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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 14 Nov 2011 11:49:02 -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/2011/Nov/14/t1321289358g7ma9wffad1cfqm.htm/, Retrieved Fri, 26 Apr 2024 00:44:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142080, Retrieved Fri, 26 Apr 2024 00:44:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [Temperatuur ] [2011-11-14 16:49:02] [2a6d487209befbc7c5ce02a41ecac161] [Current]
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Dataseries X:
18,4
17,6
19
20,5
24,3
21,2
22,1
21,5
20,8
22,5
23,7
23,8
14,1
16,3
22,2
21,1
19,2
17,3
20,8
22,6
20,2
18,6
17
13,3
19,7
18,6
21,7
24,3
18,9
16,8
18,1
21,7
26,7
23,4
25,3
22,9
24,6
20,5
19,1
17,3
20,1
21,1
21,1
20
21,3
21,1
21,8
22,2
19,4
19,7
23,1
27,4
23,4
24,2
20,9
24,2
20,9
24,2
21,2
18,3
16,6
17,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142080&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142080&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142080&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.77096774193550.35941949712952257.7903199682302
Geometric Mean20.5733491800096
Harmonic Mean20.3659290249892
Quadratic Mean20.9598002329806
Winsorized Mean ( 1 / 20 )20.77258064516130.35194683564159559.0219275797526
Winsorized Mean ( 2 / 20 )20.79838709677420.32116831225848464.7585278588604
Winsorized Mean ( 3 / 20 )20.77903225806450.3105847940804366.9029284565796
Winsorized Mean ( 4 / 20 )20.77258064516130.30398524619454768.3341737969319
Winsorized Mean ( 5 / 20 )20.78870967741940.30059085863974269.1594873227154
Winsorized Mean ( 6 / 20 )20.8080645161290.29289396838537871.0429942645681
Winsorized Mean ( 7 / 20 )20.8080645161290.29289396838537871.0429942645681
Winsorized Mean ( 8 / 20 )20.84677419354840.28548267589014573.0229045547069
Winsorized Mean ( 9 / 20 )20.83225806451610.26659390835147278.1422883716131
Winsorized Mean ( 10 / 20 )20.84838709677420.25793326911050980.8286079910146
Winsorized Mean ( 11 / 20 )20.83064516129030.24233995803428885.9562959829475
Winsorized Mean ( 12 / 20 )20.850.23905717771006487.2176280157022
Winsorized Mean ( 13 / 20 )20.82903225806450.2212696775663994.1341465633715
Winsorized Mean ( 14 / 20 )20.78387096774190.21380432036218897.2097801042266
Winsorized Mean ( 15 / 20 )20.78387096774190.190245931019905109.247387612024
Winsorized Mean ( 16 / 20 )20.78387096774190.182064567849266114.156594076829
Winsorized Mean ( 17 / 20 )20.72903225806450.165274431600116125.421894102887
Winsorized Mean ( 18 / 20 )20.7580645161290.160619971307913129.237132512838
Winsorized Mean ( 19 / 20 )20.78870967741940.146474610140134141.927052460017
Winsorized Mean ( 20 / 20 )20.78870967741940.117642649183783176.710655715878
Trimmed Mean ( 1 / 20 )20.7850.33140537076820562.7177524366003
Trimmed Mean ( 2 / 20 )20.7982758620690.30577711714233768.0177642344228
Trimmed Mean ( 3 / 20 )20.79821428571430.29531505377021170.4272065382001
Trimmed Mean ( 4 / 20 )20.80555555555560.28747942735213372.3723285077748
Trimmed Mean ( 5 / 20 )20.81538461538460.2802361724210874.2780078515618
Trimmed Mean ( 6 / 20 )20.8220.27222874535198976.4871467672428
Trimmed Mean ( 7 / 20 )20.8250.26443268593362578.7535017710606
Trimmed Mean ( 8 / 20 )20.82826086956520.25436599299256681.8830403566325
Trimmed Mean ( 9 / 20 )20.8250.24345828074002385.5382693769943
Trimmed Mean ( 10 / 20 )20.82380952380950.23455321216254388.7807475831064
Trimmed Mean ( 11 / 20 )20.820.22509826913868392.49293688337
Trimmed Mean ( 12 / 20 )20.81842105263160.21672117842336196.0608520315588
Trimmed Mean ( 13 / 20 )20.81388888888890.206103409773546100.987600892959
Trimmed Mean ( 14 / 20 )20.81176470588240.196664009735324105.823962065512
Trimmed Mean ( 15 / 20 )20.8156250.185519615463633112.201747227535
Trimmed Mean ( 16 / 20 )20.820.177103126006797117.558625132348
Trimmed Mean ( 17 / 20 )20.8250.167270730716696124.498768617631
Trimmed Mean ( 18 / 20 )20.83846153846150.158267244589837131.666293884538
Trimmed Mean ( 19 / 20 )20.850.145835921302089142.968891435264
Trimmed Mean ( 20 / 20 )20.85909090909090.13219084506831157.795276203218
Median21
Midrange20.35
Midmean - Weighted Average at Xnp20.758064516129
Midmean - Weighted Average at X(n+1)p20.815625
Midmean - Empirical Distribution Function20.815625
Midmean - Empirical Distribution Function - Averaging20.815625
Midmean - Empirical Distribution Function - Interpolation20.82
Midmean - Closest Observation20.815625
Midmean - True Basic - Statistics Graphics Toolkit20.815625
Midmean - MS Excel (old versions)20.815625
Number of observations62

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.7709677419355 & 0.359419497129522 & 57.7903199682302 \tabularnewline
Geometric Mean & 20.5733491800096 &  &  \tabularnewline
Harmonic Mean & 20.3659290249892 &  &  \tabularnewline
Quadratic Mean & 20.9598002329806 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 20.7725806451613 & 0.351946835641595 & 59.0219275797526 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 20.7983870967742 & 0.321168312258484 & 64.7585278588604 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 20.7790322580645 & 0.31058479408043 & 66.9029284565796 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 20.7725806451613 & 0.303985246194547 & 68.3341737969319 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 20.7887096774194 & 0.300590858639742 & 69.1594873227154 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 20.808064516129 & 0.292893968385378 & 71.0429942645681 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 20.808064516129 & 0.292893968385378 & 71.0429942645681 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 20.8467741935484 & 0.285482675890145 & 73.0229045547069 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 20.8322580645161 & 0.266593908351472 & 78.1422883716131 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 20.8483870967742 & 0.257933269110509 & 80.8286079910146 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 20.8306451612903 & 0.242339958034288 & 85.9562959829475 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 20.85 & 0.239057177710064 & 87.2176280157022 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 20.8290322580645 & 0.22126967756639 & 94.1341465633715 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 20.7838709677419 & 0.213804320362188 & 97.2097801042266 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 20.7838709677419 & 0.190245931019905 & 109.247387612024 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 20.7838709677419 & 0.182064567849266 & 114.156594076829 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 20.7290322580645 & 0.165274431600116 & 125.421894102887 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 20.758064516129 & 0.160619971307913 & 129.237132512838 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 20.7887096774194 & 0.146474610140134 & 141.927052460017 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 20.7887096774194 & 0.117642649183783 & 176.710655715878 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 20.785 & 0.331405370768205 & 62.7177524366003 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 20.798275862069 & 0.305777117142337 & 68.0177642344228 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 20.7982142857143 & 0.295315053770211 & 70.4272065382001 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 20.8055555555556 & 0.287479427352133 & 72.3723285077748 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 20.8153846153846 & 0.28023617242108 & 74.2780078515618 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 20.822 & 0.272228745351989 & 76.4871467672428 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 20.825 & 0.264432685933625 & 78.7535017710606 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 20.8282608695652 & 0.254365992992566 & 81.8830403566325 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 20.825 & 0.243458280740023 & 85.5382693769943 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 20.8238095238095 & 0.234553212162543 & 88.7807475831064 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 20.82 & 0.225098269138683 & 92.49293688337 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 20.8184210526316 & 0.216721178423361 & 96.0608520315588 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 20.8138888888889 & 0.206103409773546 & 100.987600892959 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 20.8117647058824 & 0.196664009735324 & 105.823962065512 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 20.815625 & 0.185519615463633 & 112.201747227535 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 20.82 & 0.177103126006797 & 117.558625132348 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 20.825 & 0.167270730716696 & 124.498768617631 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 20.8384615384615 & 0.158267244589837 & 131.666293884538 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 20.85 & 0.145835921302089 & 142.968891435264 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 20.8590909090909 & 0.13219084506831 & 157.795276203218 \tabularnewline
Median & 21 &  &  \tabularnewline
Midrange & 20.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.758064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.815625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.815625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.815625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.82 &  &  \tabularnewline
Midmean - Closest Observation & 20.815625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.815625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.815625 &  &  \tabularnewline
Number of observations & 62 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142080&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]20.7709677419355[/C][C]0.359419497129522[/C][C]57.7903199682302[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]20.5733491800096[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20.3659290249892[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.9598002329806[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]20.7725806451613[/C][C]0.351946835641595[/C][C]59.0219275797526[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]20.7983870967742[/C][C]0.321168312258484[/C][C]64.7585278588604[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]20.7790322580645[/C][C]0.31058479408043[/C][C]66.9029284565796[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]20.7725806451613[/C][C]0.303985246194547[/C][C]68.3341737969319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]20.7887096774194[/C][C]0.300590858639742[/C][C]69.1594873227154[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]20.808064516129[/C][C]0.292893968385378[/C][C]71.0429942645681[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]20.808064516129[/C][C]0.292893968385378[/C][C]71.0429942645681[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]20.8467741935484[/C][C]0.285482675890145[/C][C]73.0229045547069[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]20.8322580645161[/C][C]0.266593908351472[/C][C]78.1422883716131[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]20.8483870967742[/C][C]0.257933269110509[/C][C]80.8286079910146[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]20.8306451612903[/C][C]0.242339958034288[/C][C]85.9562959829475[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]20.85[/C][C]0.239057177710064[/C][C]87.2176280157022[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]20.8290322580645[/C][C]0.22126967756639[/C][C]94.1341465633715[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]20.7838709677419[/C][C]0.213804320362188[/C][C]97.2097801042266[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]20.7838709677419[/C][C]0.190245931019905[/C][C]109.247387612024[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]20.7838709677419[/C][C]0.182064567849266[/C][C]114.156594076829[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]20.7290322580645[/C][C]0.165274431600116[/C][C]125.421894102887[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]20.758064516129[/C][C]0.160619971307913[/C][C]129.237132512838[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]20.7887096774194[/C][C]0.146474610140134[/C][C]141.927052460017[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]20.7887096774194[/C][C]0.117642649183783[/C][C]176.710655715878[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]20.785[/C][C]0.331405370768205[/C][C]62.7177524366003[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]20.798275862069[/C][C]0.305777117142337[/C][C]68.0177642344228[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]20.7982142857143[/C][C]0.295315053770211[/C][C]70.4272065382001[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]20.8055555555556[/C][C]0.287479427352133[/C][C]72.3723285077748[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]20.8153846153846[/C][C]0.28023617242108[/C][C]74.2780078515618[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]20.822[/C][C]0.272228745351989[/C][C]76.4871467672428[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]20.825[/C][C]0.264432685933625[/C][C]78.7535017710606[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]20.8282608695652[/C][C]0.254365992992566[/C][C]81.8830403566325[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]20.825[/C][C]0.243458280740023[/C][C]85.5382693769943[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]20.8238095238095[/C][C]0.234553212162543[/C][C]88.7807475831064[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]20.82[/C][C]0.225098269138683[/C][C]92.49293688337[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]20.8184210526316[/C][C]0.216721178423361[/C][C]96.0608520315588[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]20.8138888888889[/C][C]0.206103409773546[/C][C]100.987600892959[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]20.8117647058824[/C][C]0.196664009735324[/C][C]105.823962065512[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]20.815625[/C][C]0.185519615463633[/C][C]112.201747227535[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]20.82[/C][C]0.177103126006797[/C][C]117.558625132348[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]20.825[/C][C]0.167270730716696[/C][C]124.498768617631[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]20.8384615384615[/C][C]0.158267244589837[/C][C]131.666293884538[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]20.85[/C][C]0.145835921302089[/C][C]142.968891435264[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]20.8590909090909[/C][C]0.13219084506831[/C][C]157.795276203218[/C][/ROW]
[ROW][C]Median[/C][C]21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]20.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.758064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]62[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142080&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142080&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 Mean20.77096774193550.35941949712952257.7903199682302
Geometric Mean20.5733491800096
Harmonic Mean20.3659290249892
Quadratic Mean20.9598002329806
Winsorized Mean ( 1 / 20 )20.77258064516130.35194683564159559.0219275797526
Winsorized Mean ( 2 / 20 )20.79838709677420.32116831225848464.7585278588604
Winsorized Mean ( 3 / 20 )20.77903225806450.3105847940804366.9029284565796
Winsorized Mean ( 4 / 20 )20.77258064516130.30398524619454768.3341737969319
Winsorized Mean ( 5 / 20 )20.78870967741940.30059085863974269.1594873227154
Winsorized Mean ( 6 / 20 )20.8080645161290.29289396838537871.0429942645681
Winsorized Mean ( 7 / 20 )20.8080645161290.29289396838537871.0429942645681
Winsorized Mean ( 8 / 20 )20.84677419354840.28548267589014573.0229045547069
Winsorized Mean ( 9 / 20 )20.83225806451610.26659390835147278.1422883716131
Winsorized Mean ( 10 / 20 )20.84838709677420.25793326911050980.8286079910146
Winsorized Mean ( 11 / 20 )20.83064516129030.24233995803428885.9562959829475
Winsorized Mean ( 12 / 20 )20.850.23905717771006487.2176280157022
Winsorized Mean ( 13 / 20 )20.82903225806450.2212696775663994.1341465633715
Winsorized Mean ( 14 / 20 )20.78387096774190.21380432036218897.2097801042266
Winsorized Mean ( 15 / 20 )20.78387096774190.190245931019905109.247387612024
Winsorized Mean ( 16 / 20 )20.78387096774190.182064567849266114.156594076829
Winsorized Mean ( 17 / 20 )20.72903225806450.165274431600116125.421894102887
Winsorized Mean ( 18 / 20 )20.7580645161290.160619971307913129.237132512838
Winsorized Mean ( 19 / 20 )20.78870967741940.146474610140134141.927052460017
Winsorized Mean ( 20 / 20 )20.78870967741940.117642649183783176.710655715878
Trimmed Mean ( 1 / 20 )20.7850.33140537076820562.7177524366003
Trimmed Mean ( 2 / 20 )20.7982758620690.30577711714233768.0177642344228
Trimmed Mean ( 3 / 20 )20.79821428571430.29531505377021170.4272065382001
Trimmed Mean ( 4 / 20 )20.80555555555560.28747942735213372.3723285077748
Trimmed Mean ( 5 / 20 )20.81538461538460.2802361724210874.2780078515618
Trimmed Mean ( 6 / 20 )20.8220.27222874535198976.4871467672428
Trimmed Mean ( 7 / 20 )20.8250.26443268593362578.7535017710606
Trimmed Mean ( 8 / 20 )20.82826086956520.25436599299256681.8830403566325
Trimmed Mean ( 9 / 20 )20.8250.24345828074002385.5382693769943
Trimmed Mean ( 10 / 20 )20.82380952380950.23455321216254388.7807475831064
Trimmed Mean ( 11 / 20 )20.820.22509826913868392.49293688337
Trimmed Mean ( 12 / 20 )20.81842105263160.21672117842336196.0608520315588
Trimmed Mean ( 13 / 20 )20.81388888888890.206103409773546100.987600892959
Trimmed Mean ( 14 / 20 )20.81176470588240.196664009735324105.823962065512
Trimmed Mean ( 15 / 20 )20.8156250.185519615463633112.201747227535
Trimmed Mean ( 16 / 20 )20.820.177103126006797117.558625132348
Trimmed Mean ( 17 / 20 )20.8250.167270730716696124.498768617631
Trimmed Mean ( 18 / 20 )20.83846153846150.158267244589837131.666293884538
Trimmed Mean ( 19 / 20 )20.850.145835921302089142.968891435264
Trimmed Mean ( 20 / 20 )20.85909090909090.13219084506831157.795276203218
Median21
Midrange20.35
Midmean - Weighted Average at Xnp20.758064516129
Midmean - Weighted Average at X(n+1)p20.815625
Midmean - Empirical Distribution Function20.815625
Midmean - Empirical Distribution Function - Averaging20.815625
Midmean - Empirical Distribution Function - Interpolation20.82
Midmean - Closest Observation20.815625
Midmean - True Basic - Statistics Graphics Toolkit20.815625
Midmean - MS Excel (old versions)20.815625
Number of observations62



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')