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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 04:26:37 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t125586176374rjftiuh8gobzl.htm/, Retrieved Mon, 29 Apr 2024 12:13:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47257, Retrieved Mon, 29 Apr 2024 12:13:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVraag 2
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Workshop 3] [2009-10-18 10:26:37] [ee8fc1691ecec7724e0ca78f0c288737] [Current]
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Post a new message
Dataseries X:
-7
-6
-4
-4
-2
2
-5
-15
-16
-18
-13
-23
-10
-10
-6
-3
-4
-7
-7
-7
-3
0
-5
-3
3
2
-7
-1
0
-3
4
2
3
0
-10
-10
-9
-22
-16
-18
-14
-12
-17
-23
-28
-31
-21
-19
-22
-22
-25
-16
-22
-21
-10
-7
-5
-4
7
6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47257&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47257&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47257&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-9.41.18874191674760-7.9075195949331
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean13.1047065336593
Winsorized Mean ( 1 / 20 )-9.366666666666671.17048608055945-8.00237339190717
Winsorized Mean ( 2 / 20 )-9.333333333333331.13113778693491-8.25127888143867
Winsorized Mean ( 3 / 20 )-9.283333333333331.09907297009661-8.44651227526531
Winsorized Mean ( 4 / 20 )-9.283333333333331.09907297009661-8.44651227526531
Winsorized Mean ( 5 / 20 )-9.283333333333331.06646140327273-8.70480010326197
Winsorized Mean ( 6 / 20 )-9.283333333333331.06646140327273-8.70480010326197
Winsorized Mean ( 7 / 20 )-9.283333333333331.06646140327273-8.70480010326197
Winsorized Mean ( 8 / 20 )-9.551.02136084030165-9.35027036789415
Winsorized Mean ( 9 / 20 )-9.40.99097623498502-9.4855957874127
Winsorized Mean ( 10 / 20 )-9.40.99097623498502-9.4855957874127
Winsorized Mean ( 11 / 20 )-9.216666666666670.891292360319042-10.340789483899
Winsorized Mean ( 12 / 20 )-9.216666666666670.824104261774536-11.1838599727909
Winsorized Mean ( 13 / 20 )-9.433333333333330.793108262238444-11.8941307038070
Winsorized Mean ( 14 / 20 )-9.20.751194905008503-12.2471544184606
Winsorized Mean ( 15 / 20 )-8.950.708074894694887-12.6399058447858
Winsorized Mean ( 16 / 20 )-8.950.708074894694887-12.6399058447858
Winsorized Mean ( 17 / 20 )-9.233333333333330.669077561593195-13.8000941345979
Winsorized Mean ( 18 / 20 )-8.933333333333330.618393520453893-14.4460332100123
Winsorized Mean ( 19 / 20 )-8.616666666666670.566529561346513-15.2095623151364
Winsorized Mean ( 20 / 20 )-8.283333333333330.513705749419663-16.1246654192426
Trimmed Mean ( 1 / 20 )-9.31034482758621.13600452882239-8.1956934073472
Trimmed Mean ( 2 / 20 )-9.251.09344267481971-8.4595198385916
Trimmed Mean ( 3 / 20 )-9.20370370370371.06706610367980-8.62524230876097
Trimmed Mean ( 4 / 20 )-9.173076923076921.04921185454658-8.7428262303051
Trimmed Mean ( 5 / 20 )-9.141.02619169152508-8.90671798990748
Trimmed Mean ( 6 / 20 )-9.104166666666671.00761268280918-9.03538316060554
Trimmed Mean ( 7 / 20 )-9.065217391304350.98314401219163-9.2206403933602
Trimmed Mean ( 8 / 20 )-9.022727272727270.950958477408121-9.48803495323908
Trimmed Mean ( 9 / 20 )-8.928571428571430.921036164180983-9.6940508698820
Trimmed Mean ( 10 / 20 )-8.850.889792542804652-9.94613864947051
Trimmed Mean ( 11 / 20 )-8.763157894736840.847080342962994-10.3451319199360
Trimmed Mean ( 12 / 20 )-8.694444444444440.818263205650444-10.6254862547964
Trimmed Mean ( 13 / 20 )-8.617647058823530.79662244436331-10.8177306825834
Trimmed Mean ( 14 / 20 )-8.50.772511613859874-11.0030708244366
Trimmed Mean ( 15 / 20 )-8.40.749865888392526-11.2020030915220
Trimmed Mean ( 16 / 20 )-8.321428571428570.729306352023648-11.4100590901733
Trimmed Mean ( 17 / 20 )-8.230769230769230.695718095667386-11.8306096708231
Trimmed Mean ( 18 / 20 )-8.083333333333330.6536316237124-12.3668027067338
Trimmed Mean ( 19 / 20 )-7.954545454545450.608302131894873-13.0766358318799
Trimmed Mean ( 20 / 20 )-7.850.558546044843687-14.0543471258433
Median-7
Midrange-12
Midmean - Weighted Average at Xnp-8.33333333333333
Midmean - Weighted Average at X(n+1)p-8.0625
Midmean - Empirical Distribution Function-8.33333333333333
Midmean - Empirical Distribution Function - Averaging-8.0625
Midmean - Empirical Distribution Function - Interpolation-8.0625
Midmean - Closest Observation-8.33333333333333
Midmean - True Basic - Statistics Graphics Toolkit-8.0625
Midmean - MS Excel (old versions)-8.33333333333333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -9.4 & 1.18874191674760 & -7.9075195949331 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 13.1047065336593 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -9.36666666666667 & 1.17048608055945 & -8.00237339190717 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -9.33333333333333 & 1.13113778693491 & -8.25127888143867 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -9.28333333333333 & 1.09907297009661 & -8.44651227526531 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -9.28333333333333 & 1.09907297009661 & -8.44651227526531 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -9.28333333333333 & 1.06646140327273 & -8.70480010326197 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -9.28333333333333 & 1.06646140327273 & -8.70480010326197 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -9.28333333333333 & 1.06646140327273 & -8.70480010326197 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -9.55 & 1.02136084030165 & -9.35027036789415 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -9.4 & 0.99097623498502 & -9.4855957874127 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -9.4 & 0.99097623498502 & -9.4855957874127 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -9.21666666666667 & 0.891292360319042 & -10.340789483899 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -9.21666666666667 & 0.824104261774536 & -11.1838599727909 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -9.43333333333333 & 0.793108262238444 & -11.8941307038070 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -9.2 & 0.751194905008503 & -12.2471544184606 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -8.95 & 0.708074894694887 & -12.6399058447858 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -8.95 & 0.708074894694887 & -12.6399058447858 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -9.23333333333333 & 0.669077561593195 & -13.8000941345979 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -8.93333333333333 & 0.618393520453893 & -14.4460332100123 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -8.61666666666667 & 0.566529561346513 & -15.2095623151364 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -8.28333333333333 & 0.513705749419663 & -16.1246654192426 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -9.3103448275862 & 1.13600452882239 & -8.1956934073472 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -9.25 & 1.09344267481971 & -8.4595198385916 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -9.2037037037037 & 1.06706610367980 & -8.62524230876097 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -9.17307692307692 & 1.04921185454658 & -8.7428262303051 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -9.14 & 1.02619169152508 & -8.90671798990748 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -9.10416666666667 & 1.00761268280918 & -9.03538316060554 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -9.06521739130435 & 0.98314401219163 & -9.2206403933602 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -9.02272727272727 & 0.950958477408121 & -9.48803495323908 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -8.92857142857143 & 0.921036164180983 & -9.6940508698820 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -8.85 & 0.889792542804652 & -9.94613864947051 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -8.76315789473684 & 0.847080342962994 & -10.3451319199360 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -8.69444444444444 & 0.818263205650444 & -10.6254862547964 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -8.61764705882353 & 0.79662244436331 & -10.8177306825834 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -8.5 & 0.772511613859874 & -11.0030708244366 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -8.4 & 0.749865888392526 & -11.2020030915220 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -8.32142857142857 & 0.729306352023648 & -11.4100590901733 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -8.23076923076923 & 0.695718095667386 & -11.8306096708231 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -8.08333333333333 & 0.6536316237124 & -12.3668027067338 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -7.95454545454545 & 0.608302131894873 & -13.0766358318799 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -7.85 & 0.558546044843687 & -14.0543471258433 \tabularnewline
Median & -7 &  &  \tabularnewline
Midrange & -12 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -8.33333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -8.0625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -8.33333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -8.0625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -8.0625 &  &  \tabularnewline
Midmean - Closest Observation & -8.33333333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -8.0625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -8.33333333333333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47257&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]-9.4[/C][C]1.18874191674760[/C][C]-7.9075195949331[/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]13.1047065336593[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-9.36666666666667[/C][C]1.17048608055945[/C][C]-8.00237339190717[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-9.33333333333333[/C][C]1.13113778693491[/C][C]-8.25127888143867[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-9.28333333333333[/C][C]1.09907297009661[/C][C]-8.44651227526531[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-9.28333333333333[/C][C]1.09907297009661[/C][C]-8.44651227526531[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-9.28333333333333[/C][C]1.06646140327273[/C][C]-8.70480010326197[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-9.28333333333333[/C][C]1.06646140327273[/C][C]-8.70480010326197[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-9.28333333333333[/C][C]1.06646140327273[/C][C]-8.70480010326197[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-9.55[/C][C]1.02136084030165[/C][C]-9.35027036789415[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-9.4[/C][C]0.99097623498502[/C][C]-9.4855957874127[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-9.4[/C][C]0.99097623498502[/C][C]-9.4855957874127[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-9.21666666666667[/C][C]0.891292360319042[/C][C]-10.340789483899[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-9.21666666666667[/C][C]0.824104261774536[/C][C]-11.1838599727909[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-9.43333333333333[/C][C]0.793108262238444[/C][C]-11.8941307038070[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-9.2[/C][C]0.751194905008503[/C][C]-12.2471544184606[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-8.95[/C][C]0.708074894694887[/C][C]-12.6399058447858[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-8.95[/C][C]0.708074894694887[/C][C]-12.6399058447858[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-9.23333333333333[/C][C]0.669077561593195[/C][C]-13.8000941345979[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-8.93333333333333[/C][C]0.618393520453893[/C][C]-14.4460332100123[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-8.61666666666667[/C][C]0.566529561346513[/C][C]-15.2095623151364[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-8.28333333333333[/C][C]0.513705749419663[/C][C]-16.1246654192426[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-9.3103448275862[/C][C]1.13600452882239[/C][C]-8.1956934073472[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-9.25[/C][C]1.09344267481971[/C][C]-8.4595198385916[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-9.2037037037037[/C][C]1.06706610367980[/C][C]-8.62524230876097[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-9.17307692307692[/C][C]1.04921185454658[/C][C]-8.7428262303051[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-9.14[/C][C]1.02619169152508[/C][C]-8.90671798990748[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-9.10416666666667[/C][C]1.00761268280918[/C][C]-9.03538316060554[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-9.06521739130435[/C][C]0.98314401219163[/C][C]-9.2206403933602[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-9.02272727272727[/C][C]0.950958477408121[/C][C]-9.48803495323908[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-8.92857142857143[/C][C]0.921036164180983[/C][C]-9.6940508698820[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-8.85[/C][C]0.889792542804652[/C][C]-9.94613864947051[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-8.76315789473684[/C][C]0.847080342962994[/C][C]-10.3451319199360[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-8.69444444444444[/C][C]0.818263205650444[/C][C]-10.6254862547964[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-8.61764705882353[/C][C]0.79662244436331[/C][C]-10.8177306825834[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-8.5[/C][C]0.772511613859874[/C][C]-11.0030708244366[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-8.4[/C][C]0.749865888392526[/C][C]-11.2020030915220[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-8.32142857142857[/C][C]0.729306352023648[/C][C]-11.4100590901733[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-8.23076923076923[/C][C]0.695718095667386[/C][C]-11.8306096708231[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-8.08333333333333[/C][C]0.6536316237124[/C][C]-12.3668027067338[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-7.95454545454545[/C][C]0.608302131894873[/C][C]-13.0766358318799[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-7.85[/C][C]0.558546044843687[/C][C]-14.0543471258433[/C][/ROW]
[ROW][C]Median[/C][C]-7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-8.33333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-8.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-8.33333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-8.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-8.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-8.33333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-8.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-8.33333333333333[/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=47257&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47257&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 Mean-9.41.18874191674760-7.9075195949331
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean13.1047065336593
Winsorized Mean ( 1 / 20 )-9.366666666666671.17048608055945-8.00237339190717
Winsorized Mean ( 2 / 20 )-9.333333333333331.13113778693491-8.25127888143867
Winsorized Mean ( 3 / 20 )-9.283333333333331.09907297009661-8.44651227526531
Winsorized Mean ( 4 / 20 )-9.283333333333331.09907297009661-8.44651227526531
Winsorized Mean ( 5 / 20 )-9.283333333333331.06646140327273-8.70480010326197
Winsorized Mean ( 6 / 20 )-9.283333333333331.06646140327273-8.70480010326197
Winsorized Mean ( 7 / 20 )-9.283333333333331.06646140327273-8.70480010326197
Winsorized Mean ( 8 / 20 )-9.551.02136084030165-9.35027036789415
Winsorized Mean ( 9 / 20 )-9.40.99097623498502-9.4855957874127
Winsorized Mean ( 10 / 20 )-9.40.99097623498502-9.4855957874127
Winsorized Mean ( 11 / 20 )-9.216666666666670.891292360319042-10.340789483899
Winsorized Mean ( 12 / 20 )-9.216666666666670.824104261774536-11.1838599727909
Winsorized Mean ( 13 / 20 )-9.433333333333330.793108262238444-11.8941307038070
Winsorized Mean ( 14 / 20 )-9.20.751194905008503-12.2471544184606
Winsorized Mean ( 15 / 20 )-8.950.708074894694887-12.6399058447858
Winsorized Mean ( 16 / 20 )-8.950.708074894694887-12.6399058447858
Winsorized Mean ( 17 / 20 )-9.233333333333330.669077561593195-13.8000941345979
Winsorized Mean ( 18 / 20 )-8.933333333333330.618393520453893-14.4460332100123
Winsorized Mean ( 19 / 20 )-8.616666666666670.566529561346513-15.2095623151364
Winsorized Mean ( 20 / 20 )-8.283333333333330.513705749419663-16.1246654192426
Trimmed Mean ( 1 / 20 )-9.31034482758621.13600452882239-8.1956934073472
Trimmed Mean ( 2 / 20 )-9.251.09344267481971-8.4595198385916
Trimmed Mean ( 3 / 20 )-9.20370370370371.06706610367980-8.62524230876097
Trimmed Mean ( 4 / 20 )-9.173076923076921.04921185454658-8.7428262303051
Trimmed Mean ( 5 / 20 )-9.141.02619169152508-8.90671798990748
Trimmed Mean ( 6 / 20 )-9.104166666666671.00761268280918-9.03538316060554
Trimmed Mean ( 7 / 20 )-9.065217391304350.98314401219163-9.2206403933602
Trimmed Mean ( 8 / 20 )-9.022727272727270.950958477408121-9.48803495323908
Trimmed Mean ( 9 / 20 )-8.928571428571430.921036164180983-9.6940508698820
Trimmed Mean ( 10 / 20 )-8.850.889792542804652-9.94613864947051
Trimmed Mean ( 11 / 20 )-8.763157894736840.847080342962994-10.3451319199360
Trimmed Mean ( 12 / 20 )-8.694444444444440.818263205650444-10.6254862547964
Trimmed Mean ( 13 / 20 )-8.617647058823530.79662244436331-10.8177306825834
Trimmed Mean ( 14 / 20 )-8.50.772511613859874-11.0030708244366
Trimmed Mean ( 15 / 20 )-8.40.749865888392526-11.2020030915220
Trimmed Mean ( 16 / 20 )-8.321428571428570.729306352023648-11.4100590901733
Trimmed Mean ( 17 / 20 )-8.230769230769230.695718095667386-11.8306096708231
Trimmed Mean ( 18 / 20 )-8.083333333333330.6536316237124-12.3668027067338
Trimmed Mean ( 19 / 20 )-7.954545454545450.608302131894873-13.0766358318799
Trimmed Mean ( 20 / 20 )-7.850.558546044843687-14.0543471258433
Median-7
Midrange-12
Midmean - Weighted Average at Xnp-8.33333333333333
Midmean - Weighted Average at X(n+1)p-8.0625
Midmean - Empirical Distribution Function-8.33333333333333
Midmean - Empirical Distribution Function - Averaging-8.0625
Midmean - Empirical Distribution Function - Interpolation-8.0625
Midmean - Closest Observation-8.33333333333333
Midmean - True Basic - Statistics Graphics Toolkit-8.0625
Midmean - MS Excel (old versions)-8.33333333333333
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')