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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 computationWed, 21 Oct 2009 12:55:50 -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/21/t1256151380m38hz6s7y41119w.htm/, Retrieved Thu, 02 May 2024 08:34:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49589, Retrieved Thu, 02 May 2024 08:34:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
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      [Histogram] [Workshop 3 part 2] [2009-10-21 14:40:32] [786e067c4f7cec17385c4742b96b6dfa]
- RMPD          [Central Tendency] [Workshop3] [2009-10-21 18:55:50] [5cd0e65b1f56b3935a0672588b930e12] [Current]
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Post a new message
Dataseries X:
3.04
3.12
3.21
3.34
3.45
3.74
4.02
4.24
4.87
5.62
6.02
5.98
5.89
5.76
5.58
5.39
5.19
5.16
5.2
5.25
5.26
5.21
5.18
5.13
5.03
5.01
4.87
4.86
4.82
4.69
4.65
4.61
4.47
4.37
4.29
4.2
4.19
4.09
3.88
3.87
3.74
3.61
3.43
3.29
3.18
3.07
3.02
2.97
2.98
3.01
3.06
3.12
3.16
3.19
3.21
3.27
3.36
3.45
3.52
3.58




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49589&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49589&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.19950.12208486096497034.3982043867417
Geometric Mean4.09622490819048
Harmonic Mean3.99662891557317
Quadratic Mean4.30292671716976
Winsorized Mean ( 1 / 20 )4.1990.1218897111938334.4491750687859
Winsorized Mean ( 2 / 20 )4.1970.12099453692668034.6875165326125
Winsorized Mean ( 3 / 20 )4.1910.11941659027915035.0956260784458
Winsorized Mean ( 4 / 20 )4.1830.11718576203984335.6954627182249
Winsorized Mean ( 5 / 20 )4.181333333333330.11622534770907035.9760879683481
Winsorized Mean ( 6 / 20 )4.163333333333330.11236257561682537.0526690980366
Winsorized Mean ( 7 / 20 )4.1540.10869856729080438.2157750882466
Winsorized Mean ( 8 / 20 )4.152666666666670.10846928453429738.2842634621936
Winsorized Mean ( 9 / 20 )4.152666666666670.10649178814171338.9951820617429
Winsorized Mean ( 10 / 20 )4.154333333333330.10568805144601639.3075023760402
Winsorized Mean ( 11 / 20 )4.154333333333330.10509542789397939.5291538041433
Winsorized Mean ( 12 / 20 )4.156333333333330.10414271136978439.9099781315974
Winsorized Mean ( 13 / 20 )4.1520.10342381677208740.1454919145914
Winsorized Mean ( 14 / 20 )4.1590.10013598099217741.5335223042848
Winsorized Mean ( 15 / 20 )4.1390.095346439381997243.4101160654512
Winsorized Mean ( 16 / 20 )4.1470.092510283441209344.8274488601631
Winsorized Mean ( 17 / 20 )4.1130.085552144868059448.0759425300578
Winsorized Mean ( 18 / 20 )4.1340.082465606595637450.1299895879102
Winsorized Mean ( 19 / 20 )4.137166666666670.081073688900993451.0297079453106
Winsorized Mean ( 20 / 20 )4.123833333333330.079071265741186752.1533744866475
Trimmed Mean ( 1 / 20 )4.189310344827590.12040812380240134.7925888431129
Trimmed Mean ( 2 / 20 )4.178928571428570.11850767923263835.2629348451342
Trimmed Mean ( 3 / 20 )4.168888888888890.11666836376922835.7328135426244
Trimmed Mean ( 4 / 20 )4.160384615384620.11504604676477936.1627777083975
Trimmed Mean ( 5 / 20 )4.15360.11377161512505336.5082274294386
Trimmed Mean ( 6 / 20 )4.146666666666670.11235681720982736.9062311450381
Trimmed Mean ( 7 / 20 )4.143043478260870.11158535632165937.1289174030866
Trimmed Mean ( 8 / 20 )4.140909090909090.11140028304998737.1714413782146
Trimmed Mean ( 9 / 20 )4.138809523809520.11097509026717937.2949417193091
Trimmed Mean ( 10 / 20 )4.13650.11065512953454837.3819091568504
Trimmed Mean ( 11 / 20 )4.133684210526320.11013790725023437.5318935481003
Trimmed Mean ( 12 / 20 )4.130555555555560.10928551832238037.7960009611785
Trimmed Mean ( 13 / 20 )4.126764705882350.10805088966436738.1927878493284
Trimmed Mean ( 14 / 20 )4.1231250.10621269506392338.8195120886306
Trimmed Mean ( 15 / 20 )4.1180.10421286791505439.5152737122317
Trimmed Mean ( 16 / 20 )4.1150.10242367141246440.176259484282
Trimmed Mean ( 17 / 20 )4.110384615384620.10022049655132541.0134129926169
Trimmed Mean ( 18 / 20 )4.110.098802613941834241.5980897268526
Trimmed Mean ( 19 / 20 )4.106363636363640.097015073257701442.3270683459249
Trimmed Mean ( 20 / 20 )4.10150.093879191685798843.6891277646188
Median4.14
Midrange4.495
Midmean - Weighted Average at Xnp4.09064516129032
Midmean - Weighted Average at X(n+1)p4.118
Midmean - Empirical Distribution Function4.09064516129032
Midmean - Empirical Distribution Function - Averaging4.118
Midmean - Empirical Distribution Function - Interpolation4.118
Midmean - Closest Observation4.09064516129032
Midmean - True Basic - Statistics Graphics Toolkit4.118
Midmean - MS Excel (old versions)4.123125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.1995 & 0.122084860964970 & 34.3982043867417 \tabularnewline
Geometric Mean & 4.09622490819048 &  &  \tabularnewline
Harmonic Mean & 3.99662891557317 &  &  \tabularnewline
Quadratic Mean & 4.30292671716976 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4.199 & 0.12188971119383 & 34.4491750687859 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4.197 & 0.120994536926680 & 34.6875165326125 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4.191 & 0.119416590279150 & 35.0956260784458 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4.183 & 0.117185762039843 & 35.6954627182249 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4.18133333333333 & 0.116225347709070 & 35.9760879683481 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4.16333333333333 & 0.112362575616825 & 37.0526690980366 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4.154 & 0.108698567290804 & 38.2157750882466 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4.15266666666667 & 0.108469284534297 & 38.2842634621936 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4.15266666666667 & 0.106491788141713 & 38.9951820617429 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4.15433333333333 & 0.105688051446016 & 39.3075023760402 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4.15433333333333 & 0.105095427893979 & 39.5291538041433 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4.15633333333333 & 0.104142711369784 & 39.9099781315974 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4.152 & 0.103423816772087 & 40.1454919145914 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4.159 & 0.100135980992177 & 41.5335223042848 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4.139 & 0.0953464393819972 & 43.4101160654512 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4.147 & 0.0925102834412093 & 44.8274488601631 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4.113 & 0.0855521448680594 & 48.0759425300578 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4.134 & 0.0824656065956374 & 50.1299895879102 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4.13716666666667 & 0.0810736889009934 & 51.0297079453106 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4.12383333333333 & 0.0790712657411867 & 52.1533744866475 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4.18931034482759 & 0.120408123802401 & 34.7925888431129 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4.17892857142857 & 0.118507679232638 & 35.2629348451342 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4.16888888888889 & 0.116668363769228 & 35.7328135426244 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4.16038461538462 & 0.115046046764779 & 36.1627777083975 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4.1536 & 0.113771615125053 & 36.5082274294386 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4.14666666666667 & 0.112356817209827 & 36.9062311450381 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4.14304347826087 & 0.111585356321659 & 37.1289174030866 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4.14090909090909 & 0.111400283049987 & 37.1714413782146 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4.13880952380952 & 0.110975090267179 & 37.2949417193091 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4.1365 & 0.110655129534548 & 37.3819091568504 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4.13368421052632 & 0.110137907250234 & 37.5318935481003 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4.13055555555556 & 0.109285518322380 & 37.7960009611785 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4.12676470588235 & 0.108050889664367 & 38.1927878493284 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4.123125 & 0.106212695063923 & 38.8195120886306 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4.118 & 0.104212867915054 & 39.5152737122317 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4.115 & 0.102423671412464 & 40.176259484282 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4.11038461538462 & 0.100220496551325 & 41.0134129926169 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4.11 & 0.0988026139418342 & 41.5980897268526 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4.10636363636364 & 0.0970150732577014 & 42.3270683459249 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4.1015 & 0.0938791916857988 & 43.6891277646188 \tabularnewline
Median & 4.14 &  &  \tabularnewline
Midrange & 4.495 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.09064516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.118 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.09064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.118 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.118 &  &  \tabularnewline
Midmean - Closest Observation & 4.09064516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.118 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.123125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49589&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]4.1995[/C][C]0.122084860964970[/C][C]34.3982043867417[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.09622490819048[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.99662891557317[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.30292671716976[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4.199[/C][C]0.12188971119383[/C][C]34.4491750687859[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4.197[/C][C]0.120994536926680[/C][C]34.6875165326125[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4.191[/C][C]0.119416590279150[/C][C]35.0956260784458[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4.183[/C][C]0.117185762039843[/C][C]35.6954627182249[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4.18133333333333[/C][C]0.116225347709070[/C][C]35.9760879683481[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4.16333333333333[/C][C]0.112362575616825[/C][C]37.0526690980366[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4.154[/C][C]0.108698567290804[/C][C]38.2157750882466[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4.15266666666667[/C][C]0.108469284534297[/C][C]38.2842634621936[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4.15266666666667[/C][C]0.106491788141713[/C][C]38.9951820617429[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4.15433333333333[/C][C]0.105688051446016[/C][C]39.3075023760402[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4.15433333333333[/C][C]0.105095427893979[/C][C]39.5291538041433[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4.15633333333333[/C][C]0.104142711369784[/C][C]39.9099781315974[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4.152[/C][C]0.103423816772087[/C][C]40.1454919145914[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4.159[/C][C]0.100135980992177[/C][C]41.5335223042848[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4.139[/C][C]0.0953464393819972[/C][C]43.4101160654512[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4.147[/C][C]0.0925102834412093[/C][C]44.8274488601631[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4.113[/C][C]0.0855521448680594[/C][C]48.0759425300578[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4.134[/C][C]0.0824656065956374[/C][C]50.1299895879102[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4.13716666666667[/C][C]0.0810736889009934[/C][C]51.0297079453106[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4.12383333333333[/C][C]0.0790712657411867[/C][C]52.1533744866475[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4.18931034482759[/C][C]0.120408123802401[/C][C]34.7925888431129[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4.17892857142857[/C][C]0.118507679232638[/C][C]35.2629348451342[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4.16888888888889[/C][C]0.116668363769228[/C][C]35.7328135426244[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4.16038461538462[/C][C]0.115046046764779[/C][C]36.1627777083975[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4.1536[/C][C]0.113771615125053[/C][C]36.5082274294386[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4.14666666666667[/C][C]0.112356817209827[/C][C]36.9062311450381[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4.14304347826087[/C][C]0.111585356321659[/C][C]37.1289174030866[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4.14090909090909[/C][C]0.111400283049987[/C][C]37.1714413782146[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4.13880952380952[/C][C]0.110975090267179[/C][C]37.2949417193091[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4.1365[/C][C]0.110655129534548[/C][C]37.3819091568504[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4.13368421052632[/C][C]0.110137907250234[/C][C]37.5318935481003[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4.13055555555556[/C][C]0.109285518322380[/C][C]37.7960009611785[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4.12676470588235[/C][C]0.108050889664367[/C][C]38.1927878493284[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4.123125[/C][C]0.106212695063923[/C][C]38.8195120886306[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4.118[/C][C]0.104212867915054[/C][C]39.5152737122317[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4.115[/C][C]0.102423671412464[/C][C]40.176259484282[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4.11038461538462[/C][C]0.100220496551325[/C][C]41.0134129926169[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4.11[/C][C]0.0988026139418342[/C][C]41.5980897268526[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4.10636363636364[/C][C]0.0970150732577014[/C][C]42.3270683459249[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4.1015[/C][C]0.0938791916857988[/C][C]43.6891277646188[/C][/ROW]
[ROW][C]Median[/C][C]4.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.495[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.09064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.09064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.09064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.123125[/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=49589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49589&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 Mean4.19950.12208486096497034.3982043867417
Geometric Mean4.09622490819048
Harmonic Mean3.99662891557317
Quadratic Mean4.30292671716976
Winsorized Mean ( 1 / 20 )4.1990.1218897111938334.4491750687859
Winsorized Mean ( 2 / 20 )4.1970.12099453692668034.6875165326125
Winsorized Mean ( 3 / 20 )4.1910.11941659027915035.0956260784458
Winsorized Mean ( 4 / 20 )4.1830.11718576203984335.6954627182249
Winsorized Mean ( 5 / 20 )4.181333333333330.11622534770907035.9760879683481
Winsorized Mean ( 6 / 20 )4.163333333333330.11236257561682537.0526690980366
Winsorized Mean ( 7 / 20 )4.1540.10869856729080438.2157750882466
Winsorized Mean ( 8 / 20 )4.152666666666670.10846928453429738.2842634621936
Winsorized Mean ( 9 / 20 )4.152666666666670.10649178814171338.9951820617429
Winsorized Mean ( 10 / 20 )4.154333333333330.10568805144601639.3075023760402
Winsorized Mean ( 11 / 20 )4.154333333333330.10509542789397939.5291538041433
Winsorized Mean ( 12 / 20 )4.156333333333330.10414271136978439.9099781315974
Winsorized Mean ( 13 / 20 )4.1520.10342381677208740.1454919145914
Winsorized Mean ( 14 / 20 )4.1590.10013598099217741.5335223042848
Winsorized Mean ( 15 / 20 )4.1390.095346439381997243.4101160654512
Winsorized Mean ( 16 / 20 )4.1470.092510283441209344.8274488601631
Winsorized Mean ( 17 / 20 )4.1130.085552144868059448.0759425300578
Winsorized Mean ( 18 / 20 )4.1340.082465606595637450.1299895879102
Winsorized Mean ( 19 / 20 )4.137166666666670.081073688900993451.0297079453106
Winsorized Mean ( 20 / 20 )4.123833333333330.079071265741186752.1533744866475
Trimmed Mean ( 1 / 20 )4.189310344827590.12040812380240134.7925888431129
Trimmed Mean ( 2 / 20 )4.178928571428570.11850767923263835.2629348451342
Trimmed Mean ( 3 / 20 )4.168888888888890.11666836376922835.7328135426244
Trimmed Mean ( 4 / 20 )4.160384615384620.11504604676477936.1627777083975
Trimmed Mean ( 5 / 20 )4.15360.11377161512505336.5082274294386
Trimmed Mean ( 6 / 20 )4.146666666666670.11235681720982736.9062311450381
Trimmed Mean ( 7 / 20 )4.143043478260870.11158535632165937.1289174030866
Trimmed Mean ( 8 / 20 )4.140909090909090.11140028304998737.1714413782146
Trimmed Mean ( 9 / 20 )4.138809523809520.11097509026717937.2949417193091
Trimmed Mean ( 10 / 20 )4.13650.11065512953454837.3819091568504
Trimmed Mean ( 11 / 20 )4.133684210526320.11013790725023437.5318935481003
Trimmed Mean ( 12 / 20 )4.130555555555560.10928551832238037.7960009611785
Trimmed Mean ( 13 / 20 )4.126764705882350.10805088966436738.1927878493284
Trimmed Mean ( 14 / 20 )4.1231250.10621269506392338.8195120886306
Trimmed Mean ( 15 / 20 )4.1180.10421286791505439.5152737122317
Trimmed Mean ( 16 / 20 )4.1150.10242367141246440.176259484282
Trimmed Mean ( 17 / 20 )4.110384615384620.10022049655132541.0134129926169
Trimmed Mean ( 18 / 20 )4.110.098802613941834241.5980897268526
Trimmed Mean ( 19 / 20 )4.106363636363640.097015073257701442.3270683459249
Trimmed Mean ( 20 / 20 )4.10150.093879191685798843.6891277646188
Median4.14
Midrange4.495
Midmean - Weighted Average at Xnp4.09064516129032
Midmean - Weighted Average at X(n+1)p4.118
Midmean - Empirical Distribution Function4.09064516129032
Midmean - Empirical Distribution Function - Averaging4.118
Midmean - Empirical Distribution Function - Interpolation4.118
Midmean - Closest Observation4.09064516129032
Midmean - True Basic - Statistics Graphics Toolkit4.118
Midmean - MS Excel (old versions)4.123125
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')