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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 22 Dec 2013 09:54:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/22/t13877240684z2exbejkwv5y9k.htm/, Retrieved Sun, 05 Dec 2021 18:22:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232532, Retrieved Sun, 05 Dec 2021 18:22:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-12-22 14:54:06] [818da16b08b21220aa14002c9e16e6e1] [Current]
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Dataseries X:
85,73
85,73
85,74
86,32
87,59
87,81
87,87
87,94
87,96
88,01
88,01
88,01
88,01
88,01
88,59
89,43
89,63
89,73
89,88
89,89
89,9
89,91
89,86
90,07
90,17
90,17
90,28
90,87
92,05
92,1
92,16
92,22
92,25
92,29
92,29
92,29
92,29
92,29
91,95
91,82
92,16
92,31
92,33
92,4
92,54
92,49
92,54
92,58
92,58
92,39
92,33
93,59
95,51
95,99
96,22
97,2
98,54
99,64
100,23
100,17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232532&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232532&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean91.34766666666670.435360449835079209.820774260203
Geometric Mean91.2874850988839
Harmonic Mean91.2282920347593
Quadratic Mean91.4088561901964
Winsorized Mean ( 1 / 20 )91.34666666666660.435015660908208209.984777274356
Winsorized Mean ( 2 / 20 )91.32933333333330.429004422735862212.886694153185
Winsorized Mean ( 3 / 20 )91.30333333333330.405406935593726225.214038826489
Winsorized Mean ( 4 / 20 )91.29866666666670.363302839128764251.301825456718
Winsorized Mean ( 5 / 20 )91.23533333333330.338679761969339269.385252909186
Winsorized Mean ( 6 / 20 )91.21833333333330.3319816520921274.769201124486
Winsorized Mean ( 7 / 20 )91.17050.317259043759918287.369270610902
Winsorized Mean ( 8 / 20 )90.91716666666670.264475399266786343.76417208829
Winsorized Mean ( 9 / 20 )90.77316666666670.240244048665145377.837316557995
Winsorized Mean ( 10 / 20 )90.77316666666670.240244048665145377.837316557995
Winsorized Mean ( 11 / 20 )90.76583333333330.239315914376422379.27203282673
Winsorized Mean ( 12 / 20 )90.76583333333330.239315914376422379.27203282673
Winsorized Mean ( 13 / 20 )90.7550.23796589747605381.378176295762
Winsorized Mean ( 14 / 20 )90.86933333333330.209620300622685433.494909908069
Winsorized Mean ( 15 / 20 )91.07683333333330.172759015670071527.190045509802
Winsorized Mean ( 16 / 20 )91.11416666666670.162263873061571561.518500375579
Winsorized Mean ( 17 / 20 )91.14250.157919314483712577.145995712896
Winsorized Mean ( 18 / 20 )91.17550.151324552061115602.516239157126
Winsorized Mean ( 19 / 20 )91.17550.149590859150027609.499139974582
Winsorized Mean ( 20 / 20 )91.17883333333330.149102037572551611.5197003191
Trimmed Mean ( 1 / 20 )91.29137931034480.411689923804459221.747907907762
Trimmed Mean ( 2 / 20 )91.23214285714290.382394176370992238.581412831536
Trimmed Mean ( 3 / 20 )91.17814814814820.349383411568309260.968738438005
Trimmed Mean ( 4 / 20 )91.130.319927522900894284.845764983558
Trimmed Mean ( 5 / 20 )91.07940.300976154727058302.613341852932
Trimmed Mean ( 6 / 20 )91.04041666666670.286168743047936318.135431902905
Trimmed Mean ( 7 / 20 )91.00173913043480.26930834730347337.909092093197
Trimmed Mean ( 8 / 20 )90.96886363636360.252246401212884360.634931554843
Trimmed Mean ( 9 / 20 )90.97809523809520.246293602610826369.388787502742
Trimmed Mean ( 10 / 20 )91.012250.24420868742291372.682278261416
Trimmed Mean ( 11 / 20 )91.050.240775182437791378.153591570944
Trimmed Mean ( 12 / 20 )91.09305555555560.235670546019274386.527112081734
Trimmed Mean ( 13 / 20 )91.14117647058820.227956028496648399.819110166364
Trimmed Mean ( 14 / 20 )91.1968750.21669411206963420.855343640791
Trimmed Mean ( 15 / 20 )91.24366666666670.209739018636727435.034297670205
Trimmed Mean ( 16 / 20 )91.26750.210982599774027432.583066555023
Trimmed Mean ( 17 / 20 )91.28961538461540.214222372435913426.144171341981
Trimmed Mean ( 18 / 20 )91.311250.218290718681118418.301110334374
Trimmed Mean ( 19 / 20 )91.33181818181820.224043552858215407.652070397299
Trimmed Mean ( 20 / 20 )91.35650.230287320536759396.706600203017
Median92
Midrange92.98
Midmean - Weighted Average at Xnp91.158064516129
Midmean - Weighted Average at X(n+1)p91.2436666666667
Midmean - Empirical Distribution Function91.158064516129
Midmean - Empirical Distribution Function - Averaging91.2436666666667
Midmean - Empirical Distribution Function - Interpolation91.2436666666667
Midmean - Closest Observation91.158064516129
Midmean - True Basic - Statistics Graphics Toolkit91.2436666666667
Midmean - MS Excel (old versions)91.196875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 91.3476666666667 & 0.435360449835079 & 209.820774260203 \tabularnewline
Geometric Mean & 91.2874850988839 &  &  \tabularnewline
Harmonic Mean & 91.2282920347593 &  &  \tabularnewline
Quadratic Mean & 91.4088561901964 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 91.3466666666666 & 0.435015660908208 & 209.984777274356 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 91.3293333333333 & 0.429004422735862 & 212.886694153185 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 91.3033333333333 & 0.405406935593726 & 225.214038826489 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 91.2986666666667 & 0.363302839128764 & 251.301825456718 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 91.2353333333333 & 0.338679761969339 & 269.385252909186 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 91.2183333333333 & 0.3319816520921 & 274.769201124486 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 91.1705 & 0.317259043759918 & 287.369270610902 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 90.9171666666667 & 0.264475399266786 & 343.76417208829 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 90.7731666666667 & 0.240244048665145 & 377.837316557995 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 90.7731666666667 & 0.240244048665145 & 377.837316557995 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 90.7658333333333 & 0.239315914376422 & 379.27203282673 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 90.7658333333333 & 0.239315914376422 & 379.27203282673 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 90.755 & 0.23796589747605 & 381.378176295762 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 90.8693333333333 & 0.209620300622685 & 433.494909908069 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 91.0768333333333 & 0.172759015670071 & 527.190045509802 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 91.1141666666667 & 0.162263873061571 & 561.518500375579 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 91.1425 & 0.157919314483712 & 577.145995712896 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 91.1755 & 0.151324552061115 & 602.516239157126 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 91.1755 & 0.149590859150027 & 609.499139974582 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 91.1788333333333 & 0.149102037572551 & 611.5197003191 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 91.2913793103448 & 0.411689923804459 & 221.747907907762 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 91.2321428571429 & 0.382394176370992 & 238.581412831536 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 91.1781481481482 & 0.349383411568309 & 260.968738438005 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 91.13 & 0.319927522900894 & 284.845764983558 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 91.0794 & 0.300976154727058 & 302.613341852932 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 91.0404166666667 & 0.286168743047936 & 318.135431902905 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 91.0017391304348 & 0.26930834730347 & 337.909092093197 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 90.9688636363636 & 0.252246401212884 & 360.634931554843 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 90.9780952380952 & 0.246293602610826 & 369.388787502742 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 91.01225 & 0.24420868742291 & 372.682278261416 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 91.05 & 0.240775182437791 & 378.153591570944 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 91.0930555555556 & 0.235670546019274 & 386.527112081734 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 91.1411764705882 & 0.227956028496648 & 399.819110166364 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 91.196875 & 0.21669411206963 & 420.855343640791 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 91.2436666666667 & 0.209739018636727 & 435.034297670205 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 91.2675 & 0.210982599774027 & 432.583066555023 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 91.2896153846154 & 0.214222372435913 & 426.144171341981 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 91.31125 & 0.218290718681118 & 418.301110334374 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 91.3318181818182 & 0.224043552858215 & 407.652070397299 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 91.3565 & 0.230287320536759 & 396.706600203017 \tabularnewline
Median & 92 &  &  \tabularnewline
Midrange & 92.98 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 91.158064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 91.2436666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 91.158064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 91.2436666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 91.2436666666667 &  &  \tabularnewline
Midmean - Closest Observation & 91.158064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 91.2436666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 91.196875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232532&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]91.3476666666667[/C][C]0.435360449835079[/C][C]209.820774260203[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]91.2874850988839[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]91.2282920347593[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]91.4088561901964[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]91.3466666666666[/C][C]0.435015660908208[/C][C]209.984777274356[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]91.3293333333333[/C][C]0.429004422735862[/C][C]212.886694153185[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]91.3033333333333[/C][C]0.405406935593726[/C][C]225.214038826489[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]91.2986666666667[/C][C]0.363302839128764[/C][C]251.301825456718[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]91.2353333333333[/C][C]0.338679761969339[/C][C]269.385252909186[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]91.2183333333333[/C][C]0.3319816520921[/C][C]274.769201124486[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]91.1705[/C][C]0.317259043759918[/C][C]287.369270610902[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]90.9171666666667[/C][C]0.264475399266786[/C][C]343.76417208829[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]90.7731666666667[/C][C]0.240244048665145[/C][C]377.837316557995[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]90.7731666666667[/C][C]0.240244048665145[/C][C]377.837316557995[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]90.7658333333333[/C][C]0.239315914376422[/C][C]379.27203282673[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]90.7658333333333[/C][C]0.239315914376422[/C][C]379.27203282673[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]90.755[/C][C]0.23796589747605[/C][C]381.378176295762[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]90.8693333333333[/C][C]0.209620300622685[/C][C]433.494909908069[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]91.0768333333333[/C][C]0.172759015670071[/C][C]527.190045509802[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]91.1141666666667[/C][C]0.162263873061571[/C][C]561.518500375579[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]91.1425[/C][C]0.157919314483712[/C][C]577.145995712896[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]91.1755[/C][C]0.151324552061115[/C][C]602.516239157126[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]91.1755[/C][C]0.149590859150027[/C][C]609.499139974582[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]91.1788333333333[/C][C]0.149102037572551[/C][C]611.5197003191[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]91.2913793103448[/C][C]0.411689923804459[/C][C]221.747907907762[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]91.2321428571429[/C][C]0.382394176370992[/C][C]238.581412831536[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]91.1781481481482[/C][C]0.349383411568309[/C][C]260.968738438005[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]91.13[/C][C]0.319927522900894[/C][C]284.845764983558[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]91.0794[/C][C]0.300976154727058[/C][C]302.613341852932[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]91.0404166666667[/C][C]0.286168743047936[/C][C]318.135431902905[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]91.0017391304348[/C][C]0.26930834730347[/C][C]337.909092093197[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]90.9688636363636[/C][C]0.252246401212884[/C][C]360.634931554843[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]90.9780952380952[/C][C]0.246293602610826[/C][C]369.388787502742[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]91.01225[/C][C]0.24420868742291[/C][C]372.682278261416[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]91.05[/C][C]0.240775182437791[/C][C]378.153591570944[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]91.0930555555556[/C][C]0.235670546019274[/C][C]386.527112081734[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]91.1411764705882[/C][C]0.227956028496648[/C][C]399.819110166364[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]91.196875[/C][C]0.21669411206963[/C][C]420.855343640791[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]91.2436666666667[/C][C]0.209739018636727[/C][C]435.034297670205[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]91.2675[/C][C]0.210982599774027[/C][C]432.583066555023[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]91.2896153846154[/C][C]0.214222372435913[/C][C]426.144171341981[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]91.31125[/C][C]0.218290718681118[/C][C]418.301110334374[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]91.3318181818182[/C][C]0.224043552858215[/C][C]407.652070397299[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]91.3565[/C][C]0.230287320536759[/C][C]396.706600203017[/C][/ROW]
[ROW][C]Median[/C][C]92[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]91.158064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]91.2436666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]91.158064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]91.2436666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]91.2436666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]91.158064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]91.2436666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]91.196875[/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=232532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232532&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 Mean91.34766666666670.435360449835079209.820774260203
Geometric Mean91.2874850988839
Harmonic Mean91.2282920347593
Quadratic Mean91.4088561901964
Winsorized Mean ( 1 / 20 )91.34666666666660.435015660908208209.984777274356
Winsorized Mean ( 2 / 20 )91.32933333333330.429004422735862212.886694153185
Winsorized Mean ( 3 / 20 )91.30333333333330.405406935593726225.214038826489
Winsorized Mean ( 4 / 20 )91.29866666666670.363302839128764251.301825456718
Winsorized Mean ( 5 / 20 )91.23533333333330.338679761969339269.385252909186
Winsorized Mean ( 6 / 20 )91.21833333333330.3319816520921274.769201124486
Winsorized Mean ( 7 / 20 )91.17050.317259043759918287.369270610902
Winsorized Mean ( 8 / 20 )90.91716666666670.264475399266786343.76417208829
Winsorized Mean ( 9 / 20 )90.77316666666670.240244048665145377.837316557995
Winsorized Mean ( 10 / 20 )90.77316666666670.240244048665145377.837316557995
Winsorized Mean ( 11 / 20 )90.76583333333330.239315914376422379.27203282673
Winsorized Mean ( 12 / 20 )90.76583333333330.239315914376422379.27203282673
Winsorized Mean ( 13 / 20 )90.7550.23796589747605381.378176295762
Winsorized Mean ( 14 / 20 )90.86933333333330.209620300622685433.494909908069
Winsorized Mean ( 15 / 20 )91.07683333333330.172759015670071527.190045509802
Winsorized Mean ( 16 / 20 )91.11416666666670.162263873061571561.518500375579
Winsorized Mean ( 17 / 20 )91.14250.157919314483712577.145995712896
Winsorized Mean ( 18 / 20 )91.17550.151324552061115602.516239157126
Winsorized Mean ( 19 / 20 )91.17550.149590859150027609.499139974582
Winsorized Mean ( 20 / 20 )91.17883333333330.149102037572551611.5197003191
Trimmed Mean ( 1 / 20 )91.29137931034480.411689923804459221.747907907762
Trimmed Mean ( 2 / 20 )91.23214285714290.382394176370992238.581412831536
Trimmed Mean ( 3 / 20 )91.17814814814820.349383411568309260.968738438005
Trimmed Mean ( 4 / 20 )91.130.319927522900894284.845764983558
Trimmed Mean ( 5 / 20 )91.07940.300976154727058302.613341852932
Trimmed Mean ( 6 / 20 )91.04041666666670.286168743047936318.135431902905
Trimmed Mean ( 7 / 20 )91.00173913043480.26930834730347337.909092093197
Trimmed Mean ( 8 / 20 )90.96886363636360.252246401212884360.634931554843
Trimmed Mean ( 9 / 20 )90.97809523809520.246293602610826369.388787502742
Trimmed Mean ( 10 / 20 )91.012250.24420868742291372.682278261416
Trimmed Mean ( 11 / 20 )91.050.240775182437791378.153591570944
Trimmed Mean ( 12 / 20 )91.09305555555560.235670546019274386.527112081734
Trimmed Mean ( 13 / 20 )91.14117647058820.227956028496648399.819110166364
Trimmed Mean ( 14 / 20 )91.1968750.21669411206963420.855343640791
Trimmed Mean ( 15 / 20 )91.24366666666670.209739018636727435.034297670205
Trimmed Mean ( 16 / 20 )91.26750.210982599774027432.583066555023
Trimmed Mean ( 17 / 20 )91.28961538461540.214222372435913426.144171341981
Trimmed Mean ( 18 / 20 )91.311250.218290718681118418.301110334374
Trimmed Mean ( 19 / 20 )91.33181818181820.224043552858215407.652070397299
Trimmed Mean ( 20 / 20 )91.35650.230287320536759396.706600203017
Median92
Midrange92.98
Midmean - Weighted Average at Xnp91.158064516129
Midmean - Weighted Average at X(n+1)p91.2436666666667
Midmean - Empirical Distribution Function91.158064516129
Midmean - Empirical Distribution Function - Averaging91.2436666666667
Midmean - Empirical Distribution Function - Interpolation91.2436666666667
Midmean - Closest Observation91.158064516129
Midmean - True Basic - Statistics Graphics Toolkit91.2436666666667
Midmean - MS Excel (old versions)91.196875
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')