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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 04 Dec 2007 09:15:30 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/04/t11967843430izm0o2jrw679c1.htm/, Retrieved Thu, 02 May 2024 12:05:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2413, Retrieved Thu, 02 May 2024 12:05:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTaak9.4G19
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency 2] [2007-12-04 16:15:30] [40a229849a2b804e343854d9b3fa1a24] [Current]
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Dataseries X:
-38.2209256877886 
-25.7062537484295 
-8.78614604054669 
-143.549433697964 
-42.9624591079809 
-88.9885459881577 
14.0886325887361 
-23.3914618674755 
-3.91688057556558 
-33.0598387059355 
-26.2713299071082 
43.9553272870348 
-36.9019356180568 
62.3813419251369 
2.35446996941928 
-92.274974039265 
-94.7424012613132 
31.3059146633623 
-10.6487210360685 
6.90342728015465 
19.6619133704088 
-54.7012097004945 
15.2583646523227 
11.261626980628 
-35.0793183508263 
18.5171282344817 
-52.5298586714035 
23.4750033012650 
-40.7051183197006 
-34.6020860920868 
37.3239205977251 
-4.97010837846055 
-36.163765585957 
111.429795553408 
-32.3992721559408 
-40.5775992934779 
-9.22380434616887 
54.9949346728775 
85.2961638680839 
19.5871368793974 
42.8461686673343 
66.6921201775877 
47.6411089815228 
2.92145998384694 
-75.4623334127209 
9.72848590678222 
61.3092731667239 
3.92785954109058 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2413&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2413&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2413&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-6.103629236240897.21250348571391-0.846256677494935
Geometric MeanNaN
Harmonic Mean73.7701376908618
Quadratic Mean49.82172213835
Winsorized Mean ( 1 / 16 )-5.631266720588256.68610336543003-0.84223446943765
Winsorized Mean ( 2 / 16 )-6.303625740106926.45115651588194-0.97713111200886
Winsorized Mean ( 3 / 16 )-6.367647627690896.32993602319294-1.00595765966035
Winsorized Mean ( 4 / 16 )-5.329802309605576.01226319467321-0.886488521382049
Winsorized Mean ( 5 / 16 )-3.824928849357655.36875907107302-0.712441888101562
Winsorized Mean ( 6 / 16 )-4.472738182140625.10711266006153-0.87578608107046
Winsorized Mean ( 7 / 16 )-3.615002242920994.72735384405541-0.764698891213064
Winsorized Mean ( 8 / 16 )-3.423638548157694.62227084541829-0.74068324047936
Winsorized Mean ( 9 / 16 )-4.435150243792664.40326445215271-1.00724139828221
Winsorized Mean ( 10 / 16 )-5.19792781226634.07167183180379-1.27660774909838
Winsorized Mean ( 11 / 16 )-6.69024310843343.69137266649779-1.81239980702918
Winsorized Mean ( 12 / 16 )-7.45897308312253.49757065127679-2.13261541418744
Winsorized Mean ( 13 / 16 )-7.185520589923523.4432676002716-2.08683187718455
Winsorized Mean ( 14 / 16 )-7.358413702558253.36796806939748-2.18482288161201
Winsorized Mean ( 15 / 16 )-7.894825013810653.12145375050707-2.52921415623351
Winsorized Mean ( 16 / 16 )-8.064546851674623.02253425839962-2.66814075945153
Trimmed Mean ( 1 / 16 )-5.670751417282766.39457466302682-0.886806662852936
Trimmed Mean ( 2 / 16 )-5.713825631858586.01419616737175-0.95005641200353
Trimmed Mean ( 3 / 16 )-5.376796998573815.68708150405912-0.945440467968704
Trimmed Mean ( 4 / 16 )-4.980456746926995.31724899874841-0.936660432509235
Trimmed Mean ( 5 / 16 )-4.87013709555484.97101183494395-0.979707403092456
Trimmed Mean ( 6 / 16 )-5.148859294540714.77043212638508-1.07932764959857
Trimmed Mean ( 7 / 16 )-5.307946615105434.59027572253466-1.15634592254395
Trimmed Mean ( 8 / 16 )-5.670720409144964.46675718540292-1.26953854301203
Trimmed Mean ( 9 / 16 )-6.120136781342414.31582860285723-1.41806761679337
Trimmed Mean ( 10 / 16 )-6.441086598018554.16704133079542-1.54572179316231
Trimmed Mean ( 11 / 16 )-6.67059283538824.05561277024194-1.64478050871466
Trimmed Mean ( 12 / 16 )-6.667020058470894.0082580862727-1.66332105243018
Trimmed Mean ( 13 / 16 )-6.523028599443333.97633107748862-1.64046415460031
Trimmed Mean ( 14 / 16 )-6.400722385816223.90925921141388-1.63732360523139
Trimmed Mean ( 15 / 16 )-6.218304992151073.78786405607753-1.64163890258257
Trimmed Mean ( 16 / 16 )-5.883000987819153.65544547291547-1.60938004175099
Median-4.44349447701306
Midrange-16.059819072278
Midmean - Weighted Average at Xnp-7.87641668085433
Midmean - Weighted Average at X(n+1)p-6.6670200584709
Midmean - Empirical Distribution Function-7.87641668085433
Midmean - Empirical Distribution Function - Averaging-6.6670200584709
Midmean - Empirical Distribution Function - Interpolation-6.6670200584709
Midmean - Closest Observation-7.87641668085433
Midmean - True Basic - Statistics Graphics Toolkit-6.6670200584709
Midmean - MS Excel (old versions)-6.6705928353882
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -6.10362923624089 & 7.21250348571391 & -0.846256677494935 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 73.7701376908618 &  &  \tabularnewline
Quadratic Mean & 49.82172213835 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -5.63126672058825 & 6.68610336543003 & -0.84223446943765 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -6.30362574010692 & 6.45115651588194 & -0.97713111200886 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -6.36764762769089 & 6.32993602319294 & -1.00595765966035 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -5.32980230960557 & 6.01226319467321 & -0.886488521382049 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -3.82492884935765 & 5.36875907107302 & -0.712441888101562 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -4.47273818214062 & 5.10711266006153 & -0.87578608107046 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -3.61500224292099 & 4.72735384405541 & -0.764698891213064 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -3.42363854815769 & 4.62227084541829 & -0.74068324047936 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -4.43515024379266 & 4.40326445215271 & -1.00724139828221 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -5.1979278122663 & 4.07167183180379 & -1.27660774909838 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -6.6902431084334 & 3.69137266649779 & -1.81239980702918 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -7.4589730831225 & 3.49757065127679 & -2.13261541418744 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -7.18552058992352 & 3.4432676002716 & -2.08683187718455 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -7.35841370255825 & 3.36796806939748 & -2.18482288161201 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -7.89482501381065 & 3.12145375050707 & -2.52921415623351 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -8.06454685167462 & 3.02253425839962 & -2.66814075945153 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -5.67075141728276 & 6.39457466302682 & -0.886806662852936 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -5.71382563185858 & 6.01419616737175 & -0.95005641200353 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -5.37679699857381 & 5.68708150405912 & -0.945440467968704 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -4.98045674692699 & 5.31724899874841 & -0.936660432509235 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -4.8701370955548 & 4.97101183494395 & -0.979707403092456 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -5.14885929454071 & 4.77043212638508 & -1.07932764959857 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -5.30794661510543 & 4.59027572253466 & -1.15634592254395 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -5.67072040914496 & 4.46675718540292 & -1.26953854301203 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -6.12013678134241 & 4.31582860285723 & -1.41806761679337 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -6.44108659801855 & 4.16704133079542 & -1.54572179316231 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -6.6705928353882 & 4.05561277024194 & -1.64478050871466 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -6.66702005847089 & 4.0082580862727 & -1.66332105243018 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -6.52302859944333 & 3.97633107748862 & -1.64046415460031 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -6.40072238581622 & 3.90925921141388 & -1.63732360523139 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -6.21830499215107 & 3.78786405607753 & -1.64163890258257 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -5.88300098781915 & 3.65544547291547 & -1.60938004175099 \tabularnewline
Median & -4.44349447701306 &  &  \tabularnewline
Midrange & -16.059819072278 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -7.87641668085433 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -6.6670200584709 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -7.87641668085433 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -6.6670200584709 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -6.6670200584709 &  &  \tabularnewline
Midmean - Closest Observation & -7.87641668085433 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -6.6670200584709 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -6.6705928353882 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2413&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]-6.10362923624089[/C][C]7.21250348571391[/C][C]-0.846256677494935[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]73.7701376908618[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]49.82172213835[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-5.63126672058825[/C][C]6.68610336543003[/C][C]-0.84223446943765[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-6.30362574010692[/C][C]6.45115651588194[/C][C]-0.97713111200886[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-6.36764762769089[/C][C]6.32993602319294[/C][C]-1.00595765966035[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-5.32980230960557[/C][C]6.01226319467321[/C][C]-0.886488521382049[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-3.82492884935765[/C][C]5.36875907107302[/C][C]-0.712441888101562[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-4.47273818214062[/C][C]5.10711266006153[/C][C]-0.87578608107046[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-3.61500224292099[/C][C]4.72735384405541[/C][C]-0.764698891213064[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-3.42363854815769[/C][C]4.62227084541829[/C][C]-0.74068324047936[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-4.43515024379266[/C][C]4.40326445215271[/C][C]-1.00724139828221[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-5.1979278122663[/C][C]4.07167183180379[/C][C]-1.27660774909838[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-6.6902431084334[/C][C]3.69137266649779[/C][C]-1.81239980702918[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-7.4589730831225[/C][C]3.49757065127679[/C][C]-2.13261541418744[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-7.18552058992352[/C][C]3.4432676002716[/C][C]-2.08683187718455[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-7.35841370255825[/C][C]3.36796806939748[/C][C]-2.18482288161201[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-7.89482501381065[/C][C]3.12145375050707[/C][C]-2.52921415623351[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-8.06454685167462[/C][C]3.02253425839962[/C][C]-2.66814075945153[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-5.67075141728276[/C][C]6.39457466302682[/C][C]-0.886806662852936[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-5.71382563185858[/C][C]6.01419616737175[/C][C]-0.95005641200353[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-5.37679699857381[/C][C]5.68708150405912[/C][C]-0.945440467968704[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-4.98045674692699[/C][C]5.31724899874841[/C][C]-0.936660432509235[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-4.8701370955548[/C][C]4.97101183494395[/C][C]-0.979707403092456[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-5.14885929454071[/C][C]4.77043212638508[/C][C]-1.07932764959857[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-5.30794661510543[/C][C]4.59027572253466[/C][C]-1.15634592254395[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-5.67072040914496[/C][C]4.46675718540292[/C][C]-1.26953854301203[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-6.12013678134241[/C][C]4.31582860285723[/C][C]-1.41806761679337[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-6.44108659801855[/C][C]4.16704133079542[/C][C]-1.54572179316231[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-6.6705928353882[/C][C]4.05561277024194[/C][C]-1.64478050871466[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-6.66702005847089[/C][C]4.0082580862727[/C][C]-1.66332105243018[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-6.52302859944333[/C][C]3.97633107748862[/C][C]-1.64046415460031[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-6.40072238581622[/C][C]3.90925921141388[/C][C]-1.63732360523139[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-6.21830499215107[/C][C]3.78786405607753[/C][C]-1.64163890258257[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-5.88300098781915[/C][C]3.65544547291547[/C][C]-1.60938004175099[/C][/ROW]
[ROW][C]Median[/C][C]-4.44349447701306[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-16.059819072278[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-7.87641668085433[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-6.6670200584709[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-7.87641668085433[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-6.6670200584709[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-6.6670200584709[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-7.87641668085433[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-6.6670200584709[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-6.6705928353882[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2413&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2413&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-6.103629236240897.21250348571391-0.846256677494935
Geometric MeanNaN
Harmonic Mean73.7701376908618
Quadratic Mean49.82172213835
Winsorized Mean ( 1 / 16 )-5.631266720588256.68610336543003-0.84223446943765
Winsorized Mean ( 2 / 16 )-6.303625740106926.45115651588194-0.97713111200886
Winsorized Mean ( 3 / 16 )-6.367647627690896.32993602319294-1.00595765966035
Winsorized Mean ( 4 / 16 )-5.329802309605576.01226319467321-0.886488521382049
Winsorized Mean ( 5 / 16 )-3.824928849357655.36875907107302-0.712441888101562
Winsorized Mean ( 6 / 16 )-4.472738182140625.10711266006153-0.87578608107046
Winsorized Mean ( 7 / 16 )-3.615002242920994.72735384405541-0.764698891213064
Winsorized Mean ( 8 / 16 )-3.423638548157694.62227084541829-0.74068324047936
Winsorized Mean ( 9 / 16 )-4.435150243792664.40326445215271-1.00724139828221
Winsorized Mean ( 10 / 16 )-5.19792781226634.07167183180379-1.27660774909838
Winsorized Mean ( 11 / 16 )-6.69024310843343.69137266649779-1.81239980702918
Winsorized Mean ( 12 / 16 )-7.45897308312253.49757065127679-2.13261541418744
Winsorized Mean ( 13 / 16 )-7.185520589923523.4432676002716-2.08683187718455
Winsorized Mean ( 14 / 16 )-7.358413702558253.36796806939748-2.18482288161201
Winsorized Mean ( 15 / 16 )-7.894825013810653.12145375050707-2.52921415623351
Winsorized Mean ( 16 / 16 )-8.064546851674623.02253425839962-2.66814075945153
Trimmed Mean ( 1 / 16 )-5.670751417282766.39457466302682-0.886806662852936
Trimmed Mean ( 2 / 16 )-5.713825631858586.01419616737175-0.95005641200353
Trimmed Mean ( 3 / 16 )-5.376796998573815.68708150405912-0.945440467968704
Trimmed Mean ( 4 / 16 )-4.980456746926995.31724899874841-0.936660432509235
Trimmed Mean ( 5 / 16 )-4.87013709555484.97101183494395-0.979707403092456
Trimmed Mean ( 6 / 16 )-5.148859294540714.77043212638508-1.07932764959857
Trimmed Mean ( 7 / 16 )-5.307946615105434.59027572253466-1.15634592254395
Trimmed Mean ( 8 / 16 )-5.670720409144964.46675718540292-1.26953854301203
Trimmed Mean ( 9 / 16 )-6.120136781342414.31582860285723-1.41806761679337
Trimmed Mean ( 10 / 16 )-6.441086598018554.16704133079542-1.54572179316231
Trimmed Mean ( 11 / 16 )-6.67059283538824.05561277024194-1.64478050871466
Trimmed Mean ( 12 / 16 )-6.667020058470894.0082580862727-1.66332105243018
Trimmed Mean ( 13 / 16 )-6.523028599443333.97633107748862-1.64046415460031
Trimmed Mean ( 14 / 16 )-6.400722385816223.90925921141388-1.63732360523139
Trimmed Mean ( 15 / 16 )-6.218304992151073.78786405607753-1.64163890258257
Trimmed Mean ( 16 / 16 )-5.883000987819153.65544547291547-1.60938004175099
Median-4.44349447701306
Midrange-16.059819072278
Midmean - Weighted Average at Xnp-7.87641668085433
Midmean - Weighted Average at X(n+1)p-6.6670200584709
Midmean - Empirical Distribution Function-7.87641668085433
Midmean - Empirical Distribution Function - Averaging-6.6670200584709
Midmean - Empirical Distribution Function - Interpolation-6.6670200584709
Midmean - Closest Observation-7.87641668085433
Midmean - True Basic - Statistics Graphics Toolkit-6.6670200584709
Midmean - MS Excel (old versions)-6.6705928353882
Number of observations48



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')