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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 19 Oct 2009 13:19:25 -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/19/t1255980140pbirscb2a6gvozd.htm/, Retrieved Mon, 29 Apr 2024 18:59:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48137, Retrieved Mon, 29 Apr 2024 18:59:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [JJ Workshop 3, De...] [2009-10-19 19:19:25] [e31f2fa83f4a5291b9a51009566cf69b] [Current]
-  M D          [Central Tendency] [Paper, Central Te...] [2009-12-21 15:10:03] [96e597a9107bfe8c07649cce3d4f6fec]
-    D            [Central Tendency] [Paper, Residu's e...] [2009-12-21 16:33:17] [96e597a9107bfe8c07649cce3d4f6fec]
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Dataseries X:
94.3
99.4
115.7
116.8
99.8
96
115.9
109.1
117.3
109.8
112.8
110.7
100
113.3
122.4
112.5
104.2
92.5
117.2
109.3
106.1
118.8
105.3
106
102
112.9
116.5
114.8
100.5
85.4
114.6
109.9
100.7
115.5
100.7
99
102.3
108.8
105.9
113.2
95.7
80.9
113.9
98.1
102.8
104.7
95.9
94.6
101.6
103.9
110.3
114.1
96.8
87.4
111.4
97.4
102.9
112.7
97
95.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48137&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48137&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.4183333333331.1618548672618490.7327897001231
Geometric Mean105.028441543895
Harmonic Mean104.625704721886
Quadratic Mean105.795413416651
Winsorized Mean ( 1 / 20 )105.4333333333331.1235704455615493.8377595724669
Winsorized Mean ( 2 / 20 )105.451.0945357347187396.3422176682958
Winsorized Mean ( 3 / 20 )105.71.0300320877016102.618162348571
Winsorized Mean ( 4 / 20 )105.7933333333331.00028489350447105.763202084047
Winsorized Mean ( 5 / 20 )105.7933333333330.990836166503436106.771772074760
Winsorized Mean ( 6 / 20 )105.7833333333330.97058770322016108.988948636348
Winsorized Mean ( 7 / 20 )105.830.953646880601701110.973990638156
Winsorized Mean ( 8 / 20 )105.830.94421611286644112.082391475742
Winsorized Mean ( 9 / 20 )105.740.92369376391287114.475169294284
Winsorized Mean ( 10 / 20 )105.840.894819364405607118.280855567208
Winsorized Mean ( 11 / 20 )105.7850.87355312173741121.097386487045
Winsorized Mean ( 12 / 20 )105.8250.853608574740236123.973684346135
Winsorized Mean ( 13 / 20 )105.8466666666670.807998387125239130.998611325521
Winsorized Mean ( 14 / 20 )106.0333333333330.771020552924509137.523355157194
Winsorized Mean ( 15 / 20 )106.0583333333330.743948435681479142.561403783558
Winsorized Mean ( 16 / 20 )106.1383333333330.72378123418124146.644218336774
Winsorized Mean ( 17 / 20 )106.1666666666670.710993840377407149.321499902603
Winsorized Mean ( 18 / 20 )106.2566666666670.679856941858798156.292684717097
Winsorized Mean ( 19 / 20 )105.9716666666670.617622979664306171.579863696563
Winsorized Mean ( 20 / 20 )105.7383333333330.583410446880402181.241755094950
Trimmed Mean ( 1 / 20 )105.5482758620691.0844784065498597.3263047236315
Trimmed Mean ( 2 / 20 )105.6714285714291.03600040830645101.999408228197
Trimmed Mean ( 3 / 20 )105.7944444444440.995424250569078106.280758564966
Trimmed Mean ( 4 / 20 )105.8307692307690.976528999744462108.374425396955
Trimmed Mean ( 5 / 20 )105.8420.963768496209393109.820979225082
Trimmed Mean ( 6 / 20 )105.8541666666670.949920481616645111.434766083279
Trimmed Mean ( 7 / 20 )105.8695652173910.937443690110347112.934319505558
Trimmed Mean ( 8 / 20 )105.8772727272730.925061358095035114.454324354553
Trimmed Mean ( 9 / 20 )105.8857142857140.910294533314235116.320279217982
Trimmed Mean ( 10 / 20 )105.910.895034736469585118.330602919118
Trimmed Mean ( 11 / 20 )105.9210526315790.880959953386044120.233674895734
Trimmed Mean ( 12 / 20 )105.9416666666670.865882199913466122.351131224610
Trimmed Mean ( 13 / 20 )105.9588235294120.84881292433491124.831774460122
Trimmed Mean ( 14 / 20 )105.9750.835647324900226126.817853467853
Trimmed Mean ( 15 / 20 )105.9666666666670.824806955238595128.474506663215
Trimmed Mean ( 16 / 20 )105.9535714285710.813794465667295130.196967291602
Trimmed Mean ( 17 / 20 )105.9269230769230.79991456644411132.422795534033
Trimmed Mean ( 18 / 20 )105.8916666666670.778886158140582135.952687770777
Trimmed Mean ( 19 / 20 )105.8363636363640.753162034346078140.522701370967
Trimmed Mean ( 20 / 20 )105.8150.733996809113959144.162752053015
Median105.6
Midrange101.65
Midmean - Weighted Average at Xnp105.741935483871
Midmean - Weighted Average at X(n+1)p105.966666666667
Midmean - Empirical Distribution Function105.741935483871
Midmean - Empirical Distribution Function - Averaging105.966666666667
Midmean - Empirical Distribution Function - Interpolation105.966666666667
Midmean - Closest Observation105.741935483871
Midmean - True Basic - Statistics Graphics Toolkit105.966666666667
Midmean - MS Excel (old versions)105.975
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.418333333333 & 1.16185486726184 & 90.7327897001231 \tabularnewline
Geometric Mean & 105.028441543895 &  &  \tabularnewline
Harmonic Mean & 104.625704721886 &  &  \tabularnewline
Quadratic Mean & 105.795413416651 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 105.433333333333 & 1.12357044556154 & 93.8377595724669 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 105.45 & 1.09453573471873 & 96.3422176682958 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 105.7 & 1.0300320877016 & 102.618162348571 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 105.793333333333 & 1.00028489350447 & 105.763202084047 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 105.793333333333 & 0.990836166503436 & 106.771772074760 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.783333333333 & 0.97058770322016 & 108.988948636348 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 105.83 & 0.953646880601701 & 110.973990638156 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 105.83 & 0.94421611286644 & 112.082391475742 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.74 & 0.92369376391287 & 114.475169294284 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.84 & 0.894819364405607 & 118.280855567208 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 105.785 & 0.87355312173741 & 121.097386487045 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 105.825 & 0.853608574740236 & 123.973684346135 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.846666666667 & 0.807998387125239 & 130.998611325521 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 106.033333333333 & 0.771020552924509 & 137.523355157194 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 106.058333333333 & 0.743948435681479 & 142.561403783558 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 106.138333333333 & 0.72378123418124 & 146.644218336774 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 106.166666666667 & 0.710993840377407 & 149.321499902603 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 106.256666666667 & 0.679856941858798 & 156.292684717097 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.971666666667 & 0.617622979664306 & 171.579863696563 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.738333333333 & 0.583410446880402 & 181.241755094950 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 105.548275862069 & 1.08447840654985 & 97.3263047236315 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 105.671428571429 & 1.03600040830645 & 101.999408228197 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 105.794444444444 & 0.995424250569078 & 106.280758564966 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 105.830769230769 & 0.976528999744462 & 108.374425396955 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.842 & 0.963768496209393 & 109.820979225082 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.854166666667 & 0.949920481616645 & 111.434766083279 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.869565217391 & 0.937443690110347 & 112.934319505558 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.877272727273 & 0.925061358095035 & 114.454324354553 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.885714285714 & 0.910294533314235 & 116.320279217982 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.91 & 0.895034736469585 & 118.330602919118 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.921052631579 & 0.880959953386044 & 120.233674895734 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.941666666667 & 0.865882199913466 & 122.351131224610 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.958823529412 & 0.84881292433491 & 124.831774460122 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.975 & 0.835647324900226 & 126.817853467853 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.966666666667 & 0.824806955238595 & 128.474506663215 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.953571428571 & 0.813794465667295 & 130.196967291602 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.926923076923 & 0.79991456644411 & 132.422795534033 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.891666666667 & 0.778886158140582 & 135.952687770777 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 105.836363636364 & 0.753162034346078 & 140.522701370967 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 105.815 & 0.733996809113959 & 144.162752053015 \tabularnewline
Median & 105.6 &  &  \tabularnewline
Midrange & 101.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.741935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.966666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.966666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.966666666667 &  &  \tabularnewline
Midmean - Closest Observation & 105.741935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.966666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.975 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48137&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]105.418333333333[/C][C]1.16185486726184[/C][C]90.7327897001231[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.028441543895[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.625704721886[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.795413416651[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]105.433333333333[/C][C]1.12357044556154[/C][C]93.8377595724669[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]105.45[/C][C]1.09453573471873[/C][C]96.3422176682958[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]105.7[/C][C]1.0300320877016[/C][C]102.618162348571[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]105.793333333333[/C][C]1.00028489350447[/C][C]105.763202084047[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]105.793333333333[/C][C]0.990836166503436[/C][C]106.771772074760[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.783333333333[/C][C]0.97058770322016[/C][C]108.988948636348[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]105.83[/C][C]0.953646880601701[/C][C]110.973990638156[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]105.83[/C][C]0.94421611286644[/C][C]112.082391475742[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.74[/C][C]0.92369376391287[/C][C]114.475169294284[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.84[/C][C]0.894819364405607[/C][C]118.280855567208[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]105.785[/C][C]0.87355312173741[/C][C]121.097386487045[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]105.825[/C][C]0.853608574740236[/C][C]123.973684346135[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.846666666667[/C][C]0.807998387125239[/C][C]130.998611325521[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]106.033333333333[/C][C]0.771020552924509[/C][C]137.523355157194[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]106.058333333333[/C][C]0.743948435681479[/C][C]142.561403783558[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]106.138333333333[/C][C]0.72378123418124[/C][C]146.644218336774[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]106.166666666667[/C][C]0.710993840377407[/C][C]149.321499902603[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]106.256666666667[/C][C]0.679856941858798[/C][C]156.292684717097[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.971666666667[/C][C]0.617622979664306[/C][C]171.579863696563[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.738333333333[/C][C]0.583410446880402[/C][C]181.241755094950[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]105.548275862069[/C][C]1.08447840654985[/C][C]97.3263047236315[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]105.671428571429[/C][C]1.03600040830645[/C][C]101.999408228197[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]105.794444444444[/C][C]0.995424250569078[/C][C]106.280758564966[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]105.830769230769[/C][C]0.976528999744462[/C][C]108.374425396955[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.842[/C][C]0.963768496209393[/C][C]109.820979225082[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.854166666667[/C][C]0.949920481616645[/C][C]111.434766083279[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.869565217391[/C][C]0.937443690110347[/C][C]112.934319505558[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.877272727273[/C][C]0.925061358095035[/C][C]114.454324354553[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.885714285714[/C][C]0.910294533314235[/C][C]116.320279217982[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.91[/C][C]0.895034736469585[/C][C]118.330602919118[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.921052631579[/C][C]0.880959953386044[/C][C]120.233674895734[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.941666666667[/C][C]0.865882199913466[/C][C]122.351131224610[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.958823529412[/C][C]0.84881292433491[/C][C]124.831774460122[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.975[/C][C]0.835647324900226[/C][C]126.817853467853[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.966666666667[/C][C]0.824806955238595[/C][C]128.474506663215[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.953571428571[/C][C]0.813794465667295[/C][C]130.196967291602[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.926923076923[/C][C]0.79991456644411[/C][C]132.422795534033[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.891666666667[/C][C]0.778886158140582[/C][C]135.952687770777[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]105.836363636364[/C][C]0.753162034346078[/C][C]140.522701370967[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]105.815[/C][C]0.733996809113959[/C][C]144.162752053015[/C][/ROW]
[ROW][C]Median[/C][C]105.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.966666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.975[/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=48137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48137&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 Mean105.4183333333331.1618548672618490.7327897001231
Geometric Mean105.028441543895
Harmonic Mean104.625704721886
Quadratic Mean105.795413416651
Winsorized Mean ( 1 / 20 )105.4333333333331.1235704455615493.8377595724669
Winsorized Mean ( 2 / 20 )105.451.0945357347187396.3422176682958
Winsorized Mean ( 3 / 20 )105.71.0300320877016102.618162348571
Winsorized Mean ( 4 / 20 )105.7933333333331.00028489350447105.763202084047
Winsorized Mean ( 5 / 20 )105.7933333333330.990836166503436106.771772074760
Winsorized Mean ( 6 / 20 )105.7833333333330.97058770322016108.988948636348
Winsorized Mean ( 7 / 20 )105.830.953646880601701110.973990638156
Winsorized Mean ( 8 / 20 )105.830.94421611286644112.082391475742
Winsorized Mean ( 9 / 20 )105.740.92369376391287114.475169294284
Winsorized Mean ( 10 / 20 )105.840.894819364405607118.280855567208
Winsorized Mean ( 11 / 20 )105.7850.87355312173741121.097386487045
Winsorized Mean ( 12 / 20 )105.8250.853608574740236123.973684346135
Winsorized Mean ( 13 / 20 )105.8466666666670.807998387125239130.998611325521
Winsorized Mean ( 14 / 20 )106.0333333333330.771020552924509137.523355157194
Winsorized Mean ( 15 / 20 )106.0583333333330.743948435681479142.561403783558
Winsorized Mean ( 16 / 20 )106.1383333333330.72378123418124146.644218336774
Winsorized Mean ( 17 / 20 )106.1666666666670.710993840377407149.321499902603
Winsorized Mean ( 18 / 20 )106.2566666666670.679856941858798156.292684717097
Winsorized Mean ( 19 / 20 )105.9716666666670.617622979664306171.579863696563
Winsorized Mean ( 20 / 20 )105.7383333333330.583410446880402181.241755094950
Trimmed Mean ( 1 / 20 )105.5482758620691.0844784065498597.3263047236315
Trimmed Mean ( 2 / 20 )105.6714285714291.03600040830645101.999408228197
Trimmed Mean ( 3 / 20 )105.7944444444440.995424250569078106.280758564966
Trimmed Mean ( 4 / 20 )105.8307692307690.976528999744462108.374425396955
Trimmed Mean ( 5 / 20 )105.8420.963768496209393109.820979225082
Trimmed Mean ( 6 / 20 )105.8541666666670.949920481616645111.434766083279
Trimmed Mean ( 7 / 20 )105.8695652173910.937443690110347112.934319505558
Trimmed Mean ( 8 / 20 )105.8772727272730.925061358095035114.454324354553
Trimmed Mean ( 9 / 20 )105.8857142857140.910294533314235116.320279217982
Trimmed Mean ( 10 / 20 )105.910.895034736469585118.330602919118
Trimmed Mean ( 11 / 20 )105.9210526315790.880959953386044120.233674895734
Trimmed Mean ( 12 / 20 )105.9416666666670.865882199913466122.351131224610
Trimmed Mean ( 13 / 20 )105.9588235294120.84881292433491124.831774460122
Trimmed Mean ( 14 / 20 )105.9750.835647324900226126.817853467853
Trimmed Mean ( 15 / 20 )105.9666666666670.824806955238595128.474506663215
Trimmed Mean ( 16 / 20 )105.9535714285710.813794465667295130.196967291602
Trimmed Mean ( 17 / 20 )105.9269230769230.79991456644411132.422795534033
Trimmed Mean ( 18 / 20 )105.8916666666670.778886158140582135.952687770777
Trimmed Mean ( 19 / 20 )105.8363636363640.753162034346078140.522701370967
Trimmed Mean ( 20 / 20 )105.8150.733996809113959144.162752053015
Median105.6
Midrange101.65
Midmean - Weighted Average at Xnp105.741935483871
Midmean - Weighted Average at X(n+1)p105.966666666667
Midmean - Empirical Distribution Function105.741935483871
Midmean - Empirical Distribution Function - Averaging105.966666666667
Midmean - Empirical Distribution Function - Interpolation105.966666666667
Midmean - Closest Observation105.741935483871
Midmean - True Basic - Statistics Graphics Toolkit105.966666666667
Midmean - MS Excel (old versions)105.975
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')