Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 10:10:11 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/18/t1318947121dnlykc7gn4oukj1.htm/, Retrieved Thu, 16 May 2024 06:22:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=131955, Retrieved Thu, 16 May 2024 06:22:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-18 14:10:11] [307fb8dee51f98edb4f1db3243dd69bf] [Current]
Feedback Forum

Post a new message
Dataseries X:
5,51
5,54
5,56
5,57
5,57
5,58
5,56
5,57
5,57
5,6
5,61
5,63
5,65
5,71
5,78
5,8
5,8
5,8
5,81
5,84
5,83
5,86
5,88
5,88
5,89
5,91
5,91
5,95
5,92
5,92
5,91
5,95
6,01
6,07
6,08
6,1
6,11
6,13
6,21
6,19
6,17
6,17
6,19
6,21
6,32
6,36
6,36
6,38
6,36
6,42
6,42
6,44
6,41
6,42
6,43
6,44
6,43
6,43
6,45
6,45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=131955&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=131955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131955&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.00050.0401989578806375149.270038736259
Geometric Mean5.99255365150642
Harmonic Mean5.98461393236334
Quadratic Mean6.00843920387539
Winsorized Mean ( 1 / 20 )6.0010.0400985368232711149.656333507843
Winsorized Mean ( 2 / 20 )6.001333333333330.0399084168137504150.37763490697
Winsorized Mean ( 3 / 20 )6.001333333333330.0399084168137504150.37763490697
Winsorized Mean ( 4 / 20 )6.001333333333330.0396613251875285151.314493526314
Winsorized Mean ( 5 / 20 )6.001333333333330.0396613251875285151.314493526314
Winsorized Mean ( 6 / 20 )6.001333333333330.0396613251875285151.314493526314
Winsorized Mean ( 7 / 20 )6.000166666666670.0394492391186866152.09841306735
Winsorized Mean ( 8 / 20 )6.00150.0392045375270754153.081770084783
Winsorized Mean ( 9 / 20 )6.00450.0386651750637685155.294783745246
Winsorized Mean ( 10 / 20 )6.00450.0380687936615735157.727614207563
Winsorized Mean ( 11 / 20 )6.002666666666670.036449691873386164.683605214494
Winsorized Mean ( 12 / 20 )6.002666666666670.035065609745409171.183866764289
Winsorized Mean ( 13 / 20 )6.015666666666670.0329323623453008182.667328981489
Winsorized Mean ( 14 / 20 )6.0320.0304984949151658197.78025167401
Winsorized Mean ( 15 / 20 )6.0270.0280055482799976215.207356047539
Winsorized Mean ( 16 / 20 )5.997666666666670.0230883425799366259.770342799684
Winsorized Mean ( 17 / 20 )5.997666666666670.0230883425799366259.770342799684
Winsorized Mean ( 18 / 20 )5.994666666666670.0217295480395651275.876270217475
Winsorized Mean ( 19 / 20 )6.0010.0208325310579988288.059092929846
Winsorized Mean ( 20 / 20 )5.997666666666670.0193545081781306309.884736489644
Trimmed Mean ( 1 / 20 )6.001206896551720.0399554179763252150.197575210141
Trimmed Mean ( 2 / 20 )6.001428571428570.0397381270117812151.024444852404
Trimmed Mean ( 3 / 20 )6.001481481481480.0395488246641235151.748668448438
Trimmed Mean ( 4 / 20 )6.001538461538460.039267793725728152.836151260678
Trimmed Mean ( 5 / 20 )6.00160.0389634679762299154.031463617698
Trimmed Mean ( 6 / 20 )6.001666666666670.0385328603126873155.754507139211
Trimmed Mean ( 7 / 20 )6.001739130434780.0379413536105345158.184633896888
Trimmed Mean ( 8 / 20 )6.002045454545450.0372020645859351161.336353811252
Trimmed Mean ( 9 / 20 )6.002142857142860.036273153468077165.470665858296
Trimmed Mean ( 10 / 20 )6.001750.0351678894549836170.65994272083
Trimmed Mean ( 11 / 20 )6.001315789473680.0338311661438133177.390154509089
Trimmed Mean ( 12 / 20 )6.001111111111110.0324643339774536184.852432681319
Trimmed Mean ( 13 / 20 )6.000882352941180.0309659339217607193.789806827824
Trimmed Mean ( 14 / 20 )5.998750.0294805499029554203.481618210881
Trimmed Mean ( 15 / 20 )5.9940.0280213383388241213.908412493461
Trimmed Mean ( 16 / 20 )5.989285714285710.026691102749538224.392591437212
Trimmed Mean ( 17 / 20 )5.988076923076920.0264285348746635226.576196958144
Trimmed Mean ( 18 / 20 )5.986666666666670.0258666218436785231.443700025705
Trimmed Mean ( 19 / 20 )5.985454545454550.0253437601525467236.170738257759
Trimmed Mean ( 20 / 20 )5.9830.0246352336469964242.863537879595
Median5.935
Midrange5.98
Midmean - Weighted Average at Xnp5.98709677419355
Midmean - Weighted Average at X(n+1)p5.994
Midmean - Empirical Distribution Function5.98709677419355
Midmean - Empirical Distribution Function - Averaging5.994
Midmean - Empirical Distribution Function - Interpolation5.994
Midmean - Closest Observation5.98709677419355
Midmean - True Basic - Statistics Graphics Toolkit5.994
Midmean - MS Excel (old versions)6.02
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.0005 & 0.0401989578806375 & 149.270038736259 \tabularnewline
Geometric Mean & 5.99255365150642 &  &  \tabularnewline
Harmonic Mean & 5.98461393236334 &  &  \tabularnewline
Quadratic Mean & 6.00843920387539 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6.001 & 0.0400985368232711 & 149.656333507843 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6.00133333333333 & 0.0399084168137504 & 150.37763490697 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6.00133333333333 & 0.0399084168137504 & 150.37763490697 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6.00133333333333 & 0.0396613251875285 & 151.314493526314 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6.00133333333333 & 0.0396613251875285 & 151.314493526314 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6.00133333333333 & 0.0396613251875285 & 151.314493526314 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6.00016666666667 & 0.0394492391186866 & 152.09841306735 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6.0015 & 0.0392045375270754 & 153.081770084783 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6.0045 & 0.0386651750637685 & 155.294783745246 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6.0045 & 0.0380687936615735 & 157.727614207563 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6.00266666666667 & 0.036449691873386 & 164.683605214494 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6.00266666666667 & 0.035065609745409 & 171.183866764289 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6.01566666666667 & 0.0329323623453008 & 182.667328981489 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6.032 & 0.0304984949151658 & 197.78025167401 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6.027 & 0.0280055482799976 & 215.207356047539 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 5.99766666666667 & 0.0230883425799366 & 259.770342799684 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 5.99766666666667 & 0.0230883425799366 & 259.770342799684 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 5.99466666666667 & 0.0217295480395651 & 275.876270217475 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6.001 & 0.0208325310579988 & 288.059092929846 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 5.99766666666667 & 0.0193545081781306 & 309.884736489644 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6.00120689655172 & 0.0399554179763252 & 150.197575210141 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6.00142857142857 & 0.0397381270117812 & 151.024444852404 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6.00148148148148 & 0.0395488246641235 & 151.748668448438 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6.00153846153846 & 0.039267793725728 & 152.836151260678 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6.0016 & 0.0389634679762299 & 154.031463617698 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6.00166666666667 & 0.0385328603126873 & 155.754507139211 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6.00173913043478 & 0.0379413536105345 & 158.184633896888 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6.00204545454545 & 0.0372020645859351 & 161.336353811252 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6.00214285714286 & 0.036273153468077 & 165.470665858296 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6.00175 & 0.0351678894549836 & 170.65994272083 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6.00131578947368 & 0.0338311661438133 & 177.390154509089 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6.00111111111111 & 0.0324643339774536 & 184.852432681319 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6.00088235294118 & 0.0309659339217607 & 193.789806827824 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 5.99875 & 0.0294805499029554 & 203.481618210881 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 5.994 & 0.0280213383388241 & 213.908412493461 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 5.98928571428571 & 0.026691102749538 & 224.392591437212 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 5.98807692307692 & 0.0264285348746635 & 226.576196958144 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 5.98666666666667 & 0.0258666218436785 & 231.443700025705 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 5.98545454545455 & 0.0253437601525467 & 236.170738257759 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 5.983 & 0.0246352336469964 & 242.863537879595 \tabularnewline
Median & 5.935 &  &  \tabularnewline
Midrange & 5.98 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.98709677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.994 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.98709677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.994 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.994 &  &  \tabularnewline
Midmean - Closest Observation & 5.98709677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.994 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.02 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=131955&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]6.0005[/C][C]0.0401989578806375[/C][C]149.270038736259[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.99255365150642[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5.98461393236334[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.00843920387539[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6.001[/C][C]0.0400985368232711[/C][C]149.656333507843[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6.00133333333333[/C][C]0.0399084168137504[/C][C]150.37763490697[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6.00133333333333[/C][C]0.0399084168137504[/C][C]150.37763490697[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6.00133333333333[/C][C]0.0396613251875285[/C][C]151.314493526314[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6.00133333333333[/C][C]0.0396613251875285[/C][C]151.314493526314[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6.00133333333333[/C][C]0.0396613251875285[/C][C]151.314493526314[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6.00016666666667[/C][C]0.0394492391186866[/C][C]152.09841306735[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6.0015[/C][C]0.0392045375270754[/C][C]153.081770084783[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6.0045[/C][C]0.0386651750637685[/C][C]155.294783745246[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6.0045[/C][C]0.0380687936615735[/C][C]157.727614207563[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6.00266666666667[/C][C]0.036449691873386[/C][C]164.683605214494[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6.00266666666667[/C][C]0.035065609745409[/C][C]171.183866764289[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6.01566666666667[/C][C]0.0329323623453008[/C][C]182.667328981489[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6.032[/C][C]0.0304984949151658[/C][C]197.78025167401[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6.027[/C][C]0.0280055482799976[/C][C]215.207356047539[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]5.99766666666667[/C][C]0.0230883425799366[/C][C]259.770342799684[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]5.99766666666667[/C][C]0.0230883425799366[/C][C]259.770342799684[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]5.99466666666667[/C][C]0.0217295480395651[/C][C]275.876270217475[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6.001[/C][C]0.0208325310579988[/C][C]288.059092929846[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]5.99766666666667[/C][C]0.0193545081781306[/C][C]309.884736489644[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6.00120689655172[/C][C]0.0399554179763252[/C][C]150.197575210141[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6.00142857142857[/C][C]0.0397381270117812[/C][C]151.024444852404[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6.00148148148148[/C][C]0.0395488246641235[/C][C]151.748668448438[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6.00153846153846[/C][C]0.039267793725728[/C][C]152.836151260678[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6.0016[/C][C]0.0389634679762299[/C][C]154.031463617698[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6.00166666666667[/C][C]0.0385328603126873[/C][C]155.754507139211[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6.00173913043478[/C][C]0.0379413536105345[/C][C]158.184633896888[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6.00204545454545[/C][C]0.0372020645859351[/C][C]161.336353811252[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6.00214285714286[/C][C]0.036273153468077[/C][C]165.470665858296[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6.00175[/C][C]0.0351678894549836[/C][C]170.65994272083[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6.00131578947368[/C][C]0.0338311661438133[/C][C]177.390154509089[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6.00111111111111[/C][C]0.0324643339774536[/C][C]184.852432681319[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6.00088235294118[/C][C]0.0309659339217607[/C][C]193.789806827824[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]5.99875[/C][C]0.0294805499029554[/C][C]203.481618210881[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]5.994[/C][C]0.0280213383388241[/C][C]213.908412493461[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]5.98928571428571[/C][C]0.026691102749538[/C][C]224.392591437212[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]5.98807692307692[/C][C]0.0264285348746635[/C][C]226.576196958144[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]5.98666666666667[/C][C]0.0258666218436785[/C][C]231.443700025705[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]5.98545454545455[/C][C]0.0253437601525467[/C][C]236.170738257759[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]5.983[/C][C]0.0246352336469964[/C][C]242.863537879595[/C][/ROW]
[ROW][C]Median[/C][C]5.935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.98709677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.98709677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.98709677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.994[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.02[/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=131955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=131955&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 Mean6.00050.0401989578806375149.270038736259
Geometric Mean5.99255365150642
Harmonic Mean5.98461393236334
Quadratic Mean6.00843920387539
Winsorized Mean ( 1 / 20 )6.0010.0400985368232711149.656333507843
Winsorized Mean ( 2 / 20 )6.001333333333330.0399084168137504150.37763490697
Winsorized Mean ( 3 / 20 )6.001333333333330.0399084168137504150.37763490697
Winsorized Mean ( 4 / 20 )6.001333333333330.0396613251875285151.314493526314
Winsorized Mean ( 5 / 20 )6.001333333333330.0396613251875285151.314493526314
Winsorized Mean ( 6 / 20 )6.001333333333330.0396613251875285151.314493526314
Winsorized Mean ( 7 / 20 )6.000166666666670.0394492391186866152.09841306735
Winsorized Mean ( 8 / 20 )6.00150.0392045375270754153.081770084783
Winsorized Mean ( 9 / 20 )6.00450.0386651750637685155.294783745246
Winsorized Mean ( 10 / 20 )6.00450.0380687936615735157.727614207563
Winsorized Mean ( 11 / 20 )6.002666666666670.036449691873386164.683605214494
Winsorized Mean ( 12 / 20 )6.002666666666670.035065609745409171.183866764289
Winsorized Mean ( 13 / 20 )6.015666666666670.0329323623453008182.667328981489
Winsorized Mean ( 14 / 20 )6.0320.0304984949151658197.78025167401
Winsorized Mean ( 15 / 20 )6.0270.0280055482799976215.207356047539
Winsorized Mean ( 16 / 20 )5.997666666666670.0230883425799366259.770342799684
Winsorized Mean ( 17 / 20 )5.997666666666670.0230883425799366259.770342799684
Winsorized Mean ( 18 / 20 )5.994666666666670.0217295480395651275.876270217475
Winsorized Mean ( 19 / 20 )6.0010.0208325310579988288.059092929846
Winsorized Mean ( 20 / 20 )5.997666666666670.0193545081781306309.884736489644
Trimmed Mean ( 1 / 20 )6.001206896551720.0399554179763252150.197575210141
Trimmed Mean ( 2 / 20 )6.001428571428570.0397381270117812151.024444852404
Trimmed Mean ( 3 / 20 )6.001481481481480.0395488246641235151.748668448438
Trimmed Mean ( 4 / 20 )6.001538461538460.039267793725728152.836151260678
Trimmed Mean ( 5 / 20 )6.00160.0389634679762299154.031463617698
Trimmed Mean ( 6 / 20 )6.001666666666670.0385328603126873155.754507139211
Trimmed Mean ( 7 / 20 )6.001739130434780.0379413536105345158.184633896888
Trimmed Mean ( 8 / 20 )6.002045454545450.0372020645859351161.336353811252
Trimmed Mean ( 9 / 20 )6.002142857142860.036273153468077165.470665858296
Trimmed Mean ( 10 / 20 )6.001750.0351678894549836170.65994272083
Trimmed Mean ( 11 / 20 )6.001315789473680.0338311661438133177.390154509089
Trimmed Mean ( 12 / 20 )6.001111111111110.0324643339774536184.852432681319
Trimmed Mean ( 13 / 20 )6.000882352941180.0309659339217607193.789806827824
Trimmed Mean ( 14 / 20 )5.998750.0294805499029554203.481618210881
Trimmed Mean ( 15 / 20 )5.9940.0280213383388241213.908412493461
Trimmed Mean ( 16 / 20 )5.989285714285710.026691102749538224.392591437212
Trimmed Mean ( 17 / 20 )5.988076923076920.0264285348746635226.576196958144
Trimmed Mean ( 18 / 20 )5.986666666666670.0258666218436785231.443700025705
Trimmed Mean ( 19 / 20 )5.985454545454550.0253437601525467236.170738257759
Trimmed Mean ( 20 / 20 )5.9830.0246352336469964242.863537879595
Median5.935
Midrange5.98
Midmean - Weighted Average at Xnp5.98709677419355
Midmean - Weighted Average at X(n+1)p5.994
Midmean - Empirical Distribution Function5.98709677419355
Midmean - Empirical Distribution Function - Averaging5.994
Midmean - Empirical Distribution Function - Interpolation5.994
Midmean - Closest Observation5.98709677419355
Midmean - True Basic - Statistics Graphics Toolkit5.994
Midmean - MS Excel (old versions)6.02
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')