FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 15:13:26 -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/2008/Dec/21/t1229898074yy1kdjtg4r1z5f5.htm/, Retrieved Sat, 18 May 2024 18:53:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35878, Retrieved Sat, 18 May 2024 18:53:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [] [2008-12-21 22:13:26] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
116,51
116,26
116,21
116,02
115,92
115,76
115,54
115,37
115,29
115,05
114,97
114,73
114,38
114,28
114,25
114,02
113,88
113,81
113,65
113,68
113,38
113,33
113,1
112,99
112,73
112,78
112,59
112,47
112,3
112,12
112,04
111,89
111,76
111,62
111,41
111,28
111,09
110,94
110,72
110,57
110,49
110,2
110,01
109,91
109,65
109,41
109,23
108,92
108,5
108,3
108,2
107,9
107,7
107,6
107,4
107,3
107,1
107
106,8
106,6

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35878&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35878&T=0

As an alternative you can also use a QR Code:  
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'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.8151666666670.373413744240818299.440415333389
Geometric Mean111.778239963061
Harmonic Mean111.741181275991
Quadratic Mean111.851948254527
Winsorized Mean ( 1 / 20 )111.8143333333330.371771934118374300.760555254101
Winsorized Mean ( 2 / 20 )111.8193333333330.369937303182921302.265633585058
Winsorized Mean ( 3 / 20 )111.8148333333330.366962604636367304.703618081558
Winsorized Mean ( 4 / 20 )111.82150.362816728960448308.203814968493
Winsorized Mean ( 5 / 20 )111.81650.358547274853798311.859851802233
Winsorized Mean ( 6 / 20 )111.81450.350386584324481319.117526190593
Winsorized Mean ( 7 / 20 )111.8063333333330.344492500444529324.553751356154
Winsorized Mean ( 8 / 20 )111.8223333333330.337305655839616331.516330655609
Winsorized Mean ( 9 / 20 )111.8313333333330.322388023451218346.884267399763
Winsorized Mean ( 10 / 20 )111.8346666666670.316976042747844352.817410732936
Winsorized Mean ( 11 / 20 )111.8273333333330.302830607184667369.273549899600
Winsorized Mean ( 12 / 20 )111.8413333333330.276322548227852404.74921084294
Winsorized Mean ( 13 / 20 )111.8868333333330.261137396100567428.459634675397
Winsorized Mean ( 14 / 20 )111.9218333333330.252889682706879442.571765424929
Winsorized Mean ( 15 / 20 )111.9243333333330.234039613077876478.228159162487
Winsorized Mean ( 16 / 20 )111.9563333333330.217149349353551515.572962417917
Winsorized Mean ( 17 / 20 )111.9648333333330.209679401722228533.981079751737
Winsorized Mean ( 18 / 20 )111.9828333333330.19496908224643574.362006750349
Winsorized Mean ( 19 / 20 )112.0651666666670.179604476254831623.955310042848
Winsorized Mean ( 20 / 20 )112.0018333333330.162415643757305689.600033237535
Trimmed Mean ( 1 / 20 )111.8241379310340.366622312211654305.011817901791
Trimmed Mean ( 2 / 20 )111.8346428571430.360122991642386310.545689813102
Trimmed Mean ( 3 / 20 )111.8431481481480.353142706387034316.708078987115
Trimmed Mean ( 4 / 20 )111.8540384615380.345718071393496323.541196474588
Trimmed Mean ( 5 / 20 )111.86380.337876669927997331.078792814664
Trimmed Mean ( 6 / 20 )111.8756250.329262137997397339.776767776696
Trimmed Mean ( 7 / 20 )111.8889130434780.320675800325022348.915985958631
Trimmed Mean ( 8 / 20 )111.9050.311162911179769359.634763589639
Trimmed Mean ( 9 / 20 )111.9197619047620.300677224016752372.22560594921
Trimmed Mean ( 10 / 20 )111.93450.290927771016653384.750137839515
Trimmed Mean ( 11 / 20 )111.9502631578950.279202656337886400.964176438259
Trimmed Mean ( 12 / 20 )111.9688888888890.267201480896529419.042920395519
Trimmed Mean ( 13 / 20 )111.9876470588240.258265522290905433.614390590947
Trimmed Mean ( 14 / 20 )112.00218750.249944241513837448.108693449532
Trimmed Mean ( 15 / 20 )112.0136666666670.240201775014896466.331552544607
Trimmed Mean ( 16 / 20 )112.0264285714290.231681919268202483.535482290889
Trimmed Mean ( 17 / 20 )112.0365384615380.224162676031144499.800147130526
Trimmed Mean ( 18 / 20 )112.0470833333330.214539850666851522.266996015235
Trimmed Mean ( 19 / 20 )112.0568181818180.204531336694126547.871147732231
Trimmed Mean ( 20 / 20 )112.05550.194217017791953576.960254430611
Median112.08
Midrange111.555
Midmean - Weighted Average at Xnp111.929677419355
Midmean - Weighted Average at X(n+1)p112.013666666667
Midmean - Empirical Distribution Function111.929677419355
Midmean - Empirical Distribution Function - Averaging112.013666666667
Midmean - Empirical Distribution Function - Interpolation112.013666666667
Midmean - Closest Observation111.929677419355
Midmean - True Basic - Statistics Graphics Toolkit112.013666666667
Midmean - MS Excel (old versions)112.0021875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.815166666667 & 0.373413744240818 & 299.440415333389 \tabularnewline
Geometric Mean & 111.778239963061 &  &  \tabularnewline
Harmonic Mean & 111.741181275991 &  &  \tabularnewline
Quadratic Mean & 111.851948254527 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.814333333333 & 0.371771934118374 & 300.760555254101 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 111.819333333333 & 0.369937303182921 & 302.265633585058 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 111.814833333333 & 0.366962604636367 & 304.703618081558 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 111.8215 & 0.362816728960448 & 308.203814968493 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.8165 & 0.358547274853798 & 311.859851802233 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.8145 & 0.350386584324481 & 319.117526190593 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.806333333333 & 0.344492500444529 & 324.553751356154 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.822333333333 & 0.337305655839616 & 331.516330655609 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.831333333333 & 0.322388023451218 & 346.884267399763 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.834666666667 & 0.316976042747844 & 352.817410732936 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.827333333333 & 0.302830607184667 & 369.273549899600 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.841333333333 & 0.276322548227852 & 404.74921084294 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.886833333333 & 0.261137396100567 & 428.459634675397 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.921833333333 & 0.252889682706879 & 442.571765424929 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.924333333333 & 0.234039613077876 & 478.228159162487 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.956333333333 & 0.217149349353551 & 515.572962417917 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111.964833333333 & 0.209679401722228 & 533.981079751737 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.982833333333 & 0.19496908224643 & 574.362006750349 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 112.065166666667 & 0.179604476254831 & 623.955310042848 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 112.001833333333 & 0.162415643757305 & 689.600033237535 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 111.824137931034 & 0.366622312211654 & 305.011817901791 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 111.834642857143 & 0.360122991642386 & 310.545689813102 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 111.843148148148 & 0.353142706387034 & 316.708078987115 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.854038461538 & 0.345718071393496 & 323.541196474588 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.8638 & 0.337876669927997 & 331.078792814664 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.875625 & 0.329262137997397 & 339.776767776696 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.888913043478 & 0.320675800325022 & 348.915985958631 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.905 & 0.311162911179769 & 359.634763589639 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.919761904762 & 0.300677224016752 & 372.22560594921 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.9345 & 0.290927771016653 & 384.750137839515 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.950263157895 & 0.279202656337886 & 400.964176438259 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.968888888889 & 0.267201480896529 & 419.042920395519 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.987647058824 & 0.258265522290905 & 433.614390590947 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 112.0021875 & 0.249944241513837 & 448.108693449532 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 112.013666666667 & 0.240201775014896 & 466.331552544607 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 112.026428571429 & 0.231681919268202 & 483.535482290889 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 112.036538461538 & 0.224162676031144 & 499.800147130526 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 112.047083333333 & 0.214539850666851 & 522.266996015235 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 112.056818181818 & 0.204531336694126 & 547.871147732231 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 112.0555 & 0.194217017791953 & 576.960254430611 \tabularnewline
Median & 112.08 &  &  \tabularnewline
Midrange & 111.555 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.929677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.013666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.929677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.013666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.013666666667 &  &  \tabularnewline
Midmean - Closest Observation & 111.929677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.013666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.0021875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35878&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]111.815166666667[/C][C]0.373413744240818[/C][C]299.440415333389[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.778239963061[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.741181275991[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.851948254527[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.814333333333[/C][C]0.371771934118374[/C][C]300.760555254101[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]111.819333333333[/C][C]0.369937303182921[/C][C]302.265633585058[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]111.814833333333[/C][C]0.366962604636367[/C][C]304.703618081558[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]111.8215[/C][C]0.362816728960448[/C][C]308.203814968493[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.8165[/C][C]0.358547274853798[/C][C]311.859851802233[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.8145[/C][C]0.350386584324481[/C][C]319.117526190593[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.806333333333[/C][C]0.344492500444529[/C][C]324.553751356154[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.822333333333[/C][C]0.337305655839616[/C][C]331.516330655609[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.831333333333[/C][C]0.322388023451218[/C][C]346.884267399763[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.834666666667[/C][C]0.316976042747844[/C][C]352.817410732936[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.827333333333[/C][C]0.302830607184667[/C][C]369.273549899600[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.841333333333[/C][C]0.276322548227852[/C][C]404.74921084294[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.886833333333[/C][C]0.261137396100567[/C][C]428.459634675397[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.921833333333[/C][C]0.252889682706879[/C][C]442.571765424929[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.924333333333[/C][C]0.234039613077876[/C][C]478.228159162487[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.956333333333[/C][C]0.217149349353551[/C][C]515.572962417917[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111.964833333333[/C][C]0.209679401722228[/C][C]533.981079751737[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.982833333333[/C][C]0.19496908224643[/C][C]574.362006750349[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]112.065166666667[/C][C]0.179604476254831[/C][C]623.955310042848[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]112.001833333333[/C][C]0.162415643757305[/C][C]689.600033237535[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]111.824137931034[/C][C]0.366622312211654[/C][C]305.011817901791[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]111.834642857143[/C][C]0.360122991642386[/C][C]310.545689813102[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]111.843148148148[/C][C]0.353142706387034[/C][C]316.708078987115[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.854038461538[/C][C]0.345718071393496[/C][C]323.541196474588[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.8638[/C][C]0.337876669927997[/C][C]331.078792814664[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.875625[/C][C]0.329262137997397[/C][C]339.776767776696[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.888913043478[/C][C]0.320675800325022[/C][C]348.915985958631[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.905[/C][C]0.311162911179769[/C][C]359.634763589639[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.919761904762[/C][C]0.300677224016752[/C][C]372.22560594921[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.9345[/C][C]0.290927771016653[/C][C]384.750137839515[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.950263157895[/C][C]0.279202656337886[/C][C]400.964176438259[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.968888888889[/C][C]0.267201480896529[/C][C]419.042920395519[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.987647058824[/C][C]0.258265522290905[/C][C]433.614390590947[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]112.0021875[/C][C]0.249944241513837[/C][C]448.108693449532[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]112.013666666667[/C][C]0.240201775014896[/C][C]466.331552544607[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]112.026428571429[/C][C]0.231681919268202[/C][C]483.535482290889[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]112.036538461538[/C][C]0.224162676031144[/C][C]499.800147130526[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]112.047083333333[/C][C]0.214539850666851[/C][C]522.266996015235[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]112.056818181818[/C][C]0.204531336694126[/C][C]547.871147732231[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]112.0555[/C][C]0.194217017791953[/C][C]576.960254430611[/C][/ROW]
[ROW][C]Median[/C][C]112.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.929677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.013666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.929677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.013666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.013666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.929677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.013666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.0021875[/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=35878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35878&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.8151666666670.373413744240818299.440415333389
Geometric Mean111.778239963061
Harmonic Mean111.741181275991
Quadratic Mean111.851948254527
Winsorized Mean ( 1 / 20 )111.8143333333330.371771934118374300.760555254101
Winsorized Mean ( 2 / 20 )111.8193333333330.369937303182921302.265633585058
Winsorized Mean ( 3 / 20 )111.8148333333330.366962604636367304.703618081558
Winsorized Mean ( 4 / 20 )111.82150.362816728960448308.203814968493
Winsorized Mean ( 5 / 20 )111.81650.358547274853798311.859851802233
Winsorized Mean ( 6 / 20 )111.81450.350386584324481319.117526190593
Winsorized Mean ( 7 / 20 )111.8063333333330.344492500444529324.553751356154
Winsorized Mean ( 8 / 20 )111.8223333333330.337305655839616331.516330655609
Winsorized Mean ( 9 / 20 )111.8313333333330.322388023451218346.884267399763
Winsorized Mean ( 10 / 20 )111.8346666666670.316976042747844352.817410732936
Winsorized Mean ( 11 / 20 )111.8273333333330.302830607184667369.273549899600
Winsorized Mean ( 12 / 20 )111.8413333333330.276322548227852404.74921084294
Winsorized Mean ( 13 / 20 )111.8868333333330.261137396100567428.459634675397
Winsorized Mean ( 14 / 20 )111.9218333333330.252889682706879442.571765424929
Winsorized Mean ( 15 / 20 )111.9243333333330.234039613077876478.228159162487
Winsorized Mean ( 16 / 20 )111.9563333333330.217149349353551515.572962417917
Winsorized Mean ( 17 / 20 )111.9648333333330.209679401722228533.981079751737
Winsorized Mean ( 18 / 20 )111.9828333333330.19496908224643574.362006750349
Winsorized Mean ( 19 / 20 )112.0651666666670.179604476254831623.955310042848
Winsorized Mean ( 20 / 20 )112.0018333333330.162415643757305689.600033237535
Trimmed Mean ( 1 / 20 )111.8241379310340.366622312211654305.011817901791
Trimmed Mean ( 2 / 20 )111.8346428571430.360122991642386310.545689813102
Trimmed Mean ( 3 / 20 )111.8431481481480.353142706387034316.708078987115
Trimmed Mean ( 4 / 20 )111.8540384615380.345718071393496323.541196474588
Trimmed Mean ( 5 / 20 )111.86380.337876669927997331.078792814664
Trimmed Mean ( 6 / 20 )111.8756250.329262137997397339.776767776696
Trimmed Mean ( 7 / 20 )111.8889130434780.320675800325022348.915985958631
Trimmed Mean ( 8 / 20 )111.9050.311162911179769359.634763589639
Trimmed Mean ( 9 / 20 )111.9197619047620.300677224016752372.22560594921
Trimmed Mean ( 10 / 20 )111.93450.290927771016653384.750137839515
Trimmed Mean ( 11 / 20 )111.9502631578950.279202656337886400.964176438259
Trimmed Mean ( 12 / 20 )111.9688888888890.267201480896529419.042920395519
Trimmed Mean ( 13 / 20 )111.9876470588240.258265522290905433.614390590947
Trimmed Mean ( 14 / 20 )112.00218750.249944241513837448.108693449532
Trimmed Mean ( 15 / 20 )112.0136666666670.240201775014896466.331552544607
Trimmed Mean ( 16 / 20 )112.0264285714290.231681919268202483.535482290889
Trimmed Mean ( 17 / 20 )112.0365384615380.224162676031144499.800147130526
Trimmed Mean ( 18 / 20 )112.0470833333330.214539850666851522.266996015235
Trimmed Mean ( 19 / 20 )112.0568181818180.204531336694126547.871147732231
Trimmed Mean ( 20 / 20 )112.05550.194217017791953576.960254430611
Median112.08
Midrange111.555
Midmean - Weighted Average at Xnp111.929677419355
Midmean - Weighted Average at X(n+1)p112.013666666667
Midmean - Empirical Distribution Function111.929677419355
Midmean - Empirical Distribution Function - Averaging112.013666666667
Midmean - Empirical Distribution Function - Interpolation112.013666666667
Midmean - Closest Observation111.929677419355
Midmean - True Basic - Statistics Graphics Toolkit112.013666666667
Midmean - MS Excel (old versions)112.0021875
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')