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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 computationSat, 18 Dec 2010 14:20:59 +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/Dec/18/t129268198246ih2tmnniklps5.htm/, Retrieved Tue, 30 Apr 2024 05:51:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111990, Retrieved Tue, 30 Apr 2024 05:51:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
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] [Robustness of Cen...] [2010-12-18 14:20:59] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]
-           [Central Tendency] [Central tendency ...] [2010-12-19 18:22:32] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D        [Central Tendency] [Central tendencey...] [2010-12-19 21:01:37] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D        [Central Tendency] [Central tendencey...] [2010-12-19 21:03:16] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D        [Central Tendency] [Central tendency ...] [2010-12-19 21:05:11] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D      [Central Tendency] [Central tendency ...] [2010-12-19 18:24:01] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D      [Central Tendency] [Central tendencey...] [2010-12-19 18:25:12] [1afa3497b02a8d7c9f6727c1b17b89b2]
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Dataseries X:
0,61
0,62
0,61
0,63
0,63
0,58
0,55
0,54
0,54
0,49
0,52
0,53
0,56
0,56
0,58
0,6
0,59
0,61
0,63
0,69
0,68
0,7
0,7
0,76
0,78
0,89
0,94
0,95
0,83
0,81
0,73
0,64
0,51
0,5
0,47
0,43
0,47
0,48
0,52
0,5
0,55
0,52
0,52
0,55
0,54
0,59
0,56
0,61
0,66
0,68
0,66
0,64
0,65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111990&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]3 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=111990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111990&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.6167924528301890.016031929282664638.4727528393685
Geometric Mean0.60693770043862
Harmonic Mean0.597940082767736
Quadratic Mean0.627533356250923
Winsorized Mean ( 1 / 17 )0.6173584905660380.015804848843973739.0613346992832
Winsorized Mean ( 2 / 17 )0.6154716981132070.015103815965832740.749417200627
Winsorized Mean ( 3 / 17 )0.6126415094339620.013891427809065344.1021267111336
Winsorized Mean ( 4 / 17 )0.611886792452830.013312304847806345.9640009335919
Winsorized Mean ( 5 / 17 )0.610.012368319471950649.3195539930371
Winsorized Mean ( 6 / 17 )0.6077358490566040.011787429989800151.5579604360315
Winsorized Mean ( 7 / 17 )0.6050943396226410.010614715261395957.0052351590889
Winsorized Mean ( 8 / 17 )0.6020754716981130.0093874761805090864.1360318919566
Winsorized Mean ( 9 / 17 )0.6020754716981130.0093874761805090864.1360318919566
Winsorized Mean ( 10 / 17 )0.6001886792452830.0090173617655213166.5592326061663
Winsorized Mean ( 11 / 17 )0.598113207547170.0086290115669279369.3142201639333
Winsorized Mean ( 12 / 17 )0.6003773584905660.0082458691956515872.8094691105666
Winsorized Mean ( 13 / 17 )0.5979245283018870.0069695506649055185.7909723380988
Winsorized Mean ( 14 / 17 )0.5979245283018870.0069695506649055185.7909723380988
Winsorized Mean ( 15 / 17 )0.5950943396226410.0064967483298456591.5987982617113
Winsorized Mean ( 16 / 17 )0.5950943396226410.00553142914466029107.584192811565
Winsorized Mean ( 17 / 17 )0.5950943396226420.00553142914466029107.584192811565
Trimmed Mean ( 1 / 17 )0.6139215686274510.014845817873830541.3531658440754
Trimmed Mean ( 2 / 17 )0.6102040816326530.013588616296378444.9055347743745
Trimmed Mean ( 3 / 17 )0.6072340425531910.012465315905184948.7138911819004
Trimmed Mean ( 4 / 17 )0.6051111111111110.011675850161429151.8258715849303
Trimmed Mean ( 5 / 17 )0.6030232558139540.010898377274237755.3314718916385
Trimmed Mean ( 6 / 17 )0.6012195121951220.010254060004672158.6323380125709
Trimmed Mean ( 7 / 17 )0.599743589743590.0096111101610211862.4010733095028
Trimmed Mean ( 8 / 17 )0.5986486486486490.009162875236896565.3341481981602
Trimmed Mean ( 9 / 17 )0.5980.0089517849494674866.802319691066
Trimmed Mean ( 10 / 17 )0.5972727272727270.0086413462500801469.118018186945
Trimmed Mean ( 11 / 17 )0.5967741935483870.0083135735206120871.7831137318733
Trimmed Mean ( 12 / 17 )0.5965517241379310.0079604295696427574.9396397416657
Trimmed Mean ( 13 / 17 )0.5959259259259260.0075534045315263678.8950099837303
Trimmed Mean ( 14 / 17 )0.59560.0073954941236764880.5355247451556
Trimmed Mean ( 15 / 17 )0.5952173913043480.0071092425845128683.7244452174132
Trimmed Mean ( 16 / 17 )0.5952380952380950.0068180100301315987.3037869711973
Trimmed Mean ( 17 / 17 )0.5952631578947370.0067264173728704688.4963160769062
Median0.6
Midrange0.69
Midmean - Weighted Average at Xnp0.595925925925926
Midmean - Weighted Average at X(n+1)p0.595925925925926
Midmean - Empirical Distribution Function0.595925925925926
Midmean - Empirical Distribution Function - Averaging0.595925925925926
Midmean - Empirical Distribution Function - Interpolation0.595925925925926
Midmean - Closest Observation0.593571428571429
Midmean - True Basic - Statistics Graphics Toolkit0.595925925925926
Midmean - MS Excel (old versions)0.595925925925926
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.616792452830189 & 0.0160319292826646 & 38.4727528393685 \tabularnewline
Geometric Mean & 0.60693770043862 &  &  \tabularnewline
Harmonic Mean & 0.597940082767736 &  &  \tabularnewline
Quadratic Mean & 0.627533356250923 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 0.617358490566038 & 0.0158048488439737 & 39.0613346992832 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 0.615471698113207 & 0.0151038159658327 & 40.749417200627 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 0.612641509433962 & 0.0138914278090653 & 44.1021267111336 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 0.61188679245283 & 0.0133123048478063 & 45.9640009335919 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 0.61 & 0.0123683194719506 & 49.3195539930371 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 0.607735849056604 & 0.0117874299898001 & 51.5579604360315 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 0.605094339622641 & 0.0106147152613959 & 57.0052351590889 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 0.602075471698113 & 0.00938747618050908 & 64.1360318919566 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 0.602075471698113 & 0.00938747618050908 & 64.1360318919566 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 0.600188679245283 & 0.00901736176552131 & 66.5592326061663 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 0.59811320754717 & 0.00862901156692793 & 69.3142201639333 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 0.600377358490566 & 0.00824586919565158 & 72.8094691105666 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 0.597924528301887 & 0.00696955066490551 & 85.7909723380988 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 0.597924528301887 & 0.00696955066490551 & 85.7909723380988 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 0.595094339622641 & 0.00649674832984565 & 91.5987982617113 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 0.595094339622641 & 0.00553142914466029 & 107.584192811565 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 0.595094339622642 & 0.00553142914466029 & 107.584192811565 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 0.613921568627451 & 0.0148458178738305 & 41.3531658440754 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 0.610204081632653 & 0.0135886162963784 & 44.9055347743745 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 0.607234042553191 & 0.0124653159051849 & 48.7138911819004 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 0.605111111111111 & 0.0116758501614291 & 51.8258715849303 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 0.603023255813954 & 0.0108983772742377 & 55.3314718916385 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 0.601219512195122 & 0.0102540600046721 & 58.6323380125709 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 0.59974358974359 & 0.00961111016102118 & 62.4010733095028 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 0.598648648648649 & 0.0091628752368965 & 65.3341481981602 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 0.598 & 0.00895178494946748 & 66.802319691066 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 0.597272727272727 & 0.00864134625008014 & 69.118018186945 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 0.596774193548387 & 0.00831357352061208 & 71.7831137318733 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 0.596551724137931 & 0.00796042956964275 & 74.9396397416657 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 0.595925925925926 & 0.00755340453152636 & 78.8950099837303 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 0.5956 & 0.00739549412367648 & 80.5355247451556 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 0.595217391304348 & 0.00710924258451286 & 83.7244452174132 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 0.595238095238095 & 0.00681801003013159 & 87.3037869711973 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 0.595263157894737 & 0.00672641737287046 & 88.4963160769062 \tabularnewline
Median & 0.6 &  &  \tabularnewline
Midrange & 0.69 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.595925925925926 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.595925925925926 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.595925925925926 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.595925925925926 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.595925925925926 &  &  \tabularnewline
Midmean - Closest Observation & 0.593571428571429 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.595925925925926 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.595925925925926 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111990&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.616792452830189[/C][C]0.0160319292826646[/C][C]38.4727528393685[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.60693770043862[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.597940082767736[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.627533356250923[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]0.617358490566038[/C][C]0.0158048488439737[/C][C]39.0613346992832[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]0.615471698113207[/C][C]0.0151038159658327[/C][C]40.749417200627[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]0.612641509433962[/C][C]0.0138914278090653[/C][C]44.1021267111336[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]0.61188679245283[/C][C]0.0133123048478063[/C][C]45.9640009335919[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]0.61[/C][C]0.0123683194719506[/C][C]49.3195539930371[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]0.607735849056604[/C][C]0.0117874299898001[/C][C]51.5579604360315[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]0.605094339622641[/C][C]0.0106147152613959[/C][C]57.0052351590889[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]0.602075471698113[/C][C]0.00938747618050908[/C][C]64.1360318919566[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]0.602075471698113[/C][C]0.00938747618050908[/C][C]64.1360318919566[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]0.600188679245283[/C][C]0.00901736176552131[/C][C]66.5592326061663[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]0.59811320754717[/C][C]0.00862901156692793[/C][C]69.3142201639333[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]0.600377358490566[/C][C]0.00824586919565158[/C][C]72.8094691105666[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]0.597924528301887[/C][C]0.00696955066490551[/C][C]85.7909723380988[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]0.597924528301887[/C][C]0.00696955066490551[/C][C]85.7909723380988[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]0.595094339622641[/C][C]0.00649674832984565[/C][C]91.5987982617113[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]0.595094339622641[/C][C]0.00553142914466029[/C][C]107.584192811565[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]0.595094339622642[/C][C]0.00553142914466029[/C][C]107.584192811565[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]0.613921568627451[/C][C]0.0148458178738305[/C][C]41.3531658440754[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]0.610204081632653[/C][C]0.0135886162963784[/C][C]44.9055347743745[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]0.607234042553191[/C][C]0.0124653159051849[/C][C]48.7138911819004[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]0.605111111111111[/C][C]0.0116758501614291[/C][C]51.8258715849303[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]0.603023255813954[/C][C]0.0108983772742377[/C][C]55.3314718916385[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]0.601219512195122[/C][C]0.0102540600046721[/C][C]58.6323380125709[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]0.59974358974359[/C][C]0.00961111016102118[/C][C]62.4010733095028[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]0.598648648648649[/C][C]0.0091628752368965[/C][C]65.3341481981602[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]0.598[/C][C]0.00895178494946748[/C][C]66.802319691066[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]0.597272727272727[/C][C]0.00864134625008014[/C][C]69.118018186945[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]0.596774193548387[/C][C]0.00831357352061208[/C][C]71.7831137318733[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]0.596551724137931[/C][C]0.00796042956964275[/C][C]74.9396397416657[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]0.595925925925926[/C][C]0.00755340453152636[/C][C]78.8950099837303[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]0.5956[/C][C]0.00739549412367648[/C][C]80.5355247451556[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]0.595217391304348[/C][C]0.00710924258451286[/C][C]83.7244452174132[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]0.595238095238095[/C][C]0.00681801003013159[/C][C]87.3037869711973[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]0.595263157894737[/C][C]0.00672641737287046[/C][C]88.4963160769062[/C][/ROW]
[ROW][C]Median[/C][C]0.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.595925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.595925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.595925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.595925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.595925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.593571428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.595925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.595925925925926[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]53[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111990&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.6167924528301890.016031929282664638.4727528393685
Geometric Mean0.60693770043862
Harmonic Mean0.597940082767736
Quadratic Mean0.627533356250923
Winsorized Mean ( 1 / 17 )0.6173584905660380.015804848843973739.0613346992832
Winsorized Mean ( 2 / 17 )0.6154716981132070.015103815965832740.749417200627
Winsorized Mean ( 3 / 17 )0.6126415094339620.013891427809065344.1021267111336
Winsorized Mean ( 4 / 17 )0.611886792452830.013312304847806345.9640009335919
Winsorized Mean ( 5 / 17 )0.610.012368319471950649.3195539930371
Winsorized Mean ( 6 / 17 )0.6077358490566040.011787429989800151.5579604360315
Winsorized Mean ( 7 / 17 )0.6050943396226410.010614715261395957.0052351590889
Winsorized Mean ( 8 / 17 )0.6020754716981130.0093874761805090864.1360318919566
Winsorized Mean ( 9 / 17 )0.6020754716981130.0093874761805090864.1360318919566
Winsorized Mean ( 10 / 17 )0.6001886792452830.0090173617655213166.5592326061663
Winsorized Mean ( 11 / 17 )0.598113207547170.0086290115669279369.3142201639333
Winsorized Mean ( 12 / 17 )0.6003773584905660.0082458691956515872.8094691105666
Winsorized Mean ( 13 / 17 )0.5979245283018870.0069695506649055185.7909723380988
Winsorized Mean ( 14 / 17 )0.5979245283018870.0069695506649055185.7909723380988
Winsorized Mean ( 15 / 17 )0.5950943396226410.0064967483298456591.5987982617113
Winsorized Mean ( 16 / 17 )0.5950943396226410.00553142914466029107.584192811565
Winsorized Mean ( 17 / 17 )0.5950943396226420.00553142914466029107.584192811565
Trimmed Mean ( 1 / 17 )0.6139215686274510.014845817873830541.3531658440754
Trimmed Mean ( 2 / 17 )0.6102040816326530.013588616296378444.9055347743745
Trimmed Mean ( 3 / 17 )0.6072340425531910.012465315905184948.7138911819004
Trimmed Mean ( 4 / 17 )0.6051111111111110.011675850161429151.8258715849303
Trimmed Mean ( 5 / 17 )0.6030232558139540.010898377274237755.3314718916385
Trimmed Mean ( 6 / 17 )0.6012195121951220.010254060004672158.6323380125709
Trimmed Mean ( 7 / 17 )0.599743589743590.0096111101610211862.4010733095028
Trimmed Mean ( 8 / 17 )0.5986486486486490.009162875236896565.3341481981602
Trimmed Mean ( 9 / 17 )0.5980.0089517849494674866.802319691066
Trimmed Mean ( 10 / 17 )0.5972727272727270.0086413462500801469.118018186945
Trimmed Mean ( 11 / 17 )0.5967741935483870.0083135735206120871.7831137318733
Trimmed Mean ( 12 / 17 )0.5965517241379310.0079604295696427574.9396397416657
Trimmed Mean ( 13 / 17 )0.5959259259259260.0075534045315263678.8950099837303
Trimmed Mean ( 14 / 17 )0.59560.0073954941236764880.5355247451556
Trimmed Mean ( 15 / 17 )0.5952173913043480.0071092425845128683.7244452174132
Trimmed Mean ( 16 / 17 )0.5952380952380950.0068180100301315987.3037869711973
Trimmed Mean ( 17 / 17 )0.5952631578947370.0067264173728704688.4963160769062
Median0.6
Midrange0.69
Midmean - Weighted Average at Xnp0.595925925925926
Midmean - Weighted Average at X(n+1)p0.595925925925926
Midmean - Empirical Distribution Function0.595925925925926
Midmean - Empirical Distribution Function - Averaging0.595925925925926
Midmean - Empirical Distribution Function - Interpolation0.595925925925926
Midmean - Closest Observation0.593571428571429
Midmean - True Basic - Statistics Graphics Toolkit0.595925925925926
Midmean - MS Excel (old versions)0.595925925925926
Number of observations53



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')