Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 04 Dec 2007 10:24:49 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/04/t1196788656p9zoo0dkaqjq7nl.htm/, Retrieved Thu, 02 May 2024 10:15:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2423, Retrieved Thu, 02 May 2024 10:15:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central] [2007-12-04 17:24:49] [9fe578921d87f9af8e79a90d6142ba02] [Current]
Feedback Forum

Post a new message
Dataseries X:
-0.007174068323693 
0.00837108137342834 
0.00157140918757137 
-0.000643175233148797 
0.00320366235072089 
0.0108307160449628 
0.00125184427749729 
-0.0831837638143383 
-0.00272917911556520 
0.000511718325117624 
0.0717790190606497 
0.00402557915402475 
0.000676255917209026 
-0.0363876050212324 
-0.00390996426747058 
-0.0106269563760956 
-0.0312684542171285 
0.000552710576103546 
-0.00473455864702198 
0.0668596370338132 
0.0190684020744148 
-0.0212814345312873 
-0.0438593533750941 
-0.00803310171877805 
-0.0108858054797067 
-0.00526917197785588 
-0.00457325097952925 
-0.00424020372583770 
0.0168951280464051 
0.00415591238165018 
-0.0118031861766840 
0.0357582105669633 
0.00875833814468873 
-0.00177562421384827 
-0.0838454513759895 
-0.00846121976842996 
-0.0102760050456355 
-0.0376290989835201 
-0.00591266486806886 
-0.0322946990738901 
0.0193505204486656 
-0.0081851549884289 
-0.0313613361299916 
0.059432574736996 
-0.0194438749244535 
-0.0373637573120493 
0.0334022101247666 
0.00259625475909332 
-0.0408390613352506 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2423&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2423&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2423&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.004876326457454720.00423183168998178-1.15229688104059
Geometric MeanNaN
Harmonic Mean0.0141034624812071
Quadratic Mean0.0297217383985478
Winsorized Mean ( 1 / 16 )-0.004963218181234010.00418970454560016-1.18462247808051
Winsorized Mean ( 2 / 16 )-0.003661285603992090.00356955725099609-1.02569740350023
Winsorized Mean ( 3 / 16 )-0.004925820632371030.00305200865915797-1.61396024142672
Winsorized Mean ( 4 / 16 )-0.004856109456082550.00293657692244667-1.65366329039887
Winsorized Mean ( 5 / 16 )-0.006262879660636650.00258447126332942-2.42327308858082
Winsorized Mean ( 6 / 16 )-0.006177895915751010.00254758981017996-2.42499632046911
Winsorized Mean ( 7 / 16 )-0.005903662784417780.00234307184118612-2.51962516925184
Winsorized Mean ( 8 / 16 )-0.006741385079526970.00212021232970564-3.17958016990822
Winsorized Mean ( 9 / 16 )-0.007104965975173880.00205251518520888-3.46158996843224
Winsorized Mean ( 10 / 16 )-0.005145830686483920.00156629222484354-3.28535799697144
Winsorized Mean ( 11 / 16 )-0.005679579732083680.00131755307390469-4.31070280550577
Winsorized Mean ( 12 / 16 )-0.003840308992456560.000936580287860839-4.1003521451726
Winsorized Mean ( 13 / 16 )-0.003814981836992180.000856349433038175-4.45493590561192
Winsorized Mean ( 14 / 16 )-0.003914569976425450.00081435958386195-4.80693056728249
Winsorized Mean ( 15 / 16 )-0.004120864131852550.000744729343040947-5.53337151323441
Winsorized Mean ( 16 / 16 )-0.003632628909932070.000629308723536549-5.77241149545434
Trimmed Mean ( 1 / 16 )-0.004876326457454720.00372556962963797-1.30888077320100
Trimmed Mean ( 2 / 16 )-0.00482709710850940.00307552518531188-1.56951961621472
Trimmed Mean ( 3 / 16 )-0.005258666480960890.00269003025355302-1.95487261677269
Trimmed Mean ( 4 / 16 )-0.005258666480960890.00248404923547285-2.11697353090503
Trimmed Mean ( 5 / 16 )-0.005559356898827630.00226072304578488-2.45910568709116
Trimmed Mean ( 6 / 16 )-0.005373018437591730.00211192111998014-2.54413784054693
Trimmed Mean ( 7 / 16 )-0.005185213692687890.00191861266379923-2.70258494094382
Trimmed Mean ( 8 / 16 )-0.005185213692687890.00172910868752041-2.99877834754484
Trimmed Mean ( 9 / 16 )-0.004695235101018140.00154114577858821-3.04658726400255
Trimmed Mean ( 10 / 16 )-0.004242833519280090.00127296695502234-3.33302722630819
Trimmed Mean ( 11 / 16 )-0.004078956255602360.00111046007922725-3.67321287086774
Trimmed Mean ( 12 / 16 )-0.003793754254338420.000965853735263914-3.92787656746163
Trimmed Mean ( 13 / 16 )-0.003785489101556570.000926583162750013-4.08542832822646
Trimmed Mean ( 14 / 16 )-0.003780195533657870.000893316716804075-4.23164087556973
Trimmed Mean ( 15 / 16 )-0.003755442346832270.000850897880921359-4.4135053465709
Trimmed Mean ( 16 / 16 )-0.003755442346832270.000805861792387434-4.66015684365237
Median-0.0042402037258377
Midrange-0.00603321615766991
Midmean - Weighted Average at Xnp-0.00411955981302021
Midmean - Weighted Average at X(n+1)p-0.00379375425433842
Midmean - Empirical Distribution Function-0.00379375425433842
Midmean - Empirical Distribution Function - Averaging-0.00379375425433842
Midmean - Empirical Distribution Function - Interpolation-0.00379375425433842
Midmean - Closest Observation-0.00439568197241977
Midmean - True Basic - Statistics Graphics Toolkit-0.00379375425433842
Midmean - MS Excel (old versions)-0.00379375425433842
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.00487632645745472 & 0.00423183168998178 & -1.15229688104059 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.0141034624812071 &  &  \tabularnewline
Quadratic Mean & 0.0297217383985478 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -0.00496321818123401 & 0.00418970454560016 & -1.18462247808051 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -0.00366128560399209 & 0.00356955725099609 & -1.02569740350023 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -0.00492582063237103 & 0.00305200865915797 & -1.61396024142672 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -0.00485610945608255 & 0.00293657692244667 & -1.65366329039887 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -0.00626287966063665 & 0.00258447126332942 & -2.42327308858082 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -0.00617789591575101 & 0.00254758981017996 & -2.42499632046911 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -0.00590366278441778 & 0.00234307184118612 & -2.51962516925184 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -0.00674138507952697 & 0.00212021232970564 & -3.17958016990822 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -0.00710496597517388 & 0.00205251518520888 & -3.46158996843224 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -0.00514583068648392 & 0.00156629222484354 & -3.28535799697144 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -0.00567957973208368 & 0.00131755307390469 & -4.31070280550577 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -0.00384030899245656 & 0.000936580287860839 & -4.1003521451726 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -0.00381498183699218 & 0.000856349433038175 & -4.45493590561192 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -0.00391456997642545 & 0.00081435958386195 & -4.80693056728249 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -0.00412086413185255 & 0.000744729343040947 & -5.53337151323441 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -0.00363262890993207 & 0.000629308723536549 & -5.77241149545434 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -0.00487632645745472 & 0.00372556962963797 & -1.30888077320100 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -0.0048270971085094 & 0.00307552518531188 & -1.56951961621472 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -0.00525866648096089 & 0.00269003025355302 & -1.95487261677269 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -0.00525866648096089 & 0.00248404923547285 & -2.11697353090503 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -0.00555935689882763 & 0.00226072304578488 & -2.45910568709116 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -0.00537301843759173 & 0.00211192111998014 & -2.54413784054693 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -0.00518521369268789 & 0.00191861266379923 & -2.70258494094382 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -0.00518521369268789 & 0.00172910868752041 & -2.99877834754484 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -0.00469523510101814 & 0.00154114577858821 & -3.04658726400255 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -0.00424283351928009 & 0.00127296695502234 & -3.33302722630819 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -0.00407895625560236 & 0.00111046007922725 & -3.67321287086774 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -0.00379375425433842 & 0.000965853735263914 & -3.92787656746163 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -0.00378548910155657 & 0.000926583162750013 & -4.08542832822646 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -0.00378019553365787 & 0.000893316716804075 & -4.23164087556973 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -0.00375544234683227 & 0.000850897880921359 & -4.4135053465709 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -0.00375544234683227 & 0.000805861792387434 & -4.66015684365237 \tabularnewline
Median & -0.0042402037258377 &  &  \tabularnewline
Midrange & -0.00603321615766991 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.00411955981302021 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.00379375425433842 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.00379375425433842 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.00379375425433842 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.00379375425433842 &  &  \tabularnewline
Midmean - Closest Observation & -0.00439568197241977 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.00379375425433842 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.00379375425433842 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2423&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]-0.00487632645745472[/C][C]0.00423183168998178[/C][C]-1.15229688104059[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.0141034624812071[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.0297217383985478[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-0.00496321818123401[/C][C]0.00418970454560016[/C][C]-1.18462247808051[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-0.00366128560399209[/C][C]0.00356955725099609[/C][C]-1.02569740350023[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-0.00492582063237103[/C][C]0.00305200865915797[/C][C]-1.61396024142672[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-0.00485610945608255[/C][C]0.00293657692244667[/C][C]-1.65366329039887[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-0.00626287966063665[/C][C]0.00258447126332942[/C][C]-2.42327308858082[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-0.00617789591575101[/C][C]0.00254758981017996[/C][C]-2.42499632046911[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-0.00590366278441778[/C][C]0.00234307184118612[/C][C]-2.51962516925184[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-0.00674138507952697[/C][C]0.00212021232970564[/C][C]-3.17958016990822[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-0.00710496597517388[/C][C]0.00205251518520888[/C][C]-3.46158996843224[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-0.00514583068648392[/C][C]0.00156629222484354[/C][C]-3.28535799697144[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-0.00567957973208368[/C][C]0.00131755307390469[/C][C]-4.31070280550577[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-0.00384030899245656[/C][C]0.000936580287860839[/C][C]-4.1003521451726[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-0.00381498183699218[/C][C]0.000856349433038175[/C][C]-4.45493590561192[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-0.00391456997642545[/C][C]0.00081435958386195[/C][C]-4.80693056728249[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-0.00412086413185255[/C][C]0.000744729343040947[/C][C]-5.53337151323441[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-0.00363262890993207[/C][C]0.000629308723536549[/C][C]-5.77241149545434[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-0.00487632645745472[/C][C]0.00372556962963797[/C][C]-1.30888077320100[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-0.0048270971085094[/C][C]0.00307552518531188[/C][C]-1.56951961621472[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-0.00525866648096089[/C][C]0.00269003025355302[/C][C]-1.95487261677269[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-0.00525866648096089[/C][C]0.00248404923547285[/C][C]-2.11697353090503[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-0.00555935689882763[/C][C]0.00226072304578488[/C][C]-2.45910568709116[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-0.00537301843759173[/C][C]0.00211192111998014[/C][C]-2.54413784054693[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-0.00518521369268789[/C][C]0.00191861266379923[/C][C]-2.70258494094382[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-0.00518521369268789[/C][C]0.00172910868752041[/C][C]-2.99877834754484[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-0.00469523510101814[/C][C]0.00154114577858821[/C][C]-3.04658726400255[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-0.00424283351928009[/C][C]0.00127296695502234[/C][C]-3.33302722630819[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-0.00407895625560236[/C][C]0.00111046007922725[/C][C]-3.67321287086774[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-0.00379375425433842[/C][C]0.000965853735263914[/C][C]-3.92787656746163[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-0.00378548910155657[/C][C]0.000926583162750013[/C][C]-4.08542832822646[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-0.00378019553365787[/C][C]0.000893316716804075[/C][C]-4.23164087556973[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-0.00375544234683227[/C][C]0.000850897880921359[/C][C]-4.4135053465709[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-0.00375544234683227[/C][C]0.000805861792387434[/C][C]-4.66015684365237[/C][/ROW]
[ROW][C]Median[/C][C]-0.0042402037258377[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.00603321615766991[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.00411955981302021[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.00379375425433842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.00379375425433842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.00379375425433842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.00379375425433842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.00439568197241977[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.00379375425433842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.00379375425433842[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2423&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2423&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 Mean-0.004876326457454720.00423183168998178-1.15229688104059
Geometric MeanNaN
Harmonic Mean0.0141034624812071
Quadratic Mean0.0297217383985478
Winsorized Mean ( 1 / 16 )-0.004963218181234010.00418970454560016-1.18462247808051
Winsorized Mean ( 2 / 16 )-0.003661285603992090.00356955725099609-1.02569740350023
Winsorized Mean ( 3 / 16 )-0.004925820632371030.00305200865915797-1.61396024142672
Winsorized Mean ( 4 / 16 )-0.004856109456082550.00293657692244667-1.65366329039887
Winsorized Mean ( 5 / 16 )-0.006262879660636650.00258447126332942-2.42327308858082
Winsorized Mean ( 6 / 16 )-0.006177895915751010.00254758981017996-2.42499632046911
Winsorized Mean ( 7 / 16 )-0.005903662784417780.00234307184118612-2.51962516925184
Winsorized Mean ( 8 / 16 )-0.006741385079526970.00212021232970564-3.17958016990822
Winsorized Mean ( 9 / 16 )-0.007104965975173880.00205251518520888-3.46158996843224
Winsorized Mean ( 10 / 16 )-0.005145830686483920.00156629222484354-3.28535799697144
Winsorized Mean ( 11 / 16 )-0.005679579732083680.00131755307390469-4.31070280550577
Winsorized Mean ( 12 / 16 )-0.003840308992456560.000936580287860839-4.1003521451726
Winsorized Mean ( 13 / 16 )-0.003814981836992180.000856349433038175-4.45493590561192
Winsorized Mean ( 14 / 16 )-0.003914569976425450.00081435958386195-4.80693056728249
Winsorized Mean ( 15 / 16 )-0.004120864131852550.000744729343040947-5.53337151323441
Winsorized Mean ( 16 / 16 )-0.003632628909932070.000629308723536549-5.77241149545434
Trimmed Mean ( 1 / 16 )-0.004876326457454720.00372556962963797-1.30888077320100
Trimmed Mean ( 2 / 16 )-0.00482709710850940.00307552518531188-1.56951961621472
Trimmed Mean ( 3 / 16 )-0.005258666480960890.00269003025355302-1.95487261677269
Trimmed Mean ( 4 / 16 )-0.005258666480960890.00248404923547285-2.11697353090503
Trimmed Mean ( 5 / 16 )-0.005559356898827630.00226072304578488-2.45910568709116
Trimmed Mean ( 6 / 16 )-0.005373018437591730.00211192111998014-2.54413784054693
Trimmed Mean ( 7 / 16 )-0.005185213692687890.00191861266379923-2.70258494094382
Trimmed Mean ( 8 / 16 )-0.005185213692687890.00172910868752041-2.99877834754484
Trimmed Mean ( 9 / 16 )-0.004695235101018140.00154114577858821-3.04658726400255
Trimmed Mean ( 10 / 16 )-0.004242833519280090.00127296695502234-3.33302722630819
Trimmed Mean ( 11 / 16 )-0.004078956255602360.00111046007922725-3.67321287086774
Trimmed Mean ( 12 / 16 )-0.003793754254338420.000965853735263914-3.92787656746163
Trimmed Mean ( 13 / 16 )-0.003785489101556570.000926583162750013-4.08542832822646
Trimmed Mean ( 14 / 16 )-0.003780195533657870.000893316716804075-4.23164087556973
Trimmed Mean ( 15 / 16 )-0.003755442346832270.000850897880921359-4.4135053465709
Trimmed Mean ( 16 / 16 )-0.003755442346832270.000805861792387434-4.66015684365237
Median-0.0042402037258377
Midrange-0.00603321615766991
Midmean - Weighted Average at Xnp-0.00411955981302021
Midmean - Weighted Average at X(n+1)p-0.00379375425433842
Midmean - Empirical Distribution Function-0.00379375425433842
Midmean - Empirical Distribution Function - Averaging-0.00379375425433842
Midmean - Empirical Distribution Function - Interpolation-0.00379375425433842
Midmean - Closest Observation-0.00439568197241977
Midmean - True Basic - Statistics Graphics Toolkit-0.00379375425433842
Midmean - MS Excel (old versions)-0.00379375425433842
Number of observations49



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')