Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Dec 2009 09:54:58 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t12599457805ylv6go1wle3s46.htm/, Retrieved Sun, 28 Apr 2024 00:20:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63896, Retrieved Sun, 28 Apr 2024 00:20:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robustness of cen...] [2009-12-04 16:54:58] [557d56ec4b06cd0135c259898de8ce95] [Current]
Feedback Forum

Post a new message
Dataseries X:
17,8
17,9
17,4
16,7
16
16,6
19,1
17,8
17,2
18,6
16,3
15,1
19,2
17,7
19,1
18
17,5
17,8
21,1
17,2
19,4
19,8
17,6
16,2
19,5
19,9
20
17,3
18,9
18,6
21,4
18,6
19,8
20,8
19,6
17,7
19,8
22,2
20,7
17,9
20,9
21,2
21,4
23
21,3
23,9
22,4
18,3
22,8
22,3
17,8
16,4
16
16,4
17,7
16,6
16,2
18,3
17,6
15,1




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=63896&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=63896&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63896&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 Mean18.75666666666670.27074250976035769.2786171010559
Geometric Mean18.6441387295014
Harmonic Mean18.5344546503816
Quadratic Mean18.8716012392519
Winsorized Mean ( 1 / 20 )18.74166666666670.26629166782693270.380221880796
Winsorized Mean ( 2 / 20 )18.7650.25829542276960572.649371013973
Winsorized Mean ( 3 / 20 )18.7450.25319902401611274.0326708321244
Winsorized Mean ( 4 / 20 )18.75166666666670.24919635425807975.2485594040698
Winsorized Mean ( 5 / 20 )18.74333333333330.24720318807785875.8215679946248
Winsorized Mean ( 6 / 20 )18.67333333333330.22779794132424381.9732312977935
Winsorized Mean ( 7 / 20 )18.6850.22576705408864382.7622970739729
Winsorized Mean ( 8 / 20 )18.67166666666670.22307673512757783.7006452330784
Winsorized Mean ( 9 / 20 )18.68666666666670.21503470573475686.9007009952922
Winsorized Mean ( 10 / 20 )18.670.21176284571392388.1646633386382
Winsorized Mean ( 11 / 20 )18.65166666666670.20170868498155292.4683370394912
Winsorized Mean ( 12 / 20 )18.73166666666670.182535371801108102.619379914359
Winsorized Mean ( 13 / 20 )18.710.178406315917688104.872968783416
Winsorized Mean ( 14 / 20 )18.570.145813517620637127.354447674142
Winsorized Mean ( 15 / 20 )18.570.138051411040943134.515104626439
Winsorized Mean ( 16 / 20 )18.570.129956533367783142.893931676725
Winsorized Mean ( 17 / 20 )18.59833333333330.126077092070722147.515563913075
Winsorized Mean ( 18 / 20 )18.59833333333330.126077092070722147.515563913075
Winsorized Mean ( 19 / 20 )18.56666666666670.111782341637987166.096598036887
Winsorized Mean ( 20 / 20 )18.53333333333330.106608388034182173.844982323445
Trimmed Mean ( 1 / 20 )18.73103448275860.25774402737057072.6730107923246
Trimmed Mean ( 2 / 20 )18.71964285714290.24719753448914975.7274658739147
Trimmed Mean ( 3 / 20 )18.69444444444440.23947322614938578.0648623858381
Trimmed Mean ( 4 / 20 )18.6750.23230556345353280.389809535214
Trimmed Mean ( 5 / 20 )18.6520.22481266577725982.966855695222
Trimmed Mean ( 6 / 20 )18.62916666666670.21594174281138086.2694096293315
Trimmed Mean ( 7 / 20 )18.61956521739130.21092434170765088.2760380648657
Trimmed Mean ( 8 / 20 )18.60681818181820.20489252912503990.8125750669174
Trimmed Mean ( 9 / 20 )18.59523809523810.19769144945201594.0619240072475
Trimmed Mean ( 10 / 20 )18.580.19035055380359097.6093824196145
Trimmed Mean ( 11 / 20 )18.56578947368420.18136029055417102.369650031735
Trimmed Mean ( 12 / 20 )18.55277777777780.172078152746237107.815998031647
Trimmed Mean ( 13 / 20 )18.52647058823530.164620712636791112.540337673735
Trimmed Mean ( 14 / 20 )18.50.155218368550516119.186924671091
Trimmed Mean ( 15 / 20 )18.490.152402220395929121.323691688773
Trimmed Mean ( 16 / 20 )18.47857142857140.150075566755423123.128446742339
Trimmed Mean ( 17 / 20 )18.46538461538460.148421676593550124.411642821902
Trimmed Mean ( 18 / 20 )18.44583333333330.146081569266034126.270777525268
Trimmed Mean ( 19 / 20 )18.42272727272730.141257772751977130.419211019801
Trimmed Mean ( 20 / 20 )18.40.138602042971197132.754175952686
Median18.3
Midrange19.5
Midmean - Weighted Average at Xnp18.4516129032258
Midmean - Weighted Average at X(n+1)p18.49
Midmean - Empirical Distribution Function18.4516129032258
Midmean - Empirical Distribution Function - Averaging18.49
Midmean - Empirical Distribution Function - Interpolation18.49
Midmean - Closest Observation18.4516129032258
Midmean - True Basic - Statistics Graphics Toolkit18.49
Midmean - MS Excel (old versions)18.5
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.7566666666667 & 0.270742509760357 & 69.2786171010559 \tabularnewline
Geometric Mean & 18.6441387295014 &  &  \tabularnewline
Harmonic Mean & 18.5344546503816 &  &  \tabularnewline
Quadratic Mean & 18.8716012392519 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18.7416666666667 & 0.266291667826932 & 70.380221880796 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18.765 & 0.258295422769605 & 72.649371013973 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18.745 & 0.253199024016112 & 74.0326708321244 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18.7516666666667 & 0.249196354258079 & 75.2485594040698 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18.7433333333333 & 0.247203188077858 & 75.8215679946248 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18.6733333333333 & 0.227797941324243 & 81.9732312977935 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18.685 & 0.225767054088643 & 82.7622970739729 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18.6716666666667 & 0.223076735127577 & 83.7006452330784 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18.6866666666667 & 0.215034705734756 & 86.9007009952922 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18.67 & 0.211762845713923 & 88.1646633386382 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18.6516666666667 & 0.201708684981552 & 92.4683370394912 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18.7316666666667 & 0.182535371801108 & 102.619379914359 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18.71 & 0.178406315917688 & 104.872968783416 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18.57 & 0.145813517620637 & 127.354447674142 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18.57 & 0.138051411040943 & 134.515104626439 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18.57 & 0.129956533367783 & 142.893931676725 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18.5983333333333 & 0.126077092070722 & 147.515563913075 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18.5983333333333 & 0.126077092070722 & 147.515563913075 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18.5666666666667 & 0.111782341637987 & 166.096598036887 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18.5333333333333 & 0.106608388034182 & 173.844982323445 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18.7310344827586 & 0.257744027370570 & 72.6730107923246 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18.7196428571429 & 0.247197534489149 & 75.7274658739147 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18.6944444444444 & 0.239473226149385 & 78.0648623858381 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18.675 & 0.232305563453532 & 80.389809535214 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18.652 & 0.224812665777259 & 82.966855695222 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18.6291666666667 & 0.215941742811380 & 86.2694096293315 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18.6195652173913 & 0.210924341707650 & 88.2760380648657 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18.6068181818182 & 0.204892529125039 & 90.8125750669174 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18.5952380952381 & 0.197691449452015 & 94.0619240072475 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18.58 & 0.190350553803590 & 97.6093824196145 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18.5657894736842 & 0.18136029055417 & 102.369650031735 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18.5527777777778 & 0.172078152746237 & 107.815998031647 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18.5264705882353 & 0.164620712636791 & 112.540337673735 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18.5 & 0.155218368550516 & 119.186924671091 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18.49 & 0.152402220395929 & 121.323691688773 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18.4785714285714 & 0.150075566755423 & 123.128446742339 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18.4653846153846 & 0.148421676593550 & 124.411642821902 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18.4458333333333 & 0.146081569266034 & 126.270777525268 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18.4227272727273 & 0.141257772751977 & 130.419211019801 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18.4 & 0.138602042971197 & 132.754175952686 \tabularnewline
Median & 18.3 &  &  \tabularnewline
Midrange & 19.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.4516129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18.49 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.4516129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18.49 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18.49 &  &  \tabularnewline
Midmean - Closest Observation & 18.4516129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18.49 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18.5 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63896&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]18.7566666666667[/C][C]0.270742509760357[/C][C]69.2786171010559[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18.6441387295014[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18.5344546503816[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18.8716012392519[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18.7416666666667[/C][C]0.266291667826932[/C][C]70.380221880796[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18.765[/C][C]0.258295422769605[/C][C]72.649371013973[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18.745[/C][C]0.253199024016112[/C][C]74.0326708321244[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18.7516666666667[/C][C]0.249196354258079[/C][C]75.2485594040698[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18.7433333333333[/C][C]0.247203188077858[/C][C]75.8215679946248[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18.6733333333333[/C][C]0.227797941324243[/C][C]81.9732312977935[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18.685[/C][C]0.225767054088643[/C][C]82.7622970739729[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18.6716666666667[/C][C]0.223076735127577[/C][C]83.7006452330784[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18.6866666666667[/C][C]0.215034705734756[/C][C]86.9007009952922[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18.67[/C][C]0.211762845713923[/C][C]88.1646633386382[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18.6516666666667[/C][C]0.201708684981552[/C][C]92.4683370394912[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18.7316666666667[/C][C]0.182535371801108[/C][C]102.619379914359[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18.71[/C][C]0.178406315917688[/C][C]104.872968783416[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18.57[/C][C]0.145813517620637[/C][C]127.354447674142[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18.57[/C][C]0.138051411040943[/C][C]134.515104626439[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18.57[/C][C]0.129956533367783[/C][C]142.893931676725[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18.5983333333333[/C][C]0.126077092070722[/C][C]147.515563913075[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18.5983333333333[/C][C]0.126077092070722[/C][C]147.515563913075[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18.5666666666667[/C][C]0.111782341637987[/C][C]166.096598036887[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18.5333333333333[/C][C]0.106608388034182[/C][C]173.844982323445[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18.7310344827586[/C][C]0.257744027370570[/C][C]72.6730107923246[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18.7196428571429[/C][C]0.247197534489149[/C][C]75.7274658739147[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18.6944444444444[/C][C]0.239473226149385[/C][C]78.0648623858381[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18.675[/C][C]0.232305563453532[/C][C]80.389809535214[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18.652[/C][C]0.224812665777259[/C][C]82.966855695222[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18.6291666666667[/C][C]0.215941742811380[/C][C]86.2694096293315[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18.6195652173913[/C][C]0.210924341707650[/C][C]88.2760380648657[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18.6068181818182[/C][C]0.204892529125039[/C][C]90.8125750669174[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18.5952380952381[/C][C]0.197691449452015[/C][C]94.0619240072475[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18.58[/C][C]0.190350553803590[/C][C]97.6093824196145[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18.5657894736842[/C][C]0.18136029055417[/C][C]102.369650031735[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18.5527777777778[/C][C]0.172078152746237[/C][C]107.815998031647[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18.5264705882353[/C][C]0.164620712636791[/C][C]112.540337673735[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18.5[/C][C]0.155218368550516[/C][C]119.186924671091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18.49[/C][C]0.152402220395929[/C][C]121.323691688773[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18.4785714285714[/C][C]0.150075566755423[/C][C]123.128446742339[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18.4653846153846[/C][C]0.148421676593550[/C][C]124.411642821902[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18.4458333333333[/C][C]0.146081569266034[/C][C]126.270777525268[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18.4227272727273[/C][C]0.141257772751977[/C][C]130.419211019801[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18.4[/C][C]0.138602042971197[/C][C]132.754175952686[/C][/ROW]
[ROW][C]Median[/C][C]18.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.4516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.4516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.4516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18.5[/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=63896&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63896&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 Mean18.75666666666670.27074250976035769.2786171010559
Geometric Mean18.6441387295014
Harmonic Mean18.5344546503816
Quadratic Mean18.8716012392519
Winsorized Mean ( 1 / 20 )18.74166666666670.26629166782693270.380221880796
Winsorized Mean ( 2 / 20 )18.7650.25829542276960572.649371013973
Winsorized Mean ( 3 / 20 )18.7450.25319902401611274.0326708321244
Winsorized Mean ( 4 / 20 )18.75166666666670.24919635425807975.2485594040698
Winsorized Mean ( 5 / 20 )18.74333333333330.24720318807785875.8215679946248
Winsorized Mean ( 6 / 20 )18.67333333333330.22779794132424381.9732312977935
Winsorized Mean ( 7 / 20 )18.6850.22576705408864382.7622970739729
Winsorized Mean ( 8 / 20 )18.67166666666670.22307673512757783.7006452330784
Winsorized Mean ( 9 / 20 )18.68666666666670.21503470573475686.9007009952922
Winsorized Mean ( 10 / 20 )18.670.21176284571392388.1646633386382
Winsorized Mean ( 11 / 20 )18.65166666666670.20170868498155292.4683370394912
Winsorized Mean ( 12 / 20 )18.73166666666670.182535371801108102.619379914359
Winsorized Mean ( 13 / 20 )18.710.178406315917688104.872968783416
Winsorized Mean ( 14 / 20 )18.570.145813517620637127.354447674142
Winsorized Mean ( 15 / 20 )18.570.138051411040943134.515104626439
Winsorized Mean ( 16 / 20 )18.570.129956533367783142.893931676725
Winsorized Mean ( 17 / 20 )18.59833333333330.126077092070722147.515563913075
Winsorized Mean ( 18 / 20 )18.59833333333330.126077092070722147.515563913075
Winsorized Mean ( 19 / 20 )18.56666666666670.111782341637987166.096598036887
Winsorized Mean ( 20 / 20 )18.53333333333330.106608388034182173.844982323445
Trimmed Mean ( 1 / 20 )18.73103448275860.25774402737057072.6730107923246
Trimmed Mean ( 2 / 20 )18.71964285714290.24719753448914975.7274658739147
Trimmed Mean ( 3 / 20 )18.69444444444440.23947322614938578.0648623858381
Trimmed Mean ( 4 / 20 )18.6750.23230556345353280.389809535214
Trimmed Mean ( 5 / 20 )18.6520.22481266577725982.966855695222
Trimmed Mean ( 6 / 20 )18.62916666666670.21594174281138086.2694096293315
Trimmed Mean ( 7 / 20 )18.61956521739130.21092434170765088.2760380648657
Trimmed Mean ( 8 / 20 )18.60681818181820.20489252912503990.8125750669174
Trimmed Mean ( 9 / 20 )18.59523809523810.19769144945201594.0619240072475
Trimmed Mean ( 10 / 20 )18.580.19035055380359097.6093824196145
Trimmed Mean ( 11 / 20 )18.56578947368420.18136029055417102.369650031735
Trimmed Mean ( 12 / 20 )18.55277777777780.172078152746237107.815998031647
Trimmed Mean ( 13 / 20 )18.52647058823530.164620712636791112.540337673735
Trimmed Mean ( 14 / 20 )18.50.155218368550516119.186924671091
Trimmed Mean ( 15 / 20 )18.490.152402220395929121.323691688773
Trimmed Mean ( 16 / 20 )18.47857142857140.150075566755423123.128446742339
Trimmed Mean ( 17 / 20 )18.46538461538460.148421676593550124.411642821902
Trimmed Mean ( 18 / 20 )18.44583333333330.146081569266034126.270777525268
Trimmed Mean ( 19 / 20 )18.42272727272730.141257772751977130.419211019801
Trimmed Mean ( 20 / 20 )18.40.138602042971197132.754175952686
Median18.3
Midrange19.5
Midmean - Weighted Average at Xnp18.4516129032258
Midmean - Weighted Average at X(n+1)p18.49
Midmean - Empirical Distribution Function18.4516129032258
Midmean - Empirical Distribution Function - Averaging18.49
Midmean - Empirical Distribution Function - Interpolation18.49
Midmean - Closest Observation18.4516129032258
Midmean - True Basic - Statistics Graphics Toolkit18.49
Midmean - MS Excel (old versions)18.5
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')