Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 19 Oct 2010 09:39:30 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/19/t1287481117jj46zcj18jaor2b.htm/, Retrieved Sun, 28 Apr 2024 23:08:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=86092, Retrieved Sun, 28 Apr 2024 23:08:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Quartiles] [kwartielen Maximu...] [2010-10-12 10:43:04] [c4ce808c07ea53ce320aeb10407b1705]
- RM D    [Central Tendency] [centrummaten cons...] [2010-10-19 09:39:30] [6828a15931dcaf58ef367cb5857a54a7] [Current]
Feedback Forum

Post a new message
Dataseries X:
98,2
98,71
98,54
98,2
96,92
99,06
99,65
99,82
99,99
100,33
99,31
101,1
101,1
100,93
100,85
100,93
99,6
101,88
101,81
102,38
102,74
102,82
101,72
103,47
102,98
102,68
102,9
103,03
101,29
103,69
103,68
104,2
104,08
104,16
103,05
104,66
104,46
104,95
105,85
106,23
104,86
107,44
108,23
108,45
109,39
110,15
109,13
110,28
110,17
109,99
109,26
109,11
107,06
109,53
108,92
109,24
109,12
109
107,23
109,49
109,04
109,02
109,23
109,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=86092&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=86092&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=86092&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.449218750.494298510110636211.307978101374
Geometric Mean104.375486221828
Harmonic Mean104.301748492241
Quadratic Mean104.522878603502
Winsorized Mean ( 1 / 21 )104.46750.489526769782137213.405081087788
Winsorized Mean ( 2 / 21 )104.4668750.489411386978649213.454116065668
Winsorized Mean ( 3 / 21 )104.47531250.48487479814739215.468638294214
Winsorized Mean ( 4 / 21 )104.45718750.477809281784505218.616907377515
Winsorized Mean ( 5 / 21 )104.481406250.472180219914754221.274424135901
Winsorized Mean ( 6 / 21 )104.502031250.467504837196322223.53144381716
Winsorized Mean ( 7 / 21 )104.526093750.460730883793485226.870169608278
Winsorized Mean ( 8 / 21 )104.516093750.456971874958786228.714499682122
Winsorized Mean ( 9 / 21 )104.53718750.452509726982076231.016442888841
Winsorized Mean ( 10 / 21 )104.56218750.447901769893479233.448926814617
Winsorized Mean ( 11 / 21 )104.60343750.435778143343346240.038283465685
Winsorized Mean ( 12 / 21 )104.69906250.420791824847669248.814393050298
Winsorized Mean ( 13 / 21 )104.713281250.418106206999754250.446607816233
Winsorized Mean ( 14 / 21 )104.697968750.415558417789377251.945248292541
Winsorized Mean ( 15 / 21 )104.7331250.409103917880286256.006164748213
Winsorized Mean ( 16 / 21 )104.7281250.408272886378687256.515013595248
Winsorized Mean ( 17 / 21 )104.757343750.397690395788178263.414316411596
Winsorized Mean ( 18 / 21 )104.746093750.359425703268443291.426274741872
Winsorized Mean ( 19 / 21 )104.70750.345228817609331303.298840244818
Winsorized Mean ( 20 / 21 )104.48250.303117728189654344.692805082742
Winsorized Mean ( 21 / 21 )104.577656250.27063662656827386.413537502543
Trimmed Mean ( 1 / 21 )104.4766129032260.486303410498339214.838330654855
Trimmed Mean ( 2 / 21 )104.4863333333330.482048592544764216.754773168704
Trimmed Mean ( 3 / 21 )104.4970689655170.47661306383767219.249275553026
Trimmed Mean ( 4 / 21 )104.5053571428570.471708759220185221.546356941987
Trimmed Mean ( 5 / 21 )104.519629629630.467864587295225223.397180440325
Trimmed Mean ( 6 / 21 )104.5290384615380.464407069352426225.080635846683
Trimmed Mean ( 7 / 21 )104.53480.460883290375057226.81403770341
Trimmed Mean ( 8 / 21 )104.5364583333330.457641724122809228.424229748074
Trimmed Mean ( 9 / 21 )104.540.453807084084435230.362203822604
Trimmed Mean ( 10 / 21 )104.5404545454550.449294249785861232.677036475049
Trimmed Mean ( 11 / 21 )104.5371428571430.44384437187786235.526570754647
Trimmed Mean ( 12 / 21 )104.52750.438844746508901238.187880409957
Trimmed Mean ( 13 / 21 )104.5034210526320.434791242777482240.353095395977
Trimmed Mean ( 14 / 21 )104.4747222222220.428892535863267243.591840580619
Trimmed Mean ( 15 / 21 )104.4447058823530.420442478763791248.41615954089
Trimmed Mean ( 16 / 21 )104.406250.409280384904703255.097126201907
Trimmed Mean ( 17 / 21 )104.3633333333330.392576614774025265.841951368925
Trimmed Mean ( 18 / 21 )104.3103571428570.370531750791577281.515300429764
Trimmed Mean ( 19 / 21 )104.2507692307690.350505535159596297.429737260214
Trimmed Mean ( 20 / 21 )104.1866666666670.32405082502297321.513351059302
Trimmed Mean ( 21 / 21 )104.1436363636360.301580645065558345.325995111514
Median103.885
Midrange103.6
Midmean - Weighted Average at Xnp104.306060606061
Midmean - Weighted Average at X(n+1)p104.306060606061
Midmean - Empirical Distribution Function104.306060606061
Midmean - Empirical Distribution Function - Averaging104.306060606061
Midmean - Empirical Distribution Function - Interpolation104.306060606061
Midmean - Closest Observation104.306060606061
Midmean - True Basic - Statistics Graphics Toolkit104.306060606061
Midmean - MS Excel (old versions)104.444705882353
Number of observations64

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.44921875 & 0.494298510110636 & 211.307978101374 \tabularnewline
Geometric Mean & 104.375486221828 &  &  \tabularnewline
Harmonic Mean & 104.301748492241 &  &  \tabularnewline
Quadratic Mean & 104.522878603502 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 104.4675 & 0.489526769782137 & 213.405081087788 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 104.466875 & 0.489411386978649 & 213.454116065668 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 104.4753125 & 0.48487479814739 & 215.468638294214 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 104.4571875 & 0.477809281784505 & 218.616907377515 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 104.48140625 & 0.472180219914754 & 221.274424135901 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 104.50203125 & 0.467504837196322 & 223.53144381716 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 104.52609375 & 0.460730883793485 & 226.870169608278 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 104.51609375 & 0.456971874958786 & 228.714499682122 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 104.5371875 & 0.452509726982076 & 231.016442888841 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 104.5621875 & 0.447901769893479 & 233.448926814617 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 104.6034375 & 0.435778143343346 & 240.038283465685 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 104.6990625 & 0.420791824847669 & 248.814393050298 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 104.71328125 & 0.418106206999754 & 250.446607816233 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 104.69796875 & 0.415558417789377 & 251.945248292541 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 104.733125 & 0.409103917880286 & 256.006164748213 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 104.728125 & 0.408272886378687 & 256.515013595248 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 104.75734375 & 0.397690395788178 & 263.414316411596 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 104.74609375 & 0.359425703268443 & 291.426274741872 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 104.7075 & 0.345228817609331 & 303.298840244818 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 104.4825 & 0.303117728189654 & 344.692805082742 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 104.57765625 & 0.27063662656827 & 386.413537502543 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 104.476612903226 & 0.486303410498339 & 214.838330654855 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 104.486333333333 & 0.482048592544764 & 216.754773168704 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 104.497068965517 & 0.47661306383767 & 219.249275553026 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 104.505357142857 & 0.471708759220185 & 221.546356941987 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 104.51962962963 & 0.467864587295225 & 223.397180440325 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 104.529038461538 & 0.464407069352426 & 225.080635846683 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 104.5348 & 0.460883290375057 & 226.81403770341 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 104.536458333333 & 0.457641724122809 & 228.424229748074 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 104.54 & 0.453807084084435 & 230.362203822604 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 104.540454545455 & 0.449294249785861 & 232.677036475049 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 104.537142857143 & 0.44384437187786 & 235.526570754647 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 104.5275 & 0.438844746508901 & 238.187880409957 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 104.503421052632 & 0.434791242777482 & 240.353095395977 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 104.474722222222 & 0.428892535863267 & 243.591840580619 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 104.444705882353 & 0.420442478763791 & 248.41615954089 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 104.40625 & 0.409280384904703 & 255.097126201907 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 104.363333333333 & 0.392576614774025 & 265.841951368925 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 104.310357142857 & 0.370531750791577 & 281.515300429764 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 104.250769230769 & 0.350505535159596 & 297.429737260214 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 104.186666666667 & 0.32405082502297 & 321.513351059302 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 104.143636363636 & 0.301580645065558 & 345.325995111514 \tabularnewline
Median & 103.885 &  &  \tabularnewline
Midrange & 103.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 104.306060606061 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.306060606061 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.306060606061 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.306060606061 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.306060606061 &  &  \tabularnewline
Midmean - Closest Observation & 104.306060606061 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.306060606061 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.444705882353 &  &  \tabularnewline
Number of observations & 64 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=86092&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]104.44921875[/C][C]0.494298510110636[/C][C]211.307978101374[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.375486221828[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.301748492241[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.522878603502[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]104.4675[/C][C]0.489526769782137[/C][C]213.405081087788[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]104.466875[/C][C]0.489411386978649[/C][C]213.454116065668[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]104.4753125[/C][C]0.48487479814739[/C][C]215.468638294214[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]104.4571875[/C][C]0.477809281784505[/C][C]218.616907377515[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]104.48140625[/C][C]0.472180219914754[/C][C]221.274424135901[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]104.50203125[/C][C]0.467504837196322[/C][C]223.53144381716[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]104.52609375[/C][C]0.460730883793485[/C][C]226.870169608278[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]104.51609375[/C][C]0.456971874958786[/C][C]228.714499682122[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]104.5371875[/C][C]0.452509726982076[/C][C]231.016442888841[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]104.5621875[/C][C]0.447901769893479[/C][C]233.448926814617[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]104.6034375[/C][C]0.435778143343346[/C][C]240.038283465685[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]104.6990625[/C][C]0.420791824847669[/C][C]248.814393050298[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]104.71328125[/C][C]0.418106206999754[/C][C]250.446607816233[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]104.69796875[/C][C]0.415558417789377[/C][C]251.945248292541[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]104.733125[/C][C]0.409103917880286[/C][C]256.006164748213[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]104.728125[/C][C]0.408272886378687[/C][C]256.515013595248[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]104.75734375[/C][C]0.397690395788178[/C][C]263.414316411596[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]104.74609375[/C][C]0.359425703268443[/C][C]291.426274741872[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]104.7075[/C][C]0.345228817609331[/C][C]303.298840244818[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]104.4825[/C][C]0.303117728189654[/C][C]344.692805082742[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]104.57765625[/C][C]0.27063662656827[/C][C]386.413537502543[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]104.476612903226[/C][C]0.486303410498339[/C][C]214.838330654855[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]104.486333333333[/C][C]0.482048592544764[/C][C]216.754773168704[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]104.497068965517[/C][C]0.47661306383767[/C][C]219.249275553026[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]104.505357142857[/C][C]0.471708759220185[/C][C]221.546356941987[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]104.51962962963[/C][C]0.467864587295225[/C][C]223.397180440325[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]104.529038461538[/C][C]0.464407069352426[/C][C]225.080635846683[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]104.5348[/C][C]0.460883290375057[/C][C]226.81403770341[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]104.536458333333[/C][C]0.457641724122809[/C][C]228.424229748074[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]104.54[/C][C]0.453807084084435[/C][C]230.362203822604[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]104.540454545455[/C][C]0.449294249785861[/C][C]232.677036475049[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]104.537142857143[/C][C]0.44384437187786[/C][C]235.526570754647[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]104.5275[/C][C]0.438844746508901[/C][C]238.187880409957[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]104.503421052632[/C][C]0.434791242777482[/C][C]240.353095395977[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]104.474722222222[/C][C]0.428892535863267[/C][C]243.591840580619[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]104.444705882353[/C][C]0.420442478763791[/C][C]248.41615954089[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]104.40625[/C][C]0.409280384904703[/C][C]255.097126201907[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]104.363333333333[/C][C]0.392576614774025[/C][C]265.841951368925[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]104.310357142857[/C][C]0.370531750791577[/C][C]281.515300429764[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]104.250769230769[/C][C]0.350505535159596[/C][C]297.429737260214[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]104.186666666667[/C][C]0.32405082502297[/C][C]321.513351059302[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]104.143636363636[/C][C]0.301580645065558[/C][C]345.325995111514[/C][/ROW]
[ROW][C]Median[/C][C]103.885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]104.306060606061[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.306060606061[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.306060606061[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.306060606061[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.306060606061[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.306060606061[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.306060606061[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.444705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]64[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=86092&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=86092&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 Mean104.449218750.494298510110636211.307978101374
Geometric Mean104.375486221828
Harmonic Mean104.301748492241
Quadratic Mean104.522878603502
Winsorized Mean ( 1 / 21 )104.46750.489526769782137213.405081087788
Winsorized Mean ( 2 / 21 )104.4668750.489411386978649213.454116065668
Winsorized Mean ( 3 / 21 )104.47531250.48487479814739215.468638294214
Winsorized Mean ( 4 / 21 )104.45718750.477809281784505218.616907377515
Winsorized Mean ( 5 / 21 )104.481406250.472180219914754221.274424135901
Winsorized Mean ( 6 / 21 )104.502031250.467504837196322223.53144381716
Winsorized Mean ( 7 / 21 )104.526093750.460730883793485226.870169608278
Winsorized Mean ( 8 / 21 )104.516093750.456971874958786228.714499682122
Winsorized Mean ( 9 / 21 )104.53718750.452509726982076231.016442888841
Winsorized Mean ( 10 / 21 )104.56218750.447901769893479233.448926814617
Winsorized Mean ( 11 / 21 )104.60343750.435778143343346240.038283465685
Winsorized Mean ( 12 / 21 )104.69906250.420791824847669248.814393050298
Winsorized Mean ( 13 / 21 )104.713281250.418106206999754250.446607816233
Winsorized Mean ( 14 / 21 )104.697968750.415558417789377251.945248292541
Winsorized Mean ( 15 / 21 )104.7331250.409103917880286256.006164748213
Winsorized Mean ( 16 / 21 )104.7281250.408272886378687256.515013595248
Winsorized Mean ( 17 / 21 )104.757343750.397690395788178263.414316411596
Winsorized Mean ( 18 / 21 )104.746093750.359425703268443291.426274741872
Winsorized Mean ( 19 / 21 )104.70750.345228817609331303.298840244818
Winsorized Mean ( 20 / 21 )104.48250.303117728189654344.692805082742
Winsorized Mean ( 21 / 21 )104.577656250.27063662656827386.413537502543
Trimmed Mean ( 1 / 21 )104.4766129032260.486303410498339214.838330654855
Trimmed Mean ( 2 / 21 )104.4863333333330.482048592544764216.754773168704
Trimmed Mean ( 3 / 21 )104.4970689655170.47661306383767219.249275553026
Trimmed Mean ( 4 / 21 )104.5053571428570.471708759220185221.546356941987
Trimmed Mean ( 5 / 21 )104.519629629630.467864587295225223.397180440325
Trimmed Mean ( 6 / 21 )104.5290384615380.464407069352426225.080635846683
Trimmed Mean ( 7 / 21 )104.53480.460883290375057226.81403770341
Trimmed Mean ( 8 / 21 )104.5364583333330.457641724122809228.424229748074
Trimmed Mean ( 9 / 21 )104.540.453807084084435230.362203822604
Trimmed Mean ( 10 / 21 )104.5404545454550.449294249785861232.677036475049
Trimmed Mean ( 11 / 21 )104.5371428571430.44384437187786235.526570754647
Trimmed Mean ( 12 / 21 )104.52750.438844746508901238.187880409957
Trimmed Mean ( 13 / 21 )104.5034210526320.434791242777482240.353095395977
Trimmed Mean ( 14 / 21 )104.4747222222220.428892535863267243.591840580619
Trimmed Mean ( 15 / 21 )104.4447058823530.420442478763791248.41615954089
Trimmed Mean ( 16 / 21 )104.406250.409280384904703255.097126201907
Trimmed Mean ( 17 / 21 )104.3633333333330.392576614774025265.841951368925
Trimmed Mean ( 18 / 21 )104.3103571428570.370531750791577281.515300429764
Trimmed Mean ( 19 / 21 )104.2507692307690.350505535159596297.429737260214
Trimmed Mean ( 20 / 21 )104.1866666666670.32405082502297321.513351059302
Trimmed Mean ( 21 / 21 )104.1436363636360.301580645065558345.325995111514
Median103.885
Midrange103.6
Midmean - Weighted Average at Xnp104.306060606061
Midmean - Weighted Average at X(n+1)p104.306060606061
Midmean - Empirical Distribution Function104.306060606061
Midmean - Empirical Distribution Function - Averaging104.306060606061
Midmean - Empirical Distribution Function - Interpolation104.306060606061
Midmean - Closest Observation104.306060606061
Midmean - True Basic - Statistics Graphics Toolkit104.306060606061
Midmean - MS Excel (old versions)104.444705882353
Number of observations64



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')