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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 computationThu, 22 Dec 2011 13:34:04 -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/Dec/22/t1324578889ncfnjh1nmjwnxmz.htm/, Retrieved Wed, 15 May 2024 19:51:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159831, Retrieved Wed, 15 May 2024 19:51:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2011-12-22 18:34:04] [8aedcf735e397266388b06f47fe45218] [Current]
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Dataseries X:
2.36
5.73
6.6
10.05
5.13
1.88
2.52
2
4.69
1.91
6.75
3.92
3.46
2.64
3.63
3.44
9.49
4.9
7.45
20.23
3.91
1.7
16.29
5.52
1.44
3.34
6
5.92
7.28
1.25
4.01
7.59
13.42
3.24
3.37
14.06
5.1
6.44
7.76
4.4
5.48
7.51
6.18
8.22
4.37
2.93
9.95
4.46
14.32
9.01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159831&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159831&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159831&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.0650.56840214637173910.6702623111374
Geometric Mean4.99290658739867
Harmonic Mean4.09573723534664
Quadratic Mean7.25363315863161
Winsorized Mean ( 1 / 16 )5.990.53198780099562711.2596566853405
Winsorized Mean ( 2 / 16 )5.92160.50107805086755111.8177197938475
Winsorized Mean ( 3 / 16 )5.91680.49395616098960811.9783909328028
Winsorized Mean ( 4 / 16 )5.8680.47665629597205112.3107573519685
Winsorized Mean ( 5 / 16 )5.540.37797753955514814.6569555601642
Winsorized Mean ( 6 / 16 )5.57120.36706687818601215.1776156637505
Winsorized Mean ( 7 / 16 )5.52920.34775546651317515.8996781716745
Winsorized Mean ( 8 / 16 )5.47160.32694246638595416.7356662488158
Winsorized Mean ( 9 / 16 )5.38160.28767588905373618.7071638770351
Winsorized Mean ( 10 / 16 )5.35160.25909928126303320.6546308191691
Winsorized Mean ( 11 / 16 )5.33620.24845447002110721.4775769562394
Winsorized Mean ( 12 / 16 )5.32420.24374076057842121.8436997872869
Winsorized Mean ( 13 / 16 )5.32680.23793078053612722.388023895005
Winsorized Mean ( 14 / 16 )5.28480.22844286384305423.1340122037289
Winsorized Mean ( 15 / 16 )5.17680.19260797448894726.8773918304047
Winsorized Mean ( 16 / 16 )5.21840.17024217084698530.6528046137896
Trimmed Mean ( 1 / 16 )5.870208333333330.50083958672386111.7207355187957
Trimmed Mean ( 2 / 16 )5.740.45942465594779912.4938875737052
Trimmed Mean ( 3 / 16 )5.636818181818180.42795456931328313.1715340505963
Trimmed Mean ( 4 / 16 )5.525714285714290.38926389671304114.1952909899264
Trimmed Mean ( 5 / 16 )5.418750.34444086752002715.7320182097292
Trimmed Mean ( 6 / 16 )5.386842105263160.32869263536598216.3886912137997
Trimmed Mean ( 7 / 16 )5.344166666666670.31098011343553917.1849145195402
Trimmed Mean ( 8 / 16 )5.305294117647060.29347880709321318.0772648294227
Trimmed Mean ( 9 / 16 )5.27281250.27638078365835219.0780720359994
Trimmed Mean ( 10 / 16 )5.252666666666670.26606624934806319.7419502831989
Trimmed Mean ( 11 / 16 )5.2350.26034699067889320.1077799530118
Trimmed Mean ( 12 / 16 )5.217307692307690.25448866239960620.5011399844418
Trimmed Mean ( 13 / 16 )5.198750.24605460135471221.128440481816
Trimmed Mean ( 14 / 16 )5.176363636363640.23376880710464322.143089578442
Trimmed Mean ( 15 / 16 )5.1570.21684714480602823.781728851505
Trimmed Mean ( 16 / 16 )5.153333333333330.20610771978958725.0031068151854
Median5.115
Midrange10.74
Midmean - Weighted Average at Xnp5.1256
Midmean - Weighted Average at X(n+1)p5.21730769230769
Midmean - Empirical Distribution Function5.21730769230769
Midmean - Empirical Distribution Function - Averaging5.21730769230769
Midmean - Empirical Distribution Function - Interpolation5.19875
Midmean - Closest Observation5.21730769230769
Midmean - True Basic - Statistics Graphics Toolkit5.21730769230769
Midmean - MS Excel (old versions)5.21730769230769
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.065 & 0.568402146371739 & 10.6702623111374 \tabularnewline
Geometric Mean & 4.99290658739867 &  &  \tabularnewline
Harmonic Mean & 4.09573723534664 &  &  \tabularnewline
Quadratic Mean & 7.25363315863161 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 5.99 & 0.531987800995627 & 11.2596566853405 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 5.9216 & 0.501078050867551 & 11.8177197938475 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 5.9168 & 0.493956160989608 & 11.9783909328028 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 5.868 & 0.476656295972051 & 12.3107573519685 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 5.54 & 0.377977539555148 & 14.6569555601642 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 5.5712 & 0.367066878186012 & 15.1776156637505 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 5.5292 & 0.347755466513175 & 15.8996781716745 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 5.4716 & 0.326942466385954 & 16.7356662488158 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 5.3816 & 0.287675889053736 & 18.7071638770351 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 5.3516 & 0.259099281263033 & 20.6546308191691 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 5.3362 & 0.248454470021107 & 21.4775769562394 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 5.3242 & 0.243740760578421 & 21.8436997872869 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 5.3268 & 0.237930780536127 & 22.388023895005 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 5.2848 & 0.228442863843054 & 23.1340122037289 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 5.1768 & 0.192607974488947 & 26.8773918304047 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 5.2184 & 0.170242170846985 & 30.6528046137896 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 5.87020833333333 & 0.500839586723861 & 11.7207355187957 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 5.74 & 0.459424655947799 & 12.4938875737052 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 5.63681818181818 & 0.427954569313283 & 13.1715340505963 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 5.52571428571429 & 0.389263896713041 & 14.1952909899264 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 5.41875 & 0.344440867520027 & 15.7320182097292 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 5.38684210526316 & 0.328692635365982 & 16.3886912137997 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 5.34416666666667 & 0.310980113435539 & 17.1849145195402 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 5.30529411764706 & 0.293478807093213 & 18.0772648294227 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 5.2728125 & 0.276380783658352 & 19.0780720359994 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 5.25266666666667 & 0.266066249348063 & 19.7419502831989 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 5.235 & 0.260346990678893 & 20.1077799530118 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 5.21730769230769 & 0.254488662399606 & 20.5011399844418 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 5.19875 & 0.246054601354712 & 21.128440481816 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 5.17636363636364 & 0.233768807104643 & 22.143089578442 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 5.157 & 0.216847144806028 & 23.781728851505 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 5.15333333333333 & 0.206107719789587 & 25.0031068151854 \tabularnewline
Median & 5.115 &  &  \tabularnewline
Midrange & 10.74 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.1256 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.21730769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.21730769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.21730769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.19875 &  &  \tabularnewline
Midmean - Closest Observation & 5.21730769230769 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.21730769230769 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.21730769230769 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159831&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]6.065[/C][C]0.568402146371739[/C][C]10.6702623111374[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.99290658739867[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.09573723534664[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.25363315863161[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]5.99[/C][C]0.531987800995627[/C][C]11.2596566853405[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]5.9216[/C][C]0.501078050867551[/C][C]11.8177197938475[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]5.9168[/C][C]0.493956160989608[/C][C]11.9783909328028[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]5.868[/C][C]0.476656295972051[/C][C]12.3107573519685[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]5.54[/C][C]0.377977539555148[/C][C]14.6569555601642[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]5.5712[/C][C]0.367066878186012[/C][C]15.1776156637505[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]5.5292[/C][C]0.347755466513175[/C][C]15.8996781716745[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]5.4716[/C][C]0.326942466385954[/C][C]16.7356662488158[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]5.3816[/C][C]0.287675889053736[/C][C]18.7071638770351[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]5.3516[/C][C]0.259099281263033[/C][C]20.6546308191691[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]5.3362[/C][C]0.248454470021107[/C][C]21.4775769562394[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]5.3242[/C][C]0.243740760578421[/C][C]21.8436997872869[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]5.3268[/C][C]0.237930780536127[/C][C]22.388023895005[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]5.2848[/C][C]0.228442863843054[/C][C]23.1340122037289[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]5.1768[/C][C]0.192607974488947[/C][C]26.8773918304047[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]5.2184[/C][C]0.170242170846985[/C][C]30.6528046137896[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]5.87020833333333[/C][C]0.500839586723861[/C][C]11.7207355187957[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]5.74[/C][C]0.459424655947799[/C][C]12.4938875737052[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]5.63681818181818[/C][C]0.427954569313283[/C][C]13.1715340505963[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]5.52571428571429[/C][C]0.389263896713041[/C][C]14.1952909899264[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]5.41875[/C][C]0.344440867520027[/C][C]15.7320182097292[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]5.38684210526316[/C][C]0.328692635365982[/C][C]16.3886912137997[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]5.34416666666667[/C][C]0.310980113435539[/C][C]17.1849145195402[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]5.30529411764706[/C][C]0.293478807093213[/C][C]18.0772648294227[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]5.2728125[/C][C]0.276380783658352[/C][C]19.0780720359994[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]5.25266666666667[/C][C]0.266066249348063[/C][C]19.7419502831989[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]5.235[/C][C]0.260346990678893[/C][C]20.1077799530118[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]5.21730769230769[/C][C]0.254488662399606[/C][C]20.5011399844418[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]5.19875[/C][C]0.246054601354712[/C][C]21.128440481816[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]5.17636363636364[/C][C]0.233768807104643[/C][C]22.143089578442[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]5.157[/C][C]0.216847144806028[/C][C]23.781728851505[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]5.15333333333333[/C][C]0.206107719789587[/C][C]25.0031068151854[/C][/ROW]
[ROW][C]Median[/C][C]5.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.74[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.1256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.21730769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.21730769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.21730769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.19875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.21730769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.21730769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.21730769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159831&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159831&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 Mean6.0650.56840214637173910.6702623111374
Geometric Mean4.99290658739867
Harmonic Mean4.09573723534664
Quadratic Mean7.25363315863161
Winsorized Mean ( 1 / 16 )5.990.53198780099562711.2596566853405
Winsorized Mean ( 2 / 16 )5.92160.50107805086755111.8177197938475
Winsorized Mean ( 3 / 16 )5.91680.49395616098960811.9783909328028
Winsorized Mean ( 4 / 16 )5.8680.47665629597205112.3107573519685
Winsorized Mean ( 5 / 16 )5.540.37797753955514814.6569555601642
Winsorized Mean ( 6 / 16 )5.57120.36706687818601215.1776156637505
Winsorized Mean ( 7 / 16 )5.52920.34775546651317515.8996781716745
Winsorized Mean ( 8 / 16 )5.47160.32694246638595416.7356662488158
Winsorized Mean ( 9 / 16 )5.38160.28767588905373618.7071638770351
Winsorized Mean ( 10 / 16 )5.35160.25909928126303320.6546308191691
Winsorized Mean ( 11 / 16 )5.33620.24845447002110721.4775769562394
Winsorized Mean ( 12 / 16 )5.32420.24374076057842121.8436997872869
Winsorized Mean ( 13 / 16 )5.32680.23793078053612722.388023895005
Winsorized Mean ( 14 / 16 )5.28480.22844286384305423.1340122037289
Winsorized Mean ( 15 / 16 )5.17680.19260797448894726.8773918304047
Winsorized Mean ( 16 / 16 )5.21840.17024217084698530.6528046137896
Trimmed Mean ( 1 / 16 )5.870208333333330.50083958672386111.7207355187957
Trimmed Mean ( 2 / 16 )5.740.45942465594779912.4938875737052
Trimmed Mean ( 3 / 16 )5.636818181818180.42795456931328313.1715340505963
Trimmed Mean ( 4 / 16 )5.525714285714290.38926389671304114.1952909899264
Trimmed Mean ( 5 / 16 )5.418750.34444086752002715.7320182097292
Trimmed Mean ( 6 / 16 )5.386842105263160.32869263536598216.3886912137997
Trimmed Mean ( 7 / 16 )5.344166666666670.31098011343553917.1849145195402
Trimmed Mean ( 8 / 16 )5.305294117647060.29347880709321318.0772648294227
Trimmed Mean ( 9 / 16 )5.27281250.27638078365835219.0780720359994
Trimmed Mean ( 10 / 16 )5.252666666666670.26606624934806319.7419502831989
Trimmed Mean ( 11 / 16 )5.2350.26034699067889320.1077799530118
Trimmed Mean ( 12 / 16 )5.217307692307690.25448866239960620.5011399844418
Trimmed Mean ( 13 / 16 )5.198750.24605460135471221.128440481816
Trimmed Mean ( 14 / 16 )5.176363636363640.23376880710464322.143089578442
Trimmed Mean ( 15 / 16 )5.1570.21684714480602823.781728851505
Trimmed Mean ( 16 / 16 )5.153333333333330.20610771978958725.0031068151854
Median5.115
Midrange10.74
Midmean - Weighted Average at Xnp5.1256
Midmean - Weighted Average at X(n+1)p5.21730769230769
Midmean - Empirical Distribution Function5.21730769230769
Midmean - Empirical Distribution Function - Averaging5.21730769230769
Midmean - Empirical Distribution Function - Interpolation5.19875
Midmean - Closest Observation5.21730769230769
Midmean - True Basic - Statistics Graphics Toolkit5.21730769230769
Midmean - MS Excel (old versions)5.21730769230769
Number of observations50



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')