Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Nov 2007 13:12:31 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/06/9oas3zx840rgiqw1194379788.htm/, Retrieved Fri, 03 May 2024 23:25:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=556, Retrieved Fri, 03 May 2024 23:25:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact245
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-11-06 20:12:31] [d9ccf6bb4f7743d5d52b9a9a992ccbd5] [Current]
Feedback Forum

Post a new message
Dataseries X:
88.8
93.4
92.6
90.7
81.6
84.1
88.1
85.3
82.9
84.8
71.2
68.9
94.3
97.6
85.6
91.9
75.8
79.8
99
88.5
86.7
97.9
94.3
72.9
91.8
93.2
86.5
98.9
77.2
79.4
90.4
81.4
85.8
103.6
73.6
75.7
99.2
88.7
94.6
98.7
84.2
87.7
103.3
88.2
93.4
106.3
73.1
78.6
101.6
101.4
98.5
99
89.5
83.5
97.4
87.8
90.4
97.1
79.4
85




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=556&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=556&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean88.681.1558492854267276.7228055751754
Geometric Mean88.2251385105405
Harmonic Mean87.7599691646335
Quadratic Mean89.1233171884141
Winsorized Mean ( 1 / 20 )88.67333333333331.1344424616002978.1646811846649
Winsorized Mean ( 2 / 20 )88.721.1180259035031179.354154248138
Winsorized Mean ( 3 / 20 )88.6451.0977234403129280.7534910384447
Winsorized Mean ( 4 / 20 )88.6651.0871510090066581.5572071087113
Winsorized Mean ( 5 / 20 )88.65666666666671.0131378974486787.5070085621377
Winsorized Mean ( 6 / 20 )88.64666666666671.0074677846461587.9895794363313
Winsorized Mean ( 7 / 20 )88.810.97328641245933791.247549398734
Winsorized Mean ( 8 / 20 )88.98333333333330.93442984418841395.2274094055918
Winsorized Mean ( 9 / 20 )89.07333333333330.9068785063256398.2196983521298
Winsorized Mean ( 10 / 20 )89.040.90091353510762298.8330139688304
Winsorized Mean ( 11 / 20 )89.00333333333330.868331625403615102.499241913437
Winsorized Mean ( 12 / 20 )89.26333333333330.802439665143652111.239931437529
Winsorized Mean ( 13 / 20 )89.26333333333330.78765893084323113.327393162130
Winsorized Mean ( 14 / 20 )89.49666666666670.726923579733198123.117022424165
Winsorized Mean ( 15 / 20 )89.02166666666670.598307838243158148.789069733844
Winsorized Mean ( 16 / 20 )89.10166666666670.56108999885698158.80102452045
Winsorized Mean ( 17 / 20 )89.130.556823618727583160.068641132131
Winsorized Mean ( 18 / 20 )89.040.488328175287543182.336396927272
Winsorized Mean ( 19 / 20 )89.10333333333330.47907023102292185.992214843068
Winsorized Mean ( 20 / 20 )89.13666666666670.454537491798085196.104102026996
Trimmed Mean ( 1 / 20 )88.71724137931041.1037529827324280.3778044247587
Trimmed Mean ( 2 / 20 )88.76428571428571.0658708669483783.278648912153
Trimmed Mean ( 3 / 20 )88.78888888888891.0299724429179186.2051111167116
Trimmed Mean ( 4 / 20 )88.84423076923080.99503069016517189.2879301587
Trimmed Mean ( 5 / 20 )88.8980.95522831975247893.0646612561021
Trimmed Mean ( 6 / 20 )88.95833333333330.93091045065542295.5605700534363
Trimmed Mean ( 7 / 20 )89.02608695652170.9011127569833698.7957236945051
Trimmed Mean ( 8 / 20 )89.06818181818180.872844810178854102.043548611959
Trimmed Mean ( 9 / 20 )89.08333333333330.846931447343995105.183641028683
Trimmed Mean ( 10 / 20 )89.0850.819994918683443108.640917120599
Trimmed Mean ( 11 / 20 )89.09210526315790.785034103135668113.488197400975
Trimmed Mean ( 12 / 20 )89.10555555555560.746717094857943119.329738356274
Trimmed Mean ( 13 / 20 )89.08235294117650.713387022837934124.872404584537
Trimmed Mean ( 14 / 20 )89.056250.670383518965077132.843734191859
Trimmed Mean ( 15 / 20 )88.99333333333330.627985894367783141.712312539960
Trimmed Mean ( 16 / 20 )88.98928571428570.610194246236876145.837634922143
Trimmed Mean ( 17 / 20 )88.9730769230770.594035940179424149.777262460253
Trimmed Mean ( 18 / 20 )88.950.5681778655989156.553089068755
Trimmed Mean ( 19 / 20 )88.93636363636360.55277910442781160.889517935782
Trimmed Mean ( 20 / 20 )88.910.527501558989964168.549264897417
Median88.6
Midrange87.6
Midmean - Weighted Average at Xnp88.7967741935484
Midmean - Weighted Average at X(n+1)p88.9933333333334
Midmean - Empirical Distribution Function88.7967741935484
Midmean - Empirical Distribution Function - Averaging88.9933333333334
Midmean - Empirical Distribution Function - Interpolation88.9933333333334
Midmean - Closest Observation88.7967741935484
Midmean - True Basic - Statistics Graphics Toolkit88.9933333333334
Midmean - MS Excel (old versions)89.05625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 88.68 & 1.15584928542672 & 76.7228055751754 \tabularnewline
Geometric Mean & 88.2251385105405 &  &  \tabularnewline
Harmonic Mean & 87.7599691646335 &  &  \tabularnewline
Quadratic Mean & 89.1233171884141 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 88.6733333333333 & 1.13444246160029 & 78.1646811846649 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 88.72 & 1.11802590350311 & 79.354154248138 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 88.645 & 1.09772344031292 & 80.7534910384447 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 88.665 & 1.08715100900665 & 81.5572071087113 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 88.6566666666667 & 1.01313789744867 & 87.5070085621377 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 88.6466666666667 & 1.00746778464615 & 87.9895794363313 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 88.81 & 0.973286412459337 & 91.247549398734 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 88.9833333333333 & 0.934429844188413 & 95.2274094055918 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 89.0733333333333 & 0.90687850632563 & 98.2196983521298 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 89.04 & 0.900913535107622 & 98.8330139688304 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 89.0033333333333 & 0.868331625403615 & 102.499241913437 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 89.2633333333333 & 0.802439665143652 & 111.239931437529 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 89.2633333333333 & 0.78765893084323 & 113.327393162130 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 89.4966666666667 & 0.726923579733198 & 123.117022424165 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 89.0216666666667 & 0.598307838243158 & 148.789069733844 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 89.1016666666667 & 0.56108999885698 & 158.80102452045 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 89.13 & 0.556823618727583 & 160.068641132131 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 89.04 & 0.488328175287543 & 182.336396927272 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 89.1033333333333 & 0.47907023102292 & 185.992214843068 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 89.1366666666667 & 0.454537491798085 & 196.104102026996 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 88.7172413793104 & 1.10375298273242 & 80.3778044247587 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 88.7642857142857 & 1.06587086694837 & 83.278648912153 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 88.7888888888889 & 1.02997244291791 & 86.2051111167116 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 88.8442307692308 & 0.995030690165171 & 89.2879301587 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 88.898 & 0.955228319752478 & 93.0646612561021 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 88.9583333333333 & 0.930910450655422 & 95.5605700534363 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 89.0260869565217 & 0.90111275698336 & 98.7957236945051 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 89.0681818181818 & 0.872844810178854 & 102.043548611959 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 89.0833333333333 & 0.846931447343995 & 105.183641028683 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 89.085 & 0.819994918683443 & 108.640917120599 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 89.0921052631579 & 0.785034103135668 & 113.488197400975 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 89.1055555555556 & 0.746717094857943 & 119.329738356274 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 89.0823529411765 & 0.713387022837934 & 124.872404584537 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 89.05625 & 0.670383518965077 & 132.843734191859 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 88.9933333333333 & 0.627985894367783 & 141.712312539960 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 88.9892857142857 & 0.610194246236876 & 145.837634922143 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 88.973076923077 & 0.594035940179424 & 149.777262460253 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 88.95 & 0.5681778655989 & 156.553089068755 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 88.9363636363636 & 0.55277910442781 & 160.889517935782 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 88.91 & 0.527501558989964 & 168.549264897417 \tabularnewline
Median & 88.6 &  &  \tabularnewline
Midrange & 87.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 88.7967741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 88.9933333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 88.7967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 88.9933333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 88.9933333333334 &  &  \tabularnewline
Midmean - Closest Observation & 88.7967741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 88.9933333333334 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 89.05625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=556&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]88.68[/C][C]1.15584928542672[/C][C]76.7228055751754[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]88.2251385105405[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]87.7599691646335[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]89.1233171884141[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]88.6733333333333[/C][C]1.13444246160029[/C][C]78.1646811846649[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]88.72[/C][C]1.11802590350311[/C][C]79.354154248138[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]88.645[/C][C]1.09772344031292[/C][C]80.7534910384447[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]88.665[/C][C]1.08715100900665[/C][C]81.5572071087113[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]88.6566666666667[/C][C]1.01313789744867[/C][C]87.5070085621377[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]88.6466666666667[/C][C]1.00746778464615[/C][C]87.9895794363313[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]88.81[/C][C]0.973286412459337[/C][C]91.247549398734[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]88.9833333333333[/C][C]0.934429844188413[/C][C]95.2274094055918[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]89.0733333333333[/C][C]0.90687850632563[/C][C]98.2196983521298[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]89.04[/C][C]0.900913535107622[/C][C]98.8330139688304[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]89.0033333333333[/C][C]0.868331625403615[/C][C]102.499241913437[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]89.2633333333333[/C][C]0.802439665143652[/C][C]111.239931437529[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]89.2633333333333[/C][C]0.78765893084323[/C][C]113.327393162130[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]89.4966666666667[/C][C]0.726923579733198[/C][C]123.117022424165[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]89.0216666666667[/C][C]0.598307838243158[/C][C]148.789069733844[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]89.1016666666667[/C][C]0.56108999885698[/C][C]158.80102452045[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]89.13[/C][C]0.556823618727583[/C][C]160.068641132131[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]89.04[/C][C]0.488328175287543[/C][C]182.336396927272[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]89.1033333333333[/C][C]0.47907023102292[/C][C]185.992214843068[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]89.1366666666667[/C][C]0.454537491798085[/C][C]196.104102026996[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]88.7172413793104[/C][C]1.10375298273242[/C][C]80.3778044247587[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]88.7642857142857[/C][C]1.06587086694837[/C][C]83.278648912153[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]88.7888888888889[/C][C]1.02997244291791[/C][C]86.2051111167116[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]88.8442307692308[/C][C]0.995030690165171[/C][C]89.2879301587[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]88.898[/C][C]0.955228319752478[/C][C]93.0646612561021[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]88.9583333333333[/C][C]0.930910450655422[/C][C]95.5605700534363[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]89.0260869565217[/C][C]0.90111275698336[/C][C]98.7957236945051[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]89.0681818181818[/C][C]0.872844810178854[/C][C]102.043548611959[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]89.0833333333333[/C][C]0.846931447343995[/C][C]105.183641028683[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]89.085[/C][C]0.819994918683443[/C][C]108.640917120599[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]89.0921052631579[/C][C]0.785034103135668[/C][C]113.488197400975[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]89.1055555555556[/C][C]0.746717094857943[/C][C]119.329738356274[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]89.0823529411765[/C][C]0.713387022837934[/C][C]124.872404584537[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]89.05625[/C][C]0.670383518965077[/C][C]132.843734191859[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]88.9933333333333[/C][C]0.627985894367783[/C][C]141.712312539960[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]88.9892857142857[/C][C]0.610194246236876[/C][C]145.837634922143[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]88.973076923077[/C][C]0.594035940179424[/C][C]149.777262460253[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]88.95[/C][C]0.5681778655989[/C][C]156.553089068755[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]88.9363636363636[/C][C]0.55277910442781[/C][C]160.889517935782[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]88.91[/C][C]0.527501558989964[/C][C]168.549264897417[/C][/ROW]
[ROW][C]Median[/C][C]88.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]87.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]88.7967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]88.9933333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]88.7967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]88.9933333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]88.9933333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]88.7967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]88.9933333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]89.05625[/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=556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=556&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 Mean88.681.1558492854267276.7228055751754
Geometric Mean88.2251385105405
Harmonic Mean87.7599691646335
Quadratic Mean89.1233171884141
Winsorized Mean ( 1 / 20 )88.67333333333331.1344424616002978.1646811846649
Winsorized Mean ( 2 / 20 )88.721.1180259035031179.354154248138
Winsorized Mean ( 3 / 20 )88.6451.0977234403129280.7534910384447
Winsorized Mean ( 4 / 20 )88.6651.0871510090066581.5572071087113
Winsorized Mean ( 5 / 20 )88.65666666666671.0131378974486787.5070085621377
Winsorized Mean ( 6 / 20 )88.64666666666671.0074677846461587.9895794363313
Winsorized Mean ( 7 / 20 )88.810.97328641245933791.247549398734
Winsorized Mean ( 8 / 20 )88.98333333333330.93442984418841395.2274094055918
Winsorized Mean ( 9 / 20 )89.07333333333330.9068785063256398.2196983521298
Winsorized Mean ( 10 / 20 )89.040.90091353510762298.8330139688304
Winsorized Mean ( 11 / 20 )89.00333333333330.868331625403615102.499241913437
Winsorized Mean ( 12 / 20 )89.26333333333330.802439665143652111.239931437529
Winsorized Mean ( 13 / 20 )89.26333333333330.78765893084323113.327393162130
Winsorized Mean ( 14 / 20 )89.49666666666670.726923579733198123.117022424165
Winsorized Mean ( 15 / 20 )89.02166666666670.598307838243158148.789069733844
Winsorized Mean ( 16 / 20 )89.10166666666670.56108999885698158.80102452045
Winsorized Mean ( 17 / 20 )89.130.556823618727583160.068641132131
Winsorized Mean ( 18 / 20 )89.040.488328175287543182.336396927272
Winsorized Mean ( 19 / 20 )89.10333333333330.47907023102292185.992214843068
Winsorized Mean ( 20 / 20 )89.13666666666670.454537491798085196.104102026996
Trimmed Mean ( 1 / 20 )88.71724137931041.1037529827324280.3778044247587
Trimmed Mean ( 2 / 20 )88.76428571428571.0658708669483783.278648912153
Trimmed Mean ( 3 / 20 )88.78888888888891.0299724429179186.2051111167116
Trimmed Mean ( 4 / 20 )88.84423076923080.99503069016517189.2879301587
Trimmed Mean ( 5 / 20 )88.8980.95522831975247893.0646612561021
Trimmed Mean ( 6 / 20 )88.95833333333330.93091045065542295.5605700534363
Trimmed Mean ( 7 / 20 )89.02608695652170.9011127569833698.7957236945051
Trimmed Mean ( 8 / 20 )89.06818181818180.872844810178854102.043548611959
Trimmed Mean ( 9 / 20 )89.08333333333330.846931447343995105.183641028683
Trimmed Mean ( 10 / 20 )89.0850.819994918683443108.640917120599
Trimmed Mean ( 11 / 20 )89.09210526315790.785034103135668113.488197400975
Trimmed Mean ( 12 / 20 )89.10555555555560.746717094857943119.329738356274
Trimmed Mean ( 13 / 20 )89.08235294117650.713387022837934124.872404584537
Trimmed Mean ( 14 / 20 )89.056250.670383518965077132.843734191859
Trimmed Mean ( 15 / 20 )88.99333333333330.627985894367783141.712312539960
Trimmed Mean ( 16 / 20 )88.98928571428570.610194246236876145.837634922143
Trimmed Mean ( 17 / 20 )88.9730769230770.594035940179424149.777262460253
Trimmed Mean ( 18 / 20 )88.950.5681778655989156.553089068755
Trimmed Mean ( 19 / 20 )88.93636363636360.55277910442781160.889517935782
Trimmed Mean ( 20 / 20 )88.910.527501558989964168.549264897417
Median88.6
Midrange87.6
Midmean - Weighted Average at Xnp88.7967741935484
Midmean - Weighted Average at X(n+1)p88.9933333333334
Midmean - Empirical Distribution Function88.7967741935484
Midmean - Empirical Distribution Function - Averaging88.9933333333334
Midmean - Empirical Distribution Function - Interpolation88.9933333333334
Midmean - Closest Observation88.7967741935484
Midmean - True Basic - Statistics Graphics Toolkit88.9933333333334
Midmean - MS Excel (old versions)89.05625
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')