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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, 08 Dec 2009 10:26:42 -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/2009/Dec/08/t1260293244o68llwsl5h5hu3u.htm/, Retrieved Sat, 27 Apr 2024 17:53:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64752, Retrieved Sat, 27 Apr 2024 17:53:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper: Central Te...] [2009-12-08 17:26:42] [762da55b2e2304daaed24a7cc507d14d] [Current]
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Dataseries X:
108.8
128.4
121.1
119.5
128.7
108.7
105.5
119.8
111.3
110.6
120.1
97.5
107.7
127.3
117.2
119.8
116.2
111
112.4
130.6
109.1
118.8
123.9
101.6
112.8
128
129.6
125.8
119.5
115.7
113.6
129.7
112
116.8
127
112.1
114.2
121.1
131.6
125
120.4
117.7
117.5
120.6
127.5
112.3
124.5
115.2
104.7
130.9
129.2
113.5
125.6
107.6
107
121.6
110.7
106.3
118.6
104.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64752&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64752&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64752&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.4351.08076093981951108.659552425731
Geometric Mean117.138710541647
Harmonic Mean116.839702700745
Quadratic Mean117.728050325032
Winsorized Mean ( 1 / 20 )117.4916666666671.05881900862802110.9648256305
Winsorized Mean ( 2 / 20 )117.5816666666671.03328638038032113.793880282626
Winsorized Mean ( 3 / 20 )117.5416666666671.02288307417197114.912124009695
Winsorized Mean ( 4 / 20 )117.5883333333331.01045688515682116.371450440544
Winsorized Mean ( 5 / 20 )117.6216666666670.990577334559942118.740518849969
Winsorized Mean ( 6 / 20 )117.6416666666670.96747178141498121.597000477481
Winsorized Mean ( 7 / 20 )117.6766666666670.947892001603733124.145647887703
Winsorized Mean ( 8 / 20 )117.6366666666670.935368946412789125.764990507556
Winsorized Mean ( 9 / 20 )117.7116666666670.895055758975988131.513221926350
Winsorized Mean ( 10 / 20 )117.6950.886064188285878132.828977353983
Winsorized Mean ( 11 / 20 )117.6950.866704991547229135.795918043454
Winsorized Mean ( 12 / 20 )117.7550.774930013242311151.955657914593
Winsorized Mean ( 13 / 20 )117.7333333333330.763949988996257154.11130967882
Winsorized Mean ( 14 / 20 )117.6633333333330.728898893528326161.426137943178
Winsorized Mean ( 15 / 20 )117.6133333333330.696177889252447168.941494909621
Winsorized Mean ( 16 / 20 )117.640.64124349535803183.456051954675
Winsorized Mean ( 17 / 20 )117.0166666666670.535123232370802218.672372246366
Winsorized Mean ( 18 / 20 )116.9266666666670.504369980483381231.827172891229
Winsorized Mean ( 19 / 20 )116.9583333333330.499458982252716234.170046969252
Winsorized Mean ( 20 / 20 )116.9250.455801429904322256.526180763724
Trimmed Mean ( 1 / 20 )117.5344827586211.03423711542099113.64365193061
Trimmed Mean ( 2 / 20 )117.5803571428571.00382198078617117.132678296974
Trimmed Mean ( 3 / 20 )117.5796296296300.98301216952496119.611570715803
Trimmed Mean ( 4 / 20 )117.5942307692310.96170809212623122.276428504665
Trimmed Mean ( 5 / 20 )117.5960.93946993304844125.172712678966
Trimmed Mean ( 6 / 20 )117.5895833333330.917743916904583128.128970584677
Trimmed Mean ( 7 / 20 )117.5782608695650.896730039479611131.118905013819
Trimmed Mean ( 8 / 20 )117.5590909090910.874783683208727134.386469667428
Trimmed Mean ( 9 / 20 )117.5452380952380.849138405855664138.428832431374
Trimmed Mean ( 10 / 20 )117.51750.82596398614604142.279205838427
Trimmed Mean ( 11 / 20 )117.4894736842110.796746491160245147.461551431647
Trimmed Mean ( 12 / 20 )117.4583333333330.762029193708149154.138889038835
Trimmed Mean ( 13 / 20 )117.4147058823530.740346456847407158.594270015603
Trimmed Mean ( 14 / 20 )117.368750.711957737906202164.853535190403
Trimmed Mean ( 15 / 20 )117.3266666666670.681427395266111172.177795436076
Trimmed Mean ( 16 / 20 )117.2857142857140.646678822617589181.366251968747
Trimmed Mean ( 17 / 20 )117.2346153846150.613186941194992191.189028187955
Trimmed Mean ( 18 / 20 )117.2666666666670.600352151086352195.329801774625
Trimmed Mean ( 19 / 20 )117.3181818181820.587629929029105199.646369292349
Trimmed Mean ( 20 / 20 )117.3750.56423562640555208.024794087773
Median117.6
Midrange114.55
Midmean - Weighted Average at Xnp117.122580645161
Midmean - Weighted Average at X(n+1)p117.326666666667
Midmean - Empirical Distribution Function117.122580645161
Midmean - Empirical Distribution Function - Averaging117.326666666667
Midmean - Empirical Distribution Function - Interpolation117.326666666667
Midmean - Closest Observation117.122580645161
Midmean - True Basic - Statistics Graphics Toolkit117.326666666667
Midmean - MS Excel (old versions)117.36875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 117.435 & 1.08076093981951 & 108.659552425731 \tabularnewline
Geometric Mean & 117.138710541647 &  &  \tabularnewline
Harmonic Mean & 116.839702700745 &  &  \tabularnewline
Quadratic Mean & 117.728050325032 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 117.491666666667 & 1.05881900862802 & 110.9648256305 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 117.581666666667 & 1.03328638038032 & 113.793880282626 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 117.541666666667 & 1.02288307417197 & 114.912124009695 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 117.588333333333 & 1.01045688515682 & 116.371450440544 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 117.621666666667 & 0.990577334559942 & 118.740518849969 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 117.641666666667 & 0.96747178141498 & 121.597000477481 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 117.676666666667 & 0.947892001603733 & 124.145647887703 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 117.636666666667 & 0.935368946412789 & 125.764990507556 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 117.711666666667 & 0.895055758975988 & 131.513221926350 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 117.695 & 0.886064188285878 & 132.828977353983 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 117.695 & 0.866704991547229 & 135.795918043454 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 117.755 & 0.774930013242311 & 151.955657914593 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 117.733333333333 & 0.763949988996257 & 154.11130967882 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 117.663333333333 & 0.728898893528326 & 161.426137943178 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 117.613333333333 & 0.696177889252447 & 168.941494909621 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 117.64 & 0.64124349535803 & 183.456051954675 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 117.016666666667 & 0.535123232370802 & 218.672372246366 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 116.926666666667 & 0.504369980483381 & 231.827172891229 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.958333333333 & 0.499458982252716 & 234.170046969252 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 116.925 & 0.455801429904322 & 256.526180763724 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 117.534482758621 & 1.03423711542099 & 113.64365193061 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 117.580357142857 & 1.00382198078617 & 117.132678296974 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 117.579629629630 & 0.98301216952496 & 119.611570715803 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 117.594230769231 & 0.96170809212623 & 122.276428504665 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 117.596 & 0.93946993304844 & 125.172712678966 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 117.589583333333 & 0.917743916904583 & 128.128970584677 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 117.578260869565 & 0.896730039479611 & 131.118905013819 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 117.559090909091 & 0.874783683208727 & 134.386469667428 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 117.545238095238 & 0.849138405855664 & 138.428832431374 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 117.5175 & 0.82596398614604 & 142.279205838427 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 117.489473684211 & 0.796746491160245 & 147.461551431647 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 117.458333333333 & 0.762029193708149 & 154.138889038835 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 117.414705882353 & 0.740346456847407 & 158.594270015603 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 117.36875 & 0.711957737906202 & 164.853535190403 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 117.326666666667 & 0.681427395266111 & 172.177795436076 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 117.285714285714 & 0.646678822617589 & 181.366251968747 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 117.234615384615 & 0.613186941194992 & 191.189028187955 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 117.266666666667 & 0.600352151086352 & 195.329801774625 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 117.318181818182 & 0.587629929029105 & 199.646369292349 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 117.375 & 0.56423562640555 & 208.024794087773 \tabularnewline
Median & 117.6 &  &  \tabularnewline
Midrange & 114.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 117.122580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 117.326666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 117.122580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 117.326666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 117.326666666667 &  &  \tabularnewline
Midmean - Closest Observation & 117.122580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 117.326666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 117.36875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64752&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]117.435[/C][C]1.08076093981951[/C][C]108.659552425731[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]117.138710541647[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]116.839702700745[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]117.728050325032[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]117.491666666667[/C][C]1.05881900862802[/C][C]110.9648256305[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]117.581666666667[/C][C]1.03328638038032[/C][C]113.793880282626[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]117.541666666667[/C][C]1.02288307417197[/C][C]114.912124009695[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]117.588333333333[/C][C]1.01045688515682[/C][C]116.371450440544[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]117.621666666667[/C][C]0.990577334559942[/C][C]118.740518849969[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]117.641666666667[/C][C]0.96747178141498[/C][C]121.597000477481[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]117.676666666667[/C][C]0.947892001603733[/C][C]124.145647887703[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]117.636666666667[/C][C]0.935368946412789[/C][C]125.764990507556[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]117.711666666667[/C][C]0.895055758975988[/C][C]131.513221926350[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]117.695[/C][C]0.886064188285878[/C][C]132.828977353983[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]117.695[/C][C]0.866704991547229[/C][C]135.795918043454[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]117.755[/C][C]0.774930013242311[/C][C]151.955657914593[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]117.733333333333[/C][C]0.763949988996257[/C][C]154.11130967882[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]117.663333333333[/C][C]0.728898893528326[/C][C]161.426137943178[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]117.613333333333[/C][C]0.696177889252447[/C][C]168.941494909621[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]117.64[/C][C]0.64124349535803[/C][C]183.456051954675[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]117.016666666667[/C][C]0.535123232370802[/C][C]218.672372246366[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]116.926666666667[/C][C]0.504369980483381[/C][C]231.827172891229[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.958333333333[/C][C]0.499458982252716[/C][C]234.170046969252[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]116.925[/C][C]0.455801429904322[/C][C]256.526180763724[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]117.534482758621[/C][C]1.03423711542099[/C][C]113.64365193061[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]117.580357142857[/C][C]1.00382198078617[/C][C]117.132678296974[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]117.579629629630[/C][C]0.98301216952496[/C][C]119.611570715803[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]117.594230769231[/C][C]0.96170809212623[/C][C]122.276428504665[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]117.596[/C][C]0.93946993304844[/C][C]125.172712678966[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]117.589583333333[/C][C]0.917743916904583[/C][C]128.128970584677[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]117.578260869565[/C][C]0.896730039479611[/C][C]131.118905013819[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]117.559090909091[/C][C]0.874783683208727[/C][C]134.386469667428[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]117.545238095238[/C][C]0.849138405855664[/C][C]138.428832431374[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]117.5175[/C][C]0.82596398614604[/C][C]142.279205838427[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]117.489473684211[/C][C]0.796746491160245[/C][C]147.461551431647[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]117.458333333333[/C][C]0.762029193708149[/C][C]154.138889038835[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]117.414705882353[/C][C]0.740346456847407[/C][C]158.594270015603[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]117.36875[/C][C]0.711957737906202[/C][C]164.853535190403[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]117.326666666667[/C][C]0.681427395266111[/C][C]172.177795436076[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]117.285714285714[/C][C]0.646678822617589[/C][C]181.366251968747[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]117.234615384615[/C][C]0.613186941194992[/C][C]191.189028187955[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]117.266666666667[/C][C]0.600352151086352[/C][C]195.329801774625[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]117.318181818182[/C][C]0.587629929029105[/C][C]199.646369292349[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]117.375[/C][C]0.56423562640555[/C][C]208.024794087773[/C][/ROW]
[ROW][C]Median[/C][C]117.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]117.122580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]117.326666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]117.122580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]117.326666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]117.326666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]117.122580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]117.326666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]117.36875[/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=64752&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64752&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 Mean117.4351.08076093981951108.659552425731
Geometric Mean117.138710541647
Harmonic Mean116.839702700745
Quadratic Mean117.728050325032
Winsorized Mean ( 1 / 20 )117.4916666666671.05881900862802110.9648256305
Winsorized Mean ( 2 / 20 )117.5816666666671.03328638038032113.793880282626
Winsorized Mean ( 3 / 20 )117.5416666666671.02288307417197114.912124009695
Winsorized Mean ( 4 / 20 )117.5883333333331.01045688515682116.371450440544
Winsorized Mean ( 5 / 20 )117.6216666666670.990577334559942118.740518849969
Winsorized Mean ( 6 / 20 )117.6416666666670.96747178141498121.597000477481
Winsorized Mean ( 7 / 20 )117.6766666666670.947892001603733124.145647887703
Winsorized Mean ( 8 / 20 )117.6366666666670.935368946412789125.764990507556
Winsorized Mean ( 9 / 20 )117.7116666666670.895055758975988131.513221926350
Winsorized Mean ( 10 / 20 )117.6950.886064188285878132.828977353983
Winsorized Mean ( 11 / 20 )117.6950.866704991547229135.795918043454
Winsorized Mean ( 12 / 20 )117.7550.774930013242311151.955657914593
Winsorized Mean ( 13 / 20 )117.7333333333330.763949988996257154.11130967882
Winsorized Mean ( 14 / 20 )117.6633333333330.728898893528326161.426137943178
Winsorized Mean ( 15 / 20 )117.6133333333330.696177889252447168.941494909621
Winsorized Mean ( 16 / 20 )117.640.64124349535803183.456051954675
Winsorized Mean ( 17 / 20 )117.0166666666670.535123232370802218.672372246366
Winsorized Mean ( 18 / 20 )116.9266666666670.504369980483381231.827172891229
Winsorized Mean ( 19 / 20 )116.9583333333330.499458982252716234.170046969252
Winsorized Mean ( 20 / 20 )116.9250.455801429904322256.526180763724
Trimmed Mean ( 1 / 20 )117.5344827586211.03423711542099113.64365193061
Trimmed Mean ( 2 / 20 )117.5803571428571.00382198078617117.132678296974
Trimmed Mean ( 3 / 20 )117.5796296296300.98301216952496119.611570715803
Trimmed Mean ( 4 / 20 )117.5942307692310.96170809212623122.276428504665
Trimmed Mean ( 5 / 20 )117.5960.93946993304844125.172712678966
Trimmed Mean ( 6 / 20 )117.5895833333330.917743916904583128.128970584677
Trimmed Mean ( 7 / 20 )117.5782608695650.896730039479611131.118905013819
Trimmed Mean ( 8 / 20 )117.5590909090910.874783683208727134.386469667428
Trimmed Mean ( 9 / 20 )117.5452380952380.849138405855664138.428832431374
Trimmed Mean ( 10 / 20 )117.51750.82596398614604142.279205838427
Trimmed Mean ( 11 / 20 )117.4894736842110.796746491160245147.461551431647
Trimmed Mean ( 12 / 20 )117.4583333333330.762029193708149154.138889038835
Trimmed Mean ( 13 / 20 )117.4147058823530.740346456847407158.594270015603
Trimmed Mean ( 14 / 20 )117.368750.711957737906202164.853535190403
Trimmed Mean ( 15 / 20 )117.3266666666670.681427395266111172.177795436076
Trimmed Mean ( 16 / 20 )117.2857142857140.646678822617589181.366251968747
Trimmed Mean ( 17 / 20 )117.2346153846150.613186941194992191.189028187955
Trimmed Mean ( 18 / 20 )117.2666666666670.600352151086352195.329801774625
Trimmed Mean ( 19 / 20 )117.3181818181820.587629929029105199.646369292349
Trimmed Mean ( 20 / 20 )117.3750.56423562640555208.024794087773
Median117.6
Midrange114.55
Midmean - Weighted Average at Xnp117.122580645161
Midmean - Weighted Average at X(n+1)p117.326666666667
Midmean - Empirical Distribution Function117.122580645161
Midmean - Empirical Distribution Function - Averaging117.326666666667
Midmean - Empirical Distribution Function - Interpolation117.326666666667
Midmean - Closest Observation117.122580645161
Midmean - True Basic - Statistics Graphics Toolkit117.326666666667
Midmean - MS Excel (old versions)117.36875
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')