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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 computationSun, 18 Oct 2009 04:16:40 -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/18/t1255861113k185j4e3p86uzgb.htm/, Retrieved Mon, 29 Apr 2024 10:50:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47253, Retrieved Mon, 29 Apr 2024 10:50:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
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 deel 3 voorsp...] [2009-10-18 10:16:40] [9be6fbb216efe5bb8ca600257c6e1971] [Current]
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Dataseries X:
2.34
2.45
2.11
2.17
2.12
1.84
1.27
1.47
1.19
1.23
1.31
1.23
1.09
1.14
1.24
1.28
1.13
1.26
1.35
1.35
1.58
1.46
1.46
1.58
1.58
1.73
1.95
1.49
1.73
1.38
1.88
1.59
1.38
1.89
1.49
1.60
1.39
1.37
1.40
2.14
1.51
2.00
1.54
1.66
1.67
1.53
1.70
1.65
2.08
2.26
2.26
2.24
2.13
1.91
1.92
2.05
2.39
2.26
2.24
2.56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47253&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]2 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=47253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47253&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.703333333333330.050561629154424333.6882604816994
Geometric Mean1.66005970331784
Harmonic Mean1.61844372532607
Quadratic Mean1.74704798636634
Winsorized Mean ( 1 / 20 )1.702166666666670.049932209223013334.0895524783260
Winsorized Mean ( 2 / 20 )1.70050.049377151673062634.4390055396350
Winsorized Mean ( 3 / 20 )1.70050.048336406487143835.1805217554244
Winsorized Mean ( 4 / 20 )1.697833333333330.046728626140104136.3339022260746
Winsorized Mean ( 5 / 20 )1.697833333333330.046728626140104136.3339022260746
Winsorized Mean ( 6 / 20 )1.698833333333330.046560265100752536.4867624713304
Winsorized Mean ( 7 / 20 )1.698833333333330.045702978470277137.1711733063124
Winsorized Mean ( 8 / 20 )1.700166666666670.04548762274482537.3764677966182
Winsorized Mean ( 9 / 20 )1.691166666666670.043202382537006239.1452176328018
Winsorized Mean ( 10 / 20 )1.691166666666670.041481117933457640.7695537371864
Winsorized Mean ( 11 / 20 )1.696666666666670.040035059964552942.3795210540186
Winsorized Mean ( 12 / 20 )1.694666666666670.039669871208923542.7192379259719
Winsorized Mean ( 13 / 20 )1.696833333333330.038646954599446543.9060037438923
Winsorized Mean ( 14 / 20 )1.692166666666670.037057819890893745.6628768677914
Winsorized Mean ( 15 / 20 )1.684666666666670.035742698410195447.1331696150318
Winsorized Mean ( 16 / 20 )1.6740.033086259458750450.595021237956
Winsorized Mean ( 17 / 20 )1.662666666666670.030350929272779854.7814088894414
Winsorized Mean ( 18 / 20 )1.671666666666670.026358208947265863.421102321904
Winsorized Mean ( 19 / 20 )1.66850.025854684087521564.5337608594214
Winsorized Mean ( 20 / 20 )1.665166666666670.024350885628352968.3821809227273
Trimmed Mean ( 1 / 20 )1.699137931034480.04900355215266434.6737707042348
Trimmed Mean ( 2 / 20 )1.695892857142860.047844972042229335.4455815262263
Trimmed Mean ( 3 / 20 )1.693333333333330.046766141359299836.2085321584181
Trimmed Mean ( 4 / 20 )1.690576923076920.045900914219757536.8310076566892
Trimmed Mean ( 5 / 20 )1.68840.045404629809781137.1856351890415
Trimmed Mean ( 6 / 20 )1.686041666666670.04473002107932137.6937373598989
Trimmed Mean ( 7 / 20 )1.683260869565220.043876258089592738.3638200442731
Trimmed Mean ( 8 / 20 )1.680227272727270.042982725076555239.0907572689882
Trimmed Mean ( 9 / 20 )1.676666666666670.041831844488593240.0811077580828
Trimmed Mean ( 10 / 20 )1.674250.040921888538268440.9133121613953
Trimmed Mean ( 11 / 20 )1.671578947368420.040114569769519741.6701202822955
Trimmed Mean ( 12 / 20 )1.667777777777780.039323871160320842.4113325714643
Trimmed Mean ( 13 / 20 )1.663823529411760.038259864585818943.4874390545665
Trimmed Mean ( 14 / 20 )1.65906250.036975796832675444.8688775392094
Trimmed Mean ( 15 / 20 )1.654333333333330.035566623038032546.5136465602682
Trimmed Mean ( 16 / 20 )1.650.033888238349207548.6894592453368
Trimmed Mean ( 17 / 20 )1.646538461538460.032291662690080650.9895844429296
Trimmed Mean ( 18 / 20 )1.644166666666670.030833333333333353.3243243243243
Trimmed Mean ( 19 / 20 )1.640.029949452365105154.7589311486313
Trimmed Mean ( 20 / 20 )1.63550.028501846662240957.3822468200526
Median1.595
Midrange1.825
Midmean - Weighted Average at Xnp1.64548387096774
Midmean - Weighted Average at X(n+1)p1.64548387096774
Midmean - Empirical Distribution Function1.64548387096774
Midmean - Empirical Distribution Function - Averaging1.64548387096774
Midmean - Empirical Distribution Function - Interpolation1.64548387096774
Midmean - Closest Observation1.64548387096774
Midmean - True Basic - Statistics Graphics Toolkit1.64548387096774
Midmean - MS Excel (old versions)1.6590625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.70333333333333 & 0.0505616291544243 & 33.6882604816994 \tabularnewline
Geometric Mean & 1.66005970331784 &  &  \tabularnewline
Harmonic Mean & 1.61844372532607 &  &  \tabularnewline
Quadratic Mean & 1.74704798636634 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.70216666666667 & 0.0499322092230133 & 34.0895524783260 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.7005 & 0.0493771516730626 & 34.4390055396350 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.7005 & 0.0483364064871438 & 35.1805217554244 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.69783333333333 & 0.0467286261401041 & 36.3339022260746 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.69783333333333 & 0.0467286261401041 & 36.3339022260746 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.69883333333333 & 0.0465602651007525 & 36.4867624713304 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.69883333333333 & 0.0457029784702771 & 37.1711733063124 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.70016666666667 & 0.045487622744825 & 37.3764677966182 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.69116666666667 & 0.0432023825370062 & 39.1452176328018 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.69116666666667 & 0.0414811179334576 & 40.7695537371864 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.69666666666667 & 0.0400350599645529 & 42.3795210540186 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.69466666666667 & 0.0396698712089235 & 42.7192379259719 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.69683333333333 & 0.0386469545994465 & 43.9060037438923 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.69216666666667 & 0.0370578198908937 & 45.6628768677914 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.68466666666667 & 0.0357426984101954 & 47.1331696150318 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.674 & 0.0330862594587504 & 50.595021237956 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.66266666666667 & 0.0303509292727798 & 54.7814088894414 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.67166666666667 & 0.0263582089472658 & 63.421102321904 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.6685 & 0.0258546840875215 & 64.5337608594214 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.66516666666667 & 0.0243508856283529 & 68.3821809227273 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.69913793103448 & 0.049003552152664 & 34.6737707042348 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.69589285714286 & 0.0478449720422293 & 35.4455815262263 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.69333333333333 & 0.0467661413592998 & 36.2085321584181 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.69057692307692 & 0.0459009142197575 & 36.8310076566892 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.6884 & 0.0454046298097811 & 37.1856351890415 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.68604166666667 & 0.044730021079321 & 37.6937373598989 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.68326086956522 & 0.0438762580895927 & 38.3638200442731 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.68022727272727 & 0.0429827250765552 & 39.0907572689882 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.67666666666667 & 0.0418318444885932 & 40.0811077580828 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.67425 & 0.0409218885382684 & 40.9133121613953 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.67157894736842 & 0.0401145697695197 & 41.6701202822955 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.66777777777778 & 0.0393238711603208 & 42.4113325714643 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.66382352941176 & 0.0382598645858189 & 43.4874390545665 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.6590625 & 0.0369757968326754 & 44.8688775392094 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.65433333333333 & 0.0355666230380325 & 46.5136465602682 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.65 & 0.0338882383492075 & 48.6894592453368 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.64653846153846 & 0.0322916626900806 & 50.9895844429296 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.64416666666667 & 0.0308333333333333 & 53.3243243243243 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.64 & 0.0299494523651051 & 54.7589311486313 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.6355 & 0.0285018466622409 & 57.3822468200526 \tabularnewline
Median & 1.595 &  &  \tabularnewline
Midrange & 1.825 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.64548387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.64548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.64548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.64548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.64548387096774 &  &  \tabularnewline
Midmean - Closest Observation & 1.64548387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.64548387096774 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.6590625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47253&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]1.70333333333333[/C][C]0.0505616291544243[/C][C]33.6882604816994[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.66005970331784[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.61844372532607[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.74704798636634[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.70216666666667[/C][C]0.0499322092230133[/C][C]34.0895524783260[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.7005[/C][C]0.0493771516730626[/C][C]34.4390055396350[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.7005[/C][C]0.0483364064871438[/C][C]35.1805217554244[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.69783333333333[/C][C]0.0467286261401041[/C][C]36.3339022260746[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.69783333333333[/C][C]0.0467286261401041[/C][C]36.3339022260746[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.69883333333333[/C][C]0.0465602651007525[/C][C]36.4867624713304[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.69883333333333[/C][C]0.0457029784702771[/C][C]37.1711733063124[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.70016666666667[/C][C]0.045487622744825[/C][C]37.3764677966182[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.69116666666667[/C][C]0.0432023825370062[/C][C]39.1452176328018[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.69116666666667[/C][C]0.0414811179334576[/C][C]40.7695537371864[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.69666666666667[/C][C]0.0400350599645529[/C][C]42.3795210540186[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.69466666666667[/C][C]0.0396698712089235[/C][C]42.7192379259719[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.69683333333333[/C][C]0.0386469545994465[/C][C]43.9060037438923[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.69216666666667[/C][C]0.0370578198908937[/C][C]45.6628768677914[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.68466666666667[/C][C]0.0357426984101954[/C][C]47.1331696150318[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.674[/C][C]0.0330862594587504[/C][C]50.595021237956[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.66266666666667[/C][C]0.0303509292727798[/C][C]54.7814088894414[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.67166666666667[/C][C]0.0263582089472658[/C][C]63.421102321904[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.6685[/C][C]0.0258546840875215[/C][C]64.5337608594214[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.66516666666667[/C][C]0.0243508856283529[/C][C]68.3821809227273[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.69913793103448[/C][C]0.049003552152664[/C][C]34.6737707042348[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.69589285714286[/C][C]0.0478449720422293[/C][C]35.4455815262263[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.69333333333333[/C][C]0.0467661413592998[/C][C]36.2085321584181[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.69057692307692[/C][C]0.0459009142197575[/C][C]36.8310076566892[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.6884[/C][C]0.0454046298097811[/C][C]37.1856351890415[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.68604166666667[/C][C]0.044730021079321[/C][C]37.6937373598989[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.68326086956522[/C][C]0.0438762580895927[/C][C]38.3638200442731[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.68022727272727[/C][C]0.0429827250765552[/C][C]39.0907572689882[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.67666666666667[/C][C]0.0418318444885932[/C][C]40.0811077580828[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.67425[/C][C]0.0409218885382684[/C][C]40.9133121613953[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.67157894736842[/C][C]0.0401145697695197[/C][C]41.6701202822955[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.66777777777778[/C][C]0.0393238711603208[/C][C]42.4113325714643[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.66382352941176[/C][C]0.0382598645858189[/C][C]43.4874390545665[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.6590625[/C][C]0.0369757968326754[/C][C]44.8688775392094[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.65433333333333[/C][C]0.0355666230380325[/C][C]46.5136465602682[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.65[/C][C]0.0338882383492075[/C][C]48.6894592453368[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.64653846153846[/C][C]0.0322916626900806[/C][C]50.9895844429296[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.64416666666667[/C][C]0.0308333333333333[/C][C]53.3243243243243[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.64[/C][C]0.0299494523651051[/C][C]54.7589311486313[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.6355[/C][C]0.0285018466622409[/C][C]57.3822468200526[/C][/ROW]
[ROW][C]Median[/C][C]1.595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.64548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.64548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.64548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.64548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.64548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.64548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.64548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.6590625[/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=47253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47253&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 Mean1.703333333333330.050561629154424333.6882604816994
Geometric Mean1.66005970331784
Harmonic Mean1.61844372532607
Quadratic Mean1.74704798636634
Winsorized Mean ( 1 / 20 )1.702166666666670.049932209223013334.0895524783260
Winsorized Mean ( 2 / 20 )1.70050.049377151673062634.4390055396350
Winsorized Mean ( 3 / 20 )1.70050.048336406487143835.1805217554244
Winsorized Mean ( 4 / 20 )1.697833333333330.046728626140104136.3339022260746
Winsorized Mean ( 5 / 20 )1.697833333333330.046728626140104136.3339022260746
Winsorized Mean ( 6 / 20 )1.698833333333330.046560265100752536.4867624713304
Winsorized Mean ( 7 / 20 )1.698833333333330.045702978470277137.1711733063124
Winsorized Mean ( 8 / 20 )1.700166666666670.04548762274482537.3764677966182
Winsorized Mean ( 9 / 20 )1.691166666666670.043202382537006239.1452176328018
Winsorized Mean ( 10 / 20 )1.691166666666670.041481117933457640.7695537371864
Winsorized Mean ( 11 / 20 )1.696666666666670.040035059964552942.3795210540186
Winsorized Mean ( 12 / 20 )1.694666666666670.039669871208923542.7192379259719
Winsorized Mean ( 13 / 20 )1.696833333333330.038646954599446543.9060037438923
Winsorized Mean ( 14 / 20 )1.692166666666670.037057819890893745.6628768677914
Winsorized Mean ( 15 / 20 )1.684666666666670.035742698410195447.1331696150318
Winsorized Mean ( 16 / 20 )1.6740.033086259458750450.595021237956
Winsorized Mean ( 17 / 20 )1.662666666666670.030350929272779854.7814088894414
Winsorized Mean ( 18 / 20 )1.671666666666670.026358208947265863.421102321904
Winsorized Mean ( 19 / 20 )1.66850.025854684087521564.5337608594214
Winsorized Mean ( 20 / 20 )1.665166666666670.024350885628352968.3821809227273
Trimmed Mean ( 1 / 20 )1.699137931034480.04900355215266434.6737707042348
Trimmed Mean ( 2 / 20 )1.695892857142860.047844972042229335.4455815262263
Trimmed Mean ( 3 / 20 )1.693333333333330.046766141359299836.2085321584181
Trimmed Mean ( 4 / 20 )1.690576923076920.045900914219757536.8310076566892
Trimmed Mean ( 5 / 20 )1.68840.045404629809781137.1856351890415
Trimmed Mean ( 6 / 20 )1.686041666666670.04473002107932137.6937373598989
Trimmed Mean ( 7 / 20 )1.683260869565220.043876258089592738.3638200442731
Trimmed Mean ( 8 / 20 )1.680227272727270.042982725076555239.0907572689882
Trimmed Mean ( 9 / 20 )1.676666666666670.041831844488593240.0811077580828
Trimmed Mean ( 10 / 20 )1.674250.040921888538268440.9133121613953
Trimmed Mean ( 11 / 20 )1.671578947368420.040114569769519741.6701202822955
Trimmed Mean ( 12 / 20 )1.667777777777780.039323871160320842.4113325714643
Trimmed Mean ( 13 / 20 )1.663823529411760.038259864585818943.4874390545665
Trimmed Mean ( 14 / 20 )1.65906250.036975796832675444.8688775392094
Trimmed Mean ( 15 / 20 )1.654333333333330.035566623038032546.5136465602682
Trimmed Mean ( 16 / 20 )1.650.033888238349207548.6894592453368
Trimmed Mean ( 17 / 20 )1.646538461538460.032291662690080650.9895844429296
Trimmed Mean ( 18 / 20 )1.644166666666670.030833333333333353.3243243243243
Trimmed Mean ( 19 / 20 )1.640.029949452365105154.7589311486313
Trimmed Mean ( 20 / 20 )1.63550.028501846662240957.3822468200526
Median1.595
Midrange1.825
Midmean - Weighted Average at Xnp1.64548387096774
Midmean - Weighted Average at X(n+1)p1.64548387096774
Midmean - Empirical Distribution Function1.64548387096774
Midmean - Empirical Distribution Function - Averaging1.64548387096774
Midmean - Empirical Distribution Function - Interpolation1.64548387096774
Midmean - Closest Observation1.64548387096774
Midmean - True Basic - Statistics Graphics Toolkit1.64548387096774
Midmean - MS Excel (old versions)1.6590625
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')