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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 computationMon, 19 Oct 2009 11:32:48 -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/19/t1255973766xkn5pjp6yeg6q65.htm/, Retrieved Mon, 29 Apr 2024 21:39:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47976, Retrieved Mon, 29 Apr 2024 21:39:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
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]
- RMP       [Central Tendency] [central tendency] [2009-10-17 11:29:28] [f7fc9270f813d017f9fa5b506fdc7682]
-    D          [Central Tendency] [WS 3 Part 2 Y[t]/...] [2009-10-19 17:32:48] [eba9f01697e64705b70041e6f338cb22] [Current]
- RMPD            [Univariate Data Series] [WS 3 Part 2 e[t] ...] [2009-10-19 17:45:14] [83058a88a37d754675a5cd22dab372fc]
- RMP               [Univariate Explorative Data Analysis] [WS 3 Part 3 EDA] [2009-10-19 17:59:53] [83058a88a37d754675a5cd22dab372fc]
- RMPD                [Harrell-Davis Quantiles] [WS 3 Part 3 confi...] [2009-10-19 18:14:26] [83058a88a37d754675a5cd22dab372fc]
-   P                 [Univariate Explorative Data Analysis] [WS 3 Part 3 toevo...] [2009-10-20 18:06:02] [83058a88a37d754675a5cd22dab372fc]
- RMP                 [Central Tendency] [WS 3 Part 3 toevo...] [2009-10-20 18:07:48] [83058a88a37d754675a5cd22dab372fc]
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Dataseries X:
1.049659864
1.039117043
1.076570916
1.084210526
0.984090909
1.033829974
1.050407978
1.072569779
1.064566929
1.149788584
1.141293014
1.19226361
1.121692607
1.116106014
1.090781387
1.147713226
1.028422153
1.067844523
1.054957507
1.067095588
1.069110459
1.127777778
1.134955313
1.157402597
1.134756703
1.150955414
1.143106457
1.217798595
1.083383085
1.119163763
1.136824034
1.134100974
1.140686275
1.140849057
1.126210826
1.12037037
1.140904807
1.167612077
1.155631399
1.241945946
1.09731286
1.145333333
1.134803922
1.142453663
1.1496
1.156097561
1.126152482
1.172586521
1.175703325
1.176626948
1.172562554
1.2728125
1.133066132
1.16609589
1.192739844
1.159356137
1.176564157
1.09043956
1.09860515
1.092822502




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47976&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47976&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.125137718350.0068536236503665164.166837245263
Geometric Mean1.12390031671505
Harmonic Mean1.12265584905947
Quadratic Mean1.12636860863802
Winsorized Mean ( 1 / 20 )1.125362129850.0064566007417953174.296378985498
Winsorized Mean ( 2 / 20 )1.124737478850.00618495539054613181.850540194549
Winsorized Mean ( 3 / 20 )1.123748894750.00583316230407758192.648315985390
Winsorized Mean ( 4 / 20 )1.124420000550.00566156743098985198.605777332128
Winsorized Mean ( 5 / 20 )1.123179288216670.00540542830946913207.787287873026
Winsorized Mean ( 6 / 20 )1.123627962016670.0053025151070727211.9047167858
Winsorized Mean ( 7 / 20 )1.124648630850.005049073635857222.743558910111
Winsorized Mean ( 8 / 20 )1.124570211516670.00491157326129711228.963338565712
Winsorized Mean ( 9 / 20 )1.124678956716670.00488876832628569230.053641664619
Winsorized Mean ( 10 / 20 )1.124064866550.00471398811133631238.453055035676
Winsorized Mean ( 11 / 20 )1.12442110760.004546656945007247.307224010997
Winsorized Mean ( 12 / 20 )1.12387338440.00419099749945942268.163697197377
Winsorized Mean ( 13 / 20 )1.124926087350.00385413048144600291.875454856928
Winsorized Mean ( 14 / 20 )1.124814648516670.00377576930065194297.903436081874
Winsorized Mean ( 15 / 20 )1.126255366516670.00348131766175441323.514104699395
Winsorized Mean ( 16 / 20 )1.125099591050.00329301155283274341.662813202752
Winsorized Mean ( 17 / 20 )1.125347305133330.00314752227303108357.534342100022
Winsorized Mean ( 18 / 20 )1.126637837333330.00290676223556971387.592016831235
Winsorized Mean ( 19 / 20 )1.126449584066670.00275769373245786408.475230881673
Winsorized Mean ( 20 / 20 )1.131489907733330.00169075030405231669.22354236544
Trimmed Mean ( 1 / 20 )1.125023442965520.00613861448622246183.269929312311
Trimmed Mean ( 2 / 20 )1.124660564160710.00574254401475255195.847095167485
Trimmed Mean ( 3 / 20 )1.124617833777780.00543828833268242206.796286805754
Trimmed Mean ( 4 / 20 )1.124952041096150.00523529295026842214.878527674077
Trimmed Mean ( 5 / 20 )1.125111653260.0050501872291551222.786126970630
Trimmed Mean ( 6 / 20 )1.125594744520830.0049033247548502229.557453523231
Trimmed Mean ( 7 / 20 )1.126022305934780.00474693807956907237.210236801109
Trimmed Mean ( 8 / 20 )1.126289904977270.004620712624839243.748096110287
Trimmed Mean ( 9 / 20 )1.126596993095240.00449187932760049250.807493018085
Trimmed Mean ( 10 / 20 )1.1269166658250.00432464510321341260.580149105796
Trimmed Mean ( 11 / 20 )1.127366949921050.00414620835390717271.903110913054
Trimmed Mean ( 12 / 20 )1.127813289666670.00395016323062783285.510553316404
Trimmed Mean ( 13 / 20 )1.12839268750.0037796515051557298.5441080906
Trimmed Mean ( 14 / 20 )1.128892677906250.00364132725049951310.02230786903
Trimmed Mean ( 15 / 20 )1.129475253533330.00345852400883232326.57724816971
Trimmed Mean ( 16 / 20 )1.129935237392860.00329191613251635343.245450949302
Trimmed Mean ( 17 / 20 )1.130632686384620.00308969378639615365.93680945431
Trimmed Mean ( 18 / 20 )1.131409948333330.0028213655847159401.015010058422
Trimmed Mean ( 19 / 20 )1.132132995454550.00250064334901688452.736691099768
Trimmed Mean ( 20 / 20 )1.13303037620.00199078170227982569.138431854416
Median1.1347803125
Midrange1.1284517045
Midmean - Weighted Average at Xnp1.12801510103226
Midmean - Weighted Average at X(n+1)p1.12947525353333
Midmean - Empirical Distribution Function1.12801510103226
Midmean - Empirical Distribution Function - Averaging1.12947525353333
Midmean - Empirical Distribution Function - Interpolation1.12947525353333
Midmean - Closest Observation1.12801510103226
Midmean - True Basic - Statistics Graphics Toolkit1.12947525353333
Midmean - MS Excel (old versions)1.12889267790625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.12513771835 & 0.0068536236503665 & 164.166837245263 \tabularnewline
Geometric Mean & 1.12390031671505 &  &  \tabularnewline
Harmonic Mean & 1.12265584905947 &  &  \tabularnewline
Quadratic Mean & 1.12636860863802 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.12536212985 & 0.0064566007417953 & 174.296378985498 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.12473747885 & 0.00618495539054613 & 181.850540194549 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.12374889475 & 0.00583316230407758 & 192.648315985390 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.12442000055 & 0.00566156743098985 & 198.605777332128 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.12317928821667 & 0.00540542830946913 & 207.787287873026 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.12362796201667 & 0.0053025151070727 & 211.9047167858 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.12464863085 & 0.005049073635857 & 222.743558910111 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.12457021151667 & 0.00491157326129711 & 228.963338565712 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.12467895671667 & 0.00488876832628569 & 230.053641664619 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.12406486655 & 0.00471398811133631 & 238.453055035676 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.1244211076 & 0.004546656945007 & 247.307224010997 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.1238733844 & 0.00419099749945942 & 268.163697197377 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.12492608735 & 0.00385413048144600 & 291.875454856928 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.12481464851667 & 0.00377576930065194 & 297.903436081874 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.12625536651667 & 0.00348131766175441 & 323.514104699395 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.12509959105 & 0.00329301155283274 & 341.662813202752 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.12534730513333 & 0.00314752227303108 & 357.534342100022 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.12663783733333 & 0.00290676223556971 & 387.592016831235 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.12644958406667 & 0.00275769373245786 & 408.475230881673 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.13148990773333 & 0.00169075030405231 & 669.22354236544 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.12502344296552 & 0.00613861448622246 & 183.269929312311 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.12466056416071 & 0.00574254401475255 & 195.847095167485 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.12461783377778 & 0.00543828833268242 & 206.796286805754 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.12495204109615 & 0.00523529295026842 & 214.878527674077 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.12511165326 & 0.0050501872291551 & 222.786126970630 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.12559474452083 & 0.0049033247548502 & 229.557453523231 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.12602230593478 & 0.00474693807956907 & 237.210236801109 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.12628990497727 & 0.004620712624839 & 243.748096110287 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.12659699309524 & 0.00449187932760049 & 250.807493018085 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.126916665825 & 0.00432464510321341 & 260.580149105796 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.12736694992105 & 0.00414620835390717 & 271.903110913054 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.12781328966667 & 0.00395016323062783 & 285.510553316404 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.1283926875 & 0.0037796515051557 & 298.5441080906 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.12889267790625 & 0.00364132725049951 & 310.02230786903 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.12947525353333 & 0.00345852400883232 & 326.57724816971 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.12993523739286 & 0.00329191613251635 & 343.245450949302 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.13063268638462 & 0.00308969378639615 & 365.93680945431 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.13140994833333 & 0.0028213655847159 & 401.015010058422 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.13213299545455 & 0.00250064334901688 & 452.736691099768 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.1330303762 & 0.00199078170227982 & 569.138431854416 \tabularnewline
Median & 1.1347803125 &  &  \tabularnewline
Midrange & 1.1284517045 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.12801510103226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.12947525353333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.12801510103226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.12947525353333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.12947525353333 &  &  \tabularnewline
Midmean - Closest Observation & 1.12801510103226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.12947525353333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.12889267790625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47976&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]1.12513771835[/C][C]0.0068536236503665[/C][C]164.166837245263[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.12390031671505[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.12265584905947[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.12636860863802[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.12536212985[/C][C]0.0064566007417953[/C][C]174.296378985498[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.12473747885[/C][C]0.00618495539054613[/C][C]181.850540194549[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.12374889475[/C][C]0.00583316230407758[/C][C]192.648315985390[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.12442000055[/C][C]0.00566156743098985[/C][C]198.605777332128[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.12317928821667[/C][C]0.00540542830946913[/C][C]207.787287873026[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.12362796201667[/C][C]0.0053025151070727[/C][C]211.9047167858[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.12464863085[/C][C]0.005049073635857[/C][C]222.743558910111[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.12457021151667[/C][C]0.00491157326129711[/C][C]228.963338565712[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.12467895671667[/C][C]0.00488876832628569[/C][C]230.053641664619[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.12406486655[/C][C]0.00471398811133631[/C][C]238.453055035676[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.1244211076[/C][C]0.004546656945007[/C][C]247.307224010997[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.1238733844[/C][C]0.00419099749945942[/C][C]268.163697197377[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.12492608735[/C][C]0.00385413048144600[/C][C]291.875454856928[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.12481464851667[/C][C]0.00377576930065194[/C][C]297.903436081874[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.12625536651667[/C][C]0.00348131766175441[/C][C]323.514104699395[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.12509959105[/C][C]0.00329301155283274[/C][C]341.662813202752[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.12534730513333[/C][C]0.00314752227303108[/C][C]357.534342100022[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.12663783733333[/C][C]0.00290676223556971[/C][C]387.592016831235[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.12644958406667[/C][C]0.00275769373245786[/C][C]408.475230881673[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.13148990773333[/C][C]0.00169075030405231[/C][C]669.22354236544[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.12502344296552[/C][C]0.00613861448622246[/C][C]183.269929312311[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.12466056416071[/C][C]0.00574254401475255[/C][C]195.847095167485[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.12461783377778[/C][C]0.00543828833268242[/C][C]206.796286805754[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.12495204109615[/C][C]0.00523529295026842[/C][C]214.878527674077[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.12511165326[/C][C]0.0050501872291551[/C][C]222.786126970630[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.12559474452083[/C][C]0.0049033247548502[/C][C]229.557453523231[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.12602230593478[/C][C]0.00474693807956907[/C][C]237.210236801109[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.12628990497727[/C][C]0.004620712624839[/C][C]243.748096110287[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.12659699309524[/C][C]0.00449187932760049[/C][C]250.807493018085[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.126916665825[/C][C]0.00432464510321341[/C][C]260.580149105796[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.12736694992105[/C][C]0.00414620835390717[/C][C]271.903110913054[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.12781328966667[/C][C]0.00395016323062783[/C][C]285.510553316404[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.1283926875[/C][C]0.0037796515051557[/C][C]298.5441080906[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.12889267790625[/C][C]0.00364132725049951[/C][C]310.02230786903[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.12947525353333[/C][C]0.00345852400883232[/C][C]326.57724816971[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.12993523739286[/C][C]0.00329191613251635[/C][C]343.245450949302[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.13063268638462[/C][C]0.00308969378639615[/C][C]365.93680945431[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.13140994833333[/C][C]0.0028213655847159[/C][C]401.015010058422[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.13213299545455[/C][C]0.00250064334901688[/C][C]452.736691099768[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.1330303762[/C][C]0.00199078170227982[/C][C]569.138431854416[/C][/ROW]
[ROW][C]Median[/C][C]1.1347803125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.1284517045[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.12801510103226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.12947525353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.12801510103226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.12947525353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.12947525353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.12801510103226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.12947525353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.12889267790625[/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=47976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47976&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 Mean1.125137718350.0068536236503665164.166837245263
Geometric Mean1.12390031671505
Harmonic Mean1.12265584905947
Quadratic Mean1.12636860863802
Winsorized Mean ( 1 / 20 )1.125362129850.0064566007417953174.296378985498
Winsorized Mean ( 2 / 20 )1.124737478850.00618495539054613181.850540194549
Winsorized Mean ( 3 / 20 )1.123748894750.00583316230407758192.648315985390
Winsorized Mean ( 4 / 20 )1.124420000550.00566156743098985198.605777332128
Winsorized Mean ( 5 / 20 )1.123179288216670.00540542830946913207.787287873026
Winsorized Mean ( 6 / 20 )1.123627962016670.0053025151070727211.9047167858
Winsorized Mean ( 7 / 20 )1.124648630850.005049073635857222.743558910111
Winsorized Mean ( 8 / 20 )1.124570211516670.00491157326129711228.963338565712
Winsorized Mean ( 9 / 20 )1.124678956716670.00488876832628569230.053641664619
Winsorized Mean ( 10 / 20 )1.124064866550.00471398811133631238.453055035676
Winsorized Mean ( 11 / 20 )1.12442110760.004546656945007247.307224010997
Winsorized Mean ( 12 / 20 )1.12387338440.00419099749945942268.163697197377
Winsorized Mean ( 13 / 20 )1.124926087350.00385413048144600291.875454856928
Winsorized Mean ( 14 / 20 )1.124814648516670.00377576930065194297.903436081874
Winsorized Mean ( 15 / 20 )1.126255366516670.00348131766175441323.514104699395
Winsorized Mean ( 16 / 20 )1.125099591050.00329301155283274341.662813202752
Winsorized Mean ( 17 / 20 )1.125347305133330.00314752227303108357.534342100022
Winsorized Mean ( 18 / 20 )1.126637837333330.00290676223556971387.592016831235
Winsorized Mean ( 19 / 20 )1.126449584066670.00275769373245786408.475230881673
Winsorized Mean ( 20 / 20 )1.131489907733330.00169075030405231669.22354236544
Trimmed Mean ( 1 / 20 )1.125023442965520.00613861448622246183.269929312311
Trimmed Mean ( 2 / 20 )1.124660564160710.00574254401475255195.847095167485
Trimmed Mean ( 3 / 20 )1.124617833777780.00543828833268242206.796286805754
Trimmed Mean ( 4 / 20 )1.124952041096150.00523529295026842214.878527674077
Trimmed Mean ( 5 / 20 )1.125111653260.0050501872291551222.786126970630
Trimmed Mean ( 6 / 20 )1.125594744520830.0049033247548502229.557453523231
Trimmed Mean ( 7 / 20 )1.126022305934780.00474693807956907237.210236801109
Trimmed Mean ( 8 / 20 )1.126289904977270.004620712624839243.748096110287
Trimmed Mean ( 9 / 20 )1.126596993095240.00449187932760049250.807493018085
Trimmed Mean ( 10 / 20 )1.1269166658250.00432464510321341260.580149105796
Trimmed Mean ( 11 / 20 )1.127366949921050.00414620835390717271.903110913054
Trimmed Mean ( 12 / 20 )1.127813289666670.00395016323062783285.510553316404
Trimmed Mean ( 13 / 20 )1.12839268750.0037796515051557298.5441080906
Trimmed Mean ( 14 / 20 )1.128892677906250.00364132725049951310.02230786903
Trimmed Mean ( 15 / 20 )1.129475253533330.00345852400883232326.57724816971
Trimmed Mean ( 16 / 20 )1.129935237392860.00329191613251635343.245450949302
Trimmed Mean ( 17 / 20 )1.130632686384620.00308969378639615365.93680945431
Trimmed Mean ( 18 / 20 )1.131409948333330.0028213655847159401.015010058422
Trimmed Mean ( 19 / 20 )1.132132995454550.00250064334901688452.736691099768
Trimmed Mean ( 20 / 20 )1.13303037620.00199078170227982569.138431854416
Median1.1347803125
Midrange1.1284517045
Midmean - Weighted Average at Xnp1.12801510103226
Midmean - Weighted Average at X(n+1)p1.12947525353333
Midmean - Empirical Distribution Function1.12801510103226
Midmean - Empirical Distribution Function - Averaging1.12947525353333
Midmean - Empirical Distribution Function - Interpolation1.12947525353333
Midmean - Closest Observation1.12801510103226
Midmean - True Basic - Statistics Graphics Toolkit1.12947525353333
Midmean - MS Excel (old versions)1.12889267790625
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')