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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Oct 2009 14:40:41 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t1256245305c6c5o9d41xn4nn9.htm/, Retrieved Thu, 02 May 2024 21:16:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49824, Retrieved Thu, 02 May 2024 21:16:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [] [2009-10-22 20:40:41] [17416e80e7873ecccac25c455c5f767e] [Current]
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Post a new message
Dataseries X:
98,84
99,505
100,17
100,83
101,51
102,16
102,39
102,54
102,85
103,47
103,57
103,69
103,5
103,47
103,45
103,48
103,93
103,89
104,4
104,79
104,77
105,13
105,26
104,96
104,75
105,01
105,15
105,2
105,77
105,78
106,26
106,13
106,12
106,57
106,44
106,54
107,1
108,1
108,4
108,84
109,62
110,42
110,67
111,66
112,28
112,87
112,18
112,36
112,16
111,49
111,25
111,36
111,74
111,1
111,33
111,25
111,04
110,97
111,31
111,02




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 9 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49824&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49824&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49824&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 time9 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.713250.496374423343626214.985392037666
Geometric Mean106.645127183266
Harmonic Mean106.577019289858
Quadratic Mean106.781340093124
Winsorized Mean ( 1 / 20 )106.7158333333330.491786380618616216.996316976277
Winsorized Mean ( 2 / 20 )106.7353333333330.485975660655479219.631026766587
Winsorized Mean ( 3 / 20 )106.7633333333330.47775792671063223.467424325956
Winsorized Mean ( 4 / 20 )106.8073333333330.468380239724327228.035523864535
Winsorized Mean ( 5 / 20 )106.82650.451821162623388236.435361681021
Winsorized Mean ( 6 / 20 )106.84150.446394775056496239.343079198178
Winsorized Mean ( 7 / 20 )106.8391666666670.439874487213047242.885572526784
Winsorized Mean ( 8 / 20 )106.8631666666670.430091600522406248.466062896524
Winsorized Mean ( 9 / 20 )106.9486666666670.415743800580695257.246569924278
Winsorized Mean ( 10 / 20 )106.9486666666670.414674296440062257.910045509959
Winsorized Mean ( 11 / 20 )106.9376666666670.412719817593334259.104753656476
Winsorized Mean ( 12 / 20 )106.9396666666670.412435234886058259.288386687453
Winsorized Mean ( 13 / 20 )106.91150.406099249300569263.264461050187
Winsorized Mean ( 14 / 20 )106.9138333333330.401339641704837266.392407386367
Winsorized Mean ( 15 / 20 )106.9388333333330.396264769933907269.867122810765
Winsorized Mean ( 16 / 20 )106.9788333333330.386616796779174276.705084270917
Winsorized Mean ( 17 / 20 )106.9051666666670.370315828838725288.686462584953
Winsorized Mean ( 18 / 20 )106.9711666666670.338687320731239315.840482116991
Winsorized Mean ( 19 / 20 )106.8286666666670.281389958689404379.646335513285
Winsorized Mean ( 20 / 20 )106.5753333333330.237614731926759448.521573006608
Trimmed Mean ( 1 / 20 )106.7428448275860.483317444177399220.854525557755
Trimmed Mean ( 2 / 20 )106.7717857142860.472724151953806225.864883934932
Trimmed Mean ( 3 / 20 )106.7920370370370.463306137659373230.499940226459
Trimmed Mean ( 4 / 20 )106.8030769230770.455299491911596234.577632570287
Trimmed Mean ( 5 / 20 )106.80180.448598697078367238.078711988195
Trimmed Mean ( 6 / 20 )106.7956250.445180048268982239.893107104102
Trimmed Mean ( 7 / 20 )106.7856521739130.441795704658255241.708217277747
Trimmed Mean ( 8 / 20 )106.7752272727270.438542474533559243.477504399762
Trimmed Mean ( 9 / 20 )106.7595238095240.436056788646407244.829404309753
Trimmed Mean ( 10 / 20 )106.7280.435263433348422245.203230556162
Trimmed Mean ( 11 / 20 )106.6931578947370.433232926824853246.2720427939
Trimmed Mean ( 12 / 20 )106.6561111111110.429738066729575248.188651107391
Trimmed Mean ( 13 / 20 )106.6144117647060.423717145583049251.616940395464
Trimmed Mean ( 14 / 20 )106.57156250.415865815967267256.264300666608
Trimmed Mean ( 15 / 20 )106.5226666666670.404731763970019263.193245871746
Trimmed Mean ( 16 / 20 )106.4632142857140.388600478168328273.965731559389
Trimmed Mean ( 17 / 20 )106.3888461538460.366033763437652290.653094825684
Trimmed Mean ( 18 / 20 )106.3129166666670.336690241228711315.758830070900
Trimmed Mean ( 19 / 20 )106.2131818181820.300895766828117352.989950433084
Trimmed Mean ( 20 / 20 )106.1160.270926674873285391.677932967034
Median105.95
Midrange105.855
Midmean - Weighted Average at Xnp106.427419354839
Midmean - Weighted Average at X(n+1)p106.522666666667
Midmean - Empirical Distribution Function106.427419354839
Midmean - Empirical Distribution Function - Averaging106.522666666667
Midmean - Empirical Distribution Function - Interpolation106.522666666667
Midmean - Closest Observation106.427419354839
Midmean - True Basic - Statistics Graphics Toolkit106.522666666667
Midmean - MS Excel (old versions)106.5715625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.71325 & 0.496374423343626 & 214.985392037666 \tabularnewline
Geometric Mean & 106.645127183266 &  &  \tabularnewline
Harmonic Mean & 106.577019289858 &  &  \tabularnewline
Quadratic Mean & 106.781340093124 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 106.715833333333 & 0.491786380618616 & 216.996316976277 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 106.735333333333 & 0.485975660655479 & 219.631026766587 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 106.763333333333 & 0.47775792671063 & 223.467424325956 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 106.807333333333 & 0.468380239724327 & 228.035523864535 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 106.8265 & 0.451821162623388 & 236.435361681021 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 106.8415 & 0.446394775056496 & 239.343079198178 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 106.839166666667 & 0.439874487213047 & 242.885572526784 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 106.863166666667 & 0.430091600522406 & 248.466062896524 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 106.948666666667 & 0.415743800580695 & 257.246569924278 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 106.948666666667 & 0.414674296440062 & 257.910045509959 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 106.937666666667 & 0.412719817593334 & 259.104753656476 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 106.939666666667 & 0.412435234886058 & 259.288386687453 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 106.9115 & 0.406099249300569 & 263.264461050187 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 106.913833333333 & 0.401339641704837 & 266.392407386367 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 106.938833333333 & 0.396264769933907 & 269.867122810765 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 106.978833333333 & 0.386616796779174 & 276.705084270917 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 106.905166666667 & 0.370315828838725 & 288.686462584953 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 106.971166666667 & 0.338687320731239 & 315.840482116991 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 106.828666666667 & 0.281389958689404 & 379.646335513285 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 106.575333333333 & 0.237614731926759 & 448.521573006608 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 106.742844827586 & 0.483317444177399 & 220.854525557755 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 106.771785714286 & 0.472724151953806 & 225.864883934932 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 106.792037037037 & 0.463306137659373 & 230.499940226459 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 106.803076923077 & 0.455299491911596 & 234.577632570287 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 106.8018 & 0.448598697078367 & 238.078711988195 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 106.795625 & 0.445180048268982 & 239.893107104102 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 106.785652173913 & 0.441795704658255 & 241.708217277747 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 106.775227272727 & 0.438542474533559 & 243.477504399762 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 106.759523809524 & 0.436056788646407 & 244.829404309753 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 106.728 & 0.435263433348422 & 245.203230556162 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 106.693157894737 & 0.433232926824853 & 246.2720427939 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 106.656111111111 & 0.429738066729575 & 248.188651107391 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 106.614411764706 & 0.423717145583049 & 251.616940395464 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 106.5715625 & 0.415865815967267 & 256.264300666608 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 106.522666666667 & 0.404731763970019 & 263.193245871746 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 106.463214285714 & 0.388600478168328 & 273.965731559389 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 106.388846153846 & 0.366033763437652 & 290.653094825684 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 106.312916666667 & 0.336690241228711 & 315.758830070900 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 106.213181818182 & 0.300895766828117 & 352.989950433084 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 106.116 & 0.270926674873285 & 391.677932967034 \tabularnewline
Median & 105.95 &  &  \tabularnewline
Midrange & 105.855 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.427419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 106.522666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.427419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 106.522666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 106.522666666667 &  &  \tabularnewline
Midmean - Closest Observation & 106.427419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 106.522666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 106.5715625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49824&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]106.71325[/C][C]0.496374423343626[/C][C]214.985392037666[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]106.645127183266[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.577019289858[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.781340093124[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]106.715833333333[/C][C]0.491786380618616[/C][C]216.996316976277[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]106.735333333333[/C][C]0.485975660655479[/C][C]219.631026766587[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]106.763333333333[/C][C]0.47775792671063[/C][C]223.467424325956[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]106.807333333333[/C][C]0.468380239724327[/C][C]228.035523864535[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]106.8265[/C][C]0.451821162623388[/C][C]236.435361681021[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]106.8415[/C][C]0.446394775056496[/C][C]239.343079198178[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]106.839166666667[/C][C]0.439874487213047[/C][C]242.885572526784[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]106.863166666667[/C][C]0.430091600522406[/C][C]248.466062896524[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]106.948666666667[/C][C]0.415743800580695[/C][C]257.246569924278[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]106.948666666667[/C][C]0.414674296440062[/C][C]257.910045509959[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]106.937666666667[/C][C]0.412719817593334[/C][C]259.104753656476[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]106.939666666667[/C][C]0.412435234886058[/C][C]259.288386687453[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]106.9115[/C][C]0.406099249300569[/C][C]263.264461050187[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]106.913833333333[/C][C]0.401339641704837[/C][C]266.392407386367[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]106.938833333333[/C][C]0.396264769933907[/C][C]269.867122810765[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]106.978833333333[/C][C]0.386616796779174[/C][C]276.705084270917[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]106.905166666667[/C][C]0.370315828838725[/C][C]288.686462584953[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]106.971166666667[/C][C]0.338687320731239[/C][C]315.840482116991[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]106.828666666667[/C][C]0.281389958689404[/C][C]379.646335513285[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]106.575333333333[/C][C]0.237614731926759[/C][C]448.521573006608[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]106.742844827586[/C][C]0.483317444177399[/C][C]220.854525557755[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]106.771785714286[/C][C]0.472724151953806[/C][C]225.864883934932[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]106.792037037037[/C][C]0.463306137659373[/C][C]230.499940226459[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]106.803076923077[/C][C]0.455299491911596[/C][C]234.577632570287[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]106.8018[/C][C]0.448598697078367[/C][C]238.078711988195[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]106.795625[/C][C]0.445180048268982[/C][C]239.893107104102[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]106.785652173913[/C][C]0.441795704658255[/C][C]241.708217277747[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]106.775227272727[/C][C]0.438542474533559[/C][C]243.477504399762[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]106.759523809524[/C][C]0.436056788646407[/C][C]244.829404309753[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]106.728[/C][C]0.435263433348422[/C][C]245.203230556162[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]106.693157894737[/C][C]0.433232926824853[/C][C]246.2720427939[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]106.656111111111[/C][C]0.429738066729575[/C][C]248.188651107391[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]106.614411764706[/C][C]0.423717145583049[/C][C]251.616940395464[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]106.5715625[/C][C]0.415865815967267[/C][C]256.264300666608[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]106.522666666667[/C][C]0.404731763970019[/C][C]263.193245871746[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]106.463214285714[/C][C]0.388600478168328[/C][C]273.965731559389[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]106.388846153846[/C][C]0.366033763437652[/C][C]290.653094825684[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]106.312916666667[/C][C]0.336690241228711[/C][C]315.758830070900[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]106.213181818182[/C][C]0.300895766828117[/C][C]352.989950433084[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]106.116[/C][C]0.270926674873285[/C][C]391.677932967034[/C][/ROW]
[ROW][C]Median[/C][C]105.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.855[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.427419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]106.522666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.427419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]106.522666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]106.522666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.427419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]106.522666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]106.5715625[/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=49824&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49824&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 Mean106.713250.496374423343626214.985392037666
Geometric Mean106.645127183266
Harmonic Mean106.577019289858
Quadratic Mean106.781340093124
Winsorized Mean ( 1 / 20 )106.7158333333330.491786380618616216.996316976277
Winsorized Mean ( 2 / 20 )106.7353333333330.485975660655479219.631026766587
Winsorized Mean ( 3 / 20 )106.7633333333330.47775792671063223.467424325956
Winsorized Mean ( 4 / 20 )106.8073333333330.468380239724327228.035523864535
Winsorized Mean ( 5 / 20 )106.82650.451821162623388236.435361681021
Winsorized Mean ( 6 / 20 )106.84150.446394775056496239.343079198178
Winsorized Mean ( 7 / 20 )106.8391666666670.439874487213047242.885572526784
Winsorized Mean ( 8 / 20 )106.8631666666670.430091600522406248.466062896524
Winsorized Mean ( 9 / 20 )106.9486666666670.415743800580695257.246569924278
Winsorized Mean ( 10 / 20 )106.9486666666670.414674296440062257.910045509959
Winsorized Mean ( 11 / 20 )106.9376666666670.412719817593334259.104753656476
Winsorized Mean ( 12 / 20 )106.9396666666670.412435234886058259.288386687453
Winsorized Mean ( 13 / 20 )106.91150.406099249300569263.264461050187
Winsorized Mean ( 14 / 20 )106.9138333333330.401339641704837266.392407386367
Winsorized Mean ( 15 / 20 )106.9388333333330.396264769933907269.867122810765
Winsorized Mean ( 16 / 20 )106.9788333333330.386616796779174276.705084270917
Winsorized Mean ( 17 / 20 )106.9051666666670.370315828838725288.686462584953
Winsorized Mean ( 18 / 20 )106.9711666666670.338687320731239315.840482116991
Winsorized Mean ( 19 / 20 )106.8286666666670.281389958689404379.646335513285
Winsorized Mean ( 20 / 20 )106.5753333333330.237614731926759448.521573006608
Trimmed Mean ( 1 / 20 )106.7428448275860.483317444177399220.854525557755
Trimmed Mean ( 2 / 20 )106.7717857142860.472724151953806225.864883934932
Trimmed Mean ( 3 / 20 )106.7920370370370.463306137659373230.499940226459
Trimmed Mean ( 4 / 20 )106.8030769230770.455299491911596234.577632570287
Trimmed Mean ( 5 / 20 )106.80180.448598697078367238.078711988195
Trimmed Mean ( 6 / 20 )106.7956250.445180048268982239.893107104102
Trimmed Mean ( 7 / 20 )106.7856521739130.441795704658255241.708217277747
Trimmed Mean ( 8 / 20 )106.7752272727270.438542474533559243.477504399762
Trimmed Mean ( 9 / 20 )106.7595238095240.436056788646407244.829404309753
Trimmed Mean ( 10 / 20 )106.7280.435263433348422245.203230556162
Trimmed Mean ( 11 / 20 )106.6931578947370.433232926824853246.2720427939
Trimmed Mean ( 12 / 20 )106.6561111111110.429738066729575248.188651107391
Trimmed Mean ( 13 / 20 )106.6144117647060.423717145583049251.616940395464
Trimmed Mean ( 14 / 20 )106.57156250.415865815967267256.264300666608
Trimmed Mean ( 15 / 20 )106.5226666666670.404731763970019263.193245871746
Trimmed Mean ( 16 / 20 )106.4632142857140.388600478168328273.965731559389
Trimmed Mean ( 17 / 20 )106.3888461538460.366033763437652290.653094825684
Trimmed Mean ( 18 / 20 )106.3129166666670.336690241228711315.758830070900
Trimmed Mean ( 19 / 20 )106.2131818181820.300895766828117352.989950433084
Trimmed Mean ( 20 / 20 )106.1160.270926674873285391.677932967034
Median105.95
Midrange105.855
Midmean - Weighted Average at Xnp106.427419354839
Midmean - Weighted Average at X(n+1)p106.522666666667
Midmean - Empirical Distribution Function106.427419354839
Midmean - Empirical Distribution Function - Averaging106.522666666667
Midmean - Empirical Distribution Function - Interpolation106.522666666667
Midmean - Closest Observation106.427419354839
Midmean - True Basic - Statistics Graphics Toolkit106.522666666667
Midmean - MS Excel (old versions)106.5715625
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')