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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 04:33:09 -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/t1255862069des5q5v45xuzwke.htm/, Retrieved Mon, 29 Apr 2024 11:40:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47260, Retrieved Mon, 29 Apr 2024 11:40:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVraag 2
Estimated Impact150
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] [Workshop 3] [2009-10-18 10:33:09] [ee8fc1691ecec7724e0ca78f0c288737] [Current]
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Post a new message
Dataseries X:
19
17
11
11
11
14
20
15
13
17
18
25
19
15
14
14
16
19
18
19
20
20
24
18
15
25
23
20
20
22
25
22
26
27
41
29
33
39
27
27
25
19
15
19
23
23
7
1
7
4
-8
-14
-10
-11
-10
-8
-8
-7
-8
-4




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=47260&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=47260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47260&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 Mean14.71666666666671.644729927629438.94777094977407
Geometric MeanNaN
Harmonic Mean22.1310287892498
Quadratic Mean19.3954462009342
Winsorized Mean ( 1 / 20 )14.73333333333331.621861012852039.08421450209526
Winsorized Mean ( 2 / 20 )14.56666666666671.567567958080779.29252642067345
Winsorized Mean ( 3 / 20 )14.36666666666671.531397697438949.38140803704553
Winsorized Mean ( 4 / 20 )14.36666666666671.475786999977719.73491883780226
Winsorized Mean ( 5 / 20 )14.36666666666671.475786999977719.73491883780226
Winsorized Mean ( 6 / 20 )14.36666666666671.475786999977719.73491883780226
Winsorized Mean ( 7 / 20 )14.251.459360009873539.76455425911999
Winsorized Mean ( 8 / 20 )14.251.4073304857229510.1255534109173
Winsorized Mean ( 9 / 20 )14.71.2945561811735711.3552429888936
Winsorized Mean ( 10 / 20 )15.53333333333331.0983980802739614.1418067022286
Winsorized Mean ( 11 / 20 )16.08333333333330.97895703369605316.4290492633887
Winsorized Mean ( 12 / 20 )16.48333333333330.82663693677176419.9402332512567
Winsorized Mean ( 13 / 20 )16.26666666666670.79435389893977920.4778584059041
Winsorized Mean ( 14 / 20 )17.20.62155263945688427.6726360860272
Winsorized Mean ( 15 / 20 )17.20.62155263945688427.6726360860272
Winsorized Mean ( 16 / 20 )16.93333333333330.58070027210805229.1601952791621
Winsorized Mean ( 17 / 20 )17.50.48683226035002535.9466728589798
Winsorized Mean ( 18 / 20 )17.20.35159041398911848.9205601621788
Winsorized Mean ( 19 / 20 )17.20.35159041398911848.9205601621788
Winsorized Mean ( 20 / 20 )17.20.35159041398911848.9205601621788
Trimmed Mean ( 1 / 20 )14.75862068965521.561467027179159.45176582839357
Trimmed Mean ( 2 / 20 )14.78571428571431.486893887364539.94402789019563
Trimmed Mean ( 3 / 20 )14.90740740740741.4312252350061210.4158360562610
Trimmed Mean ( 4 / 20 )15.11538461538461.3787478323953010.9631248443196
Trimmed Mean ( 5 / 20 )15.341.3345059469515211.4948907009683
Trimmed Mean ( 6 / 20 )15.58333333333331.2771287795761812.2018496353239
Trimmed Mean ( 7 / 20 )15.84782608695651.2018373178006713.1863321701124
Trimmed Mean ( 8 / 20 )16.15909090909091.1058862219776614.6118927860350
Trimmed Mean ( 9 / 20 )16.50.99198296227547816.6333501960066
Trimmed Mean ( 10 / 20 )16.80.87647311892919.1677298905968
Trimmed Mean ( 11 / 20 )170.79113149788241821.4882102981654
Trimmed Mean ( 12 / 20 )17.13888888888890.7161989368238323.9303467342408
Trimmed Mean ( 13 / 20 )17.23529411764710.66496059354033825.9192714351449
Trimmed Mean ( 14 / 20 )17.3750.60031913555718828.9429387984998
Trimmed Mean ( 15 / 20 )17.40.57255226132993630.3902388920497
Trimmed Mean ( 16 / 20 )17.42857142857140.53061951271259632.845703957388
Trimmed Mean ( 17 / 20 )17.50.48118443609333636.3685911000777
Trimmed Mean ( 18 / 20 )17.50.44640269076120139.2022726613927
Trimmed Mean ( 19 / 20 )17.54545454545450.44491972488295639.435101579437
Trimmed Mean ( 20 / 20 )17.60.43769732392193240.2104354723885
Median18
Midrange13.5
Midmean - Weighted Average at Xnp17.5454545454545
Midmean - Weighted Average at X(n+1)p17.5454545454545
Midmean - Empirical Distribution Function17.5454545454545
Midmean - Empirical Distribution Function - Averaging17.5454545454545
Midmean - Empirical Distribution Function - Interpolation17.5454545454545
Midmean - Closest Observation17.5454545454545
Midmean - True Basic - Statistics Graphics Toolkit17.5454545454545
Midmean - MS Excel (old versions)17.5454545454545
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14.7166666666667 & 1.64472992762943 & 8.94777094977407 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 22.1310287892498 &  &  \tabularnewline
Quadratic Mean & 19.3954462009342 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 14.7333333333333 & 1.62186101285203 & 9.08421450209526 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 14.5666666666667 & 1.56756795808077 & 9.29252642067345 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 14.3666666666667 & 1.53139769743894 & 9.38140803704553 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 14.3666666666667 & 1.47578699997771 & 9.73491883780226 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 14.3666666666667 & 1.47578699997771 & 9.73491883780226 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 14.3666666666667 & 1.47578699997771 & 9.73491883780226 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 14.25 & 1.45936000987353 & 9.76455425911999 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 14.25 & 1.40733048572295 & 10.1255534109173 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 14.7 & 1.29455618117357 & 11.3552429888936 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 15.5333333333333 & 1.09839808027396 & 14.1418067022286 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 16.0833333333333 & 0.978957033696053 & 16.4290492633887 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 16.4833333333333 & 0.826636936771764 & 19.9402332512567 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 16.2666666666667 & 0.794353898939779 & 20.4778584059041 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17.2 & 0.621552639456884 & 27.6726360860272 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17.2 & 0.621552639456884 & 27.6726360860272 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 16.9333333333333 & 0.580700272108052 & 29.1601952791621 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17.5 & 0.486832260350025 & 35.9466728589798 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17.2 & 0.351590413989118 & 48.9205601621788 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17.2 & 0.351590413989118 & 48.9205601621788 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 17.2 & 0.351590413989118 & 48.9205601621788 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 14.7586206896552 & 1.56146702717915 & 9.45176582839357 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 14.7857142857143 & 1.48689388736453 & 9.94402789019563 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 14.9074074074074 & 1.43122523500612 & 10.4158360562610 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 15.1153846153846 & 1.37874783239530 & 10.9631248443196 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 15.34 & 1.33450594695152 & 11.4948907009683 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 15.5833333333333 & 1.27712877957618 & 12.2018496353239 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 15.8478260869565 & 1.20183731780067 & 13.1863321701124 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 16.1590909090909 & 1.10588622197766 & 14.6118927860350 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 16.5 & 0.991982962275478 & 16.6333501960066 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 16.8 & 0.876473118929 & 19.1677298905968 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17 & 0.791131497882418 & 21.4882102981654 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17.1388888888889 & 0.71619893682383 & 23.9303467342408 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17.2352941176471 & 0.664960593540338 & 25.9192714351449 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17.375 & 0.600319135557188 & 28.9429387984998 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 17.4 & 0.572552261329936 & 30.3902388920497 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 17.4285714285714 & 0.530619512712596 & 32.845703957388 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 17.5 & 0.481184436093336 & 36.3685911000777 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 17.5 & 0.446402690761201 & 39.2022726613927 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17.5454545454545 & 0.444919724882956 & 39.435101579437 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17.6 & 0.437697323921932 & 40.2104354723885 \tabularnewline
Median & 18 &  &  \tabularnewline
Midrange & 13.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17.5454545454545 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17.5454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17.5454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17.5454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17.5454545454545 &  &  \tabularnewline
Midmean - Closest Observation & 17.5454545454545 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17.5454545454545 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17.5454545454545 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47260&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]14.7166666666667[/C][C]1.64472992762943[/C][C]8.94777094977407[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]22.1310287892498[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19.3954462009342[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]14.7333333333333[/C][C]1.62186101285203[/C][C]9.08421450209526[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]14.5666666666667[/C][C]1.56756795808077[/C][C]9.29252642067345[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]14.3666666666667[/C][C]1.53139769743894[/C][C]9.38140803704553[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]14.3666666666667[/C][C]1.47578699997771[/C][C]9.73491883780226[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]14.3666666666667[/C][C]1.47578699997771[/C][C]9.73491883780226[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]14.3666666666667[/C][C]1.47578699997771[/C][C]9.73491883780226[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]14.25[/C][C]1.45936000987353[/C][C]9.76455425911999[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]14.25[/C][C]1.40733048572295[/C][C]10.1255534109173[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]14.7[/C][C]1.29455618117357[/C][C]11.3552429888936[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]15.5333333333333[/C][C]1.09839808027396[/C][C]14.1418067022286[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]16.0833333333333[/C][C]0.978957033696053[/C][C]16.4290492633887[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]16.4833333333333[/C][C]0.826636936771764[/C][C]19.9402332512567[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]16.2666666666667[/C][C]0.794353898939779[/C][C]20.4778584059041[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17.2[/C][C]0.621552639456884[/C][C]27.6726360860272[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17.2[/C][C]0.621552639456884[/C][C]27.6726360860272[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]16.9333333333333[/C][C]0.580700272108052[/C][C]29.1601952791621[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17.5[/C][C]0.486832260350025[/C][C]35.9466728589798[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17.2[/C][C]0.351590413989118[/C][C]48.9205601621788[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17.2[/C][C]0.351590413989118[/C][C]48.9205601621788[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]17.2[/C][C]0.351590413989118[/C][C]48.9205601621788[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]14.7586206896552[/C][C]1.56146702717915[/C][C]9.45176582839357[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]14.7857142857143[/C][C]1.48689388736453[/C][C]9.94402789019563[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]14.9074074074074[/C][C]1.43122523500612[/C][C]10.4158360562610[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]15.1153846153846[/C][C]1.37874783239530[/C][C]10.9631248443196[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]15.34[/C][C]1.33450594695152[/C][C]11.4948907009683[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]15.5833333333333[/C][C]1.27712877957618[/C][C]12.2018496353239[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]15.8478260869565[/C][C]1.20183731780067[/C][C]13.1863321701124[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]16.1590909090909[/C][C]1.10588622197766[/C][C]14.6118927860350[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]16.5[/C][C]0.991982962275478[/C][C]16.6333501960066[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]16.8[/C][C]0.876473118929[/C][C]19.1677298905968[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17[/C][C]0.791131497882418[/C][C]21.4882102981654[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17.1388888888889[/C][C]0.71619893682383[/C][C]23.9303467342408[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17.2352941176471[/C][C]0.664960593540338[/C][C]25.9192714351449[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17.375[/C][C]0.600319135557188[/C][C]28.9429387984998[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]17.4[/C][C]0.572552261329936[/C][C]30.3902388920497[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]17.4285714285714[/C][C]0.530619512712596[/C][C]32.845703957388[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]17.5[/C][C]0.481184436093336[/C][C]36.3685911000777[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]17.5[/C][C]0.446402690761201[/C][C]39.2022726613927[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17.5454545454545[/C][C]0.444919724882956[/C][C]39.435101579437[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17.6[/C][C]0.437697323921932[/C][C]40.2104354723885[/C][/ROW]
[ROW][C]Median[/C][C]18[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17.5454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17.5454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17.5454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17.5454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17.5454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17.5454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17.5454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17.5454545454545[/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=47260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47260&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 Mean14.71666666666671.644729927629438.94777094977407
Geometric MeanNaN
Harmonic Mean22.1310287892498
Quadratic Mean19.3954462009342
Winsorized Mean ( 1 / 20 )14.73333333333331.621861012852039.08421450209526
Winsorized Mean ( 2 / 20 )14.56666666666671.567567958080779.29252642067345
Winsorized Mean ( 3 / 20 )14.36666666666671.531397697438949.38140803704553
Winsorized Mean ( 4 / 20 )14.36666666666671.475786999977719.73491883780226
Winsorized Mean ( 5 / 20 )14.36666666666671.475786999977719.73491883780226
Winsorized Mean ( 6 / 20 )14.36666666666671.475786999977719.73491883780226
Winsorized Mean ( 7 / 20 )14.251.459360009873539.76455425911999
Winsorized Mean ( 8 / 20 )14.251.4073304857229510.1255534109173
Winsorized Mean ( 9 / 20 )14.71.2945561811735711.3552429888936
Winsorized Mean ( 10 / 20 )15.53333333333331.0983980802739614.1418067022286
Winsorized Mean ( 11 / 20 )16.08333333333330.97895703369605316.4290492633887
Winsorized Mean ( 12 / 20 )16.48333333333330.82663693677176419.9402332512567
Winsorized Mean ( 13 / 20 )16.26666666666670.79435389893977920.4778584059041
Winsorized Mean ( 14 / 20 )17.20.62155263945688427.6726360860272
Winsorized Mean ( 15 / 20 )17.20.62155263945688427.6726360860272
Winsorized Mean ( 16 / 20 )16.93333333333330.58070027210805229.1601952791621
Winsorized Mean ( 17 / 20 )17.50.48683226035002535.9466728589798
Winsorized Mean ( 18 / 20 )17.20.35159041398911848.9205601621788
Winsorized Mean ( 19 / 20 )17.20.35159041398911848.9205601621788
Winsorized Mean ( 20 / 20 )17.20.35159041398911848.9205601621788
Trimmed Mean ( 1 / 20 )14.75862068965521.561467027179159.45176582839357
Trimmed Mean ( 2 / 20 )14.78571428571431.486893887364539.94402789019563
Trimmed Mean ( 3 / 20 )14.90740740740741.4312252350061210.4158360562610
Trimmed Mean ( 4 / 20 )15.11538461538461.3787478323953010.9631248443196
Trimmed Mean ( 5 / 20 )15.341.3345059469515211.4948907009683
Trimmed Mean ( 6 / 20 )15.58333333333331.2771287795761812.2018496353239
Trimmed Mean ( 7 / 20 )15.84782608695651.2018373178006713.1863321701124
Trimmed Mean ( 8 / 20 )16.15909090909091.1058862219776614.6118927860350
Trimmed Mean ( 9 / 20 )16.50.99198296227547816.6333501960066
Trimmed Mean ( 10 / 20 )16.80.87647311892919.1677298905968
Trimmed Mean ( 11 / 20 )170.79113149788241821.4882102981654
Trimmed Mean ( 12 / 20 )17.13888888888890.7161989368238323.9303467342408
Trimmed Mean ( 13 / 20 )17.23529411764710.66496059354033825.9192714351449
Trimmed Mean ( 14 / 20 )17.3750.60031913555718828.9429387984998
Trimmed Mean ( 15 / 20 )17.40.57255226132993630.3902388920497
Trimmed Mean ( 16 / 20 )17.42857142857140.53061951271259632.845703957388
Trimmed Mean ( 17 / 20 )17.50.48118443609333636.3685911000777
Trimmed Mean ( 18 / 20 )17.50.44640269076120139.2022726613927
Trimmed Mean ( 19 / 20 )17.54545454545450.44491972488295639.435101579437
Trimmed Mean ( 20 / 20 )17.60.43769732392193240.2104354723885
Median18
Midrange13.5
Midmean - Weighted Average at Xnp17.5454545454545
Midmean - Weighted Average at X(n+1)p17.5454545454545
Midmean - Empirical Distribution Function17.5454545454545
Midmean - Empirical Distribution Function - Averaging17.5454545454545
Midmean - Empirical Distribution Function - Interpolation17.5454545454545
Midmean - Closest Observation17.5454545454545
Midmean - True Basic - Statistics Graphics Toolkit17.5454545454545
Midmean - MS Excel (old versions)17.5454545454545
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')