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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 08:17:30 -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/Dec/13/t1197558122fun04a1cy8qk8ji.htm/, Retrieved Sun, 05 May 2024 16:11:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3604, Retrieved Sun, 05 May 2024 16:11:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-12-13 15:17:30] [919a0fafa615dc0e3c6b6d22cd1007a0] [Current]
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Dataseries X:
0.2
4.8
4
2.1
-7
-4.5
-0.5
-3.3
-5.7
-3.8
-17.4
-19.7
5.7
9
-3
3.3
-12.8
-8.8
10.4
-0.1
-1.9
9.3
5.7
-15.7
3.2
4.6
-2.1
10.3
-11.4
-9.2
1.8
-7.2
-2.8
15
-15
-12.9
10.6
0.1
6
10.1
-4.4
-0.9
14.7
-0.4
4.8
17.7
-15.5
-10
13
12.8
9.9
10.4
0.9
-5.1
8.8
-0.8
1.8
8.5
-9.2
-3.6




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3604&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3604&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3604&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.081.155849285426720.0692131759812138
Geometric MeanNaN
Harmonic Mean-156.715831984827
Quadratic Mean8.87860724813676
Winsorized Mean ( 1 / 20 )0.07333333333333341.134442461600290.0646426203316529
Winsorized Mean ( 2 / 20 )0.121.118025903503110.107332039109294
Winsorized Mean ( 3 / 20 )0.0451.097723440312920.0409939319389702
Winsorized Mean ( 4 / 20 )0.06500000000000011.087151009006650.0597893020026645
Winsorized Mean ( 5 / 20 )0.05666666666666681.013137897448670.0559318398900757
Winsorized Mean ( 6 / 20 )0.04666666666666661.007467784646150.0463207532566984
Winsorized Mean ( 7 / 20 )0.210.9732864124593370.215763825849951
Winsorized Mean ( 8 / 20 )0.3833333333333330.9344298441884130.410232331209704
Winsorized Mean ( 9 / 20 )0.4733333333333330.906878506325630.521936874710067
Winsorized Mean ( 10 / 20 )0.440.9009135351076220.488393150789369
Winsorized Mean ( 11 / 20 )0.4033333333333330.8683316254036140.464492276376387
Winsorized Mean ( 12 / 20 )0.6633333333333330.8024396651436520.826645743159498
Winsorized Mean ( 13 / 20 )0.6633333333333340.787658930843230.842158080558042
Winsorized Mean ( 14 / 20 )0.8966666666666670.7269235797331991.23350884696266
Winsorized Mean ( 15 / 20 )0.4216666666666670.5983078382431580.704765406224374
Winsorized Mean ( 16 / 20 )0.5016666666666670.561089998856980.89409304690626
Winsorized Mean ( 17 / 20 )0.530.5568236187275840.951827440817113
Winsorized Mean ( 18 / 20 )0.440.4883281752875430.901033407996404
Winsorized Mean ( 19 / 20 )0.5033333333333330.479070231022921.05064623251294
Winsorized Mean ( 20 / 20 )0.5366666666666670.4545374917980851.18068734999987
Trimmed Mean ( 1 / 20 )0.1172413793103451.103752982732420.106220668160828
Trimmed Mean ( 2 / 20 )0.1642857142857141.065870866948370.154132849841436
Trimmed Mean ( 3 / 20 )0.1888888888888891.029972442917910.1833921773225
Trimmed Mean ( 4 / 20 )0.2442307692307690.9950306901651710.245450488758521
Trimmed Mean ( 5 / 20 )0.2980.9552283197524780.311967300212811
Trimmed Mean ( 6 / 20 )0.3583333333333330.9309104506554220.384927823166066
Trimmed Mean ( 7 / 20 )0.4260869565217390.901112756983360.472845327313025
Trimmed Mean ( 8 / 20 )0.4681818181818180.8728448101788540.536386093750026
Trimmed Mean ( 9 / 20 )0.4833333333333330.8469314473439950.570687668817923
Trimmed Mean ( 10 / 20 )0.4850.8199949186834430.59146707979447
Trimmed Mean ( 11 / 20 )0.4921052631578950.7850341031356680.62685845263572
Trimmed Mean ( 12 / 20 )0.5055555555555560.7467170948579430.677037607732462
Trimmed Mean ( 13 / 20 )0.4823529411764710.7133870228379330.676144821442948
Trimmed Mean ( 14 / 20 )0.456250.6703835189650770.680580573795054
Trimmed Mean ( 15 / 20 )0.3933333333333330.6279858943677830.626341032276397
Trimmed Mean ( 16 / 20 )0.3892857142857140.6101942462368760.63797014915574
Trimmed Mean ( 17 / 20 )0.3730769230769230.5940359401794240.628037628437495
Trimmed Mean ( 18 / 20 )0.350.56817786559890.616004285262107
Trimmed Mean ( 19 / 20 )0.3363636363636360.5527791044278090.608495570236527
Trimmed Mean ( 20 / 20 )0.310.5275015589899640.587675988282526
Median0
Midrange-1
Midmean - Weighted Average at Xnp0.196774193548387
Midmean - Weighted Average at X(n+1)p0.393333333333333
Midmean - Empirical Distribution Function0.196774193548387
Midmean - Empirical Distribution Function - Averaging0.393333333333333
Midmean - Empirical Distribution Function - Interpolation0.393333333333333
Midmean - Closest Observation0.196774193548387
Midmean - True Basic - Statistics Graphics Toolkit0.393333333333333
Midmean - MS Excel (old versions)0.45625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.08 & 1.15584928542672 & 0.0692131759812138 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -156.715831984827 &  &  \tabularnewline
Quadratic Mean & 8.87860724813676 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.0733333333333334 & 1.13444246160029 & 0.0646426203316529 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.12 & 1.11802590350311 & 0.107332039109294 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.045 & 1.09772344031292 & 0.0409939319389702 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.0650000000000001 & 1.08715100900665 & 0.0597893020026645 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.0566666666666668 & 1.01313789744867 & 0.0559318398900757 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.0466666666666666 & 1.00746778464615 & 0.0463207532566984 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.21 & 0.973286412459337 & 0.215763825849951 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.383333333333333 & 0.934429844188413 & 0.410232331209704 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.473333333333333 & 0.90687850632563 & 0.521936874710067 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.44 & 0.900913535107622 & 0.488393150789369 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.403333333333333 & 0.868331625403614 & 0.464492276376387 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.663333333333333 & 0.802439665143652 & 0.826645743159498 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.663333333333334 & 0.78765893084323 & 0.842158080558042 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.896666666666667 & 0.726923579733199 & 1.23350884696266 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.421666666666667 & 0.598307838243158 & 0.704765406224374 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.501666666666667 & 0.56108999885698 & 0.89409304690626 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.53 & 0.556823618727584 & 0.951827440817113 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.44 & 0.488328175287543 & 0.901033407996404 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.503333333333333 & 0.47907023102292 & 1.05064623251294 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.536666666666667 & 0.454537491798085 & 1.18068734999987 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.117241379310345 & 1.10375298273242 & 0.106220668160828 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.164285714285714 & 1.06587086694837 & 0.154132849841436 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.188888888888889 & 1.02997244291791 & 0.1833921773225 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.244230769230769 & 0.995030690165171 & 0.245450488758521 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.298 & 0.955228319752478 & 0.311967300212811 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.358333333333333 & 0.930910450655422 & 0.384927823166066 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.426086956521739 & 0.90111275698336 & 0.472845327313025 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.468181818181818 & 0.872844810178854 & 0.536386093750026 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.483333333333333 & 0.846931447343995 & 0.570687668817923 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.485 & 0.819994918683443 & 0.59146707979447 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.492105263157895 & 0.785034103135668 & 0.62685845263572 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.505555555555556 & 0.746717094857943 & 0.677037607732462 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.482352941176471 & 0.713387022837933 & 0.676144821442948 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.45625 & 0.670383518965077 & 0.680580573795054 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.393333333333333 & 0.627985894367783 & 0.626341032276397 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.389285714285714 & 0.610194246236876 & 0.63797014915574 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.373076923076923 & 0.594035940179424 & 0.628037628437495 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.35 & 0.5681778655989 & 0.616004285262107 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.336363636363636 & 0.552779104427809 & 0.608495570236527 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.31 & 0.527501558989964 & 0.587675988282526 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & -1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.196774193548387 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.393333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.196774193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.393333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.393333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 0.196774193548387 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.393333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.45625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3604&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.08[/C][C]1.15584928542672[/C][C]0.0692131759812138[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-156.715831984827[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.87860724813676[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.0733333333333334[/C][C]1.13444246160029[/C][C]0.0646426203316529[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.12[/C][C]1.11802590350311[/C][C]0.107332039109294[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.045[/C][C]1.09772344031292[/C][C]0.0409939319389702[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.0650000000000001[/C][C]1.08715100900665[/C][C]0.0597893020026645[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.0566666666666668[/C][C]1.01313789744867[/C][C]0.0559318398900757[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.0466666666666666[/C][C]1.00746778464615[/C][C]0.0463207532566984[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.21[/C][C]0.973286412459337[/C][C]0.215763825849951[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.383333333333333[/C][C]0.934429844188413[/C][C]0.410232331209704[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.473333333333333[/C][C]0.90687850632563[/C][C]0.521936874710067[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.44[/C][C]0.900913535107622[/C][C]0.488393150789369[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.403333333333333[/C][C]0.868331625403614[/C][C]0.464492276376387[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.663333333333333[/C][C]0.802439665143652[/C][C]0.826645743159498[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.663333333333334[/C][C]0.78765893084323[/C][C]0.842158080558042[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.896666666666667[/C][C]0.726923579733199[/C][C]1.23350884696266[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.421666666666667[/C][C]0.598307838243158[/C][C]0.704765406224374[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.501666666666667[/C][C]0.56108999885698[/C][C]0.89409304690626[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.53[/C][C]0.556823618727584[/C][C]0.951827440817113[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.44[/C][C]0.488328175287543[/C][C]0.901033407996404[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.503333333333333[/C][C]0.47907023102292[/C][C]1.05064623251294[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.536666666666667[/C][C]0.454537491798085[/C][C]1.18068734999987[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.117241379310345[/C][C]1.10375298273242[/C][C]0.106220668160828[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.164285714285714[/C][C]1.06587086694837[/C][C]0.154132849841436[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.188888888888889[/C][C]1.02997244291791[/C][C]0.1833921773225[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.244230769230769[/C][C]0.995030690165171[/C][C]0.245450488758521[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.298[/C][C]0.955228319752478[/C][C]0.311967300212811[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.358333333333333[/C][C]0.930910450655422[/C][C]0.384927823166066[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.426086956521739[/C][C]0.90111275698336[/C][C]0.472845327313025[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.468181818181818[/C][C]0.872844810178854[/C][C]0.536386093750026[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.483333333333333[/C][C]0.846931447343995[/C][C]0.570687668817923[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.485[/C][C]0.819994918683443[/C][C]0.59146707979447[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.492105263157895[/C][C]0.785034103135668[/C][C]0.62685845263572[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.505555555555556[/C][C]0.746717094857943[/C][C]0.677037607732462[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.482352941176471[/C][C]0.713387022837933[/C][C]0.676144821442948[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.45625[/C][C]0.670383518965077[/C][C]0.680580573795054[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.393333333333333[/C][C]0.627985894367783[/C][C]0.626341032276397[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.389285714285714[/C][C]0.610194246236876[/C][C]0.63797014915574[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.373076923076923[/C][C]0.594035940179424[/C][C]0.628037628437495[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.35[/C][C]0.5681778655989[/C][C]0.616004285262107[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.336363636363636[/C][C]0.552779104427809[/C][C]0.608495570236527[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.31[/C][C]0.527501558989964[/C][C]0.587675988282526[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.196774193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.393333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.196774193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.393333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.393333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.196774193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.393333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.45625[/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=3604&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3604&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.081.155849285426720.0692131759812138
Geometric MeanNaN
Harmonic Mean-156.715831984827
Quadratic Mean8.87860724813676
Winsorized Mean ( 1 / 20 )0.07333333333333341.134442461600290.0646426203316529
Winsorized Mean ( 2 / 20 )0.121.118025903503110.107332039109294
Winsorized Mean ( 3 / 20 )0.0451.097723440312920.0409939319389702
Winsorized Mean ( 4 / 20 )0.06500000000000011.087151009006650.0597893020026645
Winsorized Mean ( 5 / 20 )0.05666666666666681.013137897448670.0559318398900757
Winsorized Mean ( 6 / 20 )0.04666666666666661.007467784646150.0463207532566984
Winsorized Mean ( 7 / 20 )0.210.9732864124593370.215763825849951
Winsorized Mean ( 8 / 20 )0.3833333333333330.9344298441884130.410232331209704
Winsorized Mean ( 9 / 20 )0.4733333333333330.906878506325630.521936874710067
Winsorized Mean ( 10 / 20 )0.440.9009135351076220.488393150789369
Winsorized Mean ( 11 / 20 )0.4033333333333330.8683316254036140.464492276376387
Winsorized Mean ( 12 / 20 )0.6633333333333330.8024396651436520.826645743159498
Winsorized Mean ( 13 / 20 )0.6633333333333340.787658930843230.842158080558042
Winsorized Mean ( 14 / 20 )0.8966666666666670.7269235797331991.23350884696266
Winsorized Mean ( 15 / 20 )0.4216666666666670.5983078382431580.704765406224374
Winsorized Mean ( 16 / 20 )0.5016666666666670.561089998856980.89409304690626
Winsorized Mean ( 17 / 20 )0.530.5568236187275840.951827440817113
Winsorized Mean ( 18 / 20 )0.440.4883281752875430.901033407996404
Winsorized Mean ( 19 / 20 )0.5033333333333330.479070231022921.05064623251294
Winsorized Mean ( 20 / 20 )0.5366666666666670.4545374917980851.18068734999987
Trimmed Mean ( 1 / 20 )0.1172413793103451.103752982732420.106220668160828
Trimmed Mean ( 2 / 20 )0.1642857142857141.065870866948370.154132849841436
Trimmed Mean ( 3 / 20 )0.1888888888888891.029972442917910.1833921773225
Trimmed Mean ( 4 / 20 )0.2442307692307690.9950306901651710.245450488758521
Trimmed Mean ( 5 / 20 )0.2980.9552283197524780.311967300212811
Trimmed Mean ( 6 / 20 )0.3583333333333330.9309104506554220.384927823166066
Trimmed Mean ( 7 / 20 )0.4260869565217390.901112756983360.472845327313025
Trimmed Mean ( 8 / 20 )0.4681818181818180.8728448101788540.536386093750026
Trimmed Mean ( 9 / 20 )0.4833333333333330.8469314473439950.570687668817923
Trimmed Mean ( 10 / 20 )0.4850.8199949186834430.59146707979447
Trimmed Mean ( 11 / 20 )0.4921052631578950.7850341031356680.62685845263572
Trimmed Mean ( 12 / 20 )0.5055555555555560.7467170948579430.677037607732462
Trimmed Mean ( 13 / 20 )0.4823529411764710.7133870228379330.676144821442948
Trimmed Mean ( 14 / 20 )0.456250.6703835189650770.680580573795054
Trimmed Mean ( 15 / 20 )0.3933333333333330.6279858943677830.626341032276397
Trimmed Mean ( 16 / 20 )0.3892857142857140.6101942462368760.63797014915574
Trimmed Mean ( 17 / 20 )0.3730769230769230.5940359401794240.628037628437495
Trimmed Mean ( 18 / 20 )0.350.56817786559890.616004285262107
Trimmed Mean ( 19 / 20 )0.3363636363636360.5527791044278090.608495570236527
Trimmed Mean ( 20 / 20 )0.310.5275015589899640.587675988282526
Median0
Midrange-1
Midmean - Weighted Average at Xnp0.196774193548387
Midmean - Weighted Average at X(n+1)p0.393333333333333
Midmean - Empirical Distribution Function0.196774193548387
Midmean - Empirical Distribution Function - Averaging0.393333333333333
Midmean - Empirical Distribution Function - Interpolation0.393333333333333
Midmean - Closest Observation0.196774193548387
Midmean - True Basic - Statistics Graphics Toolkit0.393333333333333
Midmean - MS Excel (old versions)0.45625
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')