Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 17 Oct 2008 04:06:12 -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/2008/Oct/17/t1224238045r81cvghmxqomqt6.htm/, Retrieved Wed, 15 May 2024 01:27:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16406, Retrieved Wed, 15 May 2024 01:27:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D    [Central Tendency] [Prijsindexcijfers...] [2008-10-17 10:06:12] [5338a3370b0f0a39c3af1ba0be9c6dab] [Current]
Feedback Forum

Post a new message
Dataseries X:
96,7
88,0
96,7
106,8
114,3
105,7
90,1
91,6
97,7
100,8
104,6
95,9
102,7
104,0
107,9
113,8
113,8
123,1
125,1
137,6
134,0
140,3
152,1
150,6
167,3
153,2
142,0
154,4
158,5
180,9
181,3
172,4
192,0
199,3
215,4
214,3
201,5
190,5
196,0
215,7
209,4
214,1
237,8
239,0
237,8
251,5
248,8
215,4
201,2
203,1
214,2
188,9
203,0
213,3
228,5
228,2
240,9
258,8
248,5
269,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16406&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16406&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean169.677.0287023739910124.1395909190644
Geometric Mean160.541810782272
Harmonic Mean151.329093293377
Quadratic Mean178.052423928085
Winsorized Mean ( 1 / 20 )169.5316666666676.9822937854684524.2802253636901
Winsorized Mean ( 2 / 20 )169.3383333333336.921864193100124.464266938686
Winsorized Mean ( 3 / 20 )169.4183333333336.8550259889260224.7144698804966
Winsorized Mean ( 4 / 20 )169.4516666666676.8414512170429824.7683804635688
Winsorized Mean ( 5 / 20 )168.8183333333336.7218416613418325.1148928877973
Winsorized Mean ( 6 / 20 )168.7283333333336.669490824832425.2985329412419
Winsorized Mean ( 7 / 20 )168.956.5801849011508325.675570297493
Winsorized Mean ( 8 / 20 )169.2033333333336.5361044077206425.8874893634602
Winsorized Mean ( 9 / 20 )168.0033333333336.2639471349925326.8206818660409
Winsorized Mean ( 10 / 20 )168.0533333333336.2384906306252726.9381398937021
Winsorized Mean ( 11 / 20 )165.9633333333335.8504550823361728.3675938021324
Winsorized Mean ( 12 / 20 )166.1233333333335.8035520813402428.624423629704
Winsorized Mean ( 13 / 20 )166.3616666666675.7624143027889628.870132886167
Winsorized Mean ( 14 / 20 )167.4816666666675.4928805959218330.4906803892684
Winsorized Mean ( 15 / 20 )167.4566666666675.4892706680435530.5061777407946
Winsorized Mean ( 16 / 20 )167.5633333333335.4633602202693830.6703798720179
Winsorized Mean ( 17 / 20 )169.835.0276047581845433.7795049866500
Winsorized Mean ( 18 / 20 )169.264.7638719237837135.52992244711
Winsorized Mean ( 19 / 20 )170.0833333333334.0481719154297142.0148493904265
Winsorized Mean ( 20 / 20 )171.253.8642980520436444.3159398404671
Trimmed Mean ( 1 / 20 )169.3620689655176.9198089397592524.4749631731031
Trimmed Mean ( 2 / 20 )169.1803571428576.8381148289031624.7407891467061
Trimmed Mean ( 3 / 20 )169.0925925925936.7713112355009424.9719126343013
Trimmed Mean ( 4 / 20 )168.9673076923086.7130738032616725.1698867976413
Trimmed Mean ( 5 / 20 )168.8226.6383015346778425.4315052002520
Trimmed Mean ( 6 / 20 )168.8229166666676.5763197038594525.6713365938687
Trimmed Mean ( 7 / 20 )168.8434782608706.5047040965229825.9571343685139
Trimmed Mean ( 8 / 20 )168.8227272727276.4289578949940626.25973447488
Trimmed Mean ( 9 / 20 )168.7547619047626.3332228754787426.6459534462547
Trimmed Mean ( 10 / 20 )168.886.2688497288638926.9395514814177
Trimmed Mean ( 11 / 20 )169.0105263157896.1774492260059727.3592740518668
Trimmed Mean ( 12 / 20 )169.4722222222226.1372135902669527.6138706482351
Trimmed Mean ( 13 / 20 )169.9647058823536.0753569650087727.9760854977363
Trimmed Mean ( 14 / 20 )170.4843755.9811483236630428.5036193343538
Trimmed Mean ( 15 / 20 )170.9133333333335.906308206346228.9374220515094
Trimmed Mean ( 16 / 20 )171.4071428571435.7743043479667629.6844663058847
Trimmed Mean ( 17 / 20 )171.9615384615385.562940774372130.9119844046782
Trimmed Mean ( 18 / 20 )172.2755.3865817250979731.9822493729763
Trimmed Mean ( 19 / 20 )172.7318181818185.1824060766225733.3304290763701
Trimmed Mean ( 20 / 20 )173.155.1253266904862333.783212360181
Median176.65
Midrange178.6
Midmean - Weighted Average at Xnp169.070967741936
Midmean - Weighted Average at X(n+1)p169.070967741936
Midmean - Empirical Distribution Function169.070967741936
Midmean - Empirical Distribution Function - Averaging169.070967741936
Midmean - Empirical Distribution Function - Interpolation169.070967741936
Midmean - Closest Observation169.070967741936
Midmean - True Basic - Statistics Graphics Toolkit169.070967741936
Midmean - MS Excel (old versions)170.484375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 169.67 & 7.02870237399101 & 24.1395909190644 \tabularnewline
Geometric Mean & 160.541810782272 &  &  \tabularnewline
Harmonic Mean & 151.329093293377 &  &  \tabularnewline
Quadratic Mean & 178.052423928085 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 169.531666666667 & 6.98229378546845 & 24.2802253636901 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 169.338333333333 & 6.9218641931001 & 24.464266938686 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 169.418333333333 & 6.85502598892602 & 24.7144698804966 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 169.451666666667 & 6.84145121704298 & 24.7683804635688 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 168.818333333333 & 6.72184166134183 & 25.1148928877973 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 168.728333333333 & 6.6694908248324 & 25.2985329412419 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 168.95 & 6.58018490115083 & 25.675570297493 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 169.203333333333 & 6.53610440772064 & 25.8874893634602 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 168.003333333333 & 6.26394713499253 & 26.8206818660409 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 168.053333333333 & 6.23849063062527 & 26.9381398937021 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 165.963333333333 & 5.85045508233617 & 28.3675938021324 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 166.123333333333 & 5.80355208134024 & 28.624423629704 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 166.361666666667 & 5.76241430278896 & 28.870132886167 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 167.481666666667 & 5.49288059592183 & 30.4906803892684 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 167.456666666667 & 5.48927066804355 & 30.5061777407946 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 167.563333333333 & 5.46336022026938 & 30.6703798720179 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 169.83 & 5.02760475818454 & 33.7795049866500 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 169.26 & 4.76387192378371 & 35.52992244711 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 170.083333333333 & 4.04817191542971 & 42.0148493904265 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 171.25 & 3.86429805204364 & 44.3159398404671 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 169.362068965517 & 6.91980893975925 & 24.4749631731031 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 169.180357142857 & 6.83811482890316 & 24.7407891467061 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 169.092592592593 & 6.77131123550094 & 24.9719126343013 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 168.967307692308 & 6.71307380326167 & 25.1698867976413 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 168.822 & 6.63830153467784 & 25.4315052002520 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 168.822916666667 & 6.57631970385945 & 25.6713365938687 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 168.843478260870 & 6.50470409652298 & 25.9571343685139 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 168.822727272727 & 6.42895789499406 & 26.25973447488 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 168.754761904762 & 6.33322287547874 & 26.6459534462547 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 168.88 & 6.26884972886389 & 26.9395514814177 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 169.010526315789 & 6.17744922600597 & 27.3592740518668 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 169.472222222222 & 6.13721359026695 & 27.6138706482351 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 169.964705882353 & 6.07535696500877 & 27.9760854977363 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 170.484375 & 5.98114832366304 & 28.5036193343538 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 170.913333333333 & 5.9063082063462 & 28.9374220515094 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 171.407142857143 & 5.77430434796676 & 29.6844663058847 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 171.961538461538 & 5.5629407743721 & 30.9119844046782 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 172.275 & 5.38658172509797 & 31.9822493729763 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 172.731818181818 & 5.18240607662257 & 33.3304290763701 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 173.15 & 5.12532669048623 & 33.783212360181 \tabularnewline
Median & 176.65 &  &  \tabularnewline
Midrange & 178.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 169.070967741936 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 169.070967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 169.070967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 169.070967741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 169.070967741936 &  &  \tabularnewline
Midmean - Closest Observation & 169.070967741936 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 169.070967741936 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 170.484375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16406&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]169.67[/C][C]7.02870237399101[/C][C]24.1395909190644[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]160.541810782272[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]151.329093293377[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]178.052423928085[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]169.531666666667[/C][C]6.98229378546845[/C][C]24.2802253636901[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]169.338333333333[/C][C]6.9218641931001[/C][C]24.464266938686[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]169.418333333333[/C][C]6.85502598892602[/C][C]24.7144698804966[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]169.451666666667[/C][C]6.84145121704298[/C][C]24.7683804635688[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]168.818333333333[/C][C]6.72184166134183[/C][C]25.1148928877973[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]168.728333333333[/C][C]6.6694908248324[/C][C]25.2985329412419[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]168.95[/C][C]6.58018490115083[/C][C]25.675570297493[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]169.203333333333[/C][C]6.53610440772064[/C][C]25.8874893634602[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]168.003333333333[/C][C]6.26394713499253[/C][C]26.8206818660409[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]168.053333333333[/C][C]6.23849063062527[/C][C]26.9381398937021[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]165.963333333333[/C][C]5.85045508233617[/C][C]28.3675938021324[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]166.123333333333[/C][C]5.80355208134024[/C][C]28.624423629704[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]166.361666666667[/C][C]5.76241430278896[/C][C]28.870132886167[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]167.481666666667[/C][C]5.49288059592183[/C][C]30.4906803892684[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]167.456666666667[/C][C]5.48927066804355[/C][C]30.5061777407946[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]167.563333333333[/C][C]5.46336022026938[/C][C]30.6703798720179[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]169.83[/C][C]5.02760475818454[/C][C]33.7795049866500[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]169.26[/C][C]4.76387192378371[/C][C]35.52992244711[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]170.083333333333[/C][C]4.04817191542971[/C][C]42.0148493904265[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]171.25[/C][C]3.86429805204364[/C][C]44.3159398404671[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]169.362068965517[/C][C]6.91980893975925[/C][C]24.4749631731031[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]169.180357142857[/C][C]6.83811482890316[/C][C]24.7407891467061[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]169.092592592593[/C][C]6.77131123550094[/C][C]24.9719126343013[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]168.967307692308[/C][C]6.71307380326167[/C][C]25.1698867976413[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]168.822[/C][C]6.63830153467784[/C][C]25.4315052002520[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]168.822916666667[/C][C]6.57631970385945[/C][C]25.6713365938687[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]168.843478260870[/C][C]6.50470409652298[/C][C]25.9571343685139[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]168.822727272727[/C][C]6.42895789499406[/C][C]26.25973447488[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]168.754761904762[/C][C]6.33322287547874[/C][C]26.6459534462547[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]168.88[/C][C]6.26884972886389[/C][C]26.9395514814177[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]169.010526315789[/C][C]6.17744922600597[/C][C]27.3592740518668[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]169.472222222222[/C][C]6.13721359026695[/C][C]27.6138706482351[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]169.964705882353[/C][C]6.07535696500877[/C][C]27.9760854977363[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]170.484375[/C][C]5.98114832366304[/C][C]28.5036193343538[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]170.913333333333[/C][C]5.9063082063462[/C][C]28.9374220515094[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]171.407142857143[/C][C]5.77430434796676[/C][C]29.6844663058847[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]171.961538461538[/C][C]5.5629407743721[/C][C]30.9119844046782[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]172.275[/C][C]5.38658172509797[/C][C]31.9822493729763[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]172.731818181818[/C][C]5.18240607662257[/C][C]33.3304290763701[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]173.15[/C][C]5.12532669048623[/C][C]33.783212360181[/C][/ROW]
[ROW][C]Median[/C][C]176.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]178.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]169.070967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]169.070967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]169.070967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]169.070967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]169.070967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]169.070967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]169.070967741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]170.484375[/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=16406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16406&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 Mean169.677.0287023739910124.1395909190644
Geometric Mean160.541810782272
Harmonic Mean151.329093293377
Quadratic Mean178.052423928085
Winsorized Mean ( 1 / 20 )169.5316666666676.9822937854684524.2802253636901
Winsorized Mean ( 2 / 20 )169.3383333333336.921864193100124.464266938686
Winsorized Mean ( 3 / 20 )169.4183333333336.8550259889260224.7144698804966
Winsorized Mean ( 4 / 20 )169.4516666666676.8414512170429824.7683804635688
Winsorized Mean ( 5 / 20 )168.8183333333336.7218416613418325.1148928877973
Winsorized Mean ( 6 / 20 )168.7283333333336.669490824832425.2985329412419
Winsorized Mean ( 7 / 20 )168.956.5801849011508325.675570297493
Winsorized Mean ( 8 / 20 )169.2033333333336.5361044077206425.8874893634602
Winsorized Mean ( 9 / 20 )168.0033333333336.2639471349925326.8206818660409
Winsorized Mean ( 10 / 20 )168.0533333333336.2384906306252726.9381398937021
Winsorized Mean ( 11 / 20 )165.9633333333335.8504550823361728.3675938021324
Winsorized Mean ( 12 / 20 )166.1233333333335.8035520813402428.624423629704
Winsorized Mean ( 13 / 20 )166.3616666666675.7624143027889628.870132886167
Winsorized Mean ( 14 / 20 )167.4816666666675.4928805959218330.4906803892684
Winsorized Mean ( 15 / 20 )167.4566666666675.4892706680435530.5061777407946
Winsorized Mean ( 16 / 20 )167.5633333333335.4633602202693830.6703798720179
Winsorized Mean ( 17 / 20 )169.835.0276047581845433.7795049866500
Winsorized Mean ( 18 / 20 )169.264.7638719237837135.52992244711
Winsorized Mean ( 19 / 20 )170.0833333333334.0481719154297142.0148493904265
Winsorized Mean ( 20 / 20 )171.253.8642980520436444.3159398404671
Trimmed Mean ( 1 / 20 )169.3620689655176.9198089397592524.4749631731031
Trimmed Mean ( 2 / 20 )169.1803571428576.8381148289031624.7407891467061
Trimmed Mean ( 3 / 20 )169.0925925925936.7713112355009424.9719126343013
Trimmed Mean ( 4 / 20 )168.9673076923086.7130738032616725.1698867976413
Trimmed Mean ( 5 / 20 )168.8226.6383015346778425.4315052002520
Trimmed Mean ( 6 / 20 )168.8229166666676.5763197038594525.6713365938687
Trimmed Mean ( 7 / 20 )168.8434782608706.5047040965229825.9571343685139
Trimmed Mean ( 8 / 20 )168.8227272727276.4289578949940626.25973447488
Trimmed Mean ( 9 / 20 )168.7547619047626.3332228754787426.6459534462547
Trimmed Mean ( 10 / 20 )168.886.2688497288638926.9395514814177
Trimmed Mean ( 11 / 20 )169.0105263157896.1774492260059727.3592740518668
Trimmed Mean ( 12 / 20 )169.4722222222226.1372135902669527.6138706482351
Trimmed Mean ( 13 / 20 )169.9647058823536.0753569650087727.9760854977363
Trimmed Mean ( 14 / 20 )170.4843755.9811483236630428.5036193343538
Trimmed Mean ( 15 / 20 )170.9133333333335.906308206346228.9374220515094
Trimmed Mean ( 16 / 20 )171.4071428571435.7743043479667629.6844663058847
Trimmed Mean ( 17 / 20 )171.9615384615385.562940774372130.9119844046782
Trimmed Mean ( 18 / 20 )172.2755.3865817250979731.9822493729763
Trimmed Mean ( 19 / 20 )172.7318181818185.1824060766225733.3304290763701
Trimmed Mean ( 20 / 20 )173.155.1253266904862333.783212360181
Median176.65
Midrange178.6
Midmean - Weighted Average at Xnp169.070967741936
Midmean - Weighted Average at X(n+1)p169.070967741936
Midmean - Empirical Distribution Function169.070967741936
Midmean - Empirical Distribution Function - Averaging169.070967741936
Midmean - Empirical Distribution Function - Interpolation169.070967741936
Midmean - Closest Observation169.070967741936
Midmean - True Basic - Statistics Graphics Toolkit169.070967741936
Midmean - MS Excel (old versions)170.484375
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')