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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 05 Dec 2007 01:47:17 -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/2007/Dec/05/t11968436887zwkpnsfgvvmkz7.htm/, Retrieved Thu, 02 May 2024 16:44:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2467, Retrieved Thu, 02 May 2024 16:44:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact257
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Q4-8] [2007-12-05 08:47:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
10.9845028700717
349.098142273962
81.4633471855314
-278.766706594484
-560.89491396613
-787.622056802042
223.81041933827
252.583430955455
-64.2640640254719
80.73040441068
270.627944194231
192.475870416700
89.0883775511372
-302.316979338774
122.280120354141
941.407337774104
198.398814682621
-512.471564985318
1093.51318763054
-48.423853621373
692.910224832028
26.079799286632
-381.837971016715
166.213763786132
575.99873286274
-138.603318979601
-400.786387170289
109.657795744652
267.895560706265
71.0440187583216
-221.237482722575
-859.12342391504
227.217599437225
783.905790519395
-660.231228952141
932.01242663218
773.101071239821
906.591178563678
-434.797368190746
1106.02138904352
-1203.47774140879
637.713874315654
-339.209390388509
-23.1384684077148
-80.7725113823799
-294.659095720157
114.889591721596
-242.372208125449
-1600.54130499084
-83.8242244224257
98.4060165844421
-164.177550448057
916.333965820262
1772.39376664942
474.247518575659
654.942821965808




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2467&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2467&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.758731984068879.67290893166561.23955223059287
Geometric MeanNaN
Harmonic Mean478.371064257256
Quadratic Mean599.066582370393
Winsorized Mean ( 1 / 18 )93.949646019357273.35106600977421.28082182209647
Winsorized Mean ( 2 / 18 )105.80129302224269.70121331181831.51792613062451
Winsorized Mean ( 3 / 18 )101.48319573241566.77097586707581.51986988979227
Winsorized Mean ( 4 / 18 )109.91147549727064.52576379770611.70337349034492
Winsorized Mean ( 5 / 18 )117.38092676281462.35978441816131.88231771257742
Winsorized Mean ( 6 / 18 )121.52527266183961.11375164164751.98850944995860
Winsorized Mean ( 7 / 18 )115.89887375562555.86226964932712.07472547182875
Winsorized Mean ( 8 / 18 )119.21405400432254.67092185520052.18057515693752
Winsorized Mean ( 9 / 18 )109.37152057060951.40974464777492.12744726354797
Winsorized Mean ( 10 / 18 )110.20387374239248.72054764739482.26195884619300
Winsorized Mean ( 11 / 18 )114.06633976731046.83882682139652.4352945517244
Winsorized Mean ( 12 / 18 )102.48264165996043.92990822474652.33286719233868
Winsorized Mean ( 13 / 18 )82.55112867606238.82497120696882.12623798832965
Winsorized Mean ( 14 / 18 )60.362409217896531.78762865810841.89892772018712
Winsorized Mean ( 15 / 18 )45.004693322309727.48311748221531.63753960413817
Winsorized Mean ( 16 / 18 )60.526850118467524.56932494740192.46351294746777
Winsorized Mean ( 17 / 18 )63.642130997038622.5807628812142.81842253655591
Winsorized Mean ( 18 / 18 )73.096394116699618.54864074019503.94079518497003
Trimmed Mean ( 1 / 18 )99.234009804616269.5961496084041.42585488368215
Trimmed Mean ( 2 / 18 )104.92486311181864.84140417291951.61817691103672
Trimmed Mean ( 3 / 18 )104.43406236198161.42319308044581.70023825080542
Trimmed Mean ( 4 / 18 )105.58162160681258.60005988489431.80173231587479
Trimmed Mean ( 5 / 18 )104.26383998797755.9394622532291.86386918622834
Trimmed Mean ( 6 / 18 )100.92494517256453.3007142503311.89350080185721
Trimmed Mean ( 7 / 18 )96.347094619391750.25414155250851.91719710342127
Trimmed Mean ( 8 / 18 )92.43673879214547.99446655983051.92598741933952
Trimmed Mean ( 9 / 18 )87.50407546358645.30530060734751.93143129590878
Trimmed Mean ( 10 / 18 )83.724517050026542.71166679615631.96022593661835
Trimmed Mean ( 11 / 18 )79.363211241872339.97315063574651.98541295793934
Trimmed Mean ( 12 / 18 )73.842258976461836.67616828926462.01335805840099
Trimmed Mean ( 13 / 18 )69.387088336806532.97212965865112.10441633752951
Trimmed Mean ( 14 / 18 )67.361851361536429.56010117295392.27880990553474
Trimmed Mean ( 15 / 18 )68.438688614404127.32290696441662.50480992756494
Trimmed Mean ( 16 / 18 )72.083976770952125.54266517815972.82210083670469
Trimmed Mean ( 17 / 18 )73.922610556574623.99062121180633.08131289739991
Trimmed Mean ( 18 / 18 )75.615866013439422.28757943455743.39273568201827
Median85.2758623683343
Midrange85.92623082929
Midmean - Weighted Average at Xnp55.4263838458115
Midmean - Weighted Average at X(n+1)p67.3618513615364
Midmean - Empirical Distribution Function55.4263838458115
Midmean - Empirical Distribution Function - Averaging67.3618513615364
Midmean - Empirical Distribution Function - Interpolation67.3618513615364
Midmean - Closest Observation55.4263838458115
Midmean - True Basic - Statistics Graphics Toolkit67.3618513615364
Midmean - MS Excel (old versions)69.3870883368065
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.7587319840688 & 79.6729089316656 & 1.23955223059287 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 478.371064257256 &  &  \tabularnewline
Quadratic Mean & 599.066582370393 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 93.9496460193572 & 73.3510660097742 & 1.28082182209647 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 105.801293022242 & 69.7012133118183 & 1.51792613062451 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 101.483195732415 & 66.7709758670758 & 1.51986988979227 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 109.911475497270 & 64.5257637977061 & 1.70337349034492 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 117.380926762814 & 62.3597844181613 & 1.88231771257742 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 121.525272661839 & 61.1137516416475 & 1.98850944995860 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 115.898873755625 & 55.8622696493271 & 2.07472547182875 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 119.214054004322 & 54.6709218552005 & 2.18057515693752 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 109.371520570609 & 51.4097446477749 & 2.12744726354797 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 110.203873742392 & 48.7205476473948 & 2.26195884619300 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 114.066339767310 & 46.8388268213965 & 2.4352945517244 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 102.482641659960 & 43.9299082247465 & 2.33286719233868 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 82.551128676062 & 38.8249712069688 & 2.12623798832965 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 60.3624092178965 & 31.7876286581084 & 1.89892772018712 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 45.0046933223097 & 27.4831174822153 & 1.63753960413817 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 60.5268501184675 & 24.5693249474019 & 2.46351294746777 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 63.6421309970386 & 22.580762881214 & 2.81842253655591 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 73.0963941166996 & 18.5486407401950 & 3.94079518497003 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 99.2340098046162 & 69.596149608404 & 1.42585488368215 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 104.924863111818 & 64.8414041729195 & 1.61817691103672 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 104.434062361981 & 61.4231930804458 & 1.70023825080542 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 105.581621606812 & 58.6000598848943 & 1.80173231587479 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 104.263839987977 & 55.939462253229 & 1.86386918622834 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 100.924945172564 & 53.300714250331 & 1.89350080185721 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 96.3470946193917 & 50.2541415525085 & 1.91719710342127 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 92.436738792145 & 47.9944665598305 & 1.92598741933952 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 87.504075463586 & 45.3053006073475 & 1.93143129590878 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 83.7245170500265 & 42.7116667961563 & 1.96022593661835 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 79.3632112418723 & 39.9731506357465 & 1.98541295793934 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 73.8422589764618 & 36.6761682892646 & 2.01335805840099 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 69.3870883368065 & 32.9721296586511 & 2.10441633752951 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 67.3618513615364 & 29.5601011729539 & 2.27880990553474 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 68.4386886144041 & 27.3229069644166 & 2.50480992756494 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 72.0839767709521 & 25.5426651781597 & 2.82210083670469 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 73.9226105565746 & 23.9906212118063 & 3.08131289739991 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 75.6158660134394 & 22.2875794345574 & 3.39273568201827 \tabularnewline
Median & 85.2758623683343 &  &  \tabularnewline
Midrange & 85.92623082929 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 55.4263838458115 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 67.3618513615364 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 55.4263838458115 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 67.3618513615364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 67.3618513615364 &  &  \tabularnewline
Midmean - Closest Observation & 55.4263838458115 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 67.3618513615364 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 69.3870883368065 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2467&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]98.7587319840688[/C][C]79.6729089316656[/C][C]1.23955223059287[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]478.371064257256[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]599.066582370393[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]93.9496460193572[/C][C]73.3510660097742[/C][C]1.28082182209647[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]105.801293022242[/C][C]69.7012133118183[/C][C]1.51792613062451[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]101.483195732415[/C][C]66.7709758670758[/C][C]1.51986988979227[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]109.911475497270[/C][C]64.5257637977061[/C][C]1.70337349034492[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]117.380926762814[/C][C]62.3597844181613[/C][C]1.88231771257742[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]121.525272661839[/C][C]61.1137516416475[/C][C]1.98850944995860[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]115.898873755625[/C][C]55.8622696493271[/C][C]2.07472547182875[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]119.214054004322[/C][C]54.6709218552005[/C][C]2.18057515693752[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]109.371520570609[/C][C]51.4097446477749[/C][C]2.12744726354797[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]110.203873742392[/C][C]48.7205476473948[/C][C]2.26195884619300[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]114.066339767310[/C][C]46.8388268213965[/C][C]2.4352945517244[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]102.482641659960[/C][C]43.9299082247465[/C][C]2.33286719233868[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]82.551128676062[/C][C]38.8249712069688[/C][C]2.12623798832965[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]60.3624092178965[/C][C]31.7876286581084[/C][C]1.89892772018712[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]45.0046933223097[/C][C]27.4831174822153[/C][C]1.63753960413817[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]60.5268501184675[/C][C]24.5693249474019[/C][C]2.46351294746777[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]63.6421309970386[/C][C]22.580762881214[/C][C]2.81842253655591[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]73.0963941166996[/C][C]18.5486407401950[/C][C]3.94079518497003[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]99.2340098046162[/C][C]69.596149608404[/C][C]1.42585488368215[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]104.924863111818[/C][C]64.8414041729195[/C][C]1.61817691103672[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]104.434062361981[/C][C]61.4231930804458[/C][C]1.70023825080542[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]105.581621606812[/C][C]58.6000598848943[/C][C]1.80173231587479[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]104.263839987977[/C][C]55.939462253229[/C][C]1.86386918622834[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]100.924945172564[/C][C]53.300714250331[/C][C]1.89350080185721[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]96.3470946193917[/C][C]50.2541415525085[/C][C]1.91719710342127[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]92.436738792145[/C][C]47.9944665598305[/C][C]1.92598741933952[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]87.504075463586[/C][C]45.3053006073475[/C][C]1.93143129590878[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]83.7245170500265[/C][C]42.7116667961563[/C][C]1.96022593661835[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]79.3632112418723[/C][C]39.9731506357465[/C][C]1.98541295793934[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]73.8422589764618[/C][C]36.6761682892646[/C][C]2.01335805840099[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]69.3870883368065[/C][C]32.9721296586511[/C][C]2.10441633752951[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]67.3618513615364[/C][C]29.5601011729539[/C][C]2.27880990553474[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]68.4386886144041[/C][C]27.3229069644166[/C][C]2.50480992756494[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]72.0839767709521[/C][C]25.5426651781597[/C][C]2.82210083670469[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]73.9226105565746[/C][C]23.9906212118063[/C][C]3.08131289739991[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]75.6158660134394[/C][C]22.2875794345574[/C][C]3.39273568201827[/C][/ROW]
[ROW][C]Median[/C][C]85.2758623683343[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]85.92623082929[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]55.4263838458115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]67.3618513615364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]55.4263838458115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]67.3618513615364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]67.3618513615364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]55.4263838458115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]67.3618513615364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]69.3870883368065[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2467&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 Mean98.758731984068879.67290893166561.23955223059287
Geometric MeanNaN
Harmonic Mean478.371064257256
Quadratic Mean599.066582370393
Winsorized Mean ( 1 / 18 )93.949646019357273.35106600977421.28082182209647
Winsorized Mean ( 2 / 18 )105.80129302224269.70121331181831.51792613062451
Winsorized Mean ( 3 / 18 )101.48319573241566.77097586707581.51986988979227
Winsorized Mean ( 4 / 18 )109.91147549727064.52576379770611.70337349034492
Winsorized Mean ( 5 / 18 )117.38092676281462.35978441816131.88231771257742
Winsorized Mean ( 6 / 18 )121.52527266183961.11375164164751.98850944995860
Winsorized Mean ( 7 / 18 )115.89887375562555.86226964932712.07472547182875
Winsorized Mean ( 8 / 18 )119.21405400432254.67092185520052.18057515693752
Winsorized Mean ( 9 / 18 )109.37152057060951.40974464777492.12744726354797
Winsorized Mean ( 10 / 18 )110.20387374239248.72054764739482.26195884619300
Winsorized Mean ( 11 / 18 )114.06633976731046.83882682139652.4352945517244
Winsorized Mean ( 12 / 18 )102.48264165996043.92990822474652.33286719233868
Winsorized Mean ( 13 / 18 )82.55112867606238.82497120696882.12623798832965
Winsorized Mean ( 14 / 18 )60.362409217896531.78762865810841.89892772018712
Winsorized Mean ( 15 / 18 )45.004693322309727.48311748221531.63753960413817
Winsorized Mean ( 16 / 18 )60.526850118467524.56932494740192.46351294746777
Winsorized Mean ( 17 / 18 )63.642130997038622.5807628812142.81842253655591
Winsorized Mean ( 18 / 18 )73.096394116699618.54864074019503.94079518497003
Trimmed Mean ( 1 / 18 )99.234009804616269.5961496084041.42585488368215
Trimmed Mean ( 2 / 18 )104.92486311181864.84140417291951.61817691103672
Trimmed Mean ( 3 / 18 )104.43406236198161.42319308044581.70023825080542
Trimmed Mean ( 4 / 18 )105.58162160681258.60005988489431.80173231587479
Trimmed Mean ( 5 / 18 )104.26383998797755.9394622532291.86386918622834
Trimmed Mean ( 6 / 18 )100.92494517256453.3007142503311.89350080185721
Trimmed Mean ( 7 / 18 )96.347094619391750.25414155250851.91719710342127
Trimmed Mean ( 8 / 18 )92.43673879214547.99446655983051.92598741933952
Trimmed Mean ( 9 / 18 )87.50407546358645.30530060734751.93143129590878
Trimmed Mean ( 10 / 18 )83.724517050026542.71166679615631.96022593661835
Trimmed Mean ( 11 / 18 )79.363211241872339.97315063574651.98541295793934
Trimmed Mean ( 12 / 18 )73.842258976461836.67616828926462.01335805840099
Trimmed Mean ( 13 / 18 )69.387088336806532.97212965865112.10441633752951
Trimmed Mean ( 14 / 18 )67.361851361536429.56010117295392.27880990553474
Trimmed Mean ( 15 / 18 )68.438688614404127.32290696441662.50480992756494
Trimmed Mean ( 16 / 18 )72.083976770952125.54266517815972.82210083670469
Trimmed Mean ( 17 / 18 )73.922610556574623.99062121180633.08131289739991
Trimmed Mean ( 18 / 18 )75.615866013439422.28757943455743.39273568201827
Median85.2758623683343
Midrange85.92623082929
Midmean - Weighted Average at Xnp55.4263838458115
Midmean - Weighted Average at X(n+1)p67.3618513615364
Midmean - Empirical Distribution Function55.4263838458115
Midmean - Empirical Distribution Function - Averaging67.3618513615364
Midmean - Empirical Distribution Function - Interpolation67.3618513615364
Midmean - Closest Observation55.4263838458115
Midmean - True Basic - Statistics Graphics Toolkit67.3618513615364
Midmean - MS Excel (old versions)69.3870883368065
Number of observations56



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')