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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 25 Nov 2011 09:46:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/25/t1322232414hae27fhk6nfndnw.htm/, Retrieved Mon, 15 Apr 2024 15:27:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147325, Retrieved Mon, 15 Apr 2024 15:27:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2011-11-25 14:46:36] [75a32e1bc492240bc1028714aca23077] [Current]
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Dataseries X:
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.249
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.202
1.2271
1.277
1.265
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227
1.4684
1.457




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147325&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147325&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147325&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 time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.249060.0115445365071033108.194902344625
Geometric Mean1.24591511659273
Harmonic Mean1.24276968802561
Quadratic Mean1.25220373209261
Winsorized Mean ( 1 / 20 )1.249121666666670.0114179930587491109.399406729322
Winsorized Mean ( 2 / 20 )1.248091666666670.0110592467872338112.85503350078
Winsorized Mean ( 3 / 20 )1.246641666666670.0105950450234515117.662705907082
Winsorized Mean ( 4 / 20 )1.247381666666670.00985445309064034126.580506821979
Winsorized Mean ( 5 / 20 )1.247290.00953436416338289130.820469894602
Winsorized Mean ( 6 / 20 )1.247730.00899906313391208138.651099723709
Winsorized Mean ( 7 / 20 )1.250121666666670.00850727408646845146.947383375727
Winsorized Mean ( 8 / 20 )1.2499750.00807147786613473154.86321349458
Winsorized Mean ( 9 / 20 )1.2502450.00796391665594416156.988709703138
Winsorized Mean ( 10 / 20 )1.2476450.00742563296965316168.01867330352
Winsorized Mean ( 11 / 20 )1.248653333333330.00706721781242705176.682446540376
Winsorized Mean ( 12 / 20 )1.249813333333330.00679545106515438183.919113146456
Winsorized Mean ( 13 / 20 )1.249813333333330.00621060486635774201.238584683346
Winsorized Mean ( 14 / 20 )1.249860.00586914425085021212.954384247575
Winsorized Mean ( 15 / 20 )1.248910.00554267863407918225.32607110235
Winsorized Mean ( 16 / 20 )1.248723333333330.00544732887772269229.235899165202
Winsorized Mean ( 17 / 20 )1.248638333333330.00539050488273335231.636620408771
Winsorized Mean ( 18 / 20 )1.247558333333330.00506647912138028246.237733038058
Winsorized Mean ( 19 / 20 )1.247843333333330.00448769401271846278.058916182086
Winsorized Mean ( 20 / 20 )1.246676666666670.00397409931285055313.700430846165
Trimmed Mean ( 1 / 20 )1.24850.0108439028898758115.133823373283
Trimmed Mean ( 2 / 20 )1.247833928571430.0101281843723555123.204108722324
Trimmed Mean ( 3 / 20 )1.247690740740740.00948413964161056131.555500856044
Trimmed Mean ( 4 / 20 )1.248094230769230.00891457845332375140.005973059095
Trimmed Mean ( 5 / 20 )1.2483080.00851144767657185146.662242127861
Trimmed Mean ( 6 / 20 )1.24856250.00811628399111737153.834254859299
Trimmed Mean ( 7 / 20 )1.248743478260870.0077892547392536160.316168884281
Trimmed Mean ( 8 / 20 )1.2484750.00751720726911597166.082290311362
Trimmed Mean ( 9 / 20 )1.248207142857140.00728664505794206171.300664837059
Trimmed Mean ( 10 / 20 )1.24786750.00700776802271996178.069179224294
Trimmed Mean ( 11 / 20 )1.247902631578950.00678625135801775183.88688625637
Trimmed Mean ( 12 / 20 )1.247788888888890.00658041318934491189.621662498234
Trimmed Mean ( 13 / 20 )1.247491176470590.00636535767961476195.981316252771
Trimmed Mean ( 14 / 20 )1.247156250.00622382573699131200.384185339176
Trimmed Mean ( 15 / 20 )1.246770.00610491633425683204.223929000294
Trimmed Mean ( 16 / 20 )1.246464285714290.006010947275631207.36569937447
Trimmed Mean ( 17 / 20 )1.246138461538460.00587504259080621212.107136633959
Trimmed Mean ( 18 / 20 )1.245770833333330.00565927313650569220.129123172615
Trimmed Mean ( 19 / 20 )1.24550.00542575627620991229.55325241222
Trimmed Mean ( 20 / 20 )1.245130.00526762754947614236.373963099162
Median1.2391
Midrange1.2653
Midmean - Weighted Average at Xnp1.24521290322581
Midmean - Weighted Average at X(n+1)p1.24677
Midmean - Empirical Distribution Function1.24521290322581
Midmean - Empirical Distribution Function - Averaging1.24677
Midmean - Empirical Distribution Function - Interpolation1.24677
Midmean - Closest Observation1.24521290322581
Midmean - True Basic - Statistics Graphics Toolkit1.24677
Midmean - MS Excel (old versions)1.24715625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.24906 & 0.0115445365071033 & 108.194902344625 \tabularnewline
Geometric Mean & 1.24591511659273 &  &  \tabularnewline
Harmonic Mean & 1.24276968802561 &  &  \tabularnewline
Quadratic Mean & 1.25220373209261 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.24912166666667 & 0.0114179930587491 & 109.399406729322 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.24809166666667 & 0.0110592467872338 & 112.85503350078 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.24664166666667 & 0.0105950450234515 & 117.662705907082 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.24738166666667 & 0.00985445309064034 & 126.580506821979 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.24729 & 0.00953436416338289 & 130.820469894602 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.24773 & 0.00899906313391208 & 138.651099723709 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.25012166666667 & 0.00850727408646845 & 146.947383375727 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.249975 & 0.00807147786613473 & 154.86321349458 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.250245 & 0.00796391665594416 & 156.988709703138 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.247645 & 0.00742563296965316 & 168.01867330352 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.24865333333333 & 0.00706721781242705 & 176.682446540376 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.24981333333333 & 0.00679545106515438 & 183.919113146456 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.24981333333333 & 0.00621060486635774 & 201.238584683346 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.24986 & 0.00586914425085021 & 212.954384247575 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.24891 & 0.00554267863407918 & 225.32607110235 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.24872333333333 & 0.00544732887772269 & 229.235899165202 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.24863833333333 & 0.00539050488273335 & 231.636620408771 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.24755833333333 & 0.00506647912138028 & 246.237733038058 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.24784333333333 & 0.00448769401271846 & 278.058916182086 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.24667666666667 & 0.00397409931285055 & 313.700430846165 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.2485 & 0.0108439028898758 & 115.133823373283 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.24783392857143 & 0.0101281843723555 & 123.204108722324 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.24769074074074 & 0.00948413964161056 & 131.555500856044 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.24809423076923 & 0.00891457845332375 & 140.005973059095 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.248308 & 0.00851144767657185 & 146.662242127861 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.2485625 & 0.00811628399111737 & 153.834254859299 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.24874347826087 & 0.0077892547392536 & 160.316168884281 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.248475 & 0.00751720726911597 & 166.082290311362 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.24820714285714 & 0.00728664505794206 & 171.300664837059 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.2478675 & 0.00700776802271996 & 178.069179224294 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.24790263157895 & 0.00678625135801775 & 183.88688625637 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.24778888888889 & 0.00658041318934491 & 189.621662498234 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.24749117647059 & 0.00636535767961476 & 195.981316252771 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.24715625 & 0.00622382573699131 & 200.384185339176 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.24677 & 0.00610491633425683 & 204.223929000294 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.24646428571429 & 0.006010947275631 & 207.36569937447 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.24613846153846 & 0.00587504259080621 & 212.107136633959 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.24577083333333 & 0.00565927313650569 & 220.129123172615 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.2455 & 0.00542575627620991 & 229.55325241222 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.24513 & 0.00526762754947614 & 236.373963099162 \tabularnewline
Median & 1.2391 &  &  \tabularnewline
Midrange & 1.2653 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.24521290322581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.24677 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.24521290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.24677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.24677 &  &  \tabularnewline
Midmean - Closest Observation & 1.24521290322581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.24677 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.24715625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147325&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]1.24906[/C][C]0.0115445365071033[/C][C]108.194902344625[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.24591511659273[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.24276968802561[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.25220373209261[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.24912166666667[/C][C]0.0114179930587491[/C][C]109.399406729322[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.24809166666667[/C][C]0.0110592467872338[/C][C]112.85503350078[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.24664166666667[/C][C]0.0105950450234515[/C][C]117.662705907082[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.24738166666667[/C][C]0.00985445309064034[/C][C]126.580506821979[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.24729[/C][C]0.00953436416338289[/C][C]130.820469894602[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.24773[/C][C]0.00899906313391208[/C][C]138.651099723709[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.25012166666667[/C][C]0.00850727408646845[/C][C]146.947383375727[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.249975[/C][C]0.00807147786613473[/C][C]154.86321349458[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.250245[/C][C]0.00796391665594416[/C][C]156.988709703138[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.247645[/C][C]0.00742563296965316[/C][C]168.01867330352[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.24865333333333[/C][C]0.00706721781242705[/C][C]176.682446540376[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.24981333333333[/C][C]0.00679545106515438[/C][C]183.919113146456[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.24981333333333[/C][C]0.00621060486635774[/C][C]201.238584683346[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.24986[/C][C]0.00586914425085021[/C][C]212.954384247575[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.24891[/C][C]0.00554267863407918[/C][C]225.32607110235[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.24872333333333[/C][C]0.00544732887772269[/C][C]229.235899165202[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.24863833333333[/C][C]0.00539050488273335[/C][C]231.636620408771[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.24755833333333[/C][C]0.00506647912138028[/C][C]246.237733038058[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.24784333333333[/C][C]0.00448769401271846[/C][C]278.058916182086[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.24667666666667[/C][C]0.00397409931285055[/C][C]313.700430846165[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.2485[/C][C]0.0108439028898758[/C][C]115.133823373283[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.24783392857143[/C][C]0.0101281843723555[/C][C]123.204108722324[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.24769074074074[/C][C]0.00948413964161056[/C][C]131.555500856044[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.24809423076923[/C][C]0.00891457845332375[/C][C]140.005973059095[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.248308[/C][C]0.00851144767657185[/C][C]146.662242127861[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.2485625[/C][C]0.00811628399111737[/C][C]153.834254859299[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.24874347826087[/C][C]0.0077892547392536[/C][C]160.316168884281[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.248475[/C][C]0.00751720726911597[/C][C]166.082290311362[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.24820714285714[/C][C]0.00728664505794206[/C][C]171.300664837059[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.2478675[/C][C]0.00700776802271996[/C][C]178.069179224294[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.24790263157895[/C][C]0.00678625135801775[/C][C]183.88688625637[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.24778888888889[/C][C]0.00658041318934491[/C][C]189.621662498234[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.24749117647059[/C][C]0.00636535767961476[/C][C]195.981316252771[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.24715625[/C][C]0.00622382573699131[/C][C]200.384185339176[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.24677[/C][C]0.00610491633425683[/C][C]204.223929000294[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.24646428571429[/C][C]0.006010947275631[/C][C]207.36569937447[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.24613846153846[/C][C]0.00587504259080621[/C][C]212.107136633959[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.24577083333333[/C][C]0.00565927313650569[/C][C]220.129123172615[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.2455[/C][C]0.00542575627620991[/C][C]229.55325241222[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.24513[/C][C]0.00526762754947614[/C][C]236.373963099162[/C][/ROW]
[ROW][C]Median[/C][C]1.2391[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2653[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.24521290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.24677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.24521290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.24677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.24677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.24521290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.24677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.24715625[/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=147325&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147325&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 Mean1.249060.0115445365071033108.194902344625
Geometric Mean1.24591511659273
Harmonic Mean1.24276968802561
Quadratic Mean1.25220373209261
Winsorized Mean ( 1 / 20 )1.249121666666670.0114179930587491109.399406729322
Winsorized Mean ( 2 / 20 )1.248091666666670.0110592467872338112.85503350078
Winsorized Mean ( 3 / 20 )1.246641666666670.0105950450234515117.662705907082
Winsorized Mean ( 4 / 20 )1.247381666666670.00985445309064034126.580506821979
Winsorized Mean ( 5 / 20 )1.247290.00953436416338289130.820469894602
Winsorized Mean ( 6 / 20 )1.247730.00899906313391208138.651099723709
Winsorized Mean ( 7 / 20 )1.250121666666670.00850727408646845146.947383375727
Winsorized Mean ( 8 / 20 )1.2499750.00807147786613473154.86321349458
Winsorized Mean ( 9 / 20 )1.2502450.00796391665594416156.988709703138
Winsorized Mean ( 10 / 20 )1.2476450.00742563296965316168.01867330352
Winsorized Mean ( 11 / 20 )1.248653333333330.00706721781242705176.682446540376
Winsorized Mean ( 12 / 20 )1.249813333333330.00679545106515438183.919113146456
Winsorized Mean ( 13 / 20 )1.249813333333330.00621060486635774201.238584683346
Winsorized Mean ( 14 / 20 )1.249860.00586914425085021212.954384247575
Winsorized Mean ( 15 / 20 )1.248910.00554267863407918225.32607110235
Winsorized Mean ( 16 / 20 )1.248723333333330.00544732887772269229.235899165202
Winsorized Mean ( 17 / 20 )1.248638333333330.00539050488273335231.636620408771
Winsorized Mean ( 18 / 20 )1.247558333333330.00506647912138028246.237733038058
Winsorized Mean ( 19 / 20 )1.247843333333330.00448769401271846278.058916182086
Winsorized Mean ( 20 / 20 )1.246676666666670.00397409931285055313.700430846165
Trimmed Mean ( 1 / 20 )1.24850.0108439028898758115.133823373283
Trimmed Mean ( 2 / 20 )1.247833928571430.0101281843723555123.204108722324
Trimmed Mean ( 3 / 20 )1.247690740740740.00948413964161056131.555500856044
Trimmed Mean ( 4 / 20 )1.248094230769230.00891457845332375140.005973059095
Trimmed Mean ( 5 / 20 )1.2483080.00851144767657185146.662242127861
Trimmed Mean ( 6 / 20 )1.24856250.00811628399111737153.834254859299
Trimmed Mean ( 7 / 20 )1.248743478260870.0077892547392536160.316168884281
Trimmed Mean ( 8 / 20 )1.2484750.00751720726911597166.082290311362
Trimmed Mean ( 9 / 20 )1.248207142857140.00728664505794206171.300664837059
Trimmed Mean ( 10 / 20 )1.24786750.00700776802271996178.069179224294
Trimmed Mean ( 11 / 20 )1.247902631578950.00678625135801775183.88688625637
Trimmed Mean ( 12 / 20 )1.247788888888890.00658041318934491189.621662498234
Trimmed Mean ( 13 / 20 )1.247491176470590.00636535767961476195.981316252771
Trimmed Mean ( 14 / 20 )1.247156250.00622382573699131200.384185339176
Trimmed Mean ( 15 / 20 )1.246770.00610491633425683204.223929000294
Trimmed Mean ( 16 / 20 )1.246464285714290.006010947275631207.36569937447
Trimmed Mean ( 17 / 20 )1.246138461538460.00587504259080621212.107136633959
Trimmed Mean ( 18 / 20 )1.245770833333330.00565927313650569220.129123172615
Trimmed Mean ( 19 / 20 )1.24550.00542575627620991229.55325241222
Trimmed Mean ( 20 / 20 )1.245130.00526762754947614236.373963099162
Median1.2391
Midrange1.2653
Midmean - Weighted Average at Xnp1.24521290322581
Midmean - Weighted Average at X(n+1)p1.24677
Midmean - Empirical Distribution Function1.24521290322581
Midmean - Empirical Distribution Function - Averaging1.24677
Midmean - Empirical Distribution Function - Interpolation1.24677
Midmean - Closest Observation1.24521290322581
Midmean - True Basic - Statistics Graphics Toolkit1.24677
Midmean - MS Excel (old versions)1.24715625
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')