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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, 15 Nov 2010 19:41:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/15/t1289849976peylzlbgl5ft7wb.htm/, Retrieved Sun, 28 Apr 2024 00:13:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95025, Retrieved Sun, 28 Apr 2024 00:13:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
0,96
0,95
0,95
0,96
0,96
0,96
0,95
0,96
0,96
0,96
0,95
0,95
0,96
0,96
0,96
0,96
0,96
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,96
0,96
0,96
0,97
0,97
0,97
0,96
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,95
0,94
0,94
0,94
0,93
0,93
0,93
0,93
0,92
0,93




Summary of computational 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 computational 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=95025&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]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=95025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95025&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.951090909090910.00141356409572007672.831824160349
Geometric Mean0.951033841271604
Harmonic Mean0.950976425692214
Quadratic Mean0.95114763216959
Winsorized Mean ( 1 / 18 )0.9512727272727270.00134976105765576704.771205153066
Winsorized Mean ( 2 / 18 )0.9512727272727270.00134976105765576704.771205153066
Winsorized Mean ( 3 / 18 )0.9507272727272730.00124057512063386766.360099371901
Winsorized Mean ( 4 / 18 )0.9507272727272730.00124057512063386766.360099371901
Winsorized Mean ( 5 / 18 )0.9507272727272730.00124057512063386766.360099371901
Winsorized Mean ( 6 / 18 )0.9518181818181820.0009389050536260411013.75339086979
Winsorized Mean ( 7 / 18 )0.9518181818181820.0009389050536260411013.75339086979
Winsorized Mean ( 8 / 18 )0.9518181818181820.0009389050536260411013.75339086979
Winsorized Mean ( 9 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 10 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 11 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 12 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 13 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 14 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 15 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 16 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 17 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 18 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Trimmed Mean ( 1 / 18 )0.9513207547169810.00129299036420788735.752393096744
Trimmed Mean ( 2 / 18 )0.9513725490196080.00122136560803117778.941655769407
Trimmed Mean ( 3 / 18 )0.9514285714285710.00112938487863156842.430768668858
Trimmed Mean ( 4 / 18 )0.9517021276595740.00106752365177628891.504488988144
Trimmed Mean ( 5 / 18 )0.9520.000984731927834662966.76057015168
Trimmed Mean ( 6 / 18 )0.952325581395350.0008701528806451031094.43478563138
Trimmed Mean ( 7 / 18 )0.952325581395350.0008396055842955381134.25351046752
Trimmed Mean ( 8 / 18 )0.9525641025641030.0007979349797082051193.78662019861
Trimmed Mean ( 9 / 18 )0.9527027027027030.0007401656182502251287.14801013714
Trimmed Mean ( 10 / 18 )0.9525714285714290.0007495496847387491270.85828727077
Trimmed Mean ( 11 / 18 )0.9524242424242420.0007575757575757581257.2
Trimmed Mean ( 12 / 18 )0.952258064516130.0007633651333031771247.44767997929
Trimmed Mean ( 13 / 18 )0.9520689655172410.0007655305550699541243.67206405006
Trimmed Mean ( 14 / 18 )0.9520689655172410.000761808658525411249.74815508150
Trimmed Mean ( 15 / 18 )0.9518518518518520.0007483314773547891271.96554021283
Trimmed Mean ( 16 / 18 )0.9513043478260870.000718019846821541324.89979495306
Trimmed Mean ( 17 / 18 )0.9509523809523810.0006563832739090591448.77607146969
Trimmed Mean ( 18 / 18 )0.9505263157894740.0005263157894736851806
Median0.95
Midrange0.945
Midmean - Weighted Average at Xnp0.953720930232558
Midmean - Weighted Average at X(n+1)p0.953720930232558
Midmean - Empirical Distribution Function0.953720930232558
Midmean - Empirical Distribution Function - Averaging0.953720930232558
Midmean - Empirical Distribution Function - Interpolation0.953720930232558
Midmean - Closest Observation0.953720930232558
Midmean - True Basic - Statistics Graphics Toolkit0.953720930232558
Midmean - MS Excel (old versions)0.953720930232558
Number of observations55

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.95109090909091 & 0.00141356409572007 & 672.831824160349 \tabularnewline
Geometric Mean & 0.951033841271604 &  &  \tabularnewline
Harmonic Mean & 0.950976425692214 &  &  \tabularnewline
Quadratic Mean & 0.95114763216959 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 0.951272727272727 & 0.00134976105765576 & 704.771205153066 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 0.951272727272727 & 0.00134976105765576 & 704.771205153066 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 0.950727272727273 & 0.00124057512063386 & 766.360099371901 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 0.950727272727273 & 0.00124057512063386 & 766.360099371901 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 0.950727272727273 & 0.00124057512063386 & 766.360099371901 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 0.951818181818182 & 0.000938905053626041 & 1013.75339086979 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 0.951818181818182 & 0.000938905053626041 & 1013.75339086979 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 0.951818181818182 & 0.000938905053626041 & 1013.75339086979 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 0.953454545454545 & 0.000647095651638262 & 1473.43679878032 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 0.951320754716981 & 0.00129299036420788 & 735.752393096744 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 0.951372549019608 & 0.00122136560803117 & 778.941655769407 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 0.951428571428571 & 0.00112938487863156 & 842.430768668858 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 0.951702127659574 & 0.00106752365177628 & 891.504488988144 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 0.952 & 0.000984731927834662 & 966.76057015168 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 0.95232558139535 & 0.000870152880645103 & 1094.43478563138 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 0.95232558139535 & 0.000839605584295538 & 1134.25351046752 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 0.952564102564103 & 0.000797934979708205 & 1193.78662019861 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 0.952702702702703 & 0.000740165618250225 & 1287.14801013714 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 0.952571428571429 & 0.000749549684738749 & 1270.85828727077 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 0.952424242424242 & 0.000757575757575758 & 1257.2 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 0.95225806451613 & 0.000763365133303177 & 1247.44767997929 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 0.952068965517241 & 0.000765530555069954 & 1243.67206405006 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 0.952068965517241 & 0.00076180865852541 & 1249.74815508150 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 0.951851851851852 & 0.000748331477354789 & 1271.96554021283 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 0.951304347826087 & 0.00071801984682154 & 1324.89979495306 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 0.950952380952381 & 0.000656383273909059 & 1448.77607146969 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 0.950526315789474 & 0.000526315789473685 & 1806 \tabularnewline
Median & 0.95 &  &  \tabularnewline
Midrange & 0.945 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.953720930232558 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.953720930232558 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.953720930232558 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.953720930232558 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.953720930232558 &  &  \tabularnewline
Midmean - Closest Observation & 0.953720930232558 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.953720930232558 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.953720930232558 &  &  \tabularnewline
Number of observations & 55 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95025&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]0.95109090909091[/C][C]0.00141356409572007[/C][C]672.831824160349[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.951033841271604[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.950976425692214[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.95114763216959[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]0.951272727272727[/C][C]0.00134976105765576[/C][C]704.771205153066[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]0.951272727272727[/C][C]0.00134976105765576[/C][C]704.771205153066[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]0.950727272727273[/C][C]0.00124057512063386[/C][C]766.360099371901[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]0.950727272727273[/C][C]0.00124057512063386[/C][C]766.360099371901[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]0.950727272727273[/C][C]0.00124057512063386[/C][C]766.360099371901[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]0.951818181818182[/C][C]0.000938905053626041[/C][C]1013.75339086979[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]0.951818181818182[/C][C]0.000938905053626041[/C][C]1013.75339086979[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]0.951818181818182[/C][C]0.000938905053626041[/C][C]1013.75339086979[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]0.953454545454545[/C][C]0.000647095651638262[/C][C]1473.43679878032[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]0.951320754716981[/C][C]0.00129299036420788[/C][C]735.752393096744[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]0.951372549019608[/C][C]0.00122136560803117[/C][C]778.941655769407[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]0.951428571428571[/C][C]0.00112938487863156[/C][C]842.430768668858[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]0.951702127659574[/C][C]0.00106752365177628[/C][C]891.504488988144[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]0.952[/C][C]0.000984731927834662[/C][C]966.76057015168[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]0.95232558139535[/C][C]0.000870152880645103[/C][C]1094.43478563138[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]0.95232558139535[/C][C]0.000839605584295538[/C][C]1134.25351046752[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]0.952564102564103[/C][C]0.000797934979708205[/C][C]1193.78662019861[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]0.952702702702703[/C][C]0.000740165618250225[/C][C]1287.14801013714[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]0.952571428571429[/C][C]0.000749549684738749[/C][C]1270.85828727077[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]0.952424242424242[/C][C]0.000757575757575758[/C][C]1257.2[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]0.95225806451613[/C][C]0.000763365133303177[/C][C]1247.44767997929[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]0.952068965517241[/C][C]0.000765530555069954[/C][C]1243.67206405006[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]0.952068965517241[/C][C]0.00076180865852541[/C][C]1249.74815508150[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]0.951851851851852[/C][C]0.000748331477354789[/C][C]1271.96554021283[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]0.951304347826087[/C][C]0.00071801984682154[/C][C]1324.89979495306[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]0.950952380952381[/C][C]0.000656383273909059[/C][C]1448.77607146969[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]0.950526315789474[/C][C]0.000526315789473685[/C][C]1806[/C][/ROW]
[ROW][C]Median[/C][C]0.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.953720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]55[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95025&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 Mean0.951090909090910.00141356409572007672.831824160349
Geometric Mean0.951033841271604
Harmonic Mean0.950976425692214
Quadratic Mean0.95114763216959
Winsorized Mean ( 1 / 18 )0.9512727272727270.00134976105765576704.771205153066
Winsorized Mean ( 2 / 18 )0.9512727272727270.00134976105765576704.771205153066
Winsorized Mean ( 3 / 18 )0.9507272727272730.00124057512063386766.360099371901
Winsorized Mean ( 4 / 18 )0.9507272727272730.00124057512063386766.360099371901
Winsorized Mean ( 5 / 18 )0.9507272727272730.00124057512063386766.360099371901
Winsorized Mean ( 6 / 18 )0.9518181818181820.0009389050536260411013.75339086979
Winsorized Mean ( 7 / 18 )0.9518181818181820.0009389050536260411013.75339086979
Winsorized Mean ( 8 / 18 )0.9518181818181820.0009389050536260411013.75339086979
Winsorized Mean ( 9 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 10 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 11 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 12 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 13 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 14 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 15 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 16 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 17 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Winsorized Mean ( 18 / 18 )0.9534545454545450.0006470956516382621473.43679878032
Trimmed Mean ( 1 / 18 )0.9513207547169810.00129299036420788735.752393096744
Trimmed Mean ( 2 / 18 )0.9513725490196080.00122136560803117778.941655769407
Trimmed Mean ( 3 / 18 )0.9514285714285710.00112938487863156842.430768668858
Trimmed Mean ( 4 / 18 )0.9517021276595740.00106752365177628891.504488988144
Trimmed Mean ( 5 / 18 )0.9520.000984731927834662966.76057015168
Trimmed Mean ( 6 / 18 )0.952325581395350.0008701528806451031094.43478563138
Trimmed Mean ( 7 / 18 )0.952325581395350.0008396055842955381134.25351046752
Trimmed Mean ( 8 / 18 )0.9525641025641030.0007979349797082051193.78662019861
Trimmed Mean ( 9 / 18 )0.9527027027027030.0007401656182502251287.14801013714
Trimmed Mean ( 10 / 18 )0.9525714285714290.0007495496847387491270.85828727077
Trimmed Mean ( 11 / 18 )0.9524242424242420.0007575757575757581257.2
Trimmed Mean ( 12 / 18 )0.952258064516130.0007633651333031771247.44767997929
Trimmed Mean ( 13 / 18 )0.9520689655172410.0007655305550699541243.67206405006
Trimmed Mean ( 14 / 18 )0.9520689655172410.000761808658525411249.74815508150
Trimmed Mean ( 15 / 18 )0.9518518518518520.0007483314773547891271.96554021283
Trimmed Mean ( 16 / 18 )0.9513043478260870.000718019846821541324.89979495306
Trimmed Mean ( 17 / 18 )0.9509523809523810.0006563832739090591448.77607146969
Trimmed Mean ( 18 / 18 )0.9505263157894740.0005263157894736851806
Median0.95
Midrange0.945
Midmean - Weighted Average at Xnp0.953720930232558
Midmean - Weighted Average at X(n+1)p0.953720930232558
Midmean - Empirical Distribution Function0.953720930232558
Midmean - Empirical Distribution Function - Averaging0.953720930232558
Midmean - Empirical Distribution Function - Interpolation0.953720930232558
Midmean - Closest Observation0.953720930232558
Midmean - True Basic - Statistics Graphics Toolkit0.953720930232558
Midmean - MS Excel (old versions)0.953720930232558
Number of observations55



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')