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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 computationMon, 20 Oct 2008 10:48:17 -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/2008/Oct/20/t12245213701ay13046lcy2hbk.htm/, Retrieved Tue, 28 May 2024 23:19:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17635, Retrieved Tue, 28 May 2024 23:19:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
- R  D    [Central Tendency] [Central Tendency ...] [2008-10-20 16:48:17] [270782e2502ae87124d0ebdcd1862d6a] [Current]
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Dataseries X:
1,6
-0,2
1,7
1,1
0,9
0
0,4
0,7
0,7
1
1,1
0,3
1,4
-0,5
1,2
1,2
0,8
-0,2
0,3
0,2
0,7
0,9
0,7
0,3
1,2
-0,6
1,1
1
0,2
-1
-0,6
0
-0,4
0,1
0,7
0,8
1,2
-0,7
0,9
0,7
0,5
-0,2
0,3
0,5
0,9
0,5
0,3
0,9
0,4
-0,1
0,6
0,2
-0,5
-1,7
-2
-1
-1,7
-1,6
-1,7
-0,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17635&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17635&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17635&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.2433333333333330.1134554011947592.14474878032140
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.904802004123923
Winsorized Mean ( 1 / 20 )0.2466666666666670.1115242788966942.21177549056522
Winsorized Mean ( 2 / 20 )0.240.1102436951321222.17699524414863
Winsorized Mean ( 3 / 20 )0.230.1085939932373412.11798086748055
Winsorized Mean ( 4 / 20 )0.2366666666666670.1066163369962642.21979739066593
Winsorized Mean ( 5 / 20 )0.2866666666666670.09338174692697563.06983619497759
Winsorized Mean ( 6 / 20 )0.2866666666666670.09338174692697563.06983619497759
Winsorized Mean ( 7 / 20 )0.2866666666666670.08882365779766923.22736840358075
Winsorized Mean ( 8 / 20 )0.3133333333333330.0830378943740243.77337763313217
Winsorized Mean ( 9 / 20 )0.3283333333333330.08001029830137464.10363841035314
Winsorized Mean ( 10 / 20 )0.3116666666666670.07739004106307144.02721929573166
Winsorized Mean ( 11 / 20 )0.330.07381072143577834.4708951976188
Winsorized Mean ( 12 / 20 )0.310.07085833722860184.37492625602946
Winsorized Mean ( 13 / 20 )0.3316666666666670.06674395237703354.9692392322393
Winsorized Mean ( 14 / 20 )0.3783333333333330.05846876932873936.47069089493167
Winsorized Mean ( 15 / 20 )0.3783333333333330.05846876932873936.47069089493167
Winsorized Mean ( 16 / 20 )0.3783333333333330.05846876932873936.47069089493167
Winsorized Mean ( 17 / 20 )0.3783333333333330.04957968343400557.63081381584304
Winsorized Mean ( 18 / 20 )0.4083333333333330.04480287436972189.11399857883423
Winsorized Mean ( 19 / 20 )0.3766666666666670.04029318167683199.34814901656786
Winsorized Mean ( 20 / 20 )0.410.035151005964822411.6639620615783
Trimmed Mean ( 1 / 20 )0.2568965517241380.1077771913822562.38358922170272
Trimmed Mean ( 2 / 20 )0.2678571428571430.1031361205844112.59712253417479
Trimmed Mean ( 3 / 20 )0.2833333333333330.0981929673651432.88547480472529
Trimmed Mean ( 4 / 20 )0.3038461538461540.09271998172466473.27702991517444
Trimmed Mean ( 5 / 20 )0.3240.08654643675094733.74365499220225
Trimmed Mean ( 6 / 20 )0.3333333333333330.08375778429650613.97972959926112
Trimmed Mean ( 7 / 20 )0.3434782608695650.08013588543483844.28619786261501
Trimmed Mean ( 8 / 20 )0.3545454545454550.07683309836785784.61448857428577
Trimmed Mean ( 9 / 20 )0.3619047619047620.07427171612356474.87271307024422
Trimmed Mean ( 10 / 20 )0.36750.07173558105810255.12298073814084
Trimmed Mean ( 11 / 20 )0.3763157894736840.06897277283810965.45600494207996
Trimmed Mean ( 12 / 20 )0.3833333333333330.0662486897145065.78627796240622
Trimmed Mean ( 13 / 20 )0.3941176470588240.06318086203480826.23792766299536
Trimmed Mean ( 14 / 20 )0.4031250.06015510446123376.70142631469936
Trimmed Mean ( 15 / 20 )0.4066666666666670.05851286003326136.9500391270483
Trimmed Mean ( 16 / 20 )0.4107142857142860.0559523809523817.3404255319149
Trimmed Mean ( 17 / 20 )0.4153846153846150.05194444004964357.99670984974775
Trimmed Mean ( 18 / 20 )0.4208333333333330.04926237307485488.5426930751767
Trimmed Mean ( 19 / 20 )0.4227272727272730.04695573036309339.0026769780485
Trimmed Mean ( 20 / 20 )0.430.04478016478190699.60246578131705
Median0.4
Midrange-0.15
Midmean - Weighted Average at Xnp0.432352941176471
Midmean - Weighted Average at X(n+1)p0.432352941176471
Midmean - Empirical Distribution Function0.432352941176471
Midmean - Empirical Distribution Function - Averaging0.432352941176471
Midmean - Empirical Distribution Function - Interpolation0.432352941176471
Midmean - Closest Observation0.432352941176471
Midmean - True Basic - Statistics Graphics Toolkit0.432352941176471
Midmean - MS Excel (old versions)0.432352941176471
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.243333333333333 & 0.113455401194759 & 2.14474878032140 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 0.904802004123923 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.246666666666667 & 0.111524278896694 & 2.21177549056522 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.24 & 0.110243695132122 & 2.17699524414863 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.23 & 0.108593993237341 & 2.11798086748055 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.236666666666667 & 0.106616336996264 & 2.21979739066593 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.286666666666667 & 0.0933817469269756 & 3.06983619497759 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.286666666666667 & 0.0933817469269756 & 3.06983619497759 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.286666666666667 & 0.0888236577976692 & 3.22736840358075 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.313333333333333 & 0.083037894374024 & 3.77337763313217 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.328333333333333 & 0.0800102983013746 & 4.10363841035314 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.311666666666667 & 0.0773900410630714 & 4.02721929573166 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.33 & 0.0738107214357783 & 4.4708951976188 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.31 & 0.0708583372286018 & 4.37492625602946 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.331666666666667 & 0.0667439523770335 & 4.9692392322393 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.378333333333333 & 0.0584687693287393 & 6.47069089493167 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.378333333333333 & 0.0584687693287393 & 6.47069089493167 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.378333333333333 & 0.0584687693287393 & 6.47069089493167 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.378333333333333 & 0.0495796834340055 & 7.63081381584304 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.408333333333333 & 0.0448028743697218 & 9.11399857883423 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.376666666666667 & 0.0402931816768319 & 9.34814901656786 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.41 & 0.0351510059648224 & 11.6639620615783 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.256896551724138 & 0.107777191382256 & 2.38358922170272 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.267857142857143 & 0.103136120584411 & 2.59712253417479 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.283333333333333 & 0.098192967365143 & 2.88547480472529 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.303846153846154 & 0.0927199817246647 & 3.27702991517444 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.324 & 0.0865464367509473 & 3.74365499220225 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.333333333333333 & 0.0837577842965061 & 3.97972959926112 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.343478260869565 & 0.0801358854348384 & 4.28619786261501 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.354545454545455 & 0.0768330983678578 & 4.61448857428577 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.361904761904762 & 0.0742717161235647 & 4.87271307024422 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.3675 & 0.0717355810581025 & 5.12298073814084 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.376315789473684 & 0.0689727728381096 & 5.45600494207996 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.383333333333333 & 0.066248689714506 & 5.78627796240622 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.394117647058824 & 0.0631808620348082 & 6.23792766299536 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.403125 & 0.0601551044612337 & 6.70142631469936 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.406666666666667 & 0.0585128600332613 & 6.9500391270483 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.410714285714286 & 0.055952380952381 & 7.3404255319149 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.415384615384615 & 0.0519444400496435 & 7.99670984974775 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.420833333333333 & 0.0492623730748548 & 8.5426930751767 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.422727272727273 & 0.0469557303630933 & 9.0026769780485 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.43 & 0.0447801647819069 & 9.60246578131705 \tabularnewline
Median & 0.4 &  &  \tabularnewline
Midrange & -0.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.432352941176471 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.432352941176471 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.432352941176471 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.432352941176471 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.432352941176471 &  &  \tabularnewline
Midmean - Closest Observation & 0.432352941176471 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.432352941176471 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.432352941176471 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17635&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]0.243333333333333[/C][C]0.113455401194759[/C][C]2.14474878032140[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.904802004123923[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.246666666666667[/C][C]0.111524278896694[/C][C]2.21177549056522[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.24[/C][C]0.110243695132122[/C][C]2.17699524414863[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.23[/C][C]0.108593993237341[/C][C]2.11798086748055[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.236666666666667[/C][C]0.106616336996264[/C][C]2.21979739066593[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.286666666666667[/C][C]0.0933817469269756[/C][C]3.06983619497759[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.286666666666667[/C][C]0.0933817469269756[/C][C]3.06983619497759[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.286666666666667[/C][C]0.0888236577976692[/C][C]3.22736840358075[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.313333333333333[/C][C]0.083037894374024[/C][C]3.77337763313217[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.328333333333333[/C][C]0.0800102983013746[/C][C]4.10363841035314[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.311666666666667[/C][C]0.0773900410630714[/C][C]4.02721929573166[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.33[/C][C]0.0738107214357783[/C][C]4.4708951976188[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.31[/C][C]0.0708583372286018[/C][C]4.37492625602946[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.331666666666667[/C][C]0.0667439523770335[/C][C]4.9692392322393[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.378333333333333[/C][C]0.0584687693287393[/C][C]6.47069089493167[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.378333333333333[/C][C]0.0584687693287393[/C][C]6.47069089493167[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.378333333333333[/C][C]0.0584687693287393[/C][C]6.47069089493167[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.378333333333333[/C][C]0.0495796834340055[/C][C]7.63081381584304[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.408333333333333[/C][C]0.0448028743697218[/C][C]9.11399857883423[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.376666666666667[/C][C]0.0402931816768319[/C][C]9.34814901656786[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.41[/C][C]0.0351510059648224[/C][C]11.6639620615783[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.256896551724138[/C][C]0.107777191382256[/C][C]2.38358922170272[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.267857142857143[/C][C]0.103136120584411[/C][C]2.59712253417479[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.283333333333333[/C][C]0.098192967365143[/C][C]2.88547480472529[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.303846153846154[/C][C]0.0927199817246647[/C][C]3.27702991517444[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.324[/C][C]0.0865464367509473[/C][C]3.74365499220225[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.333333333333333[/C][C]0.0837577842965061[/C][C]3.97972959926112[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.343478260869565[/C][C]0.0801358854348384[/C][C]4.28619786261501[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.354545454545455[/C][C]0.0768330983678578[/C][C]4.61448857428577[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.361904761904762[/C][C]0.0742717161235647[/C][C]4.87271307024422[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.3675[/C][C]0.0717355810581025[/C][C]5.12298073814084[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.376315789473684[/C][C]0.0689727728381096[/C][C]5.45600494207996[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.383333333333333[/C][C]0.066248689714506[/C][C]5.78627796240622[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.394117647058824[/C][C]0.0631808620348082[/C][C]6.23792766299536[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.403125[/C][C]0.0601551044612337[/C][C]6.70142631469936[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.406666666666667[/C][C]0.0585128600332613[/C][C]6.9500391270483[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.410714285714286[/C][C]0.055952380952381[/C][C]7.3404255319149[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.415384615384615[/C][C]0.0519444400496435[/C][C]7.99670984974775[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.420833333333333[/C][C]0.0492623730748548[/C][C]8.5426930751767[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.422727272727273[/C][C]0.0469557303630933[/C][C]9.0026769780485[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.43[/C][C]0.0447801647819069[/C][C]9.60246578131705[/C][/ROW]
[ROW][C]Median[/C][C]0.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.432352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.432352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.432352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.432352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.432352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.432352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.432352941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.432352941176471[/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=17635&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17635&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 Mean0.2433333333333330.1134554011947592.14474878032140
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.904802004123923
Winsorized Mean ( 1 / 20 )0.2466666666666670.1115242788966942.21177549056522
Winsorized Mean ( 2 / 20 )0.240.1102436951321222.17699524414863
Winsorized Mean ( 3 / 20 )0.230.1085939932373412.11798086748055
Winsorized Mean ( 4 / 20 )0.2366666666666670.1066163369962642.21979739066593
Winsorized Mean ( 5 / 20 )0.2866666666666670.09338174692697563.06983619497759
Winsorized Mean ( 6 / 20 )0.2866666666666670.09338174692697563.06983619497759
Winsorized Mean ( 7 / 20 )0.2866666666666670.08882365779766923.22736840358075
Winsorized Mean ( 8 / 20 )0.3133333333333330.0830378943740243.77337763313217
Winsorized Mean ( 9 / 20 )0.3283333333333330.08001029830137464.10363841035314
Winsorized Mean ( 10 / 20 )0.3116666666666670.07739004106307144.02721929573166
Winsorized Mean ( 11 / 20 )0.330.07381072143577834.4708951976188
Winsorized Mean ( 12 / 20 )0.310.07085833722860184.37492625602946
Winsorized Mean ( 13 / 20 )0.3316666666666670.06674395237703354.9692392322393
Winsorized Mean ( 14 / 20 )0.3783333333333330.05846876932873936.47069089493167
Winsorized Mean ( 15 / 20 )0.3783333333333330.05846876932873936.47069089493167
Winsorized Mean ( 16 / 20 )0.3783333333333330.05846876932873936.47069089493167
Winsorized Mean ( 17 / 20 )0.3783333333333330.04957968343400557.63081381584304
Winsorized Mean ( 18 / 20 )0.4083333333333330.04480287436972189.11399857883423
Winsorized Mean ( 19 / 20 )0.3766666666666670.04029318167683199.34814901656786
Winsorized Mean ( 20 / 20 )0.410.035151005964822411.6639620615783
Trimmed Mean ( 1 / 20 )0.2568965517241380.1077771913822562.38358922170272
Trimmed Mean ( 2 / 20 )0.2678571428571430.1031361205844112.59712253417479
Trimmed Mean ( 3 / 20 )0.2833333333333330.0981929673651432.88547480472529
Trimmed Mean ( 4 / 20 )0.3038461538461540.09271998172466473.27702991517444
Trimmed Mean ( 5 / 20 )0.3240.08654643675094733.74365499220225
Trimmed Mean ( 6 / 20 )0.3333333333333330.08375778429650613.97972959926112
Trimmed Mean ( 7 / 20 )0.3434782608695650.08013588543483844.28619786261501
Trimmed Mean ( 8 / 20 )0.3545454545454550.07683309836785784.61448857428577
Trimmed Mean ( 9 / 20 )0.3619047619047620.07427171612356474.87271307024422
Trimmed Mean ( 10 / 20 )0.36750.07173558105810255.12298073814084
Trimmed Mean ( 11 / 20 )0.3763157894736840.06897277283810965.45600494207996
Trimmed Mean ( 12 / 20 )0.3833333333333330.0662486897145065.78627796240622
Trimmed Mean ( 13 / 20 )0.3941176470588240.06318086203480826.23792766299536
Trimmed Mean ( 14 / 20 )0.4031250.06015510446123376.70142631469936
Trimmed Mean ( 15 / 20 )0.4066666666666670.05851286003326136.9500391270483
Trimmed Mean ( 16 / 20 )0.4107142857142860.0559523809523817.3404255319149
Trimmed Mean ( 17 / 20 )0.4153846153846150.05194444004964357.99670984974775
Trimmed Mean ( 18 / 20 )0.4208333333333330.04926237307485488.5426930751767
Trimmed Mean ( 19 / 20 )0.4227272727272730.04695573036309339.0026769780485
Trimmed Mean ( 20 / 20 )0.430.04478016478190699.60246578131705
Median0.4
Midrange-0.15
Midmean - Weighted Average at Xnp0.432352941176471
Midmean - Weighted Average at X(n+1)p0.432352941176471
Midmean - Empirical Distribution Function0.432352941176471
Midmean - Empirical Distribution Function - Averaging0.432352941176471
Midmean - Empirical Distribution Function - Interpolation0.432352941176471
Midmean - Closest Observation0.432352941176471
Midmean - True Basic - Statistics Graphics Toolkit0.432352941176471
Midmean - MS Excel (old versions)0.432352941176471
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')