625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]65.3615625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]65.4663636363636[/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=19845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19845&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 Mean65.98466666666670.602623945413462109.495593676409
Geometric Mean65.8233791336607
Harmonic Mean65.6634452815308
Quadratic Mean66.1468246907338
Winsorized Mean ( 1 / 20 )65.9930.600771457904558109.847095982519
Winsorized Mean ( 2 / 20 )66.00866666666670.5977557588759110.427487626047
Winsorized Mean ( 3 / 20 )66.03666666666670.59193700357036111.560294876577
Winsorized Mean ( 4 / 20 )66.06333333333330.586456016367562112.648402419881
Winsorized Mean ( 5 / 20 )66.0550.584313228630451113.047243778519
Winsorized Mean ( 6 / 20 )66.0410.573795555039468115.095001033003
Winsorized Mean ( 7 / 20 )65.97333333333330.55597700774853118.661981365915
Winsorized Mean ( 8 / 20 )65.95866666666670.546403933005397120.714114014284
Winsorized Mean ( 9 / 20 )65.89566666666670.533160408053365123.594448633686
Winsorized Mean ( 10 / 20 )65.8290.520706587515931126.422445151005
Winsorized Mean ( 11 / 20 )65.72633333333330.50229394497277130.852330574872
Winsorized Mean ( 12 / 20 )65.63033333333330.48585506003303135.082123728158
Winsorized Mean ( 13 / 20 )65.48733333333330.461244439690073141.979669993066
Winsorized Mean ( 14 / 20 )65.27033333333330.428967290093158152.156900632584
Winsorized Mean ( 15 / 20 )65.24283333333330.425138069408355153.462693717664
Winsorized Mean ( 16 / 20 )65.46950.387495319818647168.95558901367
Winsorized Mean ( 17 / 20 )65.73016666666670.345679833880701190.147530241383
Winsorized Mean ( 18 / 20 )65.76316666666670.339999708513224193.421244254122
Winsorized Mean ( 19 / 20 )65.75366666666670.338620412006565194.181048558266
Winsorized Mean ( 20 / 20 )65.74366666666670.331392454000899198.386130622299
Trimmed Mean ( 1 / 20 )65.98034482758620.594357567003364111.011196778812
Trimmed Mean ( 2 / 20 )65.96678571428570.586111448731341112.549901314969
Trimmed Mean ( 3 / 20 )65.94351851851850.577522429307052114.183476125147
Trimmed Mean ( 4 / 20 )65.90769230769230.569147348255256115.800754426310
Trimmed Mean ( 5 / 20 )65.8610.560237795721694117.559008876148
Trimmed Mean ( 6 / 20 )65.81250.549207964525163119.831656223159
Trimmed Mean ( 7 / 20 )65.76282608695650.537933302534074122.250892029112
Trimmed Mean ( 8 / 20 )65.72181818181820.528168809175598124.433357366182
Trimmed Mean ( 9 / 20 )65.67952380952380.517500801211424126.916757724382
Trimmed Mean ( 10 / 20 )65.64350.506516452513308129.597962068715
Trimmed Mean ( 11 / 20 )65.61421052631580.494661490584496132.644670699523
Trimmed Mean ( 12 / 20 )65.59722222222220.483075893855185135.790717476552
Trimmed Mean ( 13 / 20 )65.59235294117650.470991872348994139.264299008060
Trimmed Mean ( 14 / 20 )65.60750.460158852305200142.575764154779
Trimmed Mean ( 15 / 20 )65.65566666666670.452286828770115145.163782118532
Trimmed Mean ( 16 / 20 )65.71464285714290.440058462368744149.331619493043
Trimmed Mean ( 17 / 20 )65.750.433361458653344151.720921847356
Trimmed Mean ( 18 / 20 )65.75291666666670.434823585402983151.217456628367
Trimmed Mean ( 19 / 20 )65.75136363636360.435021667099609151.145031636569
Trimmed Mean ( 20 / 20 )65.7510.431242330214023152.468798615776
Median66.68
Midrange66.11
Midmean - Weighted Average at Xnp65.3615625
Midmean - Weighted Average at X(n+1)p65.3615625
Midmean - Empirical Distribution Function65.3615625
Midmean - Empirical Distribution Function - Averaging65.3615625
Midmean - Empirical Distribution Function - Interpolation65.3615625
Midmean - Closest Observation65.3615625
Midmean - True Basic - Statistics Graphics Toolkit65.3615625
Midmean - MS Excel (old versions)65.4663636363636
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')