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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 14:56:04 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256072370z3rargwti5qviq3.htm/, Retrieved Thu, 02 May 2024 19:09:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49169, Retrieved Thu, 02 May 2024 19:09:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHWWS3VR3
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-20 20:56:04] [71596e6a53ccce532e52aaf6113616ef] [Current]
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Dataseries X:
170.47
122.04
145.60
138.95
144.90
162.50
107.52
129.35
161.84
152.35
132.43
110.96
129.46
137.26
116.56
115.63
107.86
104.77
145.32
139.09
117.68
116.75
117.75
152.59
129.69
121.32
135.32
141.33
148.91
180.11
199.00
169.50
164.71
206.76
196.00
200.22
206.39
289.46
287.85
288.38
308.17
265.71
173.05
131.45
121.58
109.11
106.56
88.07
95.83
78.45
67.43
66.17
73.04
72.20
84.21
126.16
146.33
190.57
209.16
674.50




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49169&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49169&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean157.205511.315311341650113.8931661050588
Geometric Mean142.995222846516
Harmonic Mean132.759457703662
Quadratic Mean179.632149697653
Winsorized Mean ( 1 / 20 )151.1217.628299762803419.8105744004563
Winsorized Mean ( 2 / 20 )150.6563333333337.3909835204285720.3838004667337
Winsorized Mean ( 3 / 20 )150.6443333333337.366304335875520.4504628731755
Winsorized Mean ( 4 / 20 )150.9696666666677.2924805865673320.7021005917727
Winsorized Mean ( 5 / 20 )149.6046666666676.6443281256312622.5161466799855
Winsorized Mean ( 6 / 20 )144.3356666666675.0999510209604828.3013829100429
Winsorized Mean ( 7 / 20 )144.9614.8776329277018329.7195385853483
Winsorized Mean ( 8 / 20 )146.1036666666674.6756312300315931.2479020433097
Winsorized Mean ( 9 / 20 )145.4466666666674.4375196071289132.7765687914946
Winsorized Mean ( 10 / 20 )145.4033333333334.3714885224682433.2617442745190
Winsorized Mean ( 11 / 20 )144.9156666666674.2491056976445334.1049804308234
Winsorized Mean ( 12 / 20 )144.0796666666673.9942047706056836.0721783036723
Winsorized Mean ( 13 / 20 )142.2141666666673.5017543568617740.6122623615773
Winsorized Mean ( 14 / 20 )141.65653.0446264679096646.5267255254654
Winsorized Mean ( 15 / 20 )141.2442.8995192490663448.7129030253831
Winsorized Mean ( 16 / 20 )141.0362.8481985802507549.5176147400451
Winsorized Mean ( 17 / 20 )139.9423333333332.584543839224654.14585398378
Winsorized Mean ( 18 / 20 )139.3003333333332.4749241952286356.2846868610718
Winsorized Mean ( 19 / 20 )140.2218333333332.2784608058066361.5423504218198
Winsorized Mean ( 20 / 20 )137.2251666666671.7910637165710676.6165744953957
Trimmed Mean ( 1 / 20 )149.8562068965527.2596522760558620.6423394948013
Trimmed Mean ( 2 / 20 )148.5010714285716.796543705646621.8494984892389
Trimmed Mean ( 3 / 20 )147.3037037037046.3802676475840423.0873862728129
Trimmed Mean ( 4 / 20 )146.0188461538465.8578660015010524.9269693291771
Trimmed Mean ( 5 / 20 )144.53365.1985233598845527.8028182224442
Trimmed Mean ( 6 / 20 )143.2658333333334.6035455407227531.1207594377009
Trimmed Mean ( 7 / 20 )143.0332608695654.4188587620418732.3688238461535
Trimmed Mean ( 8 / 20 )142.6577272727274.2468753077853633.5912210587411
Trimmed Mean ( 9 / 20 )142.0423809523814.0761359946482234.8473115565516
Trimmed Mean ( 10 / 20 )141.4753.9185881647767236.1035643581241
Trimmed Mean ( 11 / 20 )140.8547368421053.721991901912337.8439127634148
Trimmed Mean ( 12 / 20 )140.2394444444443.4885698608056240.1996950154407
Trimmed Mean ( 13 / 20 )139.6747058823533.2459078923325943.0310133606346
Trimmed Mean ( 14 / 20 )139.30843753.0713064333497045.3580391677375
Trimmed Mean ( 15 / 20 )138.9732.9662707013290646.8510847434565
Trimmed Mean ( 16 / 20 )138.6485714285712.8539335480877948.5815696449798
Trimmed Mean ( 17 / 20 )138.3042307692312.6956178782539151.3070609469386
Trimmed Mean ( 18 / 20 )138.0633333333332.5534556484874154.0692114292714
Trimmed Mean ( 19 / 20 )137.8759090909092.3670537753426858.2478989396634
Trimmed Mean ( 20 / 20 )137.50552.1382728488936664.306807277259
Median138.105
Midrange370.335
Midmean - Weighted Average at Xnp138.22
Midmean - Weighted Average at X(n+1)p138.973
Midmean - Empirical Distribution Function138.22
Midmean - Empirical Distribution Function - Averaging138.973
Midmean - Empirical Distribution Function - Interpolation138.973
Midmean - Closest Observation138.22
Midmean - True Basic - Statistics Graphics Toolkit138.973
Midmean - MS Excel (old versions)139.3084375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 157.2055 & 11.3153113416501 & 13.8931661050588 \tabularnewline
Geometric Mean & 142.995222846516 &  &  \tabularnewline
Harmonic Mean & 132.759457703662 &  &  \tabularnewline
Quadratic Mean & 179.632149697653 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 151.121 & 7.6282997628034 & 19.8105744004563 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 150.656333333333 & 7.39098352042857 & 20.3838004667337 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 150.644333333333 & 7.3663043358755 & 20.4504628731755 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 150.969666666667 & 7.29248058656733 & 20.7021005917727 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 149.604666666667 & 6.64432812563126 & 22.5161466799855 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 144.335666666667 & 5.09995102096048 & 28.3013829100429 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 144.961 & 4.87763292770183 & 29.7195385853483 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 146.103666666667 & 4.67563123003159 & 31.2479020433097 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 145.446666666667 & 4.43751960712891 & 32.7765687914946 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 145.403333333333 & 4.37148852246824 & 33.2617442745190 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 144.915666666667 & 4.24910569764453 & 34.1049804308234 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 144.079666666667 & 3.99420477060568 & 36.0721783036723 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 142.214166666667 & 3.50175435686177 & 40.6122623615773 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 141.6565 & 3.04462646790966 & 46.5267255254654 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 141.244 & 2.89951924906634 & 48.7129030253831 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 141.036 & 2.84819858025075 & 49.5176147400451 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 139.942333333333 & 2.5845438392246 & 54.14585398378 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 139.300333333333 & 2.47492419522863 & 56.2846868610718 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 140.221833333333 & 2.27846080580663 & 61.5423504218198 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 137.225166666667 & 1.79106371657106 & 76.6165744953957 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 149.856206896552 & 7.25965227605586 & 20.6423394948013 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 148.501071428571 & 6.7965437056466 & 21.8494984892389 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 147.303703703704 & 6.38026764758404 & 23.0873862728129 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 146.018846153846 & 5.85786600150105 & 24.9269693291771 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 144.5336 & 5.19852335988455 & 27.8028182224442 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 143.265833333333 & 4.60354554072275 & 31.1207594377009 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 143.033260869565 & 4.41885876204187 & 32.3688238461535 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 142.657727272727 & 4.24687530778536 & 33.5912210587411 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 142.042380952381 & 4.07613599464822 & 34.8473115565516 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 141.475 & 3.91858816477672 & 36.1035643581241 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 140.854736842105 & 3.7219919019123 & 37.8439127634148 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 140.239444444444 & 3.48856986080562 & 40.1996950154407 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 139.674705882353 & 3.24590789233259 & 43.0310133606346 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 139.3084375 & 3.07130643334970 & 45.3580391677375 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 138.973 & 2.96627070132906 & 46.8510847434565 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 138.648571428571 & 2.85393354808779 & 48.5815696449798 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 138.304230769231 & 2.69561787825391 & 51.3070609469386 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 138.063333333333 & 2.55345564848741 & 54.0692114292714 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 137.875909090909 & 2.36705377534268 & 58.2478989396634 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 137.5055 & 2.13827284889366 & 64.306807277259 \tabularnewline
Median & 138.105 &  &  \tabularnewline
Midrange & 370.335 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 138.22 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 138.973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 138.22 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 138.973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 138.973 &  &  \tabularnewline
Midmean - Closest Observation & 138.22 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 138.973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 139.3084375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49169&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]157.2055[/C][C]11.3153113416501[/C][C]13.8931661050588[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]142.995222846516[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]132.759457703662[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]179.632149697653[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]151.121[/C][C]7.6282997628034[/C][C]19.8105744004563[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]150.656333333333[/C][C]7.39098352042857[/C][C]20.3838004667337[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]150.644333333333[/C][C]7.3663043358755[/C][C]20.4504628731755[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]150.969666666667[/C][C]7.29248058656733[/C][C]20.7021005917727[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]149.604666666667[/C][C]6.64432812563126[/C][C]22.5161466799855[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]144.335666666667[/C][C]5.09995102096048[/C][C]28.3013829100429[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]144.961[/C][C]4.87763292770183[/C][C]29.7195385853483[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]146.103666666667[/C][C]4.67563123003159[/C][C]31.2479020433097[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]145.446666666667[/C][C]4.43751960712891[/C][C]32.7765687914946[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]145.403333333333[/C][C]4.37148852246824[/C][C]33.2617442745190[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]144.915666666667[/C][C]4.24910569764453[/C][C]34.1049804308234[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]144.079666666667[/C][C]3.99420477060568[/C][C]36.0721783036723[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]142.214166666667[/C][C]3.50175435686177[/C][C]40.6122623615773[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]141.6565[/C][C]3.04462646790966[/C][C]46.5267255254654[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]141.244[/C][C]2.89951924906634[/C][C]48.7129030253831[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]141.036[/C][C]2.84819858025075[/C][C]49.5176147400451[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]139.942333333333[/C][C]2.5845438392246[/C][C]54.14585398378[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]139.300333333333[/C][C]2.47492419522863[/C][C]56.2846868610718[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]140.221833333333[/C][C]2.27846080580663[/C][C]61.5423504218198[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]137.225166666667[/C][C]1.79106371657106[/C][C]76.6165744953957[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]149.856206896552[/C][C]7.25965227605586[/C][C]20.6423394948013[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]148.501071428571[/C][C]6.7965437056466[/C][C]21.8494984892389[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]147.303703703704[/C][C]6.38026764758404[/C][C]23.0873862728129[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]146.018846153846[/C][C]5.85786600150105[/C][C]24.9269693291771[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]144.5336[/C][C]5.19852335988455[/C][C]27.8028182224442[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]143.265833333333[/C][C]4.60354554072275[/C][C]31.1207594377009[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]143.033260869565[/C][C]4.41885876204187[/C][C]32.3688238461535[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]142.657727272727[/C][C]4.24687530778536[/C][C]33.5912210587411[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]142.042380952381[/C][C]4.07613599464822[/C][C]34.8473115565516[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]141.475[/C][C]3.91858816477672[/C][C]36.1035643581241[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]140.854736842105[/C][C]3.7219919019123[/C][C]37.8439127634148[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]140.239444444444[/C][C]3.48856986080562[/C][C]40.1996950154407[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]139.674705882353[/C][C]3.24590789233259[/C][C]43.0310133606346[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]139.3084375[/C][C]3.07130643334970[/C][C]45.3580391677375[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]138.973[/C][C]2.96627070132906[/C][C]46.8510847434565[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]138.648571428571[/C][C]2.85393354808779[/C][C]48.5815696449798[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]138.304230769231[/C][C]2.69561787825391[/C][C]51.3070609469386[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]138.063333333333[/C][C]2.55345564848741[/C][C]54.0692114292714[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]137.875909090909[/C][C]2.36705377534268[/C][C]58.2478989396634[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]137.5055[/C][C]2.13827284889366[/C][C]64.306807277259[/C][/ROW]
[ROW][C]Median[/C][C]138.105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]370.335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]138.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]138.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]138.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]138.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]138.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]138.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]138.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]139.3084375[/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=49169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49169&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 Mean157.205511.315311341650113.8931661050588
Geometric Mean142.995222846516
Harmonic Mean132.759457703662
Quadratic Mean179.632149697653
Winsorized Mean ( 1 / 20 )151.1217.628299762803419.8105744004563
Winsorized Mean ( 2 / 20 )150.6563333333337.3909835204285720.3838004667337
Winsorized Mean ( 3 / 20 )150.6443333333337.366304335875520.4504628731755
Winsorized Mean ( 4 / 20 )150.9696666666677.2924805865673320.7021005917727
Winsorized Mean ( 5 / 20 )149.6046666666676.6443281256312622.5161466799855
Winsorized Mean ( 6 / 20 )144.3356666666675.0999510209604828.3013829100429
Winsorized Mean ( 7 / 20 )144.9614.8776329277018329.7195385853483
Winsorized Mean ( 8 / 20 )146.1036666666674.6756312300315931.2479020433097
Winsorized Mean ( 9 / 20 )145.4466666666674.4375196071289132.7765687914946
Winsorized Mean ( 10 / 20 )145.4033333333334.3714885224682433.2617442745190
Winsorized Mean ( 11 / 20 )144.9156666666674.2491056976445334.1049804308234
Winsorized Mean ( 12 / 20 )144.0796666666673.9942047706056836.0721783036723
Winsorized Mean ( 13 / 20 )142.2141666666673.5017543568617740.6122623615773
Winsorized Mean ( 14 / 20 )141.65653.0446264679096646.5267255254654
Winsorized Mean ( 15 / 20 )141.2442.8995192490663448.7129030253831
Winsorized Mean ( 16 / 20 )141.0362.8481985802507549.5176147400451
Winsorized Mean ( 17 / 20 )139.9423333333332.584543839224654.14585398378
Winsorized Mean ( 18 / 20 )139.3003333333332.4749241952286356.2846868610718
Winsorized Mean ( 19 / 20 )140.2218333333332.2784608058066361.5423504218198
Winsorized Mean ( 20 / 20 )137.2251666666671.7910637165710676.6165744953957
Trimmed Mean ( 1 / 20 )149.8562068965527.2596522760558620.6423394948013
Trimmed Mean ( 2 / 20 )148.5010714285716.796543705646621.8494984892389
Trimmed Mean ( 3 / 20 )147.3037037037046.3802676475840423.0873862728129
Trimmed Mean ( 4 / 20 )146.0188461538465.8578660015010524.9269693291771
Trimmed Mean ( 5 / 20 )144.53365.1985233598845527.8028182224442
Trimmed Mean ( 6 / 20 )143.2658333333334.6035455407227531.1207594377009
Trimmed Mean ( 7 / 20 )143.0332608695654.4188587620418732.3688238461535
Trimmed Mean ( 8 / 20 )142.6577272727274.2468753077853633.5912210587411
Trimmed Mean ( 9 / 20 )142.0423809523814.0761359946482234.8473115565516
Trimmed Mean ( 10 / 20 )141.4753.9185881647767236.1035643581241
Trimmed Mean ( 11 / 20 )140.8547368421053.721991901912337.8439127634148
Trimmed Mean ( 12 / 20 )140.2394444444443.4885698608056240.1996950154407
Trimmed Mean ( 13 / 20 )139.6747058823533.2459078923325943.0310133606346
Trimmed Mean ( 14 / 20 )139.30843753.0713064333497045.3580391677375
Trimmed Mean ( 15 / 20 )138.9732.9662707013290646.8510847434565
Trimmed Mean ( 16 / 20 )138.6485714285712.8539335480877948.5815696449798
Trimmed Mean ( 17 / 20 )138.3042307692312.6956178782539151.3070609469386
Trimmed Mean ( 18 / 20 )138.0633333333332.5534556484874154.0692114292714
Trimmed Mean ( 19 / 20 )137.8759090909092.3670537753426858.2478989396634
Trimmed Mean ( 20 / 20 )137.50552.1382728488936664.306807277259
Median138.105
Midrange370.335
Midmean - Weighted Average at Xnp138.22
Midmean - Weighted Average at X(n+1)p138.973
Midmean - Empirical Distribution Function138.22
Midmean - Empirical Distribution Function - Averaging138.973
Midmean - Empirical Distribution Function - Interpolation138.973
Midmean - Closest Observation138.22
Midmean - True Basic - Statistics Graphics Toolkit138.973
Midmean - MS Excel (old versions)139.3084375
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')