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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 computationTue, 27 Oct 2009 19:36:12 -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/28/t12566939294jhng30vk1vtbbq.htm/, Retrieved Mon, 06 May 2024 07:42:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51330, Retrieved Mon, 06 May 2024 07:42:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmediaan
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS3 Yt/Xt mediaan] [2009-10-28 01:36:12] [a54ad7d84632b3d861404e40e79a6400] [Current]
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Dataseries X:
11,80352941
11,83372093
12,11764706
12,80365854
12,95308642
13,41772152
12,53139535
12,44712644
12,60689655
12,87176471
12,76904762
12,56235294
12,22298851
12,22413793
12,39651163
12,70941176
13,07228916
13,56125
13,30365854
13,48271605
13,2345679
13,26875
13,44936709
13,4835443
13,145
13,21
13,54556962
13,4875
14,04155844
15,05972222
14,536
14,84794521
15,52142857
15,65
15,95571429
15,38333333
15,17534247
15,6
16,52647059
17,634375
18,80983607
17,87846154
15,17662338
14,49493671
15,21466667
16,24927536
16,5
15,45217391
13,75974026
13,37875
13,3875
14,02597403
14,82739726
14,82702703
13,52222222
13,33012048




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51330&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51330&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51330&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14.05860366107140.21088245245307766.6655925968975
Geometric Mean13.9763412715833
Harmonic Mean13.8985535883936
Quadratic Mean14.1453265915102
Winsorized Mean ( 1 / 18 )14.04251110732140.20452612693323168.6587641289745
Winsorized Mean ( 2 / 18 )14.04393394982140.19972855561748770.315102947612
Winsorized Mean ( 3 / 18 )13.99022521982140.18138644918107477.1293847086409
Winsorized Mean ( 4 / 18 )13.98841656482140.18089289949578977.3298266754084
Winsorized Mean ( 5 / 18 )13.98142094517860.17274176431269580.9382780175242
Winsorized Mean ( 6 / 18 )13.955390988750.16460217826549784.7825413722079
Winsorized Mean ( 7 / 18 )13.927710316250.15476143065506489.9947115847774
Winsorized Mean ( 8 / 18 )13.92498997196430.15260421749295491.2490506535787
Winsorized Mean ( 9 / 18 )13.91952121517860.14895463037100593.4480598589574
Winsorized Mean ( 10 / 18 )13.92546059910710.14367447617604896.9236914568173
Winsorized Mean ( 11 / 18 )13.92365252910710.13929539977339599.957734079934
Winsorized Mean ( 12 / 18 )13.89492629910710.131430136749424105.721006176827
Winsorized Mean ( 13 / 18 )13.90190518196430.127465525672852109.064039932212
Winsorized Mean ( 14 / 18 )13.92191538196430.124474227206957111.845766745087
Winsorized Mean ( 15 / 18 )13.92287497750.114418853791051121.683398462683
Winsorized Mean ( 16 / 18 )13.88314178607140.100893366675051137.60212632001
Winsorized Mean ( 17 / 18 )13.89663615839290.0972282142609602142.928020061073
Winsorized Mean ( 18 / 18 )13.90441398089290.0962005907791364144.535640252101
Trimmed Mean ( 1 / 18 )14.012378510.19533070059673471.73669304002
Trimmed Mean ( 2 / 18 )13.97992802057690.18365433274795176.1208723551495
Trimmed Mean ( 3 / 18 )13.94408470020.17209604518081981.0250153369251
Trimmed Mean ( 4 / 18 )13.92614116479170.16699713591217283.3914970381034
Trimmed Mean ( 5 / 18 )13.90718778217390.1605806748488586.6056130058262
Trimmed Mean ( 6 / 18 )13.88829206795450.15523648708544789.4653849021334
Trimmed Mean ( 7 / 18 )13.87338119666670.15094279626319891.911515753794
Trimmed Mean ( 8 / 18 )13.862515372750.14821925059354093.5270912330073
Trimmed Mean ( 9 / 18 )13.85100689394740.14499042998263195.5304904993153
Trimmed Mean ( 10 / 18 )13.83916491250.14146086046626397.8303459125397
Trimmed Mean ( 11 / 18 )13.82495150529410.137876277017852100.270705043073
Trimmed Mean ( 12 / 18 )13.80924906968750.133869574893498103.154500047331
Trimmed Mean ( 13 / 18 )13.79592150066670.130366216755806105.824360359466
Trimmed Mean ( 14 / 18 )13.77961631892860.126083176785175109.289888391746
Trimmed Mean ( 15 / 18 )13.75772415538460.120092549605215114.559347774787
Trimmed Mean ( 16 / 18 )13.73203402750.114157147826108120.290619457466
Trimmed Mean ( 17 / 18 )13.70799415681820.110007897921907124.609181847555
Trimmed Mean ( 18 / 18 )13.67692370950.103499730892502132.144534015314
Median13.48552215
Midrange15.30668274
Midmean - Weighted Average at Xnp13.7483110910345
Midmean - Weighted Average at X(n+1)p13.7796163189286
Midmean - Empirical Distribution Function13.7483110910345
Midmean - Empirical Distribution Function - Averaging13.7796163189286
Midmean - Empirical Distribution Function - Interpolation13.7796163189286
Midmean - Closest Observation13.7483110910345
Midmean - True Basic - Statistics Graphics Toolkit13.7796163189286
Midmean - MS Excel (old versions)13.7959215006667
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14.0586036610714 & 0.210882452453077 & 66.6655925968975 \tabularnewline
Geometric Mean & 13.9763412715833 &  &  \tabularnewline
Harmonic Mean & 13.8985535883936 &  &  \tabularnewline
Quadratic Mean & 14.1453265915102 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 14.0425111073214 & 0.204526126933231 & 68.6587641289745 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 14.0439339498214 & 0.199728555617487 & 70.315102947612 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 13.9902252198214 & 0.181386449181074 & 77.1293847086409 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 13.9884165648214 & 0.180892899495789 & 77.3298266754084 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 13.9814209451786 & 0.172741764312695 & 80.9382780175242 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 13.95539098875 & 0.164602178265497 & 84.7825413722079 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 13.92771031625 & 0.154761430655064 & 89.9947115847774 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 13.9249899719643 & 0.152604217492954 & 91.2490506535787 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 13.9195212151786 & 0.148954630371005 & 93.4480598589574 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 13.9254605991071 & 0.143674476176048 & 96.9236914568173 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 13.9236525291071 & 0.139295399773395 & 99.957734079934 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 13.8949262991071 & 0.131430136749424 & 105.721006176827 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 13.9019051819643 & 0.127465525672852 & 109.064039932212 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 13.9219153819643 & 0.124474227206957 & 111.845766745087 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 13.9228749775 & 0.114418853791051 & 121.683398462683 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 13.8831417860714 & 0.100893366675051 & 137.60212632001 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 13.8966361583929 & 0.0972282142609602 & 142.928020061073 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 13.9044139808929 & 0.0962005907791364 & 144.535640252101 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 14.01237851 & 0.195330700596734 & 71.73669304002 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 13.9799280205769 & 0.183654332747951 & 76.1208723551495 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 13.9440847002 & 0.172096045180819 & 81.0250153369251 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 13.9261411647917 & 0.166997135912172 & 83.3914970381034 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 13.9071877821739 & 0.16058067484885 & 86.6056130058262 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 13.8882920679545 & 0.155236487085447 & 89.4653849021334 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 13.8733811966667 & 0.150942796263198 & 91.911515753794 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 13.86251537275 & 0.148219250593540 & 93.5270912330073 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 13.8510068939474 & 0.144990429982631 & 95.5304904993153 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 13.8391649125 & 0.141460860466263 & 97.8303459125397 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 13.8249515052941 & 0.137876277017852 & 100.270705043073 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 13.8092490696875 & 0.133869574893498 & 103.154500047331 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 13.7959215006667 & 0.130366216755806 & 105.824360359466 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 13.7796163189286 & 0.126083176785175 & 109.289888391746 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 13.7577241553846 & 0.120092549605215 & 114.559347774787 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 13.7320340275 & 0.114157147826108 & 120.290619457466 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 13.7079941568182 & 0.110007897921907 & 124.609181847555 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 13.6769237095 & 0.103499730892502 & 132.144534015314 \tabularnewline
Median & 13.48552215 &  &  \tabularnewline
Midrange & 15.30668274 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.7483110910345 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.7796163189286 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.7483110910345 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.7796163189286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.7796163189286 &  &  \tabularnewline
Midmean - Closest Observation & 13.7483110910345 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.7796163189286 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.7959215006667 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51330&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]14.0586036610714[/C][C]0.210882452453077[/C][C]66.6655925968975[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13.9763412715833[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13.8985535883936[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14.1453265915102[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]14.0425111073214[/C][C]0.204526126933231[/C][C]68.6587641289745[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]14.0439339498214[/C][C]0.199728555617487[/C][C]70.315102947612[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]13.9902252198214[/C][C]0.181386449181074[/C][C]77.1293847086409[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]13.9884165648214[/C][C]0.180892899495789[/C][C]77.3298266754084[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]13.9814209451786[/C][C]0.172741764312695[/C][C]80.9382780175242[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]13.95539098875[/C][C]0.164602178265497[/C][C]84.7825413722079[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]13.92771031625[/C][C]0.154761430655064[/C][C]89.9947115847774[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]13.9249899719643[/C][C]0.152604217492954[/C][C]91.2490506535787[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]13.9195212151786[/C][C]0.148954630371005[/C][C]93.4480598589574[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]13.9254605991071[/C][C]0.143674476176048[/C][C]96.9236914568173[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]13.9236525291071[/C][C]0.139295399773395[/C][C]99.957734079934[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]13.8949262991071[/C][C]0.131430136749424[/C][C]105.721006176827[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]13.9019051819643[/C][C]0.127465525672852[/C][C]109.064039932212[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]13.9219153819643[/C][C]0.124474227206957[/C][C]111.845766745087[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]13.9228749775[/C][C]0.114418853791051[/C][C]121.683398462683[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]13.8831417860714[/C][C]0.100893366675051[/C][C]137.60212632001[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]13.8966361583929[/C][C]0.0972282142609602[/C][C]142.928020061073[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]13.9044139808929[/C][C]0.0962005907791364[/C][C]144.535640252101[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]14.01237851[/C][C]0.195330700596734[/C][C]71.73669304002[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]13.9799280205769[/C][C]0.183654332747951[/C][C]76.1208723551495[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]13.9440847002[/C][C]0.172096045180819[/C][C]81.0250153369251[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]13.9261411647917[/C][C]0.166997135912172[/C][C]83.3914970381034[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]13.9071877821739[/C][C]0.16058067484885[/C][C]86.6056130058262[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]13.8882920679545[/C][C]0.155236487085447[/C][C]89.4653849021334[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]13.8733811966667[/C][C]0.150942796263198[/C][C]91.911515753794[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]13.86251537275[/C][C]0.148219250593540[/C][C]93.5270912330073[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]13.8510068939474[/C][C]0.144990429982631[/C][C]95.5304904993153[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]13.8391649125[/C][C]0.141460860466263[/C][C]97.8303459125397[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]13.8249515052941[/C][C]0.137876277017852[/C][C]100.270705043073[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]13.8092490696875[/C][C]0.133869574893498[/C][C]103.154500047331[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]13.7959215006667[/C][C]0.130366216755806[/C][C]105.824360359466[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]13.7796163189286[/C][C]0.126083176785175[/C][C]109.289888391746[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]13.7577241553846[/C][C]0.120092549605215[/C][C]114.559347774787[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]13.7320340275[/C][C]0.114157147826108[/C][C]120.290619457466[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]13.7079941568182[/C][C]0.110007897921907[/C][C]124.609181847555[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]13.6769237095[/C][C]0.103499730892502[/C][C]132.144534015314[/C][/ROW]
[ROW][C]Median[/C][C]13.48552215[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.30668274[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.7483110910345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.7796163189286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.7483110910345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.7796163189286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.7796163189286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.7483110910345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.7796163189286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.7959215006667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51330&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51330&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 Mean14.05860366107140.21088245245307766.6655925968975
Geometric Mean13.9763412715833
Harmonic Mean13.8985535883936
Quadratic Mean14.1453265915102
Winsorized Mean ( 1 / 18 )14.04251110732140.20452612693323168.6587641289745
Winsorized Mean ( 2 / 18 )14.04393394982140.19972855561748770.315102947612
Winsorized Mean ( 3 / 18 )13.99022521982140.18138644918107477.1293847086409
Winsorized Mean ( 4 / 18 )13.98841656482140.18089289949578977.3298266754084
Winsorized Mean ( 5 / 18 )13.98142094517860.17274176431269580.9382780175242
Winsorized Mean ( 6 / 18 )13.955390988750.16460217826549784.7825413722079
Winsorized Mean ( 7 / 18 )13.927710316250.15476143065506489.9947115847774
Winsorized Mean ( 8 / 18 )13.92498997196430.15260421749295491.2490506535787
Winsorized Mean ( 9 / 18 )13.91952121517860.14895463037100593.4480598589574
Winsorized Mean ( 10 / 18 )13.92546059910710.14367447617604896.9236914568173
Winsorized Mean ( 11 / 18 )13.92365252910710.13929539977339599.957734079934
Winsorized Mean ( 12 / 18 )13.89492629910710.131430136749424105.721006176827
Winsorized Mean ( 13 / 18 )13.90190518196430.127465525672852109.064039932212
Winsorized Mean ( 14 / 18 )13.92191538196430.124474227206957111.845766745087
Winsorized Mean ( 15 / 18 )13.92287497750.114418853791051121.683398462683
Winsorized Mean ( 16 / 18 )13.88314178607140.100893366675051137.60212632001
Winsorized Mean ( 17 / 18 )13.89663615839290.0972282142609602142.928020061073
Winsorized Mean ( 18 / 18 )13.90441398089290.0962005907791364144.535640252101
Trimmed Mean ( 1 / 18 )14.012378510.19533070059673471.73669304002
Trimmed Mean ( 2 / 18 )13.97992802057690.18365433274795176.1208723551495
Trimmed Mean ( 3 / 18 )13.94408470020.17209604518081981.0250153369251
Trimmed Mean ( 4 / 18 )13.92614116479170.16699713591217283.3914970381034
Trimmed Mean ( 5 / 18 )13.90718778217390.1605806748488586.6056130058262
Trimmed Mean ( 6 / 18 )13.88829206795450.15523648708544789.4653849021334
Trimmed Mean ( 7 / 18 )13.87338119666670.15094279626319891.911515753794
Trimmed Mean ( 8 / 18 )13.862515372750.14821925059354093.5270912330073
Trimmed Mean ( 9 / 18 )13.85100689394740.14499042998263195.5304904993153
Trimmed Mean ( 10 / 18 )13.83916491250.14146086046626397.8303459125397
Trimmed Mean ( 11 / 18 )13.82495150529410.137876277017852100.270705043073
Trimmed Mean ( 12 / 18 )13.80924906968750.133869574893498103.154500047331
Trimmed Mean ( 13 / 18 )13.79592150066670.130366216755806105.824360359466
Trimmed Mean ( 14 / 18 )13.77961631892860.126083176785175109.289888391746
Trimmed Mean ( 15 / 18 )13.75772415538460.120092549605215114.559347774787
Trimmed Mean ( 16 / 18 )13.73203402750.114157147826108120.290619457466
Trimmed Mean ( 17 / 18 )13.70799415681820.110007897921907124.609181847555
Trimmed Mean ( 18 / 18 )13.67692370950.103499730892502132.144534015314
Median13.48552215
Midrange15.30668274
Midmean - Weighted Average at Xnp13.7483110910345
Midmean - Weighted Average at X(n+1)p13.7796163189286
Midmean - Empirical Distribution Function13.7483110910345
Midmean - Empirical Distribution Function - Averaging13.7796163189286
Midmean - Empirical Distribution Function - Interpolation13.7796163189286
Midmean - Closest Observation13.7483110910345
Midmean - True Basic - Statistics Graphics Toolkit13.7796163189286
Midmean - MS Excel (old versions)13.7959215006667
Number of observations56



Parameters (Session):
par1 = 0 ;
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')