Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 12:00:55 -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/10/t1197312404ofzg2uxd110t850.htm/, Retrieved Mon, 06 May 2024 17:58:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3022, Retrieved Mon, 06 May 2024 17:58:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact219
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-12-10 19:00:55] [40a229849a2b804e343854d9b3fa1a24] [Current]
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Dataseries X:
-0.369938394019901 
0.534373143380365 
0.0343115426927538 
-0.265677689061721 
0.414743269448613 
0.0121294714002305 
-0.00365388999556855 
0.324118555091213 
-0.51783493719443 
-0.447273140675026 
-0.093359007031772 
0.289756393379017 
-0.290816786473856 
0.0974621082103193 
0.0495174400326479 
0.378474665315993 
-0.46566630926686 
-0.149280564946482 
-0.539690417728031 
0.122421516011666 
-0.081603414117912 
-0.167909170483425 
-0.0183834213256594 
-0.140627706860251 
-0.508738649661676 
-0.28046415331831 
0.00787764423681424 
-0.0958936333648209 
-0.0319935566683973 
-0.102219467432245 
-0.0426062529085816 
0.301872003186721 
-0.0271823591238811 
-0.421491125197297 
0.0253359700850571 
0.0595014259066989 
-0.194700216228595 
-0.0280991537268318 
0.045175519112218 
-0.653201445074474 
0.166932662193915 
0.175785827586508 
0.348522996334505 
-0.0624027573238484 
-0.110743322839979 
0.0670549385107277 
0.0761178775483073 
-0.142678127397315 




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3022&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3022&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3022&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.05672175207880950.0385125506366647-1.47281213892931
Geometric MeanNaN
Harmonic Mean-0.285897072773243
Quadratic Mean0.27005283800832
Winsorized Mean ( 1 / 16 )-0.05684922804933680.0370480601855348-1.53447245995172
Winsorized Mean ( 2 / 16 )-0.05744977486596260.0364019771829376-1.57820479303224
Winsorized Mean ( 3 / 16 )-0.05875323620650840.0357841843900907-1.64187719261748
Winsorized Mean ( 4 / 16 )-0.05719757794388140.0343631431802035-1.66450367022400
Winsorized Mean ( 5 / 16 )-0.057598972038950.0333431339462345-1.72746125579640
Winsorized Mean ( 6 / 16 )-0.05589067133019690.0322064502898513-1.73538750241621
Winsorized Mean ( 7 / 16 )-0.06499327221156750.0268815189213054-2.41776785016624
Winsorized Mean ( 8 / 16 )-0.05328186518599220.0235783425453111-2.25977992658301
Winsorized Mean ( 9 / 16 )-0.0596865863784990.0215770454954863-2.76620756029758
Winsorized Mean ( 10 / 16 )-0.06180594961699020.0199991947443317-3.09042190983753
Winsorized Mean ( 11 / 16 )-0.05043166495277650.0158031147647725-3.19124841548303
Winsorized Mean ( 12 / 16 )-0.04599963827587890.0141511820574740-3.25058628240771
Winsorized Mean ( 13 / 16 )-0.04300013393988140.0128987732882430-3.33366072718520
Winsorized Mean ( 14 / 16 )-0.04398641886797250.0120762634194659-3.64238650152913
Winsorized Mean ( 15 / 16 )-0.04470251273777440.0117426071751484-3.80686435908212
Winsorized Mean ( 16 / 16 )-0.03836237687083840.00947061082697776-4.05067609383339
Trimmed Mean ( 1 / 16 )-0.05660469126279890.0357186721059466-1.58473671963228
Trimmed Mean ( 2 / 16 )-0.05633792385930290.0339864640943828-1.65765769874879
Trimmed Mean ( 3 / 16 )-0.0557025804269260.0321811838277851-1.73090526206288
Trimmed Mean ( 4 / 16 )-0.0544823181150930.0301135977234345-1.80922647022992
Trimmed Mean ( 5 / 16 )-0.05362486764284410.0279988574708759-1.91525199550103
Trimmed Mean ( 6 / 16 )-0.05256510647054910.0255236681983401-2.05946520155624
Trimmed Mean ( 7 / 16 )-0.05178262062122030.0224903502786077-2.30243726663852
Trimmed Mean ( 8 / 16 )-0.0489517667090030.020435245283386-2.39545775106508
Trimmed Mean ( 9 / 16 )-0.04808574701360520.0188500184963425-2.55096550822670
Trimmed Mean ( 10 / 16 )-0.0458760633250540.0172869501329858-2.65379740047473
Trimmed Mean ( 11 / 16 )-0.04293516124038880.0155335150273014-2.76403384326901
Trimmed Mean ( 12 / 16 )-0.04157216056540920.0147188453499575-2.82441724041413
Trimmed Mean ( 13 / 16 )-0.04076716461805110.0140971098878224-2.89188102685269
Trimmed Mean ( 14 / 16 )-0.04035492412786710.0135705004349006-2.97372409525019
Trimmed Mean ( 15 / 16 )-0.03966321084403750.0129635652072969-3.05959126288129
Trimmed Mean ( 16 / 16 )-0.03865535046529010.0119053277508726-3.24689511067487
Median-0.0300463551976146
Midrange-0.0594141508470545
Midmean - Weighted Average at Xnp-0.0476972827919367
Midmean - Weighted Average at X(n+1)p-0.0415721605654092
Midmean - Empirical Distribution Function-0.0476972827919367
Midmean - Empirical Distribution Function - Averaging-0.0415721605654092
Midmean - Empirical Distribution Function - Interpolation-0.0415721605654092
Midmean - Closest Observation-0.0476972827919367
Midmean - True Basic - Statistics Graphics Toolkit-0.0415721605654092
Midmean - MS Excel (old versions)-0.0429351612403888
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.0567217520788095 & 0.0385125506366647 & -1.47281213892931 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.285897072773243 &  &  \tabularnewline
Quadratic Mean & 0.27005283800832 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -0.0568492280493368 & 0.0370480601855348 & -1.53447245995172 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -0.0574497748659626 & 0.0364019771829376 & -1.57820479303224 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -0.0587532362065084 & 0.0357841843900907 & -1.64187719261748 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -0.0571975779438814 & 0.0343631431802035 & -1.66450367022400 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -0.05759897203895 & 0.0333431339462345 & -1.72746125579640 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -0.0558906713301969 & 0.0322064502898513 & -1.73538750241621 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -0.0649932722115675 & 0.0268815189213054 & -2.41776785016624 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -0.0532818651859922 & 0.0235783425453111 & -2.25977992658301 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -0.059686586378499 & 0.0215770454954863 & -2.76620756029758 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -0.0618059496169902 & 0.0199991947443317 & -3.09042190983753 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -0.0504316649527765 & 0.0158031147647725 & -3.19124841548303 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -0.0459996382758789 & 0.0141511820574740 & -3.25058628240771 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -0.0430001339398814 & 0.0128987732882430 & -3.33366072718520 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -0.0439864188679725 & 0.0120762634194659 & -3.64238650152913 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -0.0447025127377744 & 0.0117426071751484 & -3.80686435908212 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -0.0383623768708384 & 0.00947061082697776 & -4.05067609383339 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -0.0566046912627989 & 0.0357186721059466 & -1.58473671963228 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -0.0563379238593029 & 0.0339864640943828 & -1.65765769874879 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -0.055702580426926 & 0.0321811838277851 & -1.73090526206288 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -0.054482318115093 & 0.0301135977234345 & -1.80922647022992 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -0.0536248676428441 & 0.0279988574708759 & -1.91525199550103 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -0.0525651064705491 & 0.0255236681983401 & -2.05946520155624 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -0.0517826206212203 & 0.0224903502786077 & -2.30243726663852 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -0.048951766709003 & 0.020435245283386 & -2.39545775106508 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -0.0480857470136052 & 0.0188500184963425 & -2.55096550822670 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -0.045876063325054 & 0.0172869501329858 & -2.65379740047473 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -0.0429351612403888 & 0.0155335150273014 & -2.76403384326901 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -0.0415721605654092 & 0.0147188453499575 & -2.82441724041413 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -0.0407671646180511 & 0.0140971098878224 & -2.89188102685269 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -0.0403549241278671 & 0.0135705004349006 & -2.97372409525019 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -0.0396632108440375 & 0.0129635652072969 & -3.05959126288129 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -0.0386553504652901 & 0.0119053277508726 & -3.24689511067487 \tabularnewline
Median & -0.0300463551976146 &  &  \tabularnewline
Midrange & -0.0594141508470545 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.0476972827919367 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.0415721605654092 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.0476972827919367 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.0415721605654092 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.0415721605654092 &  &  \tabularnewline
Midmean - Closest Observation & -0.0476972827919367 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.0415721605654092 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.0429351612403888 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3022&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]-0.0567217520788095[/C][C]0.0385125506366647[/C][C]-1.47281213892931[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.285897072773243[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.27005283800832[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-0.0568492280493368[/C][C]0.0370480601855348[/C][C]-1.53447245995172[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-0.0574497748659626[/C][C]0.0364019771829376[/C][C]-1.57820479303224[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-0.0587532362065084[/C][C]0.0357841843900907[/C][C]-1.64187719261748[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-0.0571975779438814[/C][C]0.0343631431802035[/C][C]-1.66450367022400[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-0.05759897203895[/C][C]0.0333431339462345[/C][C]-1.72746125579640[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-0.0558906713301969[/C][C]0.0322064502898513[/C][C]-1.73538750241621[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-0.0649932722115675[/C][C]0.0268815189213054[/C][C]-2.41776785016624[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-0.0532818651859922[/C][C]0.0235783425453111[/C][C]-2.25977992658301[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-0.059686586378499[/C][C]0.0215770454954863[/C][C]-2.76620756029758[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-0.0618059496169902[/C][C]0.0199991947443317[/C][C]-3.09042190983753[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-0.0504316649527765[/C][C]0.0158031147647725[/C][C]-3.19124841548303[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-0.0459996382758789[/C][C]0.0141511820574740[/C][C]-3.25058628240771[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-0.0430001339398814[/C][C]0.0128987732882430[/C][C]-3.33366072718520[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-0.0439864188679725[/C][C]0.0120762634194659[/C][C]-3.64238650152913[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-0.0447025127377744[/C][C]0.0117426071751484[/C][C]-3.80686435908212[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-0.0383623768708384[/C][C]0.00947061082697776[/C][C]-4.05067609383339[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-0.0566046912627989[/C][C]0.0357186721059466[/C][C]-1.58473671963228[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-0.0563379238593029[/C][C]0.0339864640943828[/C][C]-1.65765769874879[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-0.055702580426926[/C][C]0.0321811838277851[/C][C]-1.73090526206288[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-0.054482318115093[/C][C]0.0301135977234345[/C][C]-1.80922647022992[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-0.0536248676428441[/C][C]0.0279988574708759[/C][C]-1.91525199550103[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-0.0525651064705491[/C][C]0.0255236681983401[/C][C]-2.05946520155624[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-0.0517826206212203[/C][C]0.0224903502786077[/C][C]-2.30243726663852[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-0.048951766709003[/C][C]0.020435245283386[/C][C]-2.39545775106508[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-0.0480857470136052[/C][C]0.0188500184963425[/C][C]-2.55096550822670[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-0.045876063325054[/C][C]0.0172869501329858[/C][C]-2.65379740047473[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-0.0429351612403888[/C][C]0.0155335150273014[/C][C]-2.76403384326901[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-0.0415721605654092[/C][C]0.0147188453499575[/C][C]-2.82441724041413[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-0.0407671646180511[/C][C]0.0140971098878224[/C][C]-2.89188102685269[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-0.0403549241278671[/C][C]0.0135705004349006[/C][C]-2.97372409525019[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-0.0396632108440375[/C][C]0.0129635652072969[/C][C]-3.05959126288129[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-0.0386553504652901[/C][C]0.0119053277508726[/C][C]-3.24689511067487[/C][/ROW]
[ROW][C]Median[/C][C]-0.0300463551976146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.0594141508470545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.0476972827919367[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.0415721605654092[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.0476972827919367[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.0415721605654092[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.0415721605654092[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.0476972827919367[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.0415721605654092[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.0429351612403888[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3022&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3022&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-0.05672175207880950.0385125506366647-1.47281213892931
Geometric MeanNaN
Harmonic Mean-0.285897072773243
Quadratic Mean0.27005283800832
Winsorized Mean ( 1 / 16 )-0.05684922804933680.0370480601855348-1.53447245995172
Winsorized Mean ( 2 / 16 )-0.05744977486596260.0364019771829376-1.57820479303224
Winsorized Mean ( 3 / 16 )-0.05875323620650840.0357841843900907-1.64187719261748
Winsorized Mean ( 4 / 16 )-0.05719757794388140.0343631431802035-1.66450367022400
Winsorized Mean ( 5 / 16 )-0.057598972038950.0333431339462345-1.72746125579640
Winsorized Mean ( 6 / 16 )-0.05589067133019690.0322064502898513-1.73538750241621
Winsorized Mean ( 7 / 16 )-0.06499327221156750.0268815189213054-2.41776785016624
Winsorized Mean ( 8 / 16 )-0.05328186518599220.0235783425453111-2.25977992658301
Winsorized Mean ( 9 / 16 )-0.0596865863784990.0215770454954863-2.76620756029758
Winsorized Mean ( 10 / 16 )-0.06180594961699020.0199991947443317-3.09042190983753
Winsorized Mean ( 11 / 16 )-0.05043166495277650.0158031147647725-3.19124841548303
Winsorized Mean ( 12 / 16 )-0.04599963827587890.0141511820574740-3.25058628240771
Winsorized Mean ( 13 / 16 )-0.04300013393988140.0128987732882430-3.33366072718520
Winsorized Mean ( 14 / 16 )-0.04398641886797250.0120762634194659-3.64238650152913
Winsorized Mean ( 15 / 16 )-0.04470251273777440.0117426071751484-3.80686435908212
Winsorized Mean ( 16 / 16 )-0.03836237687083840.00947061082697776-4.05067609383339
Trimmed Mean ( 1 / 16 )-0.05660469126279890.0357186721059466-1.58473671963228
Trimmed Mean ( 2 / 16 )-0.05633792385930290.0339864640943828-1.65765769874879
Trimmed Mean ( 3 / 16 )-0.0557025804269260.0321811838277851-1.73090526206288
Trimmed Mean ( 4 / 16 )-0.0544823181150930.0301135977234345-1.80922647022992
Trimmed Mean ( 5 / 16 )-0.05362486764284410.0279988574708759-1.91525199550103
Trimmed Mean ( 6 / 16 )-0.05256510647054910.0255236681983401-2.05946520155624
Trimmed Mean ( 7 / 16 )-0.05178262062122030.0224903502786077-2.30243726663852
Trimmed Mean ( 8 / 16 )-0.0489517667090030.020435245283386-2.39545775106508
Trimmed Mean ( 9 / 16 )-0.04808574701360520.0188500184963425-2.55096550822670
Trimmed Mean ( 10 / 16 )-0.0458760633250540.0172869501329858-2.65379740047473
Trimmed Mean ( 11 / 16 )-0.04293516124038880.0155335150273014-2.76403384326901
Trimmed Mean ( 12 / 16 )-0.04157216056540920.0147188453499575-2.82441724041413
Trimmed Mean ( 13 / 16 )-0.04076716461805110.0140971098878224-2.89188102685269
Trimmed Mean ( 14 / 16 )-0.04035492412786710.0135705004349006-2.97372409525019
Trimmed Mean ( 15 / 16 )-0.03966321084403750.0129635652072969-3.05959126288129
Trimmed Mean ( 16 / 16 )-0.03865535046529010.0119053277508726-3.24689511067487
Median-0.0300463551976146
Midrange-0.0594141508470545
Midmean - Weighted Average at Xnp-0.0476972827919367
Midmean - Weighted Average at X(n+1)p-0.0415721605654092
Midmean - Empirical Distribution Function-0.0476972827919367
Midmean - Empirical Distribution Function - Averaging-0.0415721605654092
Midmean - Empirical Distribution Function - Interpolation-0.0415721605654092
Midmean - Closest Observation-0.0476972827919367
Midmean - True Basic - Statistics Graphics Toolkit-0.0415721605654092
Midmean - MS Excel (old versions)-0.0429351612403888
Number of observations48



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')