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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 computationMon, 20 Oct 2008 15:24:50 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224538061p0rsgkpd84wfced.htm/, Retrieved Sun, 19 May 2024 14:55:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18180, Retrieved Sun, 19 May 2024 14:55:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [vraag 3: Q9 - cen...] [2008-10-20 21:24:50] [00a0a665d7a07edd2e460056b0c0c354] [Current]
Feedback Forum
2008-10-24 11:08:41 [2df1bcd103d52957f4a39bd4617794c8] [reply
Er zijn uitzonderlijk weinig extreme waarden. In de trimmed mean zijn deze afgezwakt, toch is de conclusie van de licht stijgende tendens naar mijn mening correct.
  2008-10-27 18:11:06 [Steffi Van Isveldt] [reply
Het gaat hier inderdaad om een vrij stabiele reeks met weinig echte outliers.

Post a new message
Dataseries X:
116,1
102,5
102,0
101,3
100,6
100,9
104,2
108,3
108,9
109,9
106,8
112,7
113,4
101,3
97,8
95,0
93,8
94,5
101,4
105,8
106,6
109,7
108,8
113,4
113,7
103,6
98,2
95,5
94,4
95,9
103,2
104,1
127,6
130,3
133,0
140,4
123,5
116,9
115,9
113,1
112,1
112,4
118,9
117,4
115,6
120,7
114,9
122,0
119,6
114,6
118,4
110,9
111,6
114,6
112,1
117,4
114,8
123,4
118,1
121,9
123,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18180&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18180&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18180&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.1426229508201.2961617550180885.7474944932852
Geometric Mean110.693629843994
Harmonic Mean110.248703190445
Quadratic Mean111.595182486066
Winsorized Mean ( 1 / 20 )111.0311475409841.2533529696685988.5872936259463
Winsorized Mean ( 2 / 20 )110.9459016393441.2280545140409090.3428148920504
Winsorized Mean ( 3 / 20 )110.8377049180331.1895197265995893.1785345291237
Winsorized Mean ( 4 / 20 )110.6016393442621.1247865415057098.3312257596943
Winsorized Mean ( 5 / 20 )110.6262295081971.1159472480024799.132131654266
Winsorized Mean ( 6 / 20 )110.8032786885251.07462782275945103.108514726524
Winsorized Mean ( 7 / 20 )110.71.03737531346355106.711619761221
Winsorized Mean ( 8 / 20 )111.0016393442620.975272112240523113.816070357282
Winsorized Mean ( 9 / 20 )110.8688524590160.935392559489104118.526549451677
Winsorized Mean ( 10 / 20 )110.7540983606560.893083850359629124.013101699305
Winsorized Mean ( 11 / 20 )110.6278688524590.872688613485235126.766715118062
Winsorized Mean ( 12 / 20 )110.5491803278690.853871360497413129.468190926874
Winsorized Mean ( 13 / 20 )110.6131147540980.821522228994045134.644092211046
Winsorized Mean ( 14 / 20 )110.5672131147540.777595148401021142.191233242793
Winsorized Mean ( 15 / 20 )110.7393442622950.748252166257391147.997358719576
Winsorized Mean ( 16 / 20 )110.7131147540980.711461496678447155.613642159101
Winsorized Mean ( 17 / 20 )110.6295081967210.656640498753089168.478046064473
Winsorized Mean ( 18 / 20 )110.60.643602395672862171.845227338490
Winsorized Mean ( 19 / 20 )111.0049180327870.549930081146975201.852784268987
Winsorized Mean ( 20 / 20 )111.0377049180330.477408555226467232.584237761219
Trimmed Mean ( 1 / 20 )110.9406779661021.2075355610395791.8736321691368
Trimmed Mean ( 2 / 20 )110.8438596491231.1510347789293396.2993140417772
Trimmed Mean ( 3 / 20 )110.7872727272731.09838894739858100.863426375202
Trimmed Mean ( 4 / 20 )110.7679245283021.05220334716259105.272355222023
Trimmed Mean ( 5 / 20 )110.8176470588241.02055619546250108.585541444490
Trimmed Mean ( 6 / 20 )110.8653061224490.983484153459278112.727089432498
Trimmed Mean ( 7 / 20 )110.8787234042550.949613759402407116.761917470563
Trimmed Mean ( 8 / 20 )110.9133333333330.917047303892094120.946141886683
Trimmed Mean ( 9 / 20 )110.8976744186050.892335323576304124.278028100634
Trimmed Mean ( 10 / 20 )110.9024390243900.870243082138955127.438460931864
Trimmed Mean ( 11 / 20 )110.9256410256410.851344241098625130.294698279154
Trimmed Mean ( 12 / 20 )110.9702702702700.830091576272143133.684371028829
Trimmed Mean ( 13 / 20 )111.0314285714290.804867246515725137.949989954349
Trimmed Mean ( 14 / 20 )111.0909090909090.778040999011781142.782847217576
Trimmed Mean ( 15 / 20 )111.1645161290320.75167981611792147.888121704725
Trimmed Mean ( 16 / 20 )111.2241379310340.721804238645388154.091832627319
Trimmed Mean ( 17 / 20 )111.2962962962960.688292024618416161.699238572462
Trimmed Mean ( 18 / 20 )111.3920.655080656611586170.043183042798
Trimmed Mean ( 19 / 20 )111.5086956521740.604852350044928184.356885848077
Trimmed Mean ( 20 / 20 )111.5857142857140.56834285905796196.335209473151
Median112.1
Midrange117.1
Midmean - Weighted Average at Xnp110.956666666667
Midmean - Weighted Average at X(n+1)p111.359375
Midmean - Empirical Distribution Function111.359375
Midmean - Empirical Distribution Function - Averaging111.359375
Midmean - Empirical Distribution Function - Interpolation111.359375
Midmean - Closest Observation111.090909090909
Midmean - True Basic - Statistics Graphics Toolkit111.359375
Midmean - MS Excel (old versions)111.359375
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.142622950820 & 1.29616175501808 & 85.7474944932852 \tabularnewline
Geometric Mean & 110.693629843994 &  &  \tabularnewline
Harmonic Mean & 110.248703190445 &  &  \tabularnewline
Quadratic Mean & 111.595182486066 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.031147540984 & 1.25335296966859 & 88.5872936259463 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 110.945901639344 & 1.22805451404090 & 90.3428148920504 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 110.837704918033 & 1.18951972659958 & 93.1785345291237 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 110.601639344262 & 1.12478654150570 & 98.3312257596943 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 110.626229508197 & 1.11594724800247 & 99.132131654266 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 110.803278688525 & 1.07462782275945 & 103.108514726524 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 110.7 & 1.03737531346355 & 106.711619761221 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.001639344262 & 0.975272112240523 & 113.816070357282 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 110.868852459016 & 0.935392559489104 & 118.526549451677 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 110.754098360656 & 0.893083850359629 & 124.013101699305 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 110.627868852459 & 0.872688613485235 & 126.766715118062 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 110.549180327869 & 0.853871360497413 & 129.468190926874 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 110.613114754098 & 0.821522228994045 & 134.644092211046 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 110.567213114754 & 0.777595148401021 & 142.191233242793 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 110.739344262295 & 0.748252166257391 & 147.997358719576 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 110.713114754098 & 0.711461496678447 & 155.613642159101 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 110.629508196721 & 0.656640498753089 & 168.478046064473 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 110.6 & 0.643602395672862 & 171.845227338490 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111.004918032787 & 0.549930081146975 & 201.852784268987 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 111.037704918033 & 0.477408555226467 & 232.584237761219 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 110.940677966102 & 1.20753556103957 & 91.8736321691368 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 110.843859649123 & 1.15103477892933 & 96.2993140417772 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 110.787272727273 & 1.09838894739858 & 100.863426375202 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 110.767924528302 & 1.05220334716259 & 105.272355222023 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 110.817647058824 & 1.02055619546250 & 108.585541444490 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 110.865306122449 & 0.983484153459278 & 112.727089432498 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 110.878723404255 & 0.949613759402407 & 116.761917470563 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 110.913333333333 & 0.917047303892094 & 120.946141886683 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 110.897674418605 & 0.892335323576304 & 124.278028100634 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 110.902439024390 & 0.870243082138955 & 127.438460931864 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 110.925641025641 & 0.851344241098625 & 130.294698279154 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 110.970270270270 & 0.830091576272143 & 133.684371028829 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.031428571429 & 0.804867246515725 & 137.949989954349 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.090909090909 & 0.778040999011781 & 142.782847217576 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.164516129032 & 0.75167981611792 & 147.888121704725 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.224137931034 & 0.721804238645388 & 154.091832627319 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.296296296296 & 0.688292024618416 & 161.699238572462 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.392 & 0.655080656611586 & 170.043183042798 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.508695652174 & 0.604852350044928 & 184.356885848077 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111.585714285714 & 0.56834285905796 & 196.335209473151 \tabularnewline
Median & 112.1 &  &  \tabularnewline
Midrange & 117.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.956666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.359375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.359375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.359375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.359375 &  &  \tabularnewline
Midmean - Closest Observation & 111.090909090909 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.359375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.359375 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18180&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]111.142622950820[/C][C]1.29616175501808[/C][C]85.7474944932852[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.693629843994[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.248703190445[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.595182486066[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.031147540984[/C][C]1.25335296966859[/C][C]88.5872936259463[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]110.945901639344[/C][C]1.22805451404090[/C][C]90.3428148920504[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]110.837704918033[/C][C]1.18951972659958[/C][C]93.1785345291237[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]110.601639344262[/C][C]1.12478654150570[/C][C]98.3312257596943[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]110.626229508197[/C][C]1.11594724800247[/C][C]99.132131654266[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]110.803278688525[/C][C]1.07462782275945[/C][C]103.108514726524[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]110.7[/C][C]1.03737531346355[/C][C]106.711619761221[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.001639344262[/C][C]0.975272112240523[/C][C]113.816070357282[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]110.868852459016[/C][C]0.935392559489104[/C][C]118.526549451677[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]110.754098360656[/C][C]0.893083850359629[/C][C]124.013101699305[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]110.627868852459[/C][C]0.872688613485235[/C][C]126.766715118062[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]110.549180327869[/C][C]0.853871360497413[/C][C]129.468190926874[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]110.613114754098[/C][C]0.821522228994045[/C][C]134.644092211046[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]110.567213114754[/C][C]0.777595148401021[/C][C]142.191233242793[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]110.739344262295[/C][C]0.748252166257391[/C][C]147.997358719576[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]110.713114754098[/C][C]0.711461496678447[/C][C]155.613642159101[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]110.629508196721[/C][C]0.656640498753089[/C][C]168.478046064473[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]110.6[/C][C]0.643602395672862[/C][C]171.845227338490[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111.004918032787[/C][C]0.549930081146975[/C][C]201.852784268987[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]111.037704918033[/C][C]0.477408555226467[/C][C]232.584237761219[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]110.940677966102[/C][C]1.20753556103957[/C][C]91.8736321691368[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]110.843859649123[/C][C]1.15103477892933[/C][C]96.2993140417772[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]110.787272727273[/C][C]1.09838894739858[/C][C]100.863426375202[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]110.767924528302[/C][C]1.05220334716259[/C][C]105.272355222023[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]110.817647058824[/C][C]1.02055619546250[/C][C]108.585541444490[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]110.865306122449[/C][C]0.983484153459278[/C][C]112.727089432498[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]110.878723404255[/C][C]0.949613759402407[/C][C]116.761917470563[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]110.913333333333[/C][C]0.917047303892094[/C][C]120.946141886683[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]110.897674418605[/C][C]0.892335323576304[/C][C]124.278028100634[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]110.902439024390[/C][C]0.870243082138955[/C][C]127.438460931864[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]110.925641025641[/C][C]0.851344241098625[/C][C]130.294698279154[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]110.970270270270[/C][C]0.830091576272143[/C][C]133.684371028829[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.031428571429[/C][C]0.804867246515725[/C][C]137.949989954349[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.090909090909[/C][C]0.778040999011781[/C][C]142.782847217576[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.164516129032[/C][C]0.75167981611792[/C][C]147.888121704725[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.224137931034[/C][C]0.721804238645388[/C][C]154.091832627319[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.296296296296[/C][C]0.688292024618416[/C][C]161.699238572462[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.392[/C][C]0.655080656611586[/C][C]170.043183042798[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.508695652174[/C][C]0.604852350044928[/C][C]184.356885848077[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111.585714285714[/C][C]0.56834285905796[/C][C]196.335209473151[/C][/ROW]
[ROW][C]Median[/C][C]112.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.956666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.359375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.359375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.359375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.359375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.090909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.359375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.359375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18180&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18180&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 Mean111.1426229508201.2961617550180885.7474944932852
Geometric Mean110.693629843994
Harmonic Mean110.248703190445
Quadratic Mean111.595182486066
Winsorized Mean ( 1 / 20 )111.0311475409841.2533529696685988.5872936259463
Winsorized Mean ( 2 / 20 )110.9459016393441.2280545140409090.3428148920504
Winsorized Mean ( 3 / 20 )110.8377049180331.1895197265995893.1785345291237
Winsorized Mean ( 4 / 20 )110.6016393442621.1247865415057098.3312257596943
Winsorized Mean ( 5 / 20 )110.6262295081971.1159472480024799.132131654266
Winsorized Mean ( 6 / 20 )110.8032786885251.07462782275945103.108514726524
Winsorized Mean ( 7 / 20 )110.71.03737531346355106.711619761221
Winsorized Mean ( 8 / 20 )111.0016393442620.975272112240523113.816070357282
Winsorized Mean ( 9 / 20 )110.8688524590160.935392559489104118.526549451677
Winsorized Mean ( 10 / 20 )110.7540983606560.893083850359629124.013101699305
Winsorized Mean ( 11 / 20 )110.6278688524590.872688613485235126.766715118062
Winsorized Mean ( 12 / 20 )110.5491803278690.853871360497413129.468190926874
Winsorized Mean ( 13 / 20 )110.6131147540980.821522228994045134.644092211046
Winsorized Mean ( 14 / 20 )110.5672131147540.777595148401021142.191233242793
Winsorized Mean ( 15 / 20 )110.7393442622950.748252166257391147.997358719576
Winsorized Mean ( 16 / 20 )110.7131147540980.711461496678447155.613642159101
Winsorized Mean ( 17 / 20 )110.6295081967210.656640498753089168.478046064473
Winsorized Mean ( 18 / 20 )110.60.643602395672862171.845227338490
Winsorized Mean ( 19 / 20 )111.0049180327870.549930081146975201.852784268987
Winsorized Mean ( 20 / 20 )111.0377049180330.477408555226467232.584237761219
Trimmed Mean ( 1 / 20 )110.9406779661021.2075355610395791.8736321691368
Trimmed Mean ( 2 / 20 )110.8438596491231.1510347789293396.2993140417772
Trimmed Mean ( 3 / 20 )110.7872727272731.09838894739858100.863426375202
Trimmed Mean ( 4 / 20 )110.7679245283021.05220334716259105.272355222023
Trimmed Mean ( 5 / 20 )110.8176470588241.02055619546250108.585541444490
Trimmed Mean ( 6 / 20 )110.8653061224490.983484153459278112.727089432498
Trimmed Mean ( 7 / 20 )110.8787234042550.949613759402407116.761917470563
Trimmed Mean ( 8 / 20 )110.9133333333330.917047303892094120.946141886683
Trimmed Mean ( 9 / 20 )110.8976744186050.892335323576304124.278028100634
Trimmed Mean ( 10 / 20 )110.9024390243900.870243082138955127.438460931864
Trimmed Mean ( 11 / 20 )110.9256410256410.851344241098625130.294698279154
Trimmed Mean ( 12 / 20 )110.9702702702700.830091576272143133.684371028829
Trimmed Mean ( 13 / 20 )111.0314285714290.804867246515725137.949989954349
Trimmed Mean ( 14 / 20 )111.0909090909090.778040999011781142.782847217576
Trimmed Mean ( 15 / 20 )111.1645161290320.75167981611792147.888121704725
Trimmed Mean ( 16 / 20 )111.2241379310340.721804238645388154.091832627319
Trimmed Mean ( 17 / 20 )111.2962962962960.688292024618416161.699238572462
Trimmed Mean ( 18 / 20 )111.3920.655080656611586170.043183042798
Trimmed Mean ( 19 / 20 )111.5086956521740.604852350044928184.356885848077
Trimmed Mean ( 20 / 20 )111.5857142857140.56834285905796196.335209473151
Median112.1
Midrange117.1
Midmean - Weighted Average at Xnp110.956666666667
Midmean - Weighted Average at X(n+1)p111.359375
Midmean - Empirical Distribution Function111.359375
Midmean - Empirical Distribution Function - Averaging111.359375
Midmean - Empirical Distribution Function - Interpolation111.359375
Midmean - Closest Observation111.090909090909
Midmean - True Basic - Statistics Graphics Toolkit111.359375
Midmean - MS Excel (old versions)111.359375
Number of observations61



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')