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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 computationSat, 17 Oct 2009 06:44:48 -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/17/t1255783597jlluzq6s93q9xw3.htm/, Retrieved Mon, 06 May 2024 05:42:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47148, Retrieved Mon, 06 May 2024 05:42:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
-    D      [Univariate Data Series] [Workshop 3 Part 2...] [2009-10-16 16:14:28] [f924a0adda9c1905a1ba8f1c751261ff]
- RMP           [Central Tendency] [Part 2: Y[t] Cent...] [2009-10-17 12:44:48] [ac86848d66148c9c4c9404e0c9a511eb] [Current]
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Dataseries X:
79.8
83.4
113.6
112.9
104
109.9
99
106.3
128.9
111.1
102.9
130
87
87.5
117.6
103.4
110.8
112.6
102.5
112.4
135.6
105.1
127.7
137
91
90.5
122.4
123.3
124.3
120
118.1
119
142.7
123.6
129.6
151.6
110.4
99.2
130.5
136.2
129.7
128
121.6
135.8
143.8
147.5
136.2
156.6
123.3
104.5
139.8
136.5
112.1
118.5
94.4
102.3
111.4
99.2
87.8
115.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47148&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47148&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.6366666666672.3021532130151250.6641634480565
Geometric Mean115.267693868378
Harmonic Mean113.870726632396
Quadratic Mean117.969515836366
Winsorized Mean ( 1 / 20 )116.6133333333332.2633626634146351.5221600224704
Winsorized Mean ( 2 / 20 )116.5966666666672.2005533031318952.985159005566
Winsorized Mean ( 3 / 20 )116.4366666666672.1528892249871854.08390980607
Winsorized Mean ( 4 / 20 )116.3833333333332.1327711565065754.5690675618319
Winsorized Mean ( 5 / 20 )116.3666666666672.0340320185174257.2098499961101
Winsorized Mean ( 6 / 20 )116.1366666666671.9707464625328458.9302931019376
Winsorized Mean ( 7 / 20 )116.4751.8777655687208362.0285098098509
Winsorized Mean ( 8 / 20 )117.0483333333331.7556599217469866.6691378458212
Winsorized Mean ( 9 / 20 )117.0783333333331.7504496462961966.8847193525742
Winsorized Mean ( 10 / 20 )117.0116666666671.7381708218775267.3188533565846
Winsorized Mean ( 11 / 20 )117.5433333333331.6370487546910271.8019747405257
Winsorized Mean ( 12 / 20 )116.5633333333331.4515352610033280.3034803665489
Winsorized Mean ( 13 / 20 )116.5416666666671.4198438118660082.0806244269252
Winsorized Mean ( 14 / 20 )116.5883333333331.3897406408982383.8921521773869
Winsorized Mean ( 15 / 20 )116.7133333333331.3618043586033685.70491979702
Winsorized Mean ( 16 / 20 )116.661.3110314221369888.9833744868177
Winsorized Mean ( 17 / 20 )116.5751.2443559017296893.6830048685895
Winsorized Mean ( 18 / 20 )116.8451.1747662948253399.4623360532942
Winsorized Mean ( 19 / 20 )116.9083333333330.841388050321672138.946985625287
Winsorized Mean ( 20 / 20 )116.8416666666670.783568152086478149.114874507778
Trimmed Mean ( 1 / 20 )116.5827586206902.1866547028878253.3155776569221
Trimmed Mean ( 2 / 20 )116.552.0920489552514955.7109333925647
Trimmed Mean ( 3 / 20 )116.5240740740742.0174811411839157.7572060999265
Trimmed Mean ( 4 / 20 )116.5576923076921.9479043659682459.8374819339529
Trimmed Mean ( 5 / 20 )116.611.8683185717950562.4144092770877
Trimmed Mean ( 6 / 20 )116.6708333333331.8028148752953864.7159255961973
Trimmed Mean ( 7 / 20 )116.7869565217391.7389307856417667.1602098749653
Trimmed Mean ( 8 / 20 )116.8477272727271.6846354824203569.3608371021902
Trimmed Mean ( 9 / 20 )116.8119047619051.6479290575266270.8840615610166
Trimmed Mean ( 10 / 20 )116.76751.5993243264835573.01051954655
Trimmed Mean ( 11 / 20 )116.7289473684211.5364972259615275.9708155641959
Trimmed Mean ( 12 / 20 )116.6055555555561.4785393073047378.8653740752547
Trimmed Mean ( 13 / 20 )116.6117647058821.4510538594880580.3634985313534
Trimmed Mean ( 14 / 20 )116.6218751.4181906803908982.2328595248249
Trimmed Mean ( 15 / 20 )116.6266666666671.3768691231832784.7042501737782
Trimmed Mean ( 16 / 20 )116.6142857142861.3221626732526988.1996505221248
Trimmed Mean ( 17 / 20 )116.6076923076921.2550687762573492.9094042602356
Trimmed Mean ( 18 / 20 )116.61251.1746617228136399.2732611740187
Trimmed Mean ( 19 / 20 )116.5772727272731.07344837821877108.600725561406
Trimmed Mean ( 20 / 20 )116.5251.06137634081513109.786694425947
Median116.7
Midrange118.2
Midmean - Weighted Average at Xnp116.2
Midmean - Weighted Average at X(n+1)p116.626666666667
Midmean - Empirical Distribution Function116.2
Midmean - Empirical Distribution Function - Averaging116.626666666667
Midmean - Empirical Distribution Function - Interpolation116.626666666667
Midmean - Closest Observation116.2
Midmean - True Basic - Statistics Graphics Toolkit116.626666666667
Midmean - MS Excel (old versions)116.621875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.636666666667 & 2.30215321301512 & 50.6641634480565 \tabularnewline
Geometric Mean & 115.267693868378 &  &  \tabularnewline
Harmonic Mean & 113.870726632396 &  &  \tabularnewline
Quadratic Mean & 117.969515836366 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 116.613333333333 & 2.26336266341463 & 51.5221600224704 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 116.596666666667 & 2.20055330313189 & 52.985159005566 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 116.436666666667 & 2.15288922498718 & 54.08390980607 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 116.383333333333 & 2.13277115650657 & 54.5690675618319 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 116.366666666667 & 2.03403201851742 & 57.2098499961101 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.136666666667 & 1.97074646253284 & 58.9302931019376 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.475 & 1.87776556872083 & 62.0285098098509 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 117.048333333333 & 1.75565992174698 & 66.6691378458212 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 117.078333333333 & 1.75044964629619 & 66.8847193525742 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 117.011666666667 & 1.73817082187752 & 67.3188533565846 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 117.543333333333 & 1.63704875469102 & 71.8019747405257 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 116.563333333333 & 1.45153526100332 & 80.3034803665489 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.541666666667 & 1.41984381186600 & 82.0806244269252 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.588333333333 & 1.38974064089823 & 83.8921521773869 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.713333333333 & 1.36180435860336 & 85.70491979702 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.66 & 1.31103142213698 & 88.9833744868177 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 116.575 & 1.24435590172968 & 93.6830048685895 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 116.845 & 1.17476629482533 & 99.4623360532942 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.908333333333 & 0.841388050321672 & 138.946985625287 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 116.841666666667 & 0.783568152086478 & 149.114874507778 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 116.582758620690 & 2.18665470288782 & 53.3155776569221 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.55 & 2.09204895525149 & 55.7109333925647 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.524074074074 & 2.01748114118391 & 57.7572060999265 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.557692307692 & 1.94790436596824 & 59.8374819339529 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.61 & 1.86831857179505 & 62.4144092770877 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.670833333333 & 1.80281487529538 & 64.7159255961973 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 116.786956521739 & 1.73893078564176 & 67.1602098749653 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 116.847727272727 & 1.68463548242035 & 69.3608371021902 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.811904761905 & 1.64792905752662 & 70.8840615610166 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.7675 & 1.59932432648355 & 73.01051954655 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.728947368421 & 1.53649722596152 & 75.9708155641959 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.605555555556 & 1.47853930730473 & 78.8653740752547 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.611764705882 & 1.45105385948805 & 80.3634985313534 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.621875 & 1.41819068039089 & 82.2328595248249 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.626666666667 & 1.37686912318327 & 84.7042501737782 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.614285714286 & 1.32216267325269 & 88.1996505221248 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.607692307692 & 1.25506877625734 & 92.9094042602356 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.6125 & 1.17466172281363 & 99.2732611740187 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 116.577272727273 & 1.07344837821877 & 108.600725561406 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 116.525 & 1.06137634081513 & 109.786694425947 \tabularnewline
Median & 116.7 &  &  \tabularnewline
Midrange & 118.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.2 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.626666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.626666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.626666666667 &  &  \tabularnewline
Midmean - Closest Observation & 116.2 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.626666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.621875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47148&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]116.636666666667[/C][C]2.30215321301512[/C][C]50.6641634480565[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.267693868378[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.870726632396[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]117.969515836366[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]116.613333333333[/C][C]2.26336266341463[/C][C]51.5221600224704[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]116.596666666667[/C][C]2.20055330313189[/C][C]52.985159005566[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]116.436666666667[/C][C]2.15288922498718[/C][C]54.08390980607[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]116.383333333333[/C][C]2.13277115650657[/C][C]54.5690675618319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]116.366666666667[/C][C]2.03403201851742[/C][C]57.2098499961101[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.136666666667[/C][C]1.97074646253284[/C][C]58.9302931019376[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.475[/C][C]1.87776556872083[/C][C]62.0285098098509[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]117.048333333333[/C][C]1.75565992174698[/C][C]66.6691378458212[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]117.078333333333[/C][C]1.75044964629619[/C][C]66.8847193525742[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]117.011666666667[/C][C]1.73817082187752[/C][C]67.3188533565846[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]117.543333333333[/C][C]1.63704875469102[/C][C]71.8019747405257[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]116.563333333333[/C][C]1.45153526100332[/C][C]80.3034803665489[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.541666666667[/C][C]1.41984381186600[/C][C]82.0806244269252[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.588333333333[/C][C]1.38974064089823[/C][C]83.8921521773869[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.713333333333[/C][C]1.36180435860336[/C][C]85.70491979702[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.66[/C][C]1.31103142213698[/C][C]88.9833744868177[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]116.575[/C][C]1.24435590172968[/C][C]93.6830048685895[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]116.845[/C][C]1.17476629482533[/C][C]99.4623360532942[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.908333333333[/C][C]0.841388050321672[/C][C]138.946985625287[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]116.841666666667[/C][C]0.783568152086478[/C][C]149.114874507778[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]116.582758620690[/C][C]2.18665470288782[/C][C]53.3155776569221[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.55[/C][C]2.09204895525149[/C][C]55.7109333925647[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.524074074074[/C][C]2.01748114118391[/C][C]57.7572060999265[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.557692307692[/C][C]1.94790436596824[/C][C]59.8374819339529[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.61[/C][C]1.86831857179505[/C][C]62.4144092770877[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.670833333333[/C][C]1.80281487529538[/C][C]64.7159255961973[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]116.786956521739[/C][C]1.73893078564176[/C][C]67.1602098749653[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]116.847727272727[/C][C]1.68463548242035[/C][C]69.3608371021902[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.811904761905[/C][C]1.64792905752662[/C][C]70.8840615610166[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.7675[/C][C]1.59932432648355[/C][C]73.01051954655[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.728947368421[/C][C]1.53649722596152[/C][C]75.9708155641959[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.605555555556[/C][C]1.47853930730473[/C][C]78.8653740752547[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.611764705882[/C][C]1.45105385948805[/C][C]80.3634985313534[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.621875[/C][C]1.41819068039089[/C][C]82.2328595248249[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.626666666667[/C][C]1.37686912318327[/C][C]84.7042501737782[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.614285714286[/C][C]1.32216267325269[/C][C]88.1996505221248[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.607692307692[/C][C]1.25506877625734[/C][C]92.9094042602356[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.6125[/C][C]1.17466172281363[/C][C]99.2732611740187[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]116.577272727273[/C][C]1.07344837821877[/C][C]108.600725561406[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]116.525[/C][C]1.06137634081513[/C][C]109.786694425947[/C][/ROW]
[ROW][C]Median[/C][C]116.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]118.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.626666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.626666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.626666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.626666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.621875[/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=47148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47148&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 Mean116.6366666666672.3021532130151250.6641634480565
Geometric Mean115.267693868378
Harmonic Mean113.870726632396
Quadratic Mean117.969515836366
Winsorized Mean ( 1 / 20 )116.6133333333332.2633626634146351.5221600224704
Winsorized Mean ( 2 / 20 )116.5966666666672.2005533031318952.985159005566
Winsorized Mean ( 3 / 20 )116.4366666666672.1528892249871854.08390980607
Winsorized Mean ( 4 / 20 )116.3833333333332.1327711565065754.5690675618319
Winsorized Mean ( 5 / 20 )116.3666666666672.0340320185174257.2098499961101
Winsorized Mean ( 6 / 20 )116.1366666666671.9707464625328458.9302931019376
Winsorized Mean ( 7 / 20 )116.4751.8777655687208362.0285098098509
Winsorized Mean ( 8 / 20 )117.0483333333331.7556599217469866.6691378458212
Winsorized Mean ( 9 / 20 )117.0783333333331.7504496462961966.8847193525742
Winsorized Mean ( 10 / 20 )117.0116666666671.7381708218775267.3188533565846
Winsorized Mean ( 11 / 20 )117.5433333333331.6370487546910271.8019747405257
Winsorized Mean ( 12 / 20 )116.5633333333331.4515352610033280.3034803665489
Winsorized Mean ( 13 / 20 )116.5416666666671.4198438118660082.0806244269252
Winsorized Mean ( 14 / 20 )116.5883333333331.3897406408982383.8921521773869
Winsorized Mean ( 15 / 20 )116.7133333333331.3618043586033685.70491979702
Winsorized Mean ( 16 / 20 )116.661.3110314221369888.9833744868177
Winsorized Mean ( 17 / 20 )116.5751.2443559017296893.6830048685895
Winsorized Mean ( 18 / 20 )116.8451.1747662948253399.4623360532942
Winsorized Mean ( 19 / 20 )116.9083333333330.841388050321672138.946985625287
Winsorized Mean ( 20 / 20 )116.8416666666670.783568152086478149.114874507778
Trimmed Mean ( 1 / 20 )116.5827586206902.1866547028878253.3155776569221
Trimmed Mean ( 2 / 20 )116.552.0920489552514955.7109333925647
Trimmed Mean ( 3 / 20 )116.5240740740742.0174811411839157.7572060999265
Trimmed Mean ( 4 / 20 )116.5576923076921.9479043659682459.8374819339529
Trimmed Mean ( 5 / 20 )116.611.8683185717950562.4144092770877
Trimmed Mean ( 6 / 20 )116.6708333333331.8028148752953864.7159255961973
Trimmed Mean ( 7 / 20 )116.7869565217391.7389307856417667.1602098749653
Trimmed Mean ( 8 / 20 )116.8477272727271.6846354824203569.3608371021902
Trimmed Mean ( 9 / 20 )116.8119047619051.6479290575266270.8840615610166
Trimmed Mean ( 10 / 20 )116.76751.5993243264835573.01051954655
Trimmed Mean ( 11 / 20 )116.7289473684211.5364972259615275.9708155641959
Trimmed Mean ( 12 / 20 )116.6055555555561.4785393073047378.8653740752547
Trimmed Mean ( 13 / 20 )116.6117647058821.4510538594880580.3634985313534
Trimmed Mean ( 14 / 20 )116.6218751.4181906803908982.2328595248249
Trimmed Mean ( 15 / 20 )116.6266666666671.3768691231832784.7042501737782
Trimmed Mean ( 16 / 20 )116.6142857142861.3221626732526988.1996505221248
Trimmed Mean ( 17 / 20 )116.6076923076921.2550687762573492.9094042602356
Trimmed Mean ( 18 / 20 )116.61251.1746617228136399.2732611740187
Trimmed Mean ( 19 / 20 )116.5772727272731.07344837821877108.600725561406
Trimmed Mean ( 20 / 20 )116.5251.06137634081513109.786694425947
Median116.7
Midrange118.2
Midmean - Weighted Average at Xnp116.2
Midmean - Weighted Average at X(n+1)p116.626666666667
Midmean - Empirical Distribution Function116.2
Midmean - Empirical Distribution Function - Averaging116.626666666667
Midmean - Empirical Distribution Function - Interpolation116.626666666667
Midmean - Closest Observation116.2
Midmean - True Basic - Statistics Graphics Toolkit116.626666666667
Midmean - MS Excel (old versions)116.621875
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')