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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 computationFri, 12 Nov 2010 14:41:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/12/t1289572790cvx4693336zfo4o.htm/, Retrieved Tue, 30 Apr 2024 08:53:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94166, Retrieved Tue, 30 Apr 2024 08:53:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [ws 6 - mini tutor...] [2010-11-12 13:22:17] [603e2f5305d3a2a4e062624458fa1155]
-    D      [Central Tendency] [ws 6 - mini tutor...] [2010-11-12 14:41:01] [0829c729852d8a4b1b0c41cf0848af95] [Current]
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Dataseries X:
102,89
102,64
103,33
103,56
103,60
104,24
105,31
105,40
105,89
105,89
105,54
106,15
106,14
105,85
106,27
106,51
106,82
106,53
107,14
107,39
107,33
107,53
107,42
108,25
108,26
108,93
109,43
109,61
109,74
110,12
110,16
110,44
111,23
112,86
112,77
113,04
112,79
113,87
114,28
115,51
116,76
116,91
116,47
116,94
117,24
116,82
117,48
117,11
117,31
117,77
118,37
117,91
118,12
118,02
117,77
117,85
118,68
118,90




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94166&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94166&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.9843103448280.6921317409046160.351424137511
Geometric Mean110.861634322167
Harmonic Mean110.739428055373
Quadratic Mean111.107258018920
Winsorized Mean ( 1 / 19 )110.9848275862070.690481268694952160.735464694031
Winsorized Mean ( 2 / 19 )110.9893103448280.685378442410152161.938723888850
Winsorized Mean ( 3 / 19 )110.9882758620690.680663182264861163.059026481736
Winsorized Mean ( 4 / 19 )110.9841379310340.678875045166601163.482423932372
Winsorized Mean ( 5 / 19 )111.0298275862070.666960786211285166.471297685909
Winsorized Mean ( 6 / 19 )111.1343103448280.647194331594064171.717063823936
Winsorized Mean ( 7 / 19 )111.1355172413790.643736172413944172.64140497905
Winsorized Mean ( 8 / 19 )111.1548275862070.640742547976655173.478143346673
Winsorized Mean ( 9 / 19 )111.1579310344830.62539544700239177.740230708872
Winsorized Mean ( 10 / 19 )111.1355172413790.61920646544508179.480550419473
Winsorized Mean ( 11 / 19 )111.1222413793100.616890316522871180.132899484718
Winsorized Mean ( 12 / 19 )111.1470689655170.604616891525942183.830571926303
Winsorized Mean ( 13 / 19 )111.1112068965520.597734940032085185.887087160385
Winsorized Mean ( 14 / 19 )111.1329310344830.592300875569405187.629185804674
Winsorized Mean ( 15 / 19 )111.1717241379310.579467971454317191.851369902151
Winsorized Mean ( 16 / 19 )111.1606896551720.57586248012128193.033395111557
Winsorized Mean ( 17 / 19 )111.1606896551720.549519773962998202.286969317791
Winsorized Mean ( 18 / 19 )110.9620689655170.486032604458315228.301698173489
Winsorized Mean ( 19 / 19 )110.6213793103450.412853851842266267.943193013029
Trimmed Mean ( 1 / 19 )110.9919642857140.686473740270307161.684209860686
Trimmed Mean ( 2 / 19 )110.9996296296300.680846934395447163.031694823141
Trimmed Mean ( 3 / 19 )111.0053846153850.67645717032451164.098171303489
Trimmed Mean ( 4 / 19 )111.0120.672335679036984165.113950458508
Trimmed Mean ( 5 / 19 )111.0204166666670.666921446771884166.467006277938
Trimmed Mean ( 6 / 19 )111.0180434782610.66303085518989167.440236919993
Trimmed Mean ( 7 / 19 )110.99250.662617983829834167.506018110888
Trimmed Mean ( 8 / 19 )110.9642857142860.661476206320472167.752497601593
Trimmed Mean ( 9 / 19 )110.929750.659095192484675168.30611308484
Trimmed Mean ( 10 / 19 )110.8910526315790.658086560939366168.505268476066
Trimmed Mean ( 11 / 19 )110.8516666666670.656250956159545168.916579284521
Trimmed Mean ( 12 / 19 )110.8097058823530.652124935441803169.920976579865
Trimmed Mean ( 13 / 19 )110.758750.64723866783835171.125050933549
Trimmed Mean ( 14 / 19 )110.7063333333330.639715900185537173.055466186201
Trimmed Mean ( 15 / 19 )110.6432142857140.627582085014857176.300785072753
Trimmed Mean ( 16 / 19 )110.5646153846150.610624958740377181.067959640387
Trimmed Mean ( 17 / 19 )110.4745833333330.58282389115741189.550540067851
Trimmed Mean ( 18 / 19 )110.3681818181820.546447256820293201.974079731684
Trimmed Mean ( 19 / 19 )110.27250.515325076248504213.986287651222
Median109.93
Midrange110.77
Midmean - Weighted Average at Xnp110.492413793103
Midmean - Weighted Average at X(n+1)p110.706333333333
Midmean - Empirical Distribution Function110.706333333333
Midmean - Empirical Distribution Function - Averaging110.706333333333
Midmean - Empirical Distribution Function - Interpolation110.643214285714
Midmean - Closest Observation110.706333333333
Midmean - True Basic - Statistics Graphics Toolkit110.706333333333
Midmean - MS Excel (old versions)110.706333333333
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.984310344828 & 0.6921317409046 & 160.351424137511 \tabularnewline
Geometric Mean & 110.861634322167 &  &  \tabularnewline
Harmonic Mean & 110.739428055373 &  &  \tabularnewline
Quadratic Mean & 111.107258018920 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 110.984827586207 & 0.690481268694952 & 160.735464694031 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 110.989310344828 & 0.685378442410152 & 161.938723888850 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 110.988275862069 & 0.680663182264861 & 163.059026481736 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 110.984137931034 & 0.678875045166601 & 163.482423932372 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 111.029827586207 & 0.666960786211285 & 166.471297685909 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 111.134310344828 & 0.647194331594064 & 171.717063823936 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 111.135517241379 & 0.643736172413944 & 172.64140497905 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 111.154827586207 & 0.640742547976655 & 173.478143346673 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 111.157931034483 & 0.62539544700239 & 177.740230708872 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 111.135517241379 & 0.61920646544508 & 179.480550419473 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 111.122241379310 & 0.616890316522871 & 180.132899484718 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 111.147068965517 & 0.604616891525942 & 183.830571926303 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 111.111206896552 & 0.597734940032085 & 185.887087160385 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 111.132931034483 & 0.592300875569405 & 187.629185804674 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 111.171724137931 & 0.579467971454317 & 191.851369902151 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 111.160689655172 & 0.57586248012128 & 193.033395111557 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 111.160689655172 & 0.549519773962998 & 202.286969317791 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 110.962068965517 & 0.486032604458315 & 228.301698173489 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 110.621379310345 & 0.412853851842266 & 267.943193013029 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 110.991964285714 & 0.686473740270307 & 161.684209860686 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 110.999629629630 & 0.680846934395447 & 163.031694823141 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 111.005384615385 & 0.67645717032451 & 164.098171303489 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 111.012 & 0.672335679036984 & 165.113950458508 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 111.020416666667 & 0.666921446771884 & 166.467006277938 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 111.018043478261 & 0.66303085518989 & 167.440236919993 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 110.9925 & 0.662617983829834 & 167.506018110888 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 110.964285714286 & 0.661476206320472 & 167.752497601593 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 110.92975 & 0.659095192484675 & 168.30611308484 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 110.891052631579 & 0.658086560939366 & 168.505268476066 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 110.851666666667 & 0.656250956159545 & 168.916579284521 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 110.809705882353 & 0.652124935441803 & 169.920976579865 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 110.75875 & 0.64723866783835 & 171.125050933549 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 110.706333333333 & 0.639715900185537 & 173.055466186201 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 110.643214285714 & 0.627582085014857 & 176.300785072753 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 110.564615384615 & 0.610624958740377 & 181.067959640387 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 110.474583333333 & 0.58282389115741 & 189.550540067851 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 110.368181818182 & 0.546447256820293 & 201.974079731684 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 110.2725 & 0.515325076248504 & 213.986287651222 \tabularnewline
Median & 109.93 &  &  \tabularnewline
Midrange & 110.77 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.492413793103 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.706333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.706333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.706333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.643214285714 &  &  \tabularnewline
Midmean - Closest Observation & 110.706333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.706333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.706333333333 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94166&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]110.984310344828[/C][C]0.6921317409046[/C][C]160.351424137511[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.861634322167[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.739428055373[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.107258018920[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]110.984827586207[/C][C]0.690481268694952[/C][C]160.735464694031[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]110.989310344828[/C][C]0.685378442410152[/C][C]161.938723888850[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]110.988275862069[/C][C]0.680663182264861[/C][C]163.059026481736[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]110.984137931034[/C][C]0.678875045166601[/C][C]163.482423932372[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]111.029827586207[/C][C]0.666960786211285[/C][C]166.471297685909[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]111.134310344828[/C][C]0.647194331594064[/C][C]171.717063823936[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]111.135517241379[/C][C]0.643736172413944[/C][C]172.64140497905[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]111.154827586207[/C][C]0.640742547976655[/C][C]173.478143346673[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]111.157931034483[/C][C]0.62539544700239[/C][C]177.740230708872[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]111.135517241379[/C][C]0.61920646544508[/C][C]179.480550419473[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]111.122241379310[/C][C]0.616890316522871[/C][C]180.132899484718[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]111.147068965517[/C][C]0.604616891525942[/C][C]183.830571926303[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]111.111206896552[/C][C]0.597734940032085[/C][C]185.887087160385[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]111.132931034483[/C][C]0.592300875569405[/C][C]187.629185804674[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]111.171724137931[/C][C]0.579467971454317[/C][C]191.851369902151[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]111.160689655172[/C][C]0.57586248012128[/C][C]193.033395111557[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]111.160689655172[/C][C]0.549519773962998[/C][C]202.286969317791[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]110.962068965517[/C][C]0.486032604458315[/C][C]228.301698173489[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]110.621379310345[/C][C]0.412853851842266[/C][C]267.943193013029[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]110.991964285714[/C][C]0.686473740270307[/C][C]161.684209860686[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]110.999629629630[/C][C]0.680846934395447[/C][C]163.031694823141[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]111.005384615385[/C][C]0.67645717032451[/C][C]164.098171303489[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]111.012[/C][C]0.672335679036984[/C][C]165.113950458508[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]111.020416666667[/C][C]0.666921446771884[/C][C]166.467006277938[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]111.018043478261[/C][C]0.66303085518989[/C][C]167.440236919993[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]110.9925[/C][C]0.662617983829834[/C][C]167.506018110888[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]110.964285714286[/C][C]0.661476206320472[/C][C]167.752497601593[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]110.92975[/C][C]0.659095192484675[/C][C]168.30611308484[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]110.891052631579[/C][C]0.658086560939366[/C][C]168.505268476066[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]110.851666666667[/C][C]0.656250956159545[/C][C]168.916579284521[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]110.809705882353[/C][C]0.652124935441803[/C][C]169.920976579865[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]110.75875[/C][C]0.64723866783835[/C][C]171.125050933549[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]110.706333333333[/C][C]0.639715900185537[/C][C]173.055466186201[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]110.643214285714[/C][C]0.627582085014857[/C][C]176.300785072753[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]110.564615384615[/C][C]0.610624958740377[/C][C]181.067959640387[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]110.474583333333[/C][C]0.58282389115741[/C][C]189.550540067851[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]110.368181818182[/C][C]0.546447256820293[/C][C]201.974079731684[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]110.2725[/C][C]0.515325076248504[/C][C]213.986287651222[/C][/ROW]
[ROW][C]Median[/C][C]109.93[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.492413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.706333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.706333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.706333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.643214285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.706333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.706333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.706333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94166&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 Mean110.9843103448280.6921317409046160.351424137511
Geometric Mean110.861634322167
Harmonic Mean110.739428055373
Quadratic Mean111.107258018920
Winsorized Mean ( 1 / 19 )110.9848275862070.690481268694952160.735464694031
Winsorized Mean ( 2 / 19 )110.9893103448280.685378442410152161.938723888850
Winsorized Mean ( 3 / 19 )110.9882758620690.680663182264861163.059026481736
Winsorized Mean ( 4 / 19 )110.9841379310340.678875045166601163.482423932372
Winsorized Mean ( 5 / 19 )111.0298275862070.666960786211285166.471297685909
Winsorized Mean ( 6 / 19 )111.1343103448280.647194331594064171.717063823936
Winsorized Mean ( 7 / 19 )111.1355172413790.643736172413944172.64140497905
Winsorized Mean ( 8 / 19 )111.1548275862070.640742547976655173.478143346673
Winsorized Mean ( 9 / 19 )111.1579310344830.62539544700239177.740230708872
Winsorized Mean ( 10 / 19 )111.1355172413790.61920646544508179.480550419473
Winsorized Mean ( 11 / 19 )111.1222413793100.616890316522871180.132899484718
Winsorized Mean ( 12 / 19 )111.1470689655170.604616891525942183.830571926303
Winsorized Mean ( 13 / 19 )111.1112068965520.597734940032085185.887087160385
Winsorized Mean ( 14 / 19 )111.1329310344830.592300875569405187.629185804674
Winsorized Mean ( 15 / 19 )111.1717241379310.579467971454317191.851369902151
Winsorized Mean ( 16 / 19 )111.1606896551720.57586248012128193.033395111557
Winsorized Mean ( 17 / 19 )111.1606896551720.549519773962998202.286969317791
Winsorized Mean ( 18 / 19 )110.9620689655170.486032604458315228.301698173489
Winsorized Mean ( 19 / 19 )110.6213793103450.412853851842266267.943193013029
Trimmed Mean ( 1 / 19 )110.9919642857140.686473740270307161.684209860686
Trimmed Mean ( 2 / 19 )110.9996296296300.680846934395447163.031694823141
Trimmed Mean ( 3 / 19 )111.0053846153850.67645717032451164.098171303489
Trimmed Mean ( 4 / 19 )111.0120.672335679036984165.113950458508
Trimmed Mean ( 5 / 19 )111.0204166666670.666921446771884166.467006277938
Trimmed Mean ( 6 / 19 )111.0180434782610.66303085518989167.440236919993
Trimmed Mean ( 7 / 19 )110.99250.662617983829834167.506018110888
Trimmed Mean ( 8 / 19 )110.9642857142860.661476206320472167.752497601593
Trimmed Mean ( 9 / 19 )110.929750.659095192484675168.30611308484
Trimmed Mean ( 10 / 19 )110.8910526315790.658086560939366168.505268476066
Trimmed Mean ( 11 / 19 )110.8516666666670.656250956159545168.916579284521
Trimmed Mean ( 12 / 19 )110.8097058823530.652124935441803169.920976579865
Trimmed Mean ( 13 / 19 )110.758750.64723866783835171.125050933549
Trimmed Mean ( 14 / 19 )110.7063333333330.639715900185537173.055466186201
Trimmed Mean ( 15 / 19 )110.6432142857140.627582085014857176.300785072753
Trimmed Mean ( 16 / 19 )110.5646153846150.610624958740377181.067959640387
Trimmed Mean ( 17 / 19 )110.4745833333330.58282389115741189.550540067851
Trimmed Mean ( 18 / 19 )110.3681818181820.546447256820293201.974079731684
Trimmed Mean ( 19 / 19 )110.27250.515325076248504213.986287651222
Median109.93
Midrange110.77
Midmean - Weighted Average at Xnp110.492413793103
Midmean - Weighted Average at X(n+1)p110.706333333333
Midmean - Empirical Distribution Function110.706333333333
Midmean - Empirical Distribution Function - Averaging110.706333333333
Midmean - Empirical Distribution Function - Interpolation110.643214285714
Midmean - Closest Observation110.706333333333
Midmean - True Basic - Statistics Graphics Toolkit110.706333333333
Midmean - MS Excel (old versions)110.706333333333
Number of observations58



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')