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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 computationTue, 20 Oct 2009 13:10:54 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256065958yqw4t8p95m4go6l.htm/, Retrieved Thu, 02 May 2024 14:43:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49025, Retrieved Thu, 02 May 2024 14:43:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheid vrouwen] [2009-10-12 19:50:51] [a94022e7c2399c0f4d62eea578db3411]
- RMP     [Central Tendency] [Ws3-Deel2CentTen] [2009-10-20 19:10:54] [30970b478e356ce7f8c2e9fca280b230] [Current]
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Dataseries X:
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1
8.5




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=49025&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=49025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49025&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 Mean8.70.12279697083070870.8486531967805
Geometric Mean8.6474701316913
Harmonic Mean8.5934916449475
Quadratic Mean8.7509808974004
Winsorized Mean ( 1 / 20 )8.6950.11868928718572473.2585072011942
Winsorized Mean ( 2 / 20 )8.6950.11705966897994874.2783580012469
Winsorized Mean ( 3 / 20 )8.70.11349606130700576.65464245906
Winsorized Mean ( 4 / 20 )8.70.11057119290558978.6823382418283
Winsorized Mean ( 5 / 20 )8.708333333333330.1086977789851780.1150990814766
Winsorized Mean ( 6 / 20 )8.708333333333330.10059966154054286.5642408729563
Winsorized Mean ( 7 / 20 )8.720.098284724172425388.7218240008703
Winsorized Mean ( 8 / 20 )8.706666666666670.09103506081478695.6408068357386
Winsorized Mean ( 9 / 20 )8.706666666666670.09103506081478695.6408068357386
Winsorized Mean ( 10 / 20 )8.706666666666670.085266834965357102.11082269213
Winsorized Mean ( 11 / 20 )8.7250.082050866130519106.336476523247
Winsorized Mean ( 12 / 20 )8.7050.0789559342166413110.251371051035
Winsorized Mean ( 13 / 20 )8.7050.0789559342166413110.251371051035
Winsorized Mean ( 14 / 20 )8.681666666666670.0755952523942968114.844072765099
Winsorized Mean ( 15 / 20 )8.706666666666670.0713021210557114122.109504426436
Winsorized Mean ( 16 / 20 )8.706666666666670.0632395975977982137.677452061615
Winsorized Mean ( 17 / 20 )8.706666666666670.0632395975977982137.677452061615
Winsorized Mean ( 18 / 20 )8.736666666666670.0584627297697265149.439937222889
Winsorized Mean ( 19 / 20 )8.736666666666670.0584627297697265149.439937222889
Winsorized Mean ( 20 / 20 )8.770.0533774535021377164.301580997092
Trimmed Mean ( 1 / 20 )8.70.11497126077676075.6710845929822
Trimmed Mean ( 2 / 20 )8.705357142857140.11038361805737378.8645751612567
Trimmed Mean ( 3 / 20 )8.711111111111110.10579527012140382.3393248215624
Trimmed Mean ( 4 / 20 )8.715384615384610.10184514223585.5748681196254
Trimmed Mean ( 5 / 20 )8.720.09806287029560388.9225450337547
Trimmed Mean ( 6 / 20 )8.722916666666670.093931070213942892.8650833722947
Trimmed Mean ( 7 / 20 )8.726086956521740.091283641544422395.593107471236
Trimmed Mean ( 8 / 20 )8.727272727272730.088525843168571598.5844631906436
Trimmed Mean ( 9 / 20 )8.730952380952380.0869196763807721100.448514588393
Trimmed Mean ( 10 / 20 )8.7350.0846978036829642103.131363744641
Trimmed Mean ( 11 / 20 )8.739473684210530.0831919641393157105.051897435372
Trimmed Mean ( 12 / 20 )8.741666666666670.0818801873432461106.761683751664
Trimmed Mean ( 13 / 20 )8.747058823529410.0806872545711244108.406945682097
Trimmed Mean ( 14 / 20 )8.7531250.0787995076075577111.080960601846
Trimmed Mean ( 15 / 20 )8.763333333333330.0767865130239385114.125944625215
Trimmed Mean ( 16 / 20 )8.771428571428570.0750409311337956116.888589185939
Trimmed Mean ( 17 / 20 )8.780769230769230.0746312433583087117.655405908384
Trimmed Mean ( 18 / 20 )8.791666666666670.0734542810254527119.688962221552
Trimmed Mean ( 19 / 20 )8.80.0729703729240527120.596889495947
Trimmed Mean ( 20 / 20 )8.810.0714142842854284123.364675402868
Median9
Midrange8.7
Midmean - Weighted Average at Xnp8.68
Midmean - Weighted Average at X(n+1)p8.78064516129032
Midmean - Empirical Distribution Function8.68
Midmean - Empirical Distribution Function - Averaging8.78064516129032
Midmean - Empirical Distribution Function - Interpolation8.78064516129032
Midmean - Closest Observation8.68
Midmean - True Basic - Statistics Graphics Toolkit8.78064516129032
Midmean - MS Excel (old versions)8.68
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.7 & 0.122796970830708 & 70.8486531967805 \tabularnewline
Geometric Mean & 8.6474701316913 &  &  \tabularnewline
Harmonic Mean & 8.5934916449475 &  &  \tabularnewline
Quadratic Mean & 8.7509808974004 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.695 & 0.118689287185724 & 73.2585072011942 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.695 & 0.117059668979948 & 74.2783580012469 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.7 & 0.113496061307005 & 76.65464245906 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.7 & 0.110571192905589 & 78.6823382418283 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.70833333333333 & 0.10869777898517 & 80.1150990814766 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.70833333333333 & 0.100599661540542 & 86.5642408729563 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.72 & 0.0982847241724253 & 88.7218240008703 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.70666666666667 & 0.091035060814786 & 95.6408068357386 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.70666666666667 & 0.091035060814786 & 95.6408068357386 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.70666666666667 & 0.085266834965357 & 102.11082269213 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.725 & 0.082050866130519 & 106.336476523247 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.705 & 0.0789559342166413 & 110.251371051035 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.705 & 0.0789559342166413 & 110.251371051035 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.68166666666667 & 0.0755952523942968 & 114.844072765099 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.70666666666667 & 0.0713021210557114 & 122.109504426436 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.70666666666667 & 0.0632395975977982 & 137.677452061615 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.70666666666667 & 0.0632395975977982 & 137.677452061615 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.73666666666667 & 0.0584627297697265 & 149.439937222889 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.73666666666667 & 0.0584627297697265 & 149.439937222889 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.77 & 0.0533774535021377 & 164.301580997092 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.7 & 0.114971260776760 & 75.6710845929822 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.70535714285714 & 0.110383618057373 & 78.8645751612567 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.71111111111111 & 0.105795270121403 & 82.3393248215624 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.71538461538461 & 0.101845142235 & 85.5748681196254 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.72 & 0.098062870295603 & 88.9225450337547 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.72291666666667 & 0.0939310702139428 & 92.8650833722947 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.72608695652174 & 0.0912836415444223 & 95.593107471236 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.72727272727273 & 0.0885258431685715 & 98.5844631906436 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.73095238095238 & 0.0869196763807721 & 100.448514588393 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.735 & 0.0846978036829642 & 103.131363744641 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.73947368421053 & 0.0831919641393157 & 105.051897435372 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.74166666666667 & 0.0818801873432461 & 106.761683751664 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.74705882352941 & 0.0806872545711244 & 108.406945682097 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.753125 & 0.0787995076075577 & 111.080960601846 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.76333333333333 & 0.0767865130239385 & 114.125944625215 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.77142857142857 & 0.0750409311337956 & 116.888589185939 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.78076923076923 & 0.0746312433583087 & 117.655405908384 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.79166666666667 & 0.0734542810254527 & 119.688962221552 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.8 & 0.0729703729240527 & 120.596889495947 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.81 & 0.0714142842854284 & 123.364675402868 \tabularnewline
Median & 9 &  &  \tabularnewline
Midrange & 8.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.68 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.78064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.68 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.78064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.78064516129032 &  &  \tabularnewline
Midmean - Closest Observation & 8.68 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.78064516129032 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.68 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49025&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]8.7[/C][C]0.122796970830708[/C][C]70.8486531967805[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.6474701316913[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.5934916449475[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.7509808974004[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.695[/C][C]0.118689287185724[/C][C]73.2585072011942[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.695[/C][C]0.117059668979948[/C][C]74.2783580012469[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.7[/C][C]0.113496061307005[/C][C]76.65464245906[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.7[/C][C]0.110571192905589[/C][C]78.6823382418283[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.70833333333333[/C][C]0.10869777898517[/C][C]80.1150990814766[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.70833333333333[/C][C]0.100599661540542[/C][C]86.5642408729563[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.72[/C][C]0.0982847241724253[/C][C]88.7218240008703[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.70666666666667[/C][C]0.091035060814786[/C][C]95.6408068357386[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.70666666666667[/C][C]0.091035060814786[/C][C]95.6408068357386[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.70666666666667[/C][C]0.085266834965357[/C][C]102.11082269213[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.725[/C][C]0.082050866130519[/C][C]106.336476523247[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.705[/C][C]0.0789559342166413[/C][C]110.251371051035[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.705[/C][C]0.0789559342166413[/C][C]110.251371051035[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.68166666666667[/C][C]0.0755952523942968[/C][C]114.844072765099[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.70666666666667[/C][C]0.0713021210557114[/C][C]122.109504426436[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.70666666666667[/C][C]0.0632395975977982[/C][C]137.677452061615[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.70666666666667[/C][C]0.0632395975977982[/C][C]137.677452061615[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.73666666666667[/C][C]0.0584627297697265[/C][C]149.439937222889[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.73666666666667[/C][C]0.0584627297697265[/C][C]149.439937222889[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.77[/C][C]0.0533774535021377[/C][C]164.301580997092[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.7[/C][C]0.114971260776760[/C][C]75.6710845929822[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.70535714285714[/C][C]0.110383618057373[/C][C]78.8645751612567[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.71111111111111[/C][C]0.105795270121403[/C][C]82.3393248215624[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.71538461538461[/C][C]0.101845142235[/C][C]85.5748681196254[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.72[/C][C]0.098062870295603[/C][C]88.9225450337547[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.72291666666667[/C][C]0.0939310702139428[/C][C]92.8650833722947[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.72608695652174[/C][C]0.0912836415444223[/C][C]95.593107471236[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.72727272727273[/C][C]0.0885258431685715[/C][C]98.5844631906436[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.73095238095238[/C][C]0.0869196763807721[/C][C]100.448514588393[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.735[/C][C]0.0846978036829642[/C][C]103.131363744641[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.73947368421053[/C][C]0.0831919641393157[/C][C]105.051897435372[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.74166666666667[/C][C]0.0818801873432461[/C][C]106.761683751664[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.74705882352941[/C][C]0.0806872545711244[/C][C]108.406945682097[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.753125[/C][C]0.0787995076075577[/C][C]111.080960601846[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.76333333333333[/C][C]0.0767865130239385[/C][C]114.125944625215[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.77142857142857[/C][C]0.0750409311337956[/C][C]116.888589185939[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.78076923076923[/C][C]0.0746312433583087[/C][C]117.655405908384[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.79166666666667[/C][C]0.0734542810254527[/C][C]119.688962221552[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.8[/C][C]0.0729703729240527[/C][C]120.596889495947[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.81[/C][C]0.0714142842854284[/C][C]123.364675402868[/C][/ROW]
[ROW][C]Median[/C][C]9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.78064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.68[/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=49025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49025&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 Mean8.70.12279697083070870.8486531967805
Geometric Mean8.6474701316913
Harmonic Mean8.5934916449475
Quadratic Mean8.7509808974004
Winsorized Mean ( 1 / 20 )8.6950.11868928718572473.2585072011942
Winsorized Mean ( 2 / 20 )8.6950.11705966897994874.2783580012469
Winsorized Mean ( 3 / 20 )8.70.11349606130700576.65464245906
Winsorized Mean ( 4 / 20 )8.70.11057119290558978.6823382418283
Winsorized Mean ( 5 / 20 )8.708333333333330.1086977789851780.1150990814766
Winsorized Mean ( 6 / 20 )8.708333333333330.10059966154054286.5642408729563
Winsorized Mean ( 7 / 20 )8.720.098284724172425388.7218240008703
Winsorized Mean ( 8 / 20 )8.706666666666670.09103506081478695.6408068357386
Winsorized Mean ( 9 / 20 )8.706666666666670.09103506081478695.6408068357386
Winsorized Mean ( 10 / 20 )8.706666666666670.085266834965357102.11082269213
Winsorized Mean ( 11 / 20 )8.7250.082050866130519106.336476523247
Winsorized Mean ( 12 / 20 )8.7050.0789559342166413110.251371051035
Winsorized Mean ( 13 / 20 )8.7050.0789559342166413110.251371051035
Winsorized Mean ( 14 / 20 )8.681666666666670.0755952523942968114.844072765099
Winsorized Mean ( 15 / 20 )8.706666666666670.0713021210557114122.109504426436
Winsorized Mean ( 16 / 20 )8.706666666666670.0632395975977982137.677452061615
Winsorized Mean ( 17 / 20 )8.706666666666670.0632395975977982137.677452061615
Winsorized Mean ( 18 / 20 )8.736666666666670.0584627297697265149.439937222889
Winsorized Mean ( 19 / 20 )8.736666666666670.0584627297697265149.439937222889
Winsorized Mean ( 20 / 20 )8.770.0533774535021377164.301580997092
Trimmed Mean ( 1 / 20 )8.70.11497126077676075.6710845929822
Trimmed Mean ( 2 / 20 )8.705357142857140.11038361805737378.8645751612567
Trimmed Mean ( 3 / 20 )8.711111111111110.10579527012140382.3393248215624
Trimmed Mean ( 4 / 20 )8.715384615384610.10184514223585.5748681196254
Trimmed Mean ( 5 / 20 )8.720.09806287029560388.9225450337547
Trimmed Mean ( 6 / 20 )8.722916666666670.093931070213942892.8650833722947
Trimmed Mean ( 7 / 20 )8.726086956521740.091283641544422395.593107471236
Trimmed Mean ( 8 / 20 )8.727272727272730.088525843168571598.5844631906436
Trimmed Mean ( 9 / 20 )8.730952380952380.0869196763807721100.448514588393
Trimmed Mean ( 10 / 20 )8.7350.0846978036829642103.131363744641
Trimmed Mean ( 11 / 20 )8.739473684210530.0831919641393157105.051897435372
Trimmed Mean ( 12 / 20 )8.741666666666670.0818801873432461106.761683751664
Trimmed Mean ( 13 / 20 )8.747058823529410.0806872545711244108.406945682097
Trimmed Mean ( 14 / 20 )8.7531250.0787995076075577111.080960601846
Trimmed Mean ( 15 / 20 )8.763333333333330.0767865130239385114.125944625215
Trimmed Mean ( 16 / 20 )8.771428571428570.0750409311337956116.888589185939
Trimmed Mean ( 17 / 20 )8.780769230769230.0746312433583087117.655405908384
Trimmed Mean ( 18 / 20 )8.791666666666670.0734542810254527119.688962221552
Trimmed Mean ( 19 / 20 )8.80.0729703729240527120.596889495947
Trimmed Mean ( 20 / 20 )8.810.0714142842854284123.364675402868
Median9
Midrange8.7
Midmean - Weighted Average at Xnp8.68
Midmean - Weighted Average at X(n+1)p8.78064516129032
Midmean - Empirical Distribution Function8.68
Midmean - Empirical Distribution Function - Averaging8.78064516129032
Midmean - Empirical Distribution Function - Interpolation8.78064516129032
Midmean - Closest Observation8.68
Midmean - True Basic - Statistics Graphics Toolkit8.78064516129032
Midmean - MS Excel (old versions)8.68
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')