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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Oct 2014 15:18:33 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413209925w4vaqmdw8uf7hed.htm/, Retrieved Fri, 10 May 2024 14:27:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240754, Retrieved Fri, 10 May 2024 14:27:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 14:18:33] [81bcec4b91879990466572cf43afb80d] [Current]
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Dataseries X:
79,26
79,38
79,35
78,91
79,11
79,22
79,22
79,21
79,26
79,82
80,04
80,2
80,2
80,27
80,37
80,57
79,99
79,86
79,86
79,81
79,88
80,2
80,53
80,52
80,52
80,48
80,29
79,54
79,39
79,3
79,3
79,49
79,63
79,74
80,17
80,06
80,06
80,22
80,5
80,58
80,24
80,34
80,34
80,41
80,59
80,77
80,94
80,8
80,8
80,76
80,94
81,03
81,35
81,41
81,41
81,44
81,55
81,8
81,97
81,99
79,36
79,44
79,46
79,77
79,49
79,42
80,32
80,48
80,6
80,53
80,84
80,68





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=240754&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=240754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240754&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'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean80.21638888888890.0864567939068913927.820536293274
Geometric Mean80.2130887502441
Harmonic Mean80.2097964437026
Quadratic Mean80.2196968054327
Winsorized Mean ( 1 / 24 )80.21888888888890.0858282749673071934.644077600827
Winsorized Mean ( 2 / 24 )80.21694444444450.0840354550354086954.56071976578
Winsorized Mean ( 3 / 24 )80.20694444444440.0813692579421918985.715569649497
Winsorized Mean ( 4 / 24 )80.20083333333330.07999186920731461002.61231707784
Winsorized Mean ( 5 / 24 )80.20152777777780.0790674965027781014.34257217136
Winsorized Mean ( 6 / 24 )80.20152777777780.0790674965027781014.34257217136
Winsorized Mean ( 7 / 24 )80.19958333333330.07718173518701731039.10054806365
Winsorized Mean ( 8 / 24 )80.16402777777780.0703366763001411139.71873558116
Winsorized Mean ( 9 / 24 )80.15902777777780.06737219388363541189.7939365939
Winsorized Mean ( 10 / 24 )80.16041666666670.06713813263472271193.96255929241
Winsorized Mean ( 11 / 24 )80.14819444444440.06421377344978871248.14646669403
Winsorized Mean ( 12 / 24 )80.14319444444440.06293699385245091273.38770949772
Winsorized Mean ( 13 / 24 )80.14861111111110.06203238387550791292.04467253685
Winsorized Mean ( 14 / 24 )80.14666666666670.06053652914978151323.93891411192
Winsorized Mean ( 15 / 24 )80.148750.05955295689782261345.83997462149
Winsorized Mean ( 16 / 24 )80.13763888888890.05596622229673291431.89294542696
Winsorized Mean ( 17 / 24 )80.118750.05347799391650121498.16296634266
Winsorized Mean ( 18 / 24 )80.128750.05111125729294591567.73192920572
Winsorized Mean ( 19 / 24 )80.14986111111110.0469935287788381705.55102359549
Winsorized Mean ( 20 / 24 )80.17763888888890.04200170140359061908.91407275313
Winsorized Mean ( 21 / 24 )80.17472222222220.03921070455139982044.71516488882
Winsorized Mean ( 22 / 24 )80.18694444444440.0374555756106182140.8546828396
Winsorized Mean ( 23 / 24 )80.18694444444440.03659277600065142191.3326401642
Winsorized Mean ( 24 / 24 )80.20027777777780.03473067189833032309.20605315538
Trimmed Mean ( 1 / 24 )80.20971428571430.0831018660558825965.197511109759
Trimmed Mean ( 2 / 24 )80.20.07983906111936331004.52083072592
Trimmed Mean ( 3 / 24 )80.19075757575760.07709084357725441040.21118273789
Trimmed Mean ( 4 / 24 )80.18468750.07503833965483751068.58291199985
Trimmed Mean ( 5 / 24 )80.180.07307443522207241097.23735471008
Trimmed Mean ( 6 / 24 )80.17483333333330.07097882698011221129.55985248668
Trimmed Mean ( 7 / 24 )80.16931034482760.06840630813512671171.95785784061
Trimmed Mean ( 8 / 24 )80.163750.06575908534335631219.05208354755
Trimmed Mean ( 9 / 24 )80.16370370370370.06427105440555861247.27537839757
Trimmed Mean ( 10 / 24 )80.16442307692310.06309477982720391270.5397070323
Trimmed Mean ( 11 / 24 )80.1650.06164033267467751300.52834761764
Trimmed Mean ( 12 / 24 )80.16729166666670.06042384250611111326.74931519886
Trimmed Mean ( 13 / 24 )80.17043478260870.05910684383053841356.36467094167
Trimmed Mean ( 14 / 24 )80.17318181818180.05757591984695821392.47765439595
Trimmed Mean ( 15 / 24 )80.17642857142860.05588359129186441434.70429723619
Trimmed Mean ( 16 / 24 )80.179750.05384865722202741488.98327528215
Trimmed Mean ( 17 / 24 )80.18473684210530.05196390152274851543.08538220523
Trimmed Mean ( 18 / 24 )80.19250.04991480837625351606.58735571047
Trimmed Mean ( 19 / 24 )80.20.04770676921441041681.10314994407
Trimmed Mean ( 20 / 24 )80.20593750.0458254476048571750.24886154083
Trimmed Mean ( 21 / 24 )80.20933333333330.0446337157581071797.05704467961
Trimmed Mean ( 22 / 24 )80.21357142857140.04359570838822911839.94192075634
Trimmed Mean ( 23 / 24 )80.21692307692310.04249079259817721887.86600983207
Trimmed Mean ( 24 / 24 )80.22083333333330.04090868528076861960.97314745643
Median80.23
Midrange80.45
Midmean - Weighted Average at Xnp80.1555263157895
Midmean - Weighted Average at X(n+1)p80.1925
Midmean - Empirical Distribution Function80.1555263157895
Midmean - Empirical Distribution Function - Averaging80.1925
Midmean - Empirical Distribution Function - Interpolation80.1925
Midmean - Closest Observation80.1555263157895
Midmean - True Basic - Statistics Graphics Toolkit80.1925
Midmean - MS Excel (old versions)80.1669230769231
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 80.2163888888889 & 0.0864567939068913 & 927.820536293274 \tabularnewline
Geometric Mean & 80.2130887502441 &  &  \tabularnewline
Harmonic Mean & 80.2097964437026 &  &  \tabularnewline
Quadratic Mean & 80.2196968054327 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 80.2188888888889 & 0.0858282749673071 & 934.644077600827 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 80.2169444444445 & 0.0840354550354086 & 954.56071976578 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 80.2069444444444 & 0.0813692579421918 & 985.715569649497 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 80.2008333333333 & 0.0799918692073146 & 1002.61231707784 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 80.2015277777778 & 0.079067496502778 & 1014.34257217136 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 80.2015277777778 & 0.079067496502778 & 1014.34257217136 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 80.1995833333333 & 0.0771817351870173 & 1039.10054806365 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 80.1640277777778 & 0.070336676300141 & 1139.71873558116 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 80.1590277777778 & 0.0673721938836354 & 1189.7939365939 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 80.1604166666667 & 0.0671381326347227 & 1193.96255929241 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 80.1481944444444 & 0.0642137734497887 & 1248.14646669403 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 80.1431944444444 & 0.0629369938524509 & 1273.38770949772 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 80.1486111111111 & 0.0620323838755079 & 1292.04467253685 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 80.1466666666667 & 0.0605365291497815 & 1323.93891411192 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 80.14875 & 0.0595529568978226 & 1345.83997462149 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 80.1376388888889 & 0.0559662222967329 & 1431.89294542696 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 80.11875 & 0.0534779939165012 & 1498.16296634266 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 80.12875 & 0.0511112572929459 & 1567.73192920572 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 80.1498611111111 & 0.046993528778838 & 1705.55102359549 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 80.1776388888889 & 0.0420017014035906 & 1908.91407275313 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 80.1747222222222 & 0.0392107045513998 & 2044.71516488882 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 80.1869444444444 & 0.037455575610618 & 2140.8546828396 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 80.1869444444444 & 0.0365927760006514 & 2191.3326401642 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 80.2002777777778 & 0.0347306718983303 & 2309.20605315538 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 80.2097142857143 & 0.0831018660558825 & 965.197511109759 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 80.2 & 0.0798390611193633 & 1004.52083072592 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 80.1907575757576 & 0.0770908435772544 & 1040.21118273789 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 80.1846875 & 0.0750383396548375 & 1068.58291199985 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 80.18 & 0.0730744352220724 & 1097.23735471008 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 80.1748333333333 & 0.0709788269801122 & 1129.55985248668 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 80.1693103448276 & 0.0684063081351267 & 1171.95785784061 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 80.16375 & 0.0657590853433563 & 1219.05208354755 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 80.1637037037037 & 0.0642710544055586 & 1247.27537839757 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 80.1644230769231 & 0.0630947798272039 & 1270.5397070323 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 80.165 & 0.0616403326746775 & 1300.52834761764 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 80.1672916666667 & 0.0604238425061111 & 1326.74931519886 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 80.1704347826087 & 0.0591068438305384 & 1356.36467094167 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 80.1731818181818 & 0.0575759198469582 & 1392.47765439595 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 80.1764285714286 & 0.0558835912918644 & 1434.70429723619 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 80.17975 & 0.0538486572220274 & 1488.98327528215 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 80.1847368421053 & 0.0519639015227485 & 1543.08538220523 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 80.1925 & 0.0499148083762535 & 1606.58735571047 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 80.2 & 0.0477067692144104 & 1681.10314994407 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 80.2059375 & 0.045825447604857 & 1750.24886154083 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 80.2093333333333 & 0.044633715758107 & 1797.05704467961 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 80.2135714285714 & 0.0435957083882291 & 1839.94192075634 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 80.2169230769231 & 0.0424907925981772 & 1887.86600983207 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 80.2208333333333 & 0.0409086852807686 & 1960.97314745643 \tabularnewline
Median & 80.23 &  &  \tabularnewline
Midrange & 80.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 80.1555263157895 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 80.1925 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 80.1555263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 80.1925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 80.1925 &  &  \tabularnewline
Midmean - Closest Observation & 80.1555263157895 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 80.1925 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 80.1669230769231 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240754&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]80.2163888888889[/C][C]0.0864567939068913[/C][C]927.820536293274[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]80.2130887502441[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]80.2097964437026[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]80.2196968054327[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]80.2188888888889[/C][C]0.0858282749673071[/C][C]934.644077600827[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]80.2169444444445[/C][C]0.0840354550354086[/C][C]954.56071976578[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]80.2069444444444[/C][C]0.0813692579421918[/C][C]985.715569649497[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]80.2008333333333[/C][C]0.0799918692073146[/C][C]1002.61231707784[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]80.2015277777778[/C][C]0.079067496502778[/C][C]1014.34257217136[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]80.2015277777778[/C][C]0.079067496502778[/C][C]1014.34257217136[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]80.1995833333333[/C][C]0.0771817351870173[/C][C]1039.10054806365[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]80.1640277777778[/C][C]0.070336676300141[/C][C]1139.71873558116[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]80.1590277777778[/C][C]0.0673721938836354[/C][C]1189.7939365939[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]80.1604166666667[/C][C]0.0671381326347227[/C][C]1193.96255929241[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]80.1481944444444[/C][C]0.0642137734497887[/C][C]1248.14646669403[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]80.1431944444444[/C][C]0.0629369938524509[/C][C]1273.38770949772[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]80.1486111111111[/C][C]0.0620323838755079[/C][C]1292.04467253685[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]80.1466666666667[/C][C]0.0605365291497815[/C][C]1323.93891411192[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]80.14875[/C][C]0.0595529568978226[/C][C]1345.83997462149[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]80.1376388888889[/C][C]0.0559662222967329[/C][C]1431.89294542696[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]80.11875[/C][C]0.0534779939165012[/C][C]1498.16296634266[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]80.12875[/C][C]0.0511112572929459[/C][C]1567.73192920572[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]80.1498611111111[/C][C]0.046993528778838[/C][C]1705.55102359549[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]80.1776388888889[/C][C]0.0420017014035906[/C][C]1908.91407275313[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]80.1747222222222[/C][C]0.0392107045513998[/C][C]2044.71516488882[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]80.1869444444444[/C][C]0.037455575610618[/C][C]2140.8546828396[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]80.1869444444444[/C][C]0.0365927760006514[/C][C]2191.3326401642[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]80.2002777777778[/C][C]0.0347306718983303[/C][C]2309.20605315538[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]80.2097142857143[/C][C]0.0831018660558825[/C][C]965.197511109759[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]80.2[/C][C]0.0798390611193633[/C][C]1004.52083072592[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]80.1907575757576[/C][C]0.0770908435772544[/C][C]1040.21118273789[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]80.1846875[/C][C]0.0750383396548375[/C][C]1068.58291199985[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]80.18[/C][C]0.0730744352220724[/C][C]1097.23735471008[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]80.1748333333333[/C][C]0.0709788269801122[/C][C]1129.55985248668[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]80.1693103448276[/C][C]0.0684063081351267[/C][C]1171.95785784061[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]80.16375[/C][C]0.0657590853433563[/C][C]1219.05208354755[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]80.1637037037037[/C][C]0.0642710544055586[/C][C]1247.27537839757[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]80.1644230769231[/C][C]0.0630947798272039[/C][C]1270.5397070323[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]80.165[/C][C]0.0616403326746775[/C][C]1300.52834761764[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]80.1672916666667[/C][C]0.0604238425061111[/C][C]1326.74931519886[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]80.1704347826087[/C][C]0.0591068438305384[/C][C]1356.36467094167[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]80.1731818181818[/C][C]0.0575759198469582[/C][C]1392.47765439595[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]80.1764285714286[/C][C]0.0558835912918644[/C][C]1434.70429723619[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]80.17975[/C][C]0.0538486572220274[/C][C]1488.98327528215[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]80.1847368421053[/C][C]0.0519639015227485[/C][C]1543.08538220523[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]80.1925[/C][C]0.0499148083762535[/C][C]1606.58735571047[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]80.2[/C][C]0.0477067692144104[/C][C]1681.10314994407[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]80.2059375[/C][C]0.045825447604857[/C][C]1750.24886154083[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]80.2093333333333[/C][C]0.044633715758107[/C][C]1797.05704467961[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]80.2135714285714[/C][C]0.0435957083882291[/C][C]1839.94192075634[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]80.2169230769231[/C][C]0.0424907925981772[/C][C]1887.86600983207[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]80.2208333333333[/C][C]0.0409086852807686[/C][C]1960.97314745643[/C][/ROW]
[ROW][C]Median[/C][C]80.23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]80.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]80.1555263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]80.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]80.1555263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]80.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]80.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]80.1555263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]80.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]80.1669230769231[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240754&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 Mean80.21638888888890.0864567939068913927.820536293274
Geometric Mean80.2130887502441
Harmonic Mean80.2097964437026
Quadratic Mean80.2196968054327
Winsorized Mean ( 1 / 24 )80.21888888888890.0858282749673071934.644077600827
Winsorized Mean ( 2 / 24 )80.21694444444450.0840354550354086954.56071976578
Winsorized Mean ( 3 / 24 )80.20694444444440.0813692579421918985.715569649497
Winsorized Mean ( 4 / 24 )80.20083333333330.07999186920731461002.61231707784
Winsorized Mean ( 5 / 24 )80.20152777777780.0790674965027781014.34257217136
Winsorized Mean ( 6 / 24 )80.20152777777780.0790674965027781014.34257217136
Winsorized Mean ( 7 / 24 )80.19958333333330.07718173518701731039.10054806365
Winsorized Mean ( 8 / 24 )80.16402777777780.0703366763001411139.71873558116
Winsorized Mean ( 9 / 24 )80.15902777777780.06737219388363541189.7939365939
Winsorized Mean ( 10 / 24 )80.16041666666670.06713813263472271193.96255929241
Winsorized Mean ( 11 / 24 )80.14819444444440.06421377344978871248.14646669403
Winsorized Mean ( 12 / 24 )80.14319444444440.06293699385245091273.38770949772
Winsorized Mean ( 13 / 24 )80.14861111111110.06203238387550791292.04467253685
Winsorized Mean ( 14 / 24 )80.14666666666670.06053652914978151323.93891411192
Winsorized Mean ( 15 / 24 )80.148750.05955295689782261345.83997462149
Winsorized Mean ( 16 / 24 )80.13763888888890.05596622229673291431.89294542696
Winsorized Mean ( 17 / 24 )80.118750.05347799391650121498.16296634266
Winsorized Mean ( 18 / 24 )80.128750.05111125729294591567.73192920572
Winsorized Mean ( 19 / 24 )80.14986111111110.0469935287788381705.55102359549
Winsorized Mean ( 20 / 24 )80.17763888888890.04200170140359061908.91407275313
Winsorized Mean ( 21 / 24 )80.17472222222220.03921070455139982044.71516488882
Winsorized Mean ( 22 / 24 )80.18694444444440.0374555756106182140.8546828396
Winsorized Mean ( 23 / 24 )80.18694444444440.03659277600065142191.3326401642
Winsorized Mean ( 24 / 24 )80.20027777777780.03473067189833032309.20605315538
Trimmed Mean ( 1 / 24 )80.20971428571430.0831018660558825965.197511109759
Trimmed Mean ( 2 / 24 )80.20.07983906111936331004.52083072592
Trimmed Mean ( 3 / 24 )80.19075757575760.07709084357725441040.21118273789
Trimmed Mean ( 4 / 24 )80.18468750.07503833965483751068.58291199985
Trimmed Mean ( 5 / 24 )80.180.07307443522207241097.23735471008
Trimmed Mean ( 6 / 24 )80.17483333333330.07097882698011221129.55985248668
Trimmed Mean ( 7 / 24 )80.16931034482760.06840630813512671171.95785784061
Trimmed Mean ( 8 / 24 )80.163750.06575908534335631219.05208354755
Trimmed Mean ( 9 / 24 )80.16370370370370.06427105440555861247.27537839757
Trimmed Mean ( 10 / 24 )80.16442307692310.06309477982720391270.5397070323
Trimmed Mean ( 11 / 24 )80.1650.06164033267467751300.52834761764
Trimmed Mean ( 12 / 24 )80.16729166666670.06042384250611111326.74931519886
Trimmed Mean ( 13 / 24 )80.17043478260870.05910684383053841356.36467094167
Trimmed Mean ( 14 / 24 )80.17318181818180.05757591984695821392.47765439595
Trimmed Mean ( 15 / 24 )80.17642857142860.05588359129186441434.70429723619
Trimmed Mean ( 16 / 24 )80.179750.05384865722202741488.98327528215
Trimmed Mean ( 17 / 24 )80.18473684210530.05196390152274851543.08538220523
Trimmed Mean ( 18 / 24 )80.19250.04991480837625351606.58735571047
Trimmed Mean ( 19 / 24 )80.20.04770676921441041681.10314994407
Trimmed Mean ( 20 / 24 )80.20593750.0458254476048571750.24886154083
Trimmed Mean ( 21 / 24 )80.20933333333330.0446337157581071797.05704467961
Trimmed Mean ( 22 / 24 )80.21357142857140.04359570838822911839.94192075634
Trimmed Mean ( 23 / 24 )80.21692307692310.04249079259817721887.86600983207
Trimmed Mean ( 24 / 24 )80.22083333333330.04090868528076861960.97314745643
Median80.23
Midrange80.45
Midmean - Weighted Average at Xnp80.1555263157895
Midmean - Weighted Average at X(n+1)p80.1925
Midmean - Empirical Distribution Function80.1555263157895
Midmean - Empirical Distribution Function - Averaging80.1925
Midmean - Empirical Distribution Function - Interpolation80.1925
Midmean - Closest Observation80.1555263157895
Midmean - True Basic - Statistics Graphics Toolkit80.1925
Midmean - MS Excel (old versions)80.1669230769231
Number of observations72



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')