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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 computationTue, 20 Oct 2009 09:40:45 -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/20/t1256053374jvuiw724tgsfay9.htm/, Retrieved Fri, 03 May 2024 03:12:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48744, Retrieved Fri, 03 May 2024 03:12:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscentral tendency
Estimated Impact111
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] [ws3 part2 ex1] [2009-10-20 15:40:45] [95523ebdb89b97dbf680ec91e0b4bca2] [Current]
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Dataseries X:
-0.62
-0.56
-0.58
-0.62
-0.59
-0.61
-0.61
-0.59
-0.60
-0.61
-0.60
-0.61
-0.58
-0.60
-0.58
-0.39
-0.34
-0.32
-0.15
-0.04
-0.09
0.03
0.14
0.30
0.37
0.61
0.66
0.83
0.89
0.90
1.02
1.15
1.12
1.29
1.39
1.38
1.36
1.27
1.35
1.21
1.35
1.36
1.42
1.32
1.34
1.34
1.52
1.63
1.60
1.15
0.48
-0.18
-0.86
-1.41
-1.61
-1.83
-1.89
-1.97
-2.31
-2.32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48744&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48744&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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.11850.1417246126091340.83612858640732
Geometric MeanNaN
Harmonic Mean-3.61508591693716
Quadratic Mean1.09503805108925
Winsorized Mean ( 1 / 20 )0.1181666666666670.1415865492962510.834589636190787
Winsorized Mean ( 2 / 20 )0.1268333333333330.1380130370626150.918995306767944
Winsorized Mean ( 3 / 20 )0.1258333333333330.1361654634167390.924120773181788
Winsorized Mean ( 4 / 20 )0.1278333333333330.1348516849368970.94795503217592
Winsorized Mean ( 5 / 20 )0.1453333333333330.1303683323187161.11479015454483
Winsorized Mean ( 6 / 20 )0.1633333333333330.1256388570886661.30002243826578
Winsorized Mean ( 7 / 20 )0.22750.1135397650543082.00370328308485
Winsorized Mean ( 8 / 20 )0.2581666666666670.1085121492499342.37914987815822
Winsorized Mean ( 9 / 20 )0.2581666666666670.1085121492499342.37914987815822
Winsorized Mean ( 10 / 20 )0.2581666666666670.1080007040327202.39041651606691
Winsorized Mean ( 11 / 20 )0.2581666666666670.1080007040327202.39041651606691
Winsorized Mean ( 12 / 20 )0.2541666666666670.1073244965130942.36820739835158
Winsorized Mean ( 13 / 20 )0.2476666666666670.1062369610920402.33126648316020
Winsorized Mean ( 14 / 20 )0.2453333333333330.1051449004667462.33328798871158
Winsorized Mean ( 15 / 20 )0.2303333333333330.1026931050410662.24292890200588
Winsorized Mean ( 16 / 20 )0.2143333333333330.1001322195579272.14050316950519
Winsorized Mean ( 17 / 20 )0.2171666666666670.0997426325576442.17727025142594
Winsorized Mean ( 18 / 20 )0.2081666666666670.09832193508582262.11719456584091
Winsorized Mean ( 19 / 20 )0.1796666666666670.0929686073821091.93255198422217
Winsorized Mean ( 20 / 20 )0.1396666666666670.08693655283283171.60653559539252
Trimmed Mean ( 1 / 20 )0.1344827586206900.1378890135628310.975297125897642
Trimmed Mean ( 2 / 20 )0.1519642857142860.1332874590126761.14012441110333
Trimmed Mean ( 3 / 20 )0.1659259259259260.1299533643487421.27681131425462
Trimmed Mean ( 4 / 20 )0.1813461538461540.1266239991782161.43216258389469
Trimmed Mean ( 5 / 20 )0.19740.1228936191698051.60626728493729
Trimmed Mean ( 6 / 20 )0.2104166666666670.1197081847562481.7577466995688
Trimmed Mean ( 7 / 20 )0.2206521739130430.1170830673260841.88457800903450
Trimmed Mean ( 8 / 20 )0.2193181818181820.1170245984004641.87412035431785
Trimmed Mean ( 9 / 20 )0.2123809523809520.1178730441296151.80177710645545
Trimmed Mean ( 10 / 20 )0.204750.1185818918052101.72665486174175
Trimmed Mean ( 11 / 20 )0.1963157894736840.1192105498667001.64679879166067
Trimmed Mean ( 12 / 20 )0.1869444444444440.1195877969596311.56324013985768
Trimmed Mean ( 13 / 20 )0.1770588235294120.1197788584839101.47821431737218
Trimmed Mean ( 14 / 20 )0.1668750.1197943781834311.39301194705881
Trimmed Mean ( 15 / 20 )0.1556666666666670.1195159618381561.30247595611927
Trimmed Mean ( 16 / 20 )0.1450.1191976039317431.21646740552798
Trimmed Mean ( 17 / 20 )0.1350.1187994431481381.13636896287182
Trimmed Mean ( 18 / 20 )0.1229166666666670.117447921185611.04656315263694
Trimmed Mean ( 19 / 20 )0.110.1149835297823650.95665875111159
Trimmed Mean ( 20 / 20 )0.0990.1124087934376370.880714016870258
Median-0.005
Midrange-0.345
Midmean - Weighted Average at Xnp0.131290322580645
Midmean - Weighted Average at X(n+1)p0.131290322580645
Midmean - Empirical Distribution Function0.131290322580645
Midmean - Empirical Distribution Function - Averaging0.131290322580645
Midmean - Empirical Distribution Function - Interpolation0.131290322580645
Midmean - Closest Observation0.131290322580645
Midmean - True Basic - Statistics Graphics Toolkit0.131290322580645
Midmean - MS Excel (old versions)0.166875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.1185 & 0.141724612609134 & 0.83612858640732 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -3.61508591693716 &  &  \tabularnewline
Quadratic Mean & 1.09503805108925 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.118166666666667 & 0.141586549296251 & 0.834589636190787 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.126833333333333 & 0.138013037062615 & 0.918995306767944 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.125833333333333 & 0.136165463416739 & 0.924120773181788 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.127833333333333 & 0.134851684936897 & 0.94795503217592 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.145333333333333 & 0.130368332318716 & 1.11479015454483 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.163333333333333 & 0.125638857088666 & 1.30002243826578 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.2275 & 0.113539765054308 & 2.00370328308485 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.258166666666667 & 0.108512149249934 & 2.37914987815822 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.258166666666667 & 0.108512149249934 & 2.37914987815822 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.258166666666667 & 0.108000704032720 & 2.39041651606691 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.258166666666667 & 0.108000704032720 & 2.39041651606691 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.254166666666667 & 0.107324496513094 & 2.36820739835158 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.247666666666667 & 0.106236961092040 & 2.33126648316020 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.245333333333333 & 0.105144900466746 & 2.33328798871158 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.230333333333333 & 0.102693105041066 & 2.24292890200588 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.214333333333333 & 0.100132219557927 & 2.14050316950519 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.217166666666667 & 0.099742632557644 & 2.17727025142594 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.208166666666667 & 0.0983219350858226 & 2.11719456584091 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.179666666666667 & 0.092968607382109 & 1.93255198422217 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.139666666666667 & 0.0869365528328317 & 1.60653559539252 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.134482758620690 & 0.137889013562831 & 0.975297125897642 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.151964285714286 & 0.133287459012676 & 1.14012441110333 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.165925925925926 & 0.129953364348742 & 1.27681131425462 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.181346153846154 & 0.126623999178216 & 1.43216258389469 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.1974 & 0.122893619169805 & 1.60626728493729 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.210416666666667 & 0.119708184756248 & 1.7577466995688 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.220652173913043 & 0.117083067326084 & 1.88457800903450 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.219318181818182 & 0.117024598400464 & 1.87412035431785 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.212380952380952 & 0.117873044129615 & 1.80177710645545 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.20475 & 0.118581891805210 & 1.72665486174175 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.196315789473684 & 0.119210549866700 & 1.64679879166067 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.186944444444444 & 0.119587796959631 & 1.56324013985768 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.177058823529412 & 0.119778858483910 & 1.47821431737218 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.166875 & 0.119794378183431 & 1.39301194705881 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.155666666666667 & 0.119515961838156 & 1.30247595611927 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.145 & 0.119197603931743 & 1.21646740552798 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.135 & 0.118799443148138 & 1.13636896287182 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.122916666666667 & 0.11744792118561 & 1.04656315263694 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.11 & 0.114983529782365 & 0.95665875111159 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.099 & 0.112408793437637 & 0.880714016870258 \tabularnewline
Median & -0.005 &  &  \tabularnewline
Midrange & -0.345 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.131290322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.131290322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.131290322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.131290322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.131290322580645 &  &  \tabularnewline
Midmean - Closest Observation & 0.131290322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.131290322580645 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.166875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48744&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]0.1185[/C][C]0.141724612609134[/C][C]0.83612858640732[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-3.61508591693716[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.09503805108925[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.118166666666667[/C][C]0.141586549296251[/C][C]0.834589636190787[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.126833333333333[/C][C]0.138013037062615[/C][C]0.918995306767944[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.125833333333333[/C][C]0.136165463416739[/C][C]0.924120773181788[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.127833333333333[/C][C]0.134851684936897[/C][C]0.94795503217592[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.145333333333333[/C][C]0.130368332318716[/C][C]1.11479015454483[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.163333333333333[/C][C]0.125638857088666[/C][C]1.30002243826578[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.2275[/C][C]0.113539765054308[/C][C]2.00370328308485[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.258166666666667[/C][C]0.108512149249934[/C][C]2.37914987815822[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.258166666666667[/C][C]0.108512149249934[/C][C]2.37914987815822[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.258166666666667[/C][C]0.108000704032720[/C][C]2.39041651606691[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.258166666666667[/C][C]0.108000704032720[/C][C]2.39041651606691[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.254166666666667[/C][C]0.107324496513094[/C][C]2.36820739835158[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.247666666666667[/C][C]0.106236961092040[/C][C]2.33126648316020[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.245333333333333[/C][C]0.105144900466746[/C][C]2.33328798871158[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.230333333333333[/C][C]0.102693105041066[/C][C]2.24292890200588[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.214333333333333[/C][C]0.100132219557927[/C][C]2.14050316950519[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.217166666666667[/C][C]0.099742632557644[/C][C]2.17727025142594[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.208166666666667[/C][C]0.0983219350858226[/C][C]2.11719456584091[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.179666666666667[/C][C]0.092968607382109[/C][C]1.93255198422217[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.139666666666667[/C][C]0.0869365528328317[/C][C]1.60653559539252[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.134482758620690[/C][C]0.137889013562831[/C][C]0.975297125897642[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.151964285714286[/C][C]0.133287459012676[/C][C]1.14012441110333[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.165925925925926[/C][C]0.129953364348742[/C][C]1.27681131425462[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.181346153846154[/C][C]0.126623999178216[/C][C]1.43216258389469[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.1974[/C][C]0.122893619169805[/C][C]1.60626728493729[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.210416666666667[/C][C]0.119708184756248[/C][C]1.7577466995688[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.220652173913043[/C][C]0.117083067326084[/C][C]1.88457800903450[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.219318181818182[/C][C]0.117024598400464[/C][C]1.87412035431785[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.212380952380952[/C][C]0.117873044129615[/C][C]1.80177710645545[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.20475[/C][C]0.118581891805210[/C][C]1.72665486174175[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.196315789473684[/C][C]0.119210549866700[/C][C]1.64679879166067[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.186944444444444[/C][C]0.119587796959631[/C][C]1.56324013985768[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.177058823529412[/C][C]0.119778858483910[/C][C]1.47821431737218[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.166875[/C][C]0.119794378183431[/C][C]1.39301194705881[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.155666666666667[/C][C]0.119515961838156[/C][C]1.30247595611927[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.145[/C][C]0.119197603931743[/C][C]1.21646740552798[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.135[/C][C]0.118799443148138[/C][C]1.13636896287182[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.122916666666667[/C][C]0.11744792118561[/C][C]1.04656315263694[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.11[/C][C]0.114983529782365[/C][C]0.95665875111159[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.099[/C][C]0.112408793437637[/C][C]0.880714016870258[/C][/ROW]
[ROW][C]Median[/C][C]-0.005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.131290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.131290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.131290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.131290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.131290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.131290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.131290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.166875[/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=48744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48744&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 Mean0.11850.1417246126091340.83612858640732
Geometric MeanNaN
Harmonic Mean-3.61508591693716
Quadratic Mean1.09503805108925
Winsorized Mean ( 1 / 20 )0.1181666666666670.1415865492962510.834589636190787
Winsorized Mean ( 2 / 20 )0.1268333333333330.1380130370626150.918995306767944
Winsorized Mean ( 3 / 20 )0.1258333333333330.1361654634167390.924120773181788
Winsorized Mean ( 4 / 20 )0.1278333333333330.1348516849368970.94795503217592
Winsorized Mean ( 5 / 20 )0.1453333333333330.1303683323187161.11479015454483
Winsorized Mean ( 6 / 20 )0.1633333333333330.1256388570886661.30002243826578
Winsorized Mean ( 7 / 20 )0.22750.1135397650543082.00370328308485
Winsorized Mean ( 8 / 20 )0.2581666666666670.1085121492499342.37914987815822
Winsorized Mean ( 9 / 20 )0.2581666666666670.1085121492499342.37914987815822
Winsorized Mean ( 10 / 20 )0.2581666666666670.1080007040327202.39041651606691
Winsorized Mean ( 11 / 20 )0.2581666666666670.1080007040327202.39041651606691
Winsorized Mean ( 12 / 20 )0.2541666666666670.1073244965130942.36820739835158
Winsorized Mean ( 13 / 20 )0.2476666666666670.1062369610920402.33126648316020
Winsorized Mean ( 14 / 20 )0.2453333333333330.1051449004667462.33328798871158
Winsorized Mean ( 15 / 20 )0.2303333333333330.1026931050410662.24292890200588
Winsorized Mean ( 16 / 20 )0.2143333333333330.1001322195579272.14050316950519
Winsorized Mean ( 17 / 20 )0.2171666666666670.0997426325576442.17727025142594
Winsorized Mean ( 18 / 20 )0.2081666666666670.09832193508582262.11719456584091
Winsorized Mean ( 19 / 20 )0.1796666666666670.0929686073821091.93255198422217
Winsorized Mean ( 20 / 20 )0.1396666666666670.08693655283283171.60653559539252
Trimmed Mean ( 1 / 20 )0.1344827586206900.1378890135628310.975297125897642
Trimmed Mean ( 2 / 20 )0.1519642857142860.1332874590126761.14012441110333
Trimmed Mean ( 3 / 20 )0.1659259259259260.1299533643487421.27681131425462
Trimmed Mean ( 4 / 20 )0.1813461538461540.1266239991782161.43216258389469
Trimmed Mean ( 5 / 20 )0.19740.1228936191698051.60626728493729
Trimmed Mean ( 6 / 20 )0.2104166666666670.1197081847562481.7577466995688
Trimmed Mean ( 7 / 20 )0.2206521739130430.1170830673260841.88457800903450
Trimmed Mean ( 8 / 20 )0.2193181818181820.1170245984004641.87412035431785
Trimmed Mean ( 9 / 20 )0.2123809523809520.1178730441296151.80177710645545
Trimmed Mean ( 10 / 20 )0.204750.1185818918052101.72665486174175
Trimmed Mean ( 11 / 20 )0.1963157894736840.1192105498667001.64679879166067
Trimmed Mean ( 12 / 20 )0.1869444444444440.1195877969596311.56324013985768
Trimmed Mean ( 13 / 20 )0.1770588235294120.1197788584839101.47821431737218
Trimmed Mean ( 14 / 20 )0.1668750.1197943781834311.39301194705881
Trimmed Mean ( 15 / 20 )0.1556666666666670.1195159618381561.30247595611927
Trimmed Mean ( 16 / 20 )0.1450.1191976039317431.21646740552798
Trimmed Mean ( 17 / 20 )0.1350.1187994431481381.13636896287182
Trimmed Mean ( 18 / 20 )0.1229166666666670.117447921185611.04656315263694
Trimmed Mean ( 19 / 20 )0.110.1149835297823650.95665875111159
Trimmed Mean ( 20 / 20 )0.0990.1124087934376370.880714016870258
Median-0.005
Midrange-0.345
Midmean - Weighted Average at Xnp0.131290322580645
Midmean - Weighted Average at X(n+1)p0.131290322580645
Midmean - Empirical Distribution Function0.131290322580645
Midmean - Empirical Distribution Function - Averaging0.131290322580645
Midmean - Empirical Distribution Function - Interpolation0.131290322580645
Midmean - Closest Observation0.131290322580645
Midmean - True Basic - Statistics Graphics Toolkit0.131290322580645
Midmean - MS Excel (old versions)0.166875
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')