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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, 12 Oct 2016 19:19:41 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t14762964505g4pa7orvrvjy24.htm/, Retrieved Sun, 05 May 2024 11:17:19 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 11:17:19 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
103,75
103,89
104,01
104,28
104,34
104,48
104,56
104,71
104,79
104,87
104,95
105
105,05
105,57
105,98
106,45
107,13
107,87
108,56
109,04
109,98
110,4
110,99
111,23
111,76
112,18
112,88
113,54
114,11
114,8
115,56
116,03
116,98
117,65
118,12
118,6
119,03
119,82
120,76
121,4
122,12
123,08
123,86
124,46
125,14
125,89
126,32
126,93
127,48
128,28
129,11
130,23
131,04
132,2
133,12
134,48
135,74
136,88
138,12
139,99




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.8261666666671.3843187986343284.3925306670113
Geometric Mean116.352752692228
Harmonic Mean115.890925471772
Quadratic Mean117.309066962732
Winsorized Mean ( 1 / 20 )116.7973333333331.3754312085365184.9168846892813
Winsorized Mean ( 2 / 20 )116.761.3641987569953285.5887013540218
Winsorized Mean ( 3 / 20 )116.71651.3481315344508586.5764927363292
Winsorized Mean ( 4 / 20 )116.63651.3278905114699787.8359314962526
Winsorized Mean ( 5 / 20 )116.5348333333331.3009011542344589.5800829709555
Winsorized Mean ( 6 / 20 )116.4508333333331.2801083175317490.9695154218434
Winsorized Mean ( 7 / 20 )116.3331.2497371542857693.0859737994155
Winsorized Mean ( 8 / 20 )116.2356666666671.22683915592194.7440144094585
Winsorized Mean ( 9 / 20 )116.0796666666671.193136562541797.2895059215904
Winsorized Mean ( 10 / 20 )115.9546666666671.1658065626936599.4630416205138
Winsorized Mean ( 11 / 20 )115.8171666666671.13845638609128101.731755455567
Winsorized Mean ( 12 / 20 )115.7171666666671.11794095666097103.509193376623
Winsorized Mean ( 13 / 20 )115.6976666666671.07757544249809107.368507209528
Winsorized Mean ( 14 / 20 )115.6931.04575005655795110.631598128523
Winsorized Mean ( 15 / 20 )115.6230.996659825572198116.010495289723
Winsorized Mean ( 16 / 20 )115.6230.93948138416173123.071092146405
Winsorized Mean ( 17 / 20 )115.6626666666670.880720938208078131.327258895417
Winsorized Mean ( 18 / 20 )115.6356666666670.813306683132891142.179658749678
Winsorized Mean ( 19 / 20 )115.4836666666670.744370244074582155.142776845196
Winsorized Mean ( 20 / 20 )115.5570.662936725257332174.310753345494
Trimmed Mean ( 1 / 20 )116.652241379311.3555173500675586.0573576380246
Trimmed Mean ( 2 / 20 )116.4967857142861.3301501015568287.5816838851021
Trimmed Mean ( 3 / 20 )116.3505555555561.305379382823489.1316019591956
Trimmed Mean ( 4 / 20 )116.2098076923081.281350875891690.6931972176989
Trimmed Mean ( 5 / 20 )116.08181.2582302663921792.2579937079811
Trimmed Mean ( 6 / 20 )115.9685416666671.2372010703350793.7345953275478
Trimmed Mean ( 7 / 20 )115.8636956521741.2156513277246195.3099733531662
Trimmed Mean ( 8 / 20 )115.7722727272731.1954746358813196.8420987384016
Trimmed Mean ( 9 / 20 )115.6895238095241.1741619668164898.5294423419234
Trimmed Mean ( 10 / 20 )115.62451.15378579478879100.213142268029
Trimmed Mean ( 11 / 20 )115.5723684210531.13225560915726102.072683488028
Trimmed Mean ( 12 / 20 )115.5352777777781.10872431242849104.205596001332
Trimmed Mean ( 13 / 20 )115.5085294117651.08015423837179106.937070011298
Trimmed Mean ( 14 / 20 )115.481251.04986008572418109.996800116792
Trimmed Mean ( 15 / 20 )115.4511.01412170821872113.843337603715
Trimmed Mean ( 16 / 20 )115.4264285714290.975787324805046118.290559466418
Trimmed Mean ( 17 / 20 )115.3980769230770.935929487684387123.297832199504
Trimmed Mean ( 18 / 20 )115.3591666666670.8938843983608129.053786908253
Trimmed Mean ( 19 / 20 )115.3172727272730.851768768750725135.3856550721
Trimmed Mean ( 20 / 20 )115.2910.810280295882071142.285330873675
Median115.18
Midrange121.87
Midmean - Weighted Average at Xnp115.145483870968
Midmean - Weighted Average at X(n+1)p115.451
Midmean - Empirical Distribution Function115.145483870968
Midmean - Empirical Distribution Function - Averaging115.451
Midmean - Empirical Distribution Function - Interpolation115.451
Midmean - Closest Observation115.145483870968
Midmean - True Basic - Statistics Graphics Toolkit115.451
Midmean - MS Excel (old versions)115.48125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.826166666667 & 1.38431879863432 & 84.3925306670113 \tabularnewline
Geometric Mean & 116.352752692228 &  &  \tabularnewline
Harmonic Mean & 115.890925471772 &  &  \tabularnewline
Quadratic Mean & 117.309066962732 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 116.797333333333 & 1.37543120853651 & 84.9168846892813 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 116.76 & 1.36419875699532 & 85.5887013540218 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 116.7165 & 1.34813153445085 & 86.5764927363292 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 116.6365 & 1.32789051146997 & 87.8359314962526 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 116.534833333333 & 1.30090115423445 & 89.5800829709555 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.450833333333 & 1.28010831753174 & 90.9695154218434 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.333 & 1.24973715428576 & 93.0859737994155 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.235666666667 & 1.226839155921 & 94.7440144094585 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.079666666667 & 1.1931365625417 & 97.2895059215904 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 115.954666666667 & 1.16580656269365 & 99.4630416205138 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 115.817166666667 & 1.13845638609128 & 101.731755455567 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 115.717166666667 & 1.11794095666097 & 103.509193376623 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 115.697666666667 & 1.07757544249809 & 107.368507209528 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 115.693 & 1.04575005655795 & 110.631598128523 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 115.623 & 0.996659825572198 & 116.010495289723 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 115.623 & 0.93948138416173 & 123.071092146405 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 115.662666666667 & 0.880720938208078 & 131.327258895417 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 115.635666666667 & 0.813306683132891 & 142.179658749678 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 115.483666666667 & 0.744370244074582 & 155.142776845196 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 115.557 & 0.662936725257332 & 174.310753345494 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 116.65224137931 & 1.35551735006755 & 86.0573576380246 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.496785714286 & 1.33015010155682 & 87.5816838851021 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.350555555556 & 1.3053793828234 & 89.1316019591956 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.209807692308 & 1.2813508758916 & 90.6931972176989 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.0818 & 1.25823026639217 & 92.2579937079811 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 115.968541666667 & 1.23720107033507 & 93.7345953275478 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 115.863695652174 & 1.21565132772461 & 95.3099733531662 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 115.772272727273 & 1.19547463588131 & 96.8420987384016 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 115.689523809524 & 1.17416196681648 & 98.5294423419234 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 115.6245 & 1.15378579478879 & 100.213142268029 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 115.572368421053 & 1.13225560915726 & 102.072683488028 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 115.535277777778 & 1.10872431242849 & 104.205596001332 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 115.508529411765 & 1.08015423837179 & 106.937070011298 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 115.48125 & 1.04986008572418 & 109.996800116792 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 115.451 & 1.01412170821872 & 113.843337603715 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 115.426428571429 & 0.975787324805046 & 118.290559466418 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 115.398076923077 & 0.935929487684387 & 123.297832199504 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 115.359166666667 & 0.8938843983608 & 129.053786908253 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 115.317272727273 & 0.851768768750725 & 135.3856550721 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 115.291 & 0.810280295882071 & 142.285330873675 \tabularnewline
Median & 115.18 &  &  \tabularnewline
Midrange & 121.87 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.145483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 115.451 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.145483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 115.451 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.451 &  &  \tabularnewline
Midmean - Closest Observation & 115.145483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 115.451 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 115.48125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]116.826166666667[/C][C]1.38431879863432[/C][C]84.3925306670113[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]116.352752692228[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.890925471772[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]117.309066962732[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]116.797333333333[/C][C]1.37543120853651[/C][C]84.9168846892813[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]116.76[/C][C]1.36419875699532[/C][C]85.5887013540218[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]116.7165[/C][C]1.34813153445085[/C][C]86.5764927363292[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]116.6365[/C][C]1.32789051146997[/C][C]87.8359314962526[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]116.534833333333[/C][C]1.30090115423445[/C][C]89.5800829709555[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.450833333333[/C][C]1.28010831753174[/C][C]90.9695154218434[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.333[/C][C]1.24973715428576[/C][C]93.0859737994155[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.235666666667[/C][C]1.226839155921[/C][C]94.7440144094585[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.079666666667[/C][C]1.1931365625417[/C][C]97.2895059215904[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]115.954666666667[/C][C]1.16580656269365[/C][C]99.4630416205138[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]115.817166666667[/C][C]1.13845638609128[/C][C]101.731755455567[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]115.717166666667[/C][C]1.11794095666097[/C][C]103.509193376623[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]115.697666666667[/C][C]1.07757544249809[/C][C]107.368507209528[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]115.693[/C][C]1.04575005655795[/C][C]110.631598128523[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]115.623[/C][C]0.996659825572198[/C][C]116.010495289723[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]115.623[/C][C]0.93948138416173[/C][C]123.071092146405[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]115.662666666667[/C][C]0.880720938208078[/C][C]131.327258895417[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]115.635666666667[/C][C]0.813306683132891[/C][C]142.179658749678[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]115.483666666667[/C][C]0.744370244074582[/C][C]155.142776845196[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]115.557[/C][C]0.662936725257332[/C][C]174.310753345494[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]116.65224137931[/C][C]1.35551735006755[/C][C]86.0573576380246[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.496785714286[/C][C]1.33015010155682[/C][C]87.5816838851021[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.350555555556[/C][C]1.3053793828234[/C][C]89.1316019591956[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.209807692308[/C][C]1.2813508758916[/C][C]90.6931972176989[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.0818[/C][C]1.25823026639217[/C][C]92.2579937079811[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]115.968541666667[/C][C]1.23720107033507[/C][C]93.7345953275478[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]115.863695652174[/C][C]1.21565132772461[/C][C]95.3099733531662[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]115.772272727273[/C][C]1.19547463588131[/C][C]96.8420987384016[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]115.689523809524[/C][C]1.17416196681648[/C][C]98.5294423419234[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]115.6245[/C][C]1.15378579478879[/C][C]100.213142268029[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]115.572368421053[/C][C]1.13225560915726[/C][C]102.072683488028[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]115.535277777778[/C][C]1.10872431242849[/C][C]104.205596001332[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]115.508529411765[/C][C]1.08015423837179[/C][C]106.937070011298[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]115.48125[/C][C]1.04986008572418[/C][C]109.996800116792[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]115.451[/C][C]1.01412170821872[/C][C]113.843337603715[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]115.426428571429[/C][C]0.975787324805046[/C][C]118.290559466418[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]115.398076923077[/C][C]0.935929487684387[/C][C]123.297832199504[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]115.359166666667[/C][C]0.8938843983608[/C][C]129.053786908253[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]115.317272727273[/C][C]0.851768768750725[/C][C]135.3856550721[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]115.291[/C][C]0.810280295882071[/C][C]142.285330873675[/C][/ROW]
[ROW][C]Median[/C][C]115.18[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]121.87[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.145483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]115.451[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.145483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]115.451[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.451[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.145483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]115.451[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]115.48125[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.8261666666671.3843187986343284.3925306670113
Geometric Mean116.352752692228
Harmonic Mean115.890925471772
Quadratic Mean117.309066962732
Winsorized Mean ( 1 / 20 )116.7973333333331.3754312085365184.9168846892813
Winsorized Mean ( 2 / 20 )116.761.3641987569953285.5887013540218
Winsorized Mean ( 3 / 20 )116.71651.3481315344508586.5764927363292
Winsorized Mean ( 4 / 20 )116.63651.3278905114699787.8359314962526
Winsorized Mean ( 5 / 20 )116.5348333333331.3009011542344589.5800829709555
Winsorized Mean ( 6 / 20 )116.4508333333331.2801083175317490.9695154218434
Winsorized Mean ( 7 / 20 )116.3331.2497371542857693.0859737994155
Winsorized Mean ( 8 / 20 )116.2356666666671.22683915592194.7440144094585
Winsorized Mean ( 9 / 20 )116.0796666666671.193136562541797.2895059215904
Winsorized Mean ( 10 / 20 )115.9546666666671.1658065626936599.4630416205138
Winsorized Mean ( 11 / 20 )115.8171666666671.13845638609128101.731755455567
Winsorized Mean ( 12 / 20 )115.7171666666671.11794095666097103.509193376623
Winsorized Mean ( 13 / 20 )115.6976666666671.07757544249809107.368507209528
Winsorized Mean ( 14 / 20 )115.6931.04575005655795110.631598128523
Winsorized Mean ( 15 / 20 )115.6230.996659825572198116.010495289723
Winsorized Mean ( 16 / 20 )115.6230.93948138416173123.071092146405
Winsorized Mean ( 17 / 20 )115.6626666666670.880720938208078131.327258895417
Winsorized Mean ( 18 / 20 )115.6356666666670.813306683132891142.179658749678
Winsorized Mean ( 19 / 20 )115.4836666666670.744370244074582155.142776845196
Winsorized Mean ( 20 / 20 )115.5570.662936725257332174.310753345494
Trimmed Mean ( 1 / 20 )116.652241379311.3555173500675586.0573576380246
Trimmed Mean ( 2 / 20 )116.4967857142861.3301501015568287.5816838851021
Trimmed Mean ( 3 / 20 )116.3505555555561.305379382823489.1316019591956
Trimmed Mean ( 4 / 20 )116.2098076923081.281350875891690.6931972176989
Trimmed Mean ( 5 / 20 )116.08181.2582302663921792.2579937079811
Trimmed Mean ( 6 / 20 )115.9685416666671.2372010703350793.7345953275478
Trimmed Mean ( 7 / 20 )115.8636956521741.2156513277246195.3099733531662
Trimmed Mean ( 8 / 20 )115.7722727272731.1954746358813196.8420987384016
Trimmed Mean ( 9 / 20 )115.6895238095241.1741619668164898.5294423419234
Trimmed Mean ( 10 / 20 )115.62451.15378579478879100.213142268029
Trimmed Mean ( 11 / 20 )115.5723684210531.13225560915726102.072683488028
Trimmed Mean ( 12 / 20 )115.5352777777781.10872431242849104.205596001332
Trimmed Mean ( 13 / 20 )115.5085294117651.08015423837179106.937070011298
Trimmed Mean ( 14 / 20 )115.481251.04986008572418109.996800116792
Trimmed Mean ( 15 / 20 )115.4511.01412170821872113.843337603715
Trimmed Mean ( 16 / 20 )115.4264285714290.975787324805046118.290559466418
Trimmed Mean ( 17 / 20 )115.3980769230770.935929487684387123.297832199504
Trimmed Mean ( 18 / 20 )115.3591666666670.8938843983608129.053786908253
Trimmed Mean ( 19 / 20 )115.3172727272730.851768768750725135.3856550721
Trimmed Mean ( 20 / 20 )115.2910.810280295882071142.285330873675
Median115.18
Midrange121.87
Midmean - Weighted Average at Xnp115.145483870968
Midmean - Weighted Average at X(n+1)p115.451
Midmean - Empirical Distribution Function115.145483870968
Midmean - Empirical Distribution Function - Averaging115.451
Midmean - Empirical Distribution Function - Interpolation115.451
Midmean - Closest Observation115.145483870968
Midmean - True Basic - Statistics Graphics Toolkit115.451
Midmean - MS Excel (old versions)115.48125
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')