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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 05:21:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t13311157084f0tlewlmjfcawr.htm/, Retrieved Sun, 28 Apr 2024 21:04:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163582, Retrieved Sun, 28 Apr 2024 21:04:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten gemi...] [2012-03-07 10:21:32] [c6701916d11cfe737d4a1a362ef25325] [Current]
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Dataseries X:
7,72
7,67
7,84
7,79
7,83
7,94
8,02
8,06
8,12
8,13
7,97
8,01
8,00
7,90
7,99
8,02
8,08
8,02
8,07
8,11
8,19
8,16
8,08
8,22
8,15
8,19
8,31
8,30
8,34
8,31
8,38
8,34
8,44
8,64
8,60
8,61
8,54
8,69
8,73
8,91
9,01
9,08
8,94
9,03
9,02
8,96
9,03
8,94
8,95
8,95
8,99
8,93
8,98
8,95
9,02
8,92
9,10
9,06
8,97
8,89




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=163582&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=163582&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163582&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 Mean8.452333333333330.0579413139035854145.8774881667
Geometric Mean8.44062084192582
Harmonic Mean8.42892893682298
Quadratic Mean8.46404237544528
Winsorized Mean ( 1 / 20 )8.452833333333330.057693957651813146.511587649209
Winsorized Mean ( 2 / 20 )8.45450.057091177447771148.087679707332
Winsorized Mean ( 3 / 20 )8.4550.0564418104431608149.800297573986
Winsorized Mean ( 4 / 20 )8.455666666666670.0563174851507947150.142831201108
Winsorized Mean ( 5 / 20 )8.459833333333330.0552812488855195153.032601540037
Winsorized Mean ( 6 / 20 )8.463833333333330.0546127050400278154.979199933969
Winsorized Mean ( 7 / 20 )8.466166666666670.0538543189055755157.20497146219
Winsorized Mean ( 8 / 20 )8.466166666666670.052991360380282159.765037279868
Winsorized Mean ( 9 / 20 )8.466166666666670.0525142389443289161.216592620561
Winsorized Mean ( 10 / 20 )8.466166666666670.0519898358529345162.842727386469
Winsorized Mean ( 11 / 20 )8.466166666666670.0514189020107632164.650864479652
Winsorized Mean ( 12 / 20 )8.464166666666670.0510949551760684165.655623681437
Winsorized Mean ( 13 / 20 )8.464166666666670.0510949551760684165.655623681437
Winsorized Mean ( 14 / 20 )8.47350.0497495563958305170.323126754758
Winsorized Mean ( 15 / 20 )8.47350.0489943067141018172.948666249034
Winsorized Mean ( 16 / 20 )8.476166666666670.0486240574635484174.320431260203
Winsorized Mean ( 17 / 20 )8.473333333333330.0481673557708804175.914438268913
Winsorized Mean ( 18 / 20 )8.479333333333330.0464556569242504182.525313271526
Winsorized Mean ( 19 / 20 )8.479333333333330.0455219985726568186.268916110957
Winsorized Mean ( 20 / 20 )8.4760.0440109128737112192.588597839853
Trimmed Mean ( 1 / 20 )8.454655172413790.0572949488399068147.563709255379
Trimmed Mean ( 2 / 20 )8.456607142857140.0567566443193837148.997659115816
Trimmed Mean ( 3 / 20 )8.457777777777780.0564285703755093149.884672276733
Trimmed Mean ( 4 / 20 )8.458846153846150.0562514647680268150.375571351417
Trimmed Mean ( 5 / 20 )8.45980.055996712731505151.076725531432
Trimmed Mean ( 6 / 20 )8.459791666666670.0559219072889553151.278668357177
Trimmed Mean ( 7 / 20 )8.458913043478260.0559116178509622151.290793731391
Trimmed Mean ( 8 / 20 )8.45750.0559759886985683151.091569736156
Trimmed Mean ( 9 / 20 )8.455952380952380.0561337165836398150.639453355149
Trimmed Mean ( 10 / 20 )8.454250.0562923771994862150.184632815208
Trimmed Mean ( 11 / 20 )8.452368421052630.0564469995378995149.739906288156
Trimmed Mean ( 12 / 20 )8.450277777777780.0565902651776326149.323876664175
Trimmed Mean ( 13 / 20 )8.448235294117650.0566448588448548149.143902313476
Trimmed Mean ( 14 / 20 )8.44593750.0564826896387791149.531432621461
Trimmed Mean ( 15 / 20 )8.4420.0563372439641066149.847585824016
Trimmed Mean ( 16 / 20 )8.43750.0560414269482098150.558264831433
Trimmed Mean ( 17 / 20 )8.431923076923080.0553756937258695152.267583656184
Trimmed Mean ( 18 / 20 )8.425833333333330.0541800429414752155.515442142319
Trimmed Mean ( 19 / 20 )8.417727272727270.0525329491253028160.237097153048
Trimmed Mean ( 20 / 20 )8.4080.0497921997695898168.861790378965
Median8.34
Midrange8.385
Midmean - Weighted Average at Xnp8.42967741935484
Midmean - Weighted Average at X(n+1)p8.442
Midmean - Empirical Distribution Function8.42967741935484
Midmean - Empirical Distribution Function - Averaging8.442
Midmean - Empirical Distribution Function - Interpolation8.442
Midmean - Closest Observation8.42967741935484
Midmean - True Basic - Statistics Graphics Toolkit8.442
Midmean - MS Excel (old versions)8.47558823529411
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.45233333333333 & 0.0579413139035854 & 145.8774881667 \tabularnewline
Geometric Mean & 8.44062084192582 &  &  \tabularnewline
Harmonic Mean & 8.42892893682298 &  &  \tabularnewline
Quadratic Mean & 8.46404237544528 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.45283333333333 & 0.057693957651813 & 146.511587649209 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.4545 & 0.057091177447771 & 148.087679707332 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.455 & 0.0564418104431608 & 149.800297573986 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.45566666666667 & 0.0563174851507947 & 150.142831201108 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.45983333333333 & 0.0552812488855195 & 153.032601540037 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.46383333333333 & 0.0546127050400278 & 154.979199933969 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.46616666666667 & 0.0538543189055755 & 157.20497146219 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.46616666666667 & 0.052991360380282 & 159.765037279868 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.46616666666667 & 0.0525142389443289 & 161.216592620561 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.46616666666667 & 0.0519898358529345 & 162.842727386469 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.46616666666667 & 0.0514189020107632 & 164.650864479652 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.46416666666667 & 0.0510949551760684 & 165.655623681437 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.46416666666667 & 0.0510949551760684 & 165.655623681437 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.4735 & 0.0497495563958305 & 170.323126754758 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.4735 & 0.0489943067141018 & 172.948666249034 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.47616666666667 & 0.0486240574635484 & 174.320431260203 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.47333333333333 & 0.0481673557708804 & 175.914438268913 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.47933333333333 & 0.0464556569242504 & 182.525313271526 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.47933333333333 & 0.0455219985726568 & 186.268916110957 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.476 & 0.0440109128737112 & 192.588597839853 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.45465517241379 & 0.0572949488399068 & 147.563709255379 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.45660714285714 & 0.0567566443193837 & 148.997659115816 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.45777777777778 & 0.0564285703755093 & 149.884672276733 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.45884615384615 & 0.0562514647680268 & 150.375571351417 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.4598 & 0.055996712731505 & 151.076725531432 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.45979166666667 & 0.0559219072889553 & 151.278668357177 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.45891304347826 & 0.0559116178509622 & 151.290793731391 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.4575 & 0.0559759886985683 & 151.091569736156 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.45595238095238 & 0.0561337165836398 & 150.639453355149 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.45425 & 0.0562923771994862 & 150.184632815208 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.45236842105263 & 0.0564469995378995 & 149.739906288156 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.45027777777778 & 0.0565902651776326 & 149.323876664175 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.44823529411765 & 0.0566448588448548 & 149.143902313476 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.4459375 & 0.0564826896387791 & 149.531432621461 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.442 & 0.0563372439641066 & 149.847585824016 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.4375 & 0.0560414269482098 & 150.558264831433 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.43192307692308 & 0.0553756937258695 & 152.267583656184 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.42583333333333 & 0.0541800429414752 & 155.515442142319 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.41772727272727 & 0.0525329491253028 & 160.237097153048 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.408 & 0.0497921997695898 & 168.861790378965 \tabularnewline
Median & 8.34 &  &  \tabularnewline
Midrange & 8.385 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.42967741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.442 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.42967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.442 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.442 &  &  \tabularnewline
Midmean - Closest Observation & 8.42967741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.442 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.47558823529411 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163582&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]8.45233333333333[/C][C]0.0579413139035854[/C][C]145.8774881667[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.44062084192582[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.42892893682298[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.46404237544528[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.45283333333333[/C][C]0.057693957651813[/C][C]146.511587649209[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.4545[/C][C]0.057091177447771[/C][C]148.087679707332[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.455[/C][C]0.0564418104431608[/C][C]149.800297573986[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.45566666666667[/C][C]0.0563174851507947[/C][C]150.142831201108[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.45983333333333[/C][C]0.0552812488855195[/C][C]153.032601540037[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.46383333333333[/C][C]0.0546127050400278[/C][C]154.979199933969[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.46616666666667[/C][C]0.0538543189055755[/C][C]157.20497146219[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.46616666666667[/C][C]0.052991360380282[/C][C]159.765037279868[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.46616666666667[/C][C]0.0525142389443289[/C][C]161.216592620561[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.46616666666667[/C][C]0.0519898358529345[/C][C]162.842727386469[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.46616666666667[/C][C]0.0514189020107632[/C][C]164.650864479652[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.46416666666667[/C][C]0.0510949551760684[/C][C]165.655623681437[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.46416666666667[/C][C]0.0510949551760684[/C][C]165.655623681437[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.4735[/C][C]0.0497495563958305[/C][C]170.323126754758[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.4735[/C][C]0.0489943067141018[/C][C]172.948666249034[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.47616666666667[/C][C]0.0486240574635484[/C][C]174.320431260203[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.47333333333333[/C][C]0.0481673557708804[/C][C]175.914438268913[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.47933333333333[/C][C]0.0464556569242504[/C][C]182.525313271526[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.47933333333333[/C][C]0.0455219985726568[/C][C]186.268916110957[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.476[/C][C]0.0440109128737112[/C][C]192.588597839853[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.45465517241379[/C][C]0.0572949488399068[/C][C]147.563709255379[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.45660714285714[/C][C]0.0567566443193837[/C][C]148.997659115816[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.45777777777778[/C][C]0.0564285703755093[/C][C]149.884672276733[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.45884615384615[/C][C]0.0562514647680268[/C][C]150.375571351417[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.4598[/C][C]0.055996712731505[/C][C]151.076725531432[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.45979166666667[/C][C]0.0559219072889553[/C][C]151.278668357177[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.45891304347826[/C][C]0.0559116178509622[/C][C]151.290793731391[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.4575[/C][C]0.0559759886985683[/C][C]151.091569736156[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.45595238095238[/C][C]0.0561337165836398[/C][C]150.639453355149[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.45425[/C][C]0.0562923771994862[/C][C]150.184632815208[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.45236842105263[/C][C]0.0564469995378995[/C][C]149.739906288156[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.45027777777778[/C][C]0.0565902651776326[/C][C]149.323876664175[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.44823529411765[/C][C]0.0566448588448548[/C][C]149.143902313476[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.4459375[/C][C]0.0564826896387791[/C][C]149.531432621461[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.442[/C][C]0.0563372439641066[/C][C]149.847585824016[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.4375[/C][C]0.0560414269482098[/C][C]150.558264831433[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.43192307692308[/C][C]0.0553756937258695[/C][C]152.267583656184[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.42583333333333[/C][C]0.0541800429414752[/C][C]155.515442142319[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.41772727272727[/C][C]0.0525329491253028[/C][C]160.237097153048[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.408[/C][C]0.0497921997695898[/C][C]168.861790378965[/C][/ROW]
[ROW][C]Median[/C][C]8.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.42967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.42967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.42967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.47558823529411[/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=163582&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163582&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 Mean8.452333333333330.0579413139035854145.8774881667
Geometric Mean8.44062084192582
Harmonic Mean8.42892893682298
Quadratic Mean8.46404237544528
Winsorized Mean ( 1 / 20 )8.452833333333330.057693957651813146.511587649209
Winsorized Mean ( 2 / 20 )8.45450.057091177447771148.087679707332
Winsorized Mean ( 3 / 20 )8.4550.0564418104431608149.800297573986
Winsorized Mean ( 4 / 20 )8.455666666666670.0563174851507947150.142831201108
Winsorized Mean ( 5 / 20 )8.459833333333330.0552812488855195153.032601540037
Winsorized Mean ( 6 / 20 )8.463833333333330.0546127050400278154.979199933969
Winsorized Mean ( 7 / 20 )8.466166666666670.0538543189055755157.20497146219
Winsorized Mean ( 8 / 20 )8.466166666666670.052991360380282159.765037279868
Winsorized Mean ( 9 / 20 )8.466166666666670.0525142389443289161.216592620561
Winsorized Mean ( 10 / 20 )8.466166666666670.0519898358529345162.842727386469
Winsorized Mean ( 11 / 20 )8.466166666666670.0514189020107632164.650864479652
Winsorized Mean ( 12 / 20 )8.464166666666670.0510949551760684165.655623681437
Winsorized Mean ( 13 / 20 )8.464166666666670.0510949551760684165.655623681437
Winsorized Mean ( 14 / 20 )8.47350.0497495563958305170.323126754758
Winsorized Mean ( 15 / 20 )8.47350.0489943067141018172.948666249034
Winsorized Mean ( 16 / 20 )8.476166666666670.0486240574635484174.320431260203
Winsorized Mean ( 17 / 20 )8.473333333333330.0481673557708804175.914438268913
Winsorized Mean ( 18 / 20 )8.479333333333330.0464556569242504182.525313271526
Winsorized Mean ( 19 / 20 )8.479333333333330.0455219985726568186.268916110957
Winsorized Mean ( 20 / 20 )8.4760.0440109128737112192.588597839853
Trimmed Mean ( 1 / 20 )8.454655172413790.0572949488399068147.563709255379
Trimmed Mean ( 2 / 20 )8.456607142857140.0567566443193837148.997659115816
Trimmed Mean ( 3 / 20 )8.457777777777780.0564285703755093149.884672276733
Trimmed Mean ( 4 / 20 )8.458846153846150.0562514647680268150.375571351417
Trimmed Mean ( 5 / 20 )8.45980.055996712731505151.076725531432
Trimmed Mean ( 6 / 20 )8.459791666666670.0559219072889553151.278668357177
Trimmed Mean ( 7 / 20 )8.458913043478260.0559116178509622151.290793731391
Trimmed Mean ( 8 / 20 )8.45750.0559759886985683151.091569736156
Trimmed Mean ( 9 / 20 )8.455952380952380.0561337165836398150.639453355149
Trimmed Mean ( 10 / 20 )8.454250.0562923771994862150.184632815208
Trimmed Mean ( 11 / 20 )8.452368421052630.0564469995378995149.739906288156
Trimmed Mean ( 12 / 20 )8.450277777777780.0565902651776326149.323876664175
Trimmed Mean ( 13 / 20 )8.448235294117650.0566448588448548149.143902313476
Trimmed Mean ( 14 / 20 )8.44593750.0564826896387791149.531432621461
Trimmed Mean ( 15 / 20 )8.4420.0563372439641066149.847585824016
Trimmed Mean ( 16 / 20 )8.43750.0560414269482098150.558264831433
Trimmed Mean ( 17 / 20 )8.431923076923080.0553756937258695152.267583656184
Trimmed Mean ( 18 / 20 )8.425833333333330.0541800429414752155.515442142319
Trimmed Mean ( 19 / 20 )8.417727272727270.0525329491253028160.237097153048
Trimmed Mean ( 20 / 20 )8.4080.0497921997695898168.861790378965
Median8.34
Midrange8.385
Midmean - Weighted Average at Xnp8.42967741935484
Midmean - Weighted Average at X(n+1)p8.442
Midmean - Empirical Distribution Function8.42967741935484
Midmean - Empirical Distribution Function - Averaging8.442
Midmean - Empirical Distribution Function - Interpolation8.442
Midmean - Closest Observation8.42967741935484
Midmean - True Basic - Statistics Graphics Toolkit8.442
Midmean - MS Excel (old versions)8.47558823529411
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')