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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, 15 Nov 2011 14:14:54 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t132138451594z84brzh4gc2tg.htm/, Retrieved Fri, 29 Mar 2024 07:13:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143392, Retrieved Fri, 29 Mar 2024 07:13:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [Aantal geboorten ...] [2011-11-15 19:14:54] [e7912d585babb6fa20e6bf5178c462ce] [Current]
- R  D      [Central Tendency] [Aantal geboorten ...] [2011-11-15 19:22:37] [379dab8110dbf77cfcc4b7951c3a599f]
- RMP         [Mean versus Median] [WS 6 tutorial blo...] [2011-11-15 19:33:07] [60c0c94f647e2c90e494ab0f2a2f1926]
- RM D      [Mean versus Median] [Verschil tussen r...] [2011-11-15 19:33:10] [379dab8110dbf77cfcc4b7951c3a599f]
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Dataseries X:
76.035
74.427
73.354
73.081
75.309
75.463
75.910
76.151
76.882
78.632
80.137
82.490
79.896
81.303
79.344
81.355
82.328
79.669
77.249
75.101
72.520
72.438
72.653
71.429
69.189
66.451
63.354
61.379
61.880
62.274
62.429
63.905
63.917
64.295
61.930
60.440
59.353
58.695
60.569
60.386
60.938
61.795
63.304
64.270
63.492
61.333
59.341
58.412
58.725
59.277
58.562
57.858
58.790
58.243
57.044
57.339
59.429
60.575
61.950
61.712




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143392&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143392&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean67.43318333333331.0655924090376663.2823420675758
Geometric Mean66.9503064163769
Harmonic Mean66.4843851753748
Quadratic Mean67.9281087490051
Winsorized Mean ( 1 / 20 )67.43541.0641473035857563.3703621413784
Winsorized Mean ( 2 / 20 )67.42026666666671.0539441507053563.9694870184019
Winsorized Mean ( 3 / 20 )67.43691666666671.0504539732336264.1978786172565
Winsorized Mean ( 4 / 20 )67.370451.0319390946927965.2852967258272
Winsorized Mean ( 5 / 20 )67.36286666666671.0259258405007465.6605614239988
Winsorized Mean ( 6 / 20 )67.35346666666671.0193270637903866.0764037954727
Winsorized Mean ( 7 / 20 )67.319051.0111190169024766.5787596461493
Winsorized Mean ( 8 / 20 )67.23278333333330.9910442321653967.8403457194161
Winsorized Mean ( 9 / 20 )67.09838333333330.94141384149360371.2740565051372
Winsorized Mean ( 10 / 20 )67.04788333333330.92883476180699472.1849419189433
Winsorized Mean ( 11 / 20 )66.91606666666670.90490323915933473.9483115662538
Winsorized Mean ( 12 / 20 )66.90806666666670.89875155150747874.4455645772645
Winsorized Mean ( 13 / 20 )67.08833333333330.86583833698928877.4836715669282
Winsorized Mean ( 14 / 20 )66.99663333333330.84633487647916879.1609033200257
Winsorized Mean ( 15 / 20 )66.99038333333330.83560510673527580.1699065663516
Winsorized Mean ( 16 / 20 )66.93651666666670.8260709793895781.0299820920109
Winsorized Mean ( 17 / 20 )66.84840.78105352298207685.5874764443436
Winsorized Mean ( 18 / 20 )66.6450.71382947804697393.3626335834992
Winsorized Mean ( 19 / 20 )66.57311666666670.6982782728822995.3389490294066
Winsorized Mean ( 20 / 20 )66.541450.661981768496712100.518553782997
Trimmed Mean ( 1 / 20 )67.35270689655171.055708724542963.7985699376635
Trimmed Mean ( 2 / 20 )67.26410714285711.0444088627154464.4039988017453
Trimmed Mean ( 3 / 20 )67.17735185185191.0360716851635564.8385172704028
Trimmed Mean ( 4 / 20 )67.07751923076921.0261151504723865.3703623807618
Trimmed Mean ( 5 / 20 )66.989641.0194628488631965.7107221461781
Trimmed Mean ( 6 / 20 )66.89633333333331.0115202743229866.1344463689647
Trimmed Mean ( 7 / 20 )66.79695652173911.00179108198266.6775315962927
Trimmed Mean ( 8 / 20 )66.695250.99000870013741867.3683473597175
Trimmed Mean ( 9 / 20 )66.59926190476190.9785788832440468.0571214494041
Trimmed Mean ( 10 / 20 )66.5160750.97458294656102268.250809471593
Trimmed Mean ( 11 / 20 )66.43210526315790.96985303310201368.4970846053644
Trimmed Mean ( 12 / 20 )66.35877777777780.96680637012755868.6370920053233
Trimmed Mean ( 13 / 20 )66.2780.96085012956209868.9784993110276
Trimmed Mean ( 14 / 20 )66.1611250.95669288895139269.1560748115496
Trimmed Mean ( 15 / 20 )66.04176666666670.95186184847506969.3816721118395
Trimmed Mean ( 16 / 20 )65.906250.94274495732594269.9088862664834
Trimmed Mean ( 17 / 20 )65.75765384615380.92683820999934770.948363087232
Trimmed Mean ( 18 / 20 )65.597250.91224039636538271.9078548388753
Trimmed Mean ( 19 / 20 )65.43850.90747178590179472.1107818630095
Trimmed Mean ( 20 / 20 )65.259350.89579439686089172.8508128971186
Median63.6985
Midrange69.767
Midmean - Weighted Average at Xnp65.861064516129
Midmean - Weighted Average at X(n+1)p66.0417666666667
Midmean - Empirical Distribution Function65.861064516129
Midmean - Empirical Distribution Function - Averaging66.0417666666667
Midmean - Empirical Distribution Function - Interpolation66.0417666666667
Midmean - Closest Observation65.861064516129
Midmean - True Basic - Statistics Graphics Toolkit66.0417666666667
Midmean - MS Excel (old versions)66.161125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 67.4331833333333 & 1.06559240903766 & 63.2823420675758 \tabularnewline
Geometric Mean & 66.9503064163769 &  &  \tabularnewline
Harmonic Mean & 66.4843851753748 &  &  \tabularnewline
Quadratic Mean & 67.9281087490051 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 67.4354 & 1.06414730358575 & 63.3703621413784 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 67.4202666666667 & 1.05394415070535 & 63.9694870184019 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 67.4369166666667 & 1.05045397323362 & 64.1978786172565 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 67.37045 & 1.03193909469279 & 65.2852967258272 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 67.3628666666667 & 1.02592584050074 & 65.6605614239988 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 67.3534666666667 & 1.01932706379038 & 66.0764037954727 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 67.31905 & 1.01111901690247 & 66.5787596461493 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 67.2327833333333 & 0.99104423216539 & 67.8403457194161 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 67.0983833333333 & 0.941413841493603 & 71.2740565051372 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 67.0478833333333 & 0.928834761806994 & 72.1849419189433 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 66.9160666666667 & 0.904903239159334 & 73.9483115662538 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 66.9080666666667 & 0.898751551507478 & 74.4455645772645 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 67.0883333333333 & 0.865838336989288 & 77.4836715669282 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 66.9966333333333 & 0.846334876479168 & 79.1609033200257 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 66.9903833333333 & 0.835605106735275 & 80.1699065663516 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 66.9365166666667 & 0.82607097938957 & 81.0299820920109 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 66.8484 & 0.781053522982076 & 85.5874764443436 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 66.645 & 0.713829478046973 & 93.3626335834992 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 66.5731166666667 & 0.69827827288229 & 95.3389490294066 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 66.54145 & 0.661981768496712 & 100.518553782997 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 67.3527068965517 & 1.0557087245429 & 63.7985699376635 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 67.2641071428571 & 1.04440886271544 & 64.4039988017453 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 67.1773518518519 & 1.03607168516355 & 64.8385172704028 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 67.0775192307692 & 1.02611515047238 & 65.3703623807618 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 66.98964 & 1.01946284886319 & 65.7107221461781 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 66.8963333333333 & 1.01152027432298 & 66.1344463689647 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 66.7969565217391 & 1.001791081982 & 66.6775315962927 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 66.69525 & 0.990008700137418 & 67.3683473597175 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 66.5992619047619 & 0.97857888324404 & 68.0571214494041 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 66.516075 & 0.974582946561022 & 68.250809471593 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 66.4321052631579 & 0.969853033102013 & 68.4970846053644 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 66.3587777777778 & 0.966806370127558 & 68.6370920053233 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 66.278 & 0.960850129562098 & 68.9784993110276 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 66.161125 & 0.956692888951392 & 69.1560748115496 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 66.0417666666667 & 0.951861848475069 & 69.3816721118395 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 65.90625 & 0.942744957325942 & 69.9088862664834 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 65.7576538461538 & 0.926838209999347 & 70.948363087232 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 65.59725 & 0.912240396365382 & 71.9078548388753 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 65.4385 & 0.907471785901794 & 72.1107818630095 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 65.25935 & 0.895794396860891 & 72.8508128971186 \tabularnewline
Median & 63.6985 &  &  \tabularnewline
Midrange & 69.767 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 65.861064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 66.0417666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 65.861064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 66.0417666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 66.0417666666667 &  &  \tabularnewline
Midmean - Closest Observation & 65.861064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 66.0417666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 66.161125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143392&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]67.4331833333333[/C][C]1.06559240903766[/C][C]63.2823420675758[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]66.9503064163769[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]66.4843851753748[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]67.9281087490051[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]67.4354[/C][C]1.06414730358575[/C][C]63.3703621413784[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]67.4202666666667[/C][C]1.05394415070535[/C][C]63.9694870184019[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]67.4369166666667[/C][C]1.05045397323362[/C][C]64.1978786172565[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]67.37045[/C][C]1.03193909469279[/C][C]65.2852967258272[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]67.3628666666667[/C][C]1.02592584050074[/C][C]65.6605614239988[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]67.3534666666667[/C][C]1.01932706379038[/C][C]66.0764037954727[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]67.31905[/C][C]1.01111901690247[/C][C]66.5787596461493[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]67.2327833333333[/C][C]0.99104423216539[/C][C]67.8403457194161[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]67.0983833333333[/C][C]0.941413841493603[/C][C]71.2740565051372[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]67.0478833333333[/C][C]0.928834761806994[/C][C]72.1849419189433[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]66.9160666666667[/C][C]0.904903239159334[/C][C]73.9483115662538[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]66.9080666666667[/C][C]0.898751551507478[/C][C]74.4455645772645[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]67.0883333333333[/C][C]0.865838336989288[/C][C]77.4836715669282[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]66.9966333333333[/C][C]0.846334876479168[/C][C]79.1609033200257[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]66.9903833333333[/C][C]0.835605106735275[/C][C]80.1699065663516[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]66.9365166666667[/C][C]0.82607097938957[/C][C]81.0299820920109[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]66.8484[/C][C]0.781053522982076[/C][C]85.5874764443436[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]66.645[/C][C]0.713829478046973[/C][C]93.3626335834992[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]66.5731166666667[/C][C]0.69827827288229[/C][C]95.3389490294066[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]66.54145[/C][C]0.661981768496712[/C][C]100.518553782997[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]67.3527068965517[/C][C]1.0557087245429[/C][C]63.7985699376635[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]67.2641071428571[/C][C]1.04440886271544[/C][C]64.4039988017453[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]67.1773518518519[/C][C]1.03607168516355[/C][C]64.8385172704028[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]67.0775192307692[/C][C]1.02611515047238[/C][C]65.3703623807618[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]66.98964[/C][C]1.01946284886319[/C][C]65.7107221461781[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]66.8963333333333[/C][C]1.01152027432298[/C][C]66.1344463689647[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]66.7969565217391[/C][C]1.001791081982[/C][C]66.6775315962927[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]66.69525[/C][C]0.990008700137418[/C][C]67.3683473597175[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]66.5992619047619[/C][C]0.97857888324404[/C][C]68.0571214494041[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]66.516075[/C][C]0.974582946561022[/C][C]68.250809471593[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]66.4321052631579[/C][C]0.969853033102013[/C][C]68.4970846053644[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]66.3587777777778[/C][C]0.966806370127558[/C][C]68.6370920053233[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]66.278[/C][C]0.960850129562098[/C][C]68.9784993110276[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]66.161125[/C][C]0.956692888951392[/C][C]69.1560748115496[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]66.0417666666667[/C][C]0.951861848475069[/C][C]69.3816721118395[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]65.90625[/C][C]0.942744957325942[/C][C]69.9088862664834[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]65.7576538461538[/C][C]0.926838209999347[/C][C]70.948363087232[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]65.59725[/C][C]0.912240396365382[/C][C]71.9078548388753[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]65.4385[/C][C]0.907471785901794[/C][C]72.1107818630095[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]65.25935[/C][C]0.895794396860891[/C][C]72.8508128971186[/C][/ROW]
[ROW][C]Median[/C][C]63.6985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]69.767[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]65.861064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]66.0417666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]65.861064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]66.0417666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]66.0417666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]65.861064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]66.0417666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]66.161125[/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=143392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143392&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 Mean67.43318333333331.0655924090376663.2823420675758
Geometric Mean66.9503064163769
Harmonic Mean66.4843851753748
Quadratic Mean67.9281087490051
Winsorized Mean ( 1 / 20 )67.43541.0641473035857563.3703621413784
Winsorized Mean ( 2 / 20 )67.42026666666671.0539441507053563.9694870184019
Winsorized Mean ( 3 / 20 )67.43691666666671.0504539732336264.1978786172565
Winsorized Mean ( 4 / 20 )67.370451.0319390946927965.2852967258272
Winsorized Mean ( 5 / 20 )67.36286666666671.0259258405007465.6605614239988
Winsorized Mean ( 6 / 20 )67.35346666666671.0193270637903866.0764037954727
Winsorized Mean ( 7 / 20 )67.319051.0111190169024766.5787596461493
Winsorized Mean ( 8 / 20 )67.23278333333330.9910442321653967.8403457194161
Winsorized Mean ( 9 / 20 )67.09838333333330.94141384149360371.2740565051372
Winsorized Mean ( 10 / 20 )67.04788333333330.92883476180699472.1849419189433
Winsorized Mean ( 11 / 20 )66.91606666666670.90490323915933473.9483115662538
Winsorized Mean ( 12 / 20 )66.90806666666670.89875155150747874.4455645772645
Winsorized Mean ( 13 / 20 )67.08833333333330.86583833698928877.4836715669282
Winsorized Mean ( 14 / 20 )66.99663333333330.84633487647916879.1609033200257
Winsorized Mean ( 15 / 20 )66.99038333333330.83560510673527580.1699065663516
Winsorized Mean ( 16 / 20 )66.93651666666670.8260709793895781.0299820920109
Winsorized Mean ( 17 / 20 )66.84840.78105352298207685.5874764443436
Winsorized Mean ( 18 / 20 )66.6450.71382947804697393.3626335834992
Winsorized Mean ( 19 / 20 )66.57311666666670.6982782728822995.3389490294066
Winsorized Mean ( 20 / 20 )66.541450.661981768496712100.518553782997
Trimmed Mean ( 1 / 20 )67.35270689655171.055708724542963.7985699376635
Trimmed Mean ( 2 / 20 )67.26410714285711.0444088627154464.4039988017453
Trimmed Mean ( 3 / 20 )67.17735185185191.0360716851635564.8385172704028
Trimmed Mean ( 4 / 20 )67.07751923076921.0261151504723865.3703623807618
Trimmed Mean ( 5 / 20 )66.989641.0194628488631965.7107221461781
Trimmed Mean ( 6 / 20 )66.89633333333331.0115202743229866.1344463689647
Trimmed Mean ( 7 / 20 )66.79695652173911.00179108198266.6775315962927
Trimmed Mean ( 8 / 20 )66.695250.99000870013741867.3683473597175
Trimmed Mean ( 9 / 20 )66.59926190476190.9785788832440468.0571214494041
Trimmed Mean ( 10 / 20 )66.5160750.97458294656102268.250809471593
Trimmed Mean ( 11 / 20 )66.43210526315790.96985303310201368.4970846053644
Trimmed Mean ( 12 / 20 )66.35877777777780.96680637012755868.6370920053233
Trimmed Mean ( 13 / 20 )66.2780.96085012956209868.9784993110276
Trimmed Mean ( 14 / 20 )66.1611250.95669288895139269.1560748115496
Trimmed Mean ( 15 / 20 )66.04176666666670.95186184847506969.3816721118395
Trimmed Mean ( 16 / 20 )65.906250.94274495732594269.9088862664834
Trimmed Mean ( 17 / 20 )65.75765384615380.92683820999934770.948363087232
Trimmed Mean ( 18 / 20 )65.597250.91224039636538271.9078548388753
Trimmed Mean ( 19 / 20 )65.43850.90747178590179472.1107818630095
Trimmed Mean ( 20 / 20 )65.259350.89579439686089172.8508128971186
Median63.6985
Midrange69.767
Midmean - Weighted Average at Xnp65.861064516129
Midmean - Weighted Average at X(n+1)p66.0417666666667
Midmean - Empirical Distribution Function65.861064516129
Midmean - Empirical Distribution Function - Averaging66.0417666666667
Midmean - Empirical Distribution Function - Interpolation66.0417666666667
Midmean - Closest Observation65.861064516129
Midmean - True Basic - Statistics Graphics Toolkit66.0417666666667
Midmean - MS Excel (old versions)66.161125
Number of observations60



Parameters (Session):
par1 = Geboorten ; par2 = Nis ; par3 = aantal geboortes in België ; par4 = No season ;
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')