Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 15:45:53 -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/t1224539249lwg05ovcffgbvii.htm/, Retrieved Sun, 19 May 2024 14:44:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18202, Retrieved Sun, 19 May 2024 14:44:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordshoutindustrie
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
F    D  [Central Tendency] [Q1 Central tenden...] [2008-10-19 16:46:20] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D      [Central Tendency] [Q9 voorspelling h...] [2008-10-20 21:45:53] [e4cb5a8878d0401c2e8d19a1768b515b] [Current]
Feedback Forum
2008-10-24 10:16:36 [Kim Wester] [reply
Correct.
Toevoeging: wellicht kunt u informatie zoeken waarom er sprake is van een neerwaartse tendens? Daarnaast hadden de exacte waarden van de trimmed mean, winsorized mean, mid-range en median in het Word-document kunnen staan om uw woorden te ondersteunen.

Post a new message
Dataseries X:
112,5
111,3
104,5
112,3
109
110,3
114,1
108,3
112,1
114,5
110,3
112,6
108,2
110,5
115,1
115,9
112,6
115,3
113,8
111,2
119,9
107,3
110,9
117,8
112,7
111,8
102,1
115,5
109,4
114,8
111,8
114,8
111,1
107,1
112,5
113,5
115,3
114,7
116,9
113,7
123,8
117,6
118,1
120,7
120,8
125,7
125
124
123,4
125,1
124,4
121,1
122,5
142,4
133,8
131,4
126,7
128,7
110,7
110,2




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=18202&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=18202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18202&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 Mean116.0683333333330.961232999575386120.749426397768
Geometric Mean115.842687957451
Harmonic Mean115.625555424339
Quadratic Mean116.302932751787
Winsorized Mean ( 1 / 20 )115.9650.8941075941018129.699155632937
Winsorized Mean ( 2 / 20 )115.9716666666670.85114775173991136.253272630514
Winsorized Mean ( 3 / 20 )115.8466666666670.810424547548569142.945653629432
Winsorized Mean ( 4 / 20 )115.7733333333330.765933818248006151.153181352082
Winsorized Mean ( 5 / 20 )115.6983333333330.744969918122686155.306047289656
Winsorized Mean ( 6 / 20 )115.7083333333330.720084315789182160.687201201601
Winsorized Mean ( 7 / 20 )115.7433333333330.710289058158268162.952437467428
Winsorized Mean ( 8 / 20 )115.770.677288128524004170.931683465786
Winsorized Mean ( 9 / 20 )115.7250.662368737662617174.713861660158
Winsorized Mean ( 10 / 20 )115.6916666666670.655344355362478176.535688024163
Winsorized Mean ( 11 / 20 )115.6550.634993771934403182.135644649988
Winsorized Mean ( 12 / 20 )115.5150.592890196672819194.833715666488
Winsorized Mean ( 13 / 20 )115.2550.528035614489677218.271262084071
Winsorized Mean ( 14 / 20 )115.2316666666670.508495574739044226.612919347042
Winsorized Mean ( 15 / 20 )115.2316666666670.50043196971102230.264398841682
Winsorized Mean ( 16 / 20 )115.0450.457809973407540251.294219616285
Winsorized Mean ( 17 / 20 )114.6766666666670.349473911853107328.140850510376
Winsorized Mean ( 18 / 20 )114.5866666666670.334676390342005342.380490448014
Winsorized Mean ( 19 / 20 )114.6183333333330.311153237328188368.366192547243
Winsorized Mean ( 20 / 20 )114.4516666666670.264697798763861432.386167173116
Trimmed Mean ( 1 / 20 )115.8551724137930.848425367630624136.553168768797
Trimmed Mean ( 2 / 20 )115.73750.791187511637683146.283274568420
Trimmed Mean ( 3 / 20 )115.6074074074070.749371280158619154.272535481927
Trimmed Mean ( 4 / 20 )115.5153846153850.717773626570303160.935677126151
Trimmed Mean ( 5 / 20 )115.4380.696169636845292165.818780208671
Trimmed Mean ( 6 / 20 )115.3729166666670.675998995336692170.670248717165
Trimmed Mean ( 7 / 20 )115.30.657715266647108175.303821952887
Trimmed Mean ( 8 / 20 )115.2136363636360.636384400144489181.044092748781
Trimmed Mean ( 9 / 20 )115.1142857142860.617350483420447186.465045068876
Trimmed Mean ( 10 / 20 )115.01250.595788504679045193.04249594738
Trimmed Mean ( 11 / 20 )114.9052631578950.568168770736415202.237907248869
Trimmed Mean ( 12 / 20 )114.7916666666670.535892298466357214.206598966216
Trimmed Mean ( 13 / 20 )114.6852941176470.504262267177283227.431837721317
Trimmed Mean ( 14 / 20 )114.6031250.481104332269234238.208466050283
Trimmed Mean ( 15 / 20 )114.5133333333330.453206540754186252.673611335729
Trimmed Mean ( 16 / 20 )114.4107142857140.413314748869010276.812561368271
Trimmed Mean ( 17 / 20 )114.3192307692310.370281357920796308.736122745029
Trimmed Mean ( 18 / 20 )114.2666666666670.352047153187798324.577732363345
Trimmed Mean ( 19 / 20 )114.2181818181820.328293262127453347.915096027281
Trimmed Mean ( 20 / 20 )114.1550.298194126102620382.821088704862
Median114.3
Midrange122.25
Midmean - Weighted Average at Xnp114.403225806452
Midmean - Weighted Average at X(n+1)p114.513333333333
Midmean - Empirical Distribution Function114.403225806452
Midmean - Empirical Distribution Function - Averaging114.513333333333
Midmean - Empirical Distribution Function - Interpolation114.513333333333
Midmean - Closest Observation114.403225806452
Midmean - True Basic - Statistics Graphics Toolkit114.513333333333
Midmean - MS Excel (old versions)114.603125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.068333333333 & 0.961232999575386 & 120.749426397768 \tabularnewline
Geometric Mean & 115.842687957451 &  &  \tabularnewline
Harmonic Mean & 115.625555424339 &  &  \tabularnewline
Quadratic Mean & 116.302932751787 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 115.965 & 0.8941075941018 & 129.699155632937 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 115.971666666667 & 0.85114775173991 & 136.253272630514 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 115.846666666667 & 0.810424547548569 & 142.945653629432 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 115.773333333333 & 0.765933818248006 & 151.153181352082 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 115.698333333333 & 0.744969918122686 & 155.306047289656 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 115.708333333333 & 0.720084315789182 & 160.687201201601 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 115.743333333333 & 0.710289058158268 & 162.952437467428 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 115.77 & 0.677288128524004 & 170.931683465786 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 115.725 & 0.662368737662617 & 174.713861660158 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 115.691666666667 & 0.655344355362478 & 176.535688024163 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 115.655 & 0.634993771934403 & 182.135644649988 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 115.515 & 0.592890196672819 & 194.833715666488 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 115.255 & 0.528035614489677 & 218.271262084071 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 115.231666666667 & 0.508495574739044 & 226.612919347042 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 115.231666666667 & 0.50043196971102 & 230.264398841682 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 115.045 & 0.457809973407540 & 251.294219616285 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.676666666667 & 0.349473911853107 & 328.140850510376 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.586666666667 & 0.334676390342005 & 342.380490448014 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.618333333333 & 0.311153237328188 & 368.366192547243 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.451666666667 & 0.264697798763861 & 432.386167173116 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 115.855172413793 & 0.848425367630624 & 136.553168768797 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 115.7375 & 0.791187511637683 & 146.283274568420 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 115.607407407407 & 0.749371280158619 & 154.272535481927 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 115.515384615385 & 0.717773626570303 & 160.935677126151 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 115.438 & 0.696169636845292 & 165.818780208671 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 115.372916666667 & 0.675998995336692 & 170.670248717165 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 115.3 & 0.657715266647108 & 175.303821952887 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 115.213636363636 & 0.636384400144489 & 181.044092748781 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 115.114285714286 & 0.617350483420447 & 186.465045068876 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 115.0125 & 0.595788504679045 & 193.04249594738 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 114.905263157895 & 0.568168770736415 & 202.237907248869 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 114.791666666667 & 0.535892298466357 & 214.206598966216 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 114.685294117647 & 0.504262267177283 & 227.431837721317 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.603125 & 0.481104332269234 & 238.208466050283 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.513333333333 & 0.453206540754186 & 252.673611335729 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.410714285714 & 0.413314748869010 & 276.812561368271 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.319230769231 & 0.370281357920796 & 308.736122745029 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.266666666667 & 0.352047153187798 & 324.577732363345 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.218181818182 & 0.328293262127453 & 347.915096027281 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.155 & 0.298194126102620 & 382.821088704862 \tabularnewline
Median & 114.3 &  &  \tabularnewline
Midrange & 122.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.403225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.513333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.403225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.513333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.513333333333 &  &  \tabularnewline
Midmean - Closest Observation & 114.403225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.513333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.603125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18202&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]116.068333333333[/C][C]0.961232999575386[/C][C]120.749426397768[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.842687957451[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.625555424339[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]116.302932751787[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]115.965[/C][C]0.8941075941018[/C][C]129.699155632937[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]115.971666666667[/C][C]0.85114775173991[/C][C]136.253272630514[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]115.846666666667[/C][C]0.810424547548569[/C][C]142.945653629432[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]115.773333333333[/C][C]0.765933818248006[/C][C]151.153181352082[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]115.698333333333[/C][C]0.744969918122686[/C][C]155.306047289656[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]115.708333333333[/C][C]0.720084315789182[/C][C]160.687201201601[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]115.743333333333[/C][C]0.710289058158268[/C][C]162.952437467428[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]115.77[/C][C]0.677288128524004[/C][C]170.931683465786[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]115.725[/C][C]0.662368737662617[/C][C]174.713861660158[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]115.691666666667[/C][C]0.655344355362478[/C][C]176.535688024163[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]115.655[/C][C]0.634993771934403[/C][C]182.135644649988[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]115.515[/C][C]0.592890196672819[/C][C]194.833715666488[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]115.255[/C][C]0.528035614489677[/C][C]218.271262084071[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]115.231666666667[/C][C]0.508495574739044[/C][C]226.612919347042[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]115.231666666667[/C][C]0.50043196971102[/C][C]230.264398841682[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]115.045[/C][C]0.457809973407540[/C][C]251.294219616285[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.676666666667[/C][C]0.349473911853107[/C][C]328.140850510376[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.586666666667[/C][C]0.334676390342005[/C][C]342.380490448014[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.618333333333[/C][C]0.311153237328188[/C][C]368.366192547243[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.451666666667[/C][C]0.264697798763861[/C][C]432.386167173116[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]115.855172413793[/C][C]0.848425367630624[/C][C]136.553168768797[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]115.7375[/C][C]0.791187511637683[/C][C]146.283274568420[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]115.607407407407[/C][C]0.749371280158619[/C][C]154.272535481927[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]115.515384615385[/C][C]0.717773626570303[/C][C]160.935677126151[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]115.438[/C][C]0.696169636845292[/C][C]165.818780208671[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]115.372916666667[/C][C]0.675998995336692[/C][C]170.670248717165[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]115.3[/C][C]0.657715266647108[/C][C]175.303821952887[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]115.213636363636[/C][C]0.636384400144489[/C][C]181.044092748781[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]115.114285714286[/C][C]0.617350483420447[/C][C]186.465045068876[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]115.0125[/C][C]0.595788504679045[/C][C]193.04249594738[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]114.905263157895[/C][C]0.568168770736415[/C][C]202.237907248869[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]114.791666666667[/C][C]0.535892298466357[/C][C]214.206598966216[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]114.685294117647[/C][C]0.504262267177283[/C][C]227.431837721317[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.603125[/C][C]0.481104332269234[/C][C]238.208466050283[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.513333333333[/C][C]0.453206540754186[/C][C]252.673611335729[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.410714285714[/C][C]0.413314748869010[/C][C]276.812561368271[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.319230769231[/C][C]0.370281357920796[/C][C]308.736122745029[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.266666666667[/C][C]0.352047153187798[/C][C]324.577732363345[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.218181818182[/C][C]0.328293262127453[/C][C]347.915096027281[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.155[/C][C]0.298194126102620[/C][C]382.821088704862[/C][/ROW]
[ROW][C]Median[/C][C]114.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]122.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.403225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.403225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.403225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.513333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.603125[/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=18202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18202&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 Mean116.0683333333330.961232999575386120.749426397768
Geometric Mean115.842687957451
Harmonic Mean115.625555424339
Quadratic Mean116.302932751787
Winsorized Mean ( 1 / 20 )115.9650.8941075941018129.699155632937
Winsorized Mean ( 2 / 20 )115.9716666666670.85114775173991136.253272630514
Winsorized Mean ( 3 / 20 )115.8466666666670.810424547548569142.945653629432
Winsorized Mean ( 4 / 20 )115.7733333333330.765933818248006151.153181352082
Winsorized Mean ( 5 / 20 )115.6983333333330.744969918122686155.306047289656
Winsorized Mean ( 6 / 20 )115.7083333333330.720084315789182160.687201201601
Winsorized Mean ( 7 / 20 )115.7433333333330.710289058158268162.952437467428
Winsorized Mean ( 8 / 20 )115.770.677288128524004170.931683465786
Winsorized Mean ( 9 / 20 )115.7250.662368737662617174.713861660158
Winsorized Mean ( 10 / 20 )115.6916666666670.655344355362478176.535688024163
Winsorized Mean ( 11 / 20 )115.6550.634993771934403182.135644649988
Winsorized Mean ( 12 / 20 )115.5150.592890196672819194.833715666488
Winsorized Mean ( 13 / 20 )115.2550.528035614489677218.271262084071
Winsorized Mean ( 14 / 20 )115.2316666666670.508495574739044226.612919347042
Winsorized Mean ( 15 / 20 )115.2316666666670.50043196971102230.264398841682
Winsorized Mean ( 16 / 20 )115.0450.457809973407540251.294219616285
Winsorized Mean ( 17 / 20 )114.6766666666670.349473911853107328.140850510376
Winsorized Mean ( 18 / 20 )114.5866666666670.334676390342005342.380490448014
Winsorized Mean ( 19 / 20 )114.6183333333330.311153237328188368.366192547243
Winsorized Mean ( 20 / 20 )114.4516666666670.264697798763861432.386167173116
Trimmed Mean ( 1 / 20 )115.8551724137930.848425367630624136.553168768797
Trimmed Mean ( 2 / 20 )115.73750.791187511637683146.283274568420
Trimmed Mean ( 3 / 20 )115.6074074074070.749371280158619154.272535481927
Trimmed Mean ( 4 / 20 )115.5153846153850.717773626570303160.935677126151
Trimmed Mean ( 5 / 20 )115.4380.696169636845292165.818780208671
Trimmed Mean ( 6 / 20 )115.3729166666670.675998995336692170.670248717165
Trimmed Mean ( 7 / 20 )115.30.657715266647108175.303821952887
Trimmed Mean ( 8 / 20 )115.2136363636360.636384400144489181.044092748781
Trimmed Mean ( 9 / 20 )115.1142857142860.617350483420447186.465045068876
Trimmed Mean ( 10 / 20 )115.01250.595788504679045193.04249594738
Trimmed Mean ( 11 / 20 )114.9052631578950.568168770736415202.237907248869
Trimmed Mean ( 12 / 20 )114.7916666666670.535892298466357214.206598966216
Trimmed Mean ( 13 / 20 )114.6852941176470.504262267177283227.431837721317
Trimmed Mean ( 14 / 20 )114.6031250.481104332269234238.208466050283
Trimmed Mean ( 15 / 20 )114.5133333333330.453206540754186252.673611335729
Trimmed Mean ( 16 / 20 )114.4107142857140.413314748869010276.812561368271
Trimmed Mean ( 17 / 20 )114.3192307692310.370281357920796308.736122745029
Trimmed Mean ( 18 / 20 )114.2666666666670.352047153187798324.577732363345
Trimmed Mean ( 19 / 20 )114.2181818181820.328293262127453347.915096027281
Trimmed Mean ( 20 / 20 )114.1550.298194126102620382.821088704862
Median114.3
Midrange122.25
Midmean - Weighted Average at Xnp114.403225806452
Midmean - Weighted Average at X(n+1)p114.513333333333
Midmean - Empirical Distribution Function114.403225806452
Midmean - Empirical Distribution Function - Averaging114.513333333333
Midmean - Empirical Distribution Function - Interpolation114.513333333333
Midmean - Closest Observation114.403225806452
Midmean - True Basic - Statistics Graphics Toolkit114.513333333333
Midmean - MS Excel (old versions)114.603125
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')