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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 17 Oct 2009 07:01:20 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/17/t12557847090fayqwqwbxt6egd.htm/, Retrieved Mon, 06 May 2024 03:31:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47160, Retrieved Mon, 06 May 2024 03:31:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS 3 dee l 2] [2009-10-17 13:01:20] [9f6463b67b1eb7bae5c03a796abf0348] [Current]
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Dataseries X:
5548.9
3911.1
3749
4128.8
4624.8
3986.5
4298.4
4133.5
4419.9
5210.1
4920
5744.9
5581.7
4152.8
4952.4
5198.8
4745.7
4481.6
5722.6
5721.8
5031
6093
4895
5359.2
5568
4609.2
4721.7
5002
5290
4136.9
4615.9
4726.9
4209.8
5107.2
4196.7
4112.6
5094.9
4292.3
4570.1
3801.1
5518
4239.1
3822.4
4386.9
4819.2
4402.5
4562.1
4097.8
4785.3
3905.7
3785.1
4397.5
4014.2
4091.7
4779.6
3154.8
3577.3
3895.8
4170.7
3854.9
3851.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47160&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47160&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47160&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4570.1459016393481.661239629215655.9646892747426
Geometric Mean4527.00081521529
Harmonic Mean4484.48946516694
Quadratic Mean4613.71293490803
Winsorized Mean ( 1 / 20 )4571.3655737704978.319670877548158.3680386108589
Winsorized Mean ( 2 / 20 )4576.2639344262377.037749813672759.402876453357
Winsorized Mean ( 3 / 20 )457876.71617985383659.6745042404648
Winsorized Mean ( 4 / 20 )4569.8622950819774.350551835698361.4637306953761
Winsorized Mean ( 5 / 20 )4570.4852459016473.79878080486561.9317175169422
Winsorized Mean ( 6 / 20 )4571.4688524590272.89985032782762.708892156861
Winsorized Mean ( 7 / 20 )4568.313114754172.04982832846163.4049132487596
Winsorized Mean ( 8 / 20 )4552.8508196721366.776739578683368.1801904135719
Winsorized Mean ( 9 / 20 )4544.1016393442664.524875556090670.4240279455345
Winsorized Mean ( 10 / 20 )4531.8885245901661.919218442736773.1903379688373
Winsorized Mean ( 11 / 20 )4543.4475409836159.344842222357476.5601081886763
Winsorized Mean ( 12 / 20 )4530.8770491803355.266604872850881.9821854373775
Winsorized Mean ( 13 / 20 )4544.7721311475452.328182239156386.8513282264707
Winsorized Mean ( 14 / 20 )4531.5065573770549.608388143001991.3455713238345
Winsorized Mean ( 15 / 20 )4528.0147540983647.893504347322894.5434003171137
Winsorized Mean ( 16 / 20 )4519.2540983606645.1666093343719100.057413318416
Winsorized Mean ( 17 / 20 )4511.5344262295143.5498611219888103.594691463932
Winsorized Mean ( 18 / 20 )4505.160655737742.2606096407275106.604251430296
Winsorized Mean ( 19 / 20 )4486.5032786885237.9960835605600118.078045373748
Winsorized Mean ( 20 / 20 )4481.2573770491835.5349288228176126.108522670564
Trimmed Mean ( 1 / 20 )4568.3237288135676.61077204652859.6303053314628
Trimmed Mean ( 2 / 20 )4565.0684210526374.502052466971161.2743980855622
Trimmed Mean ( 3 / 20 )4558.8672.728004906247162.6836939343624
Trimmed Mean ( 4 / 20 )4551.5169811320870.647573456123664.4256661406614
Trimmed Mean ( 5 / 20 )4546.0313725490268.968529594539865.9145758112397
Trimmed Mean ( 6 / 20 )4539.9428571428667.00466852198867.7556199782265
Trimmed Mean ( 7 / 20 )4533.1234042553264.754091174939570.0052046442694
Trimmed Mean ( 8 / 20 )4526.3088888888962.09070839434372.8983290082945
Trimmed Mean ( 9 / 20 )4521.6023255814060.182471840351975.1315488931063
Trimmed Mean ( 10 / 20 )4517.8829268292758.282677309986377.5167362816939
Trimmed Mean ( 11 / 20 )4515.6923076923156.454694599320179.9878971933486
Trimmed Mean ( 12 / 20 )4511.5324324324354.635081659669682.5757424604115
Trimmed Mean ( 13 / 20 )4508.7228571428653.244117217278584.6802068056395
Trimmed Mean ( 14 / 20 )4503.5969696969751.997915620529586.611105771303
Trimmed Mean ( 15 / 20 )4499.6741935483950.925762111313688.3575229313798
Trimmed Mean ( 16 / 20 )4495.749.744138947276190.376476407904
Trimmed Mean ( 17 / 20 )4492.3740740740748.712600846910792.222012291897
Trimmed Mean ( 18 / 20 )4489.62447.503411554680394.5116119677442
Trimmed Mean ( 19 / 20 )4487.334782608745.879202366975397.807602379739
Trimmed Mean ( 20 / 20 )4487.4619047619044.8019884104811100.162114762569
Median4481.6
Midrange4623.9
Midmean - Weighted Average at Xnp4482.93
Midmean - Weighted Average at X(n+1)p4499.67419354839
Midmean - Empirical Distribution Function4499.67419354839
Midmean - Empirical Distribution Function - Averaging4499.67419354839
Midmean - Empirical Distribution Function - Interpolation4499.67419354839
Midmean - Closest Observation4487.115625
Midmean - True Basic - Statistics Graphics Toolkit4499.67419354839
Midmean - MS Excel (old versions)4499.67419354839
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4570.14590163934 & 81.6612396292156 & 55.9646892747426 \tabularnewline
Geometric Mean & 4527.00081521529 &  &  \tabularnewline
Harmonic Mean & 4484.48946516694 &  &  \tabularnewline
Quadratic Mean & 4613.71293490803 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4571.36557377049 & 78.3196708775481 & 58.3680386108589 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4576.26393442623 & 77.0377498136727 & 59.402876453357 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4578 & 76.716179853836 & 59.6745042404648 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4569.86229508197 & 74.3505518356983 & 61.4637306953761 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4570.48524590164 & 73.798780804865 & 61.9317175169422 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4571.46885245902 & 72.899850327827 & 62.708892156861 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4568.3131147541 & 72.049828328461 & 63.4049132487596 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4552.85081967213 & 66.7767395786833 & 68.1801904135719 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4544.10163934426 & 64.5248755560906 & 70.4240279455345 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4531.88852459016 & 61.9192184427367 & 73.1903379688373 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4543.44754098361 & 59.3448422223574 & 76.5601081886763 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4530.87704918033 & 55.2666048728508 & 81.9821854373775 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4544.77213114754 & 52.3281822391563 & 86.8513282264707 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4531.50655737705 & 49.6083881430019 & 91.3455713238345 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4528.01475409836 & 47.8935043473228 & 94.5434003171137 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4519.25409836066 & 45.1666093343719 & 100.057413318416 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4511.53442622951 & 43.5498611219888 & 103.594691463932 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4505.1606557377 & 42.2606096407275 & 106.604251430296 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4486.50327868852 & 37.9960835605600 & 118.078045373748 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4481.25737704918 & 35.5349288228176 & 126.108522670564 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4568.32372881356 & 76.610772046528 & 59.6303053314628 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4565.06842105263 & 74.5020524669711 & 61.2743980855622 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4558.86 & 72.7280049062471 & 62.6836939343624 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4551.51698113208 & 70.6475734561236 & 64.4256661406614 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4546.03137254902 & 68.9685295945398 & 65.9145758112397 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4539.94285714286 & 67.004668521988 & 67.7556199782265 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4533.12340425532 & 64.7540911749395 & 70.0052046442694 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4526.30888888889 & 62.090708394343 & 72.8983290082945 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4521.60232558140 & 60.1824718403519 & 75.1315488931063 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4517.88292682927 & 58.2826773099863 & 77.5167362816939 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4515.69230769231 & 56.4546945993201 & 79.9878971933486 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4511.53243243243 & 54.6350816596696 & 82.5757424604115 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4508.72285714286 & 53.2441172172785 & 84.6802068056395 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4503.59696969697 & 51.9979156205295 & 86.611105771303 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4499.67419354839 & 50.9257621113136 & 88.3575229313798 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4495.7 & 49.7441389472761 & 90.376476407904 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4492.37407407407 & 48.7126008469107 & 92.222012291897 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4489.624 & 47.5034115546803 & 94.5116119677442 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4487.3347826087 & 45.8792023669753 & 97.807602379739 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4487.46190476190 & 44.8019884104811 & 100.162114762569 \tabularnewline
Median & 4481.6 &  &  \tabularnewline
Midrange & 4623.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4482.93 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4499.67419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4499.67419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4499.67419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4499.67419354839 &  &  \tabularnewline
Midmean - Closest Observation & 4487.115625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4499.67419354839 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4499.67419354839 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47160&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]4570.14590163934[/C][C]81.6612396292156[/C][C]55.9646892747426[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4527.00081521529[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4484.48946516694[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4613.71293490803[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4571.36557377049[/C][C]78.3196708775481[/C][C]58.3680386108589[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4576.26393442623[/C][C]77.0377498136727[/C][C]59.402876453357[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4578[/C][C]76.716179853836[/C][C]59.6745042404648[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4569.86229508197[/C][C]74.3505518356983[/C][C]61.4637306953761[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4570.48524590164[/C][C]73.798780804865[/C][C]61.9317175169422[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4571.46885245902[/C][C]72.899850327827[/C][C]62.708892156861[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4568.3131147541[/C][C]72.049828328461[/C][C]63.4049132487596[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4552.85081967213[/C][C]66.7767395786833[/C][C]68.1801904135719[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4544.10163934426[/C][C]64.5248755560906[/C][C]70.4240279455345[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4531.88852459016[/C][C]61.9192184427367[/C][C]73.1903379688373[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4543.44754098361[/C][C]59.3448422223574[/C][C]76.5601081886763[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4530.87704918033[/C][C]55.2666048728508[/C][C]81.9821854373775[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4544.77213114754[/C][C]52.3281822391563[/C][C]86.8513282264707[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4531.50655737705[/C][C]49.6083881430019[/C][C]91.3455713238345[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4528.01475409836[/C][C]47.8935043473228[/C][C]94.5434003171137[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4519.25409836066[/C][C]45.1666093343719[/C][C]100.057413318416[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4511.53442622951[/C][C]43.5498611219888[/C][C]103.594691463932[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4505.1606557377[/C][C]42.2606096407275[/C][C]106.604251430296[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4486.50327868852[/C][C]37.9960835605600[/C][C]118.078045373748[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4481.25737704918[/C][C]35.5349288228176[/C][C]126.108522670564[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4568.32372881356[/C][C]76.610772046528[/C][C]59.6303053314628[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4565.06842105263[/C][C]74.5020524669711[/C][C]61.2743980855622[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4558.86[/C][C]72.7280049062471[/C][C]62.6836939343624[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4551.51698113208[/C][C]70.6475734561236[/C][C]64.4256661406614[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4546.03137254902[/C][C]68.9685295945398[/C][C]65.9145758112397[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4539.94285714286[/C][C]67.004668521988[/C][C]67.7556199782265[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4533.12340425532[/C][C]64.7540911749395[/C][C]70.0052046442694[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4526.30888888889[/C][C]62.090708394343[/C][C]72.8983290082945[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4521.60232558140[/C][C]60.1824718403519[/C][C]75.1315488931063[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4517.88292682927[/C][C]58.2826773099863[/C][C]77.5167362816939[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4515.69230769231[/C][C]56.4546945993201[/C][C]79.9878971933486[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4511.53243243243[/C][C]54.6350816596696[/C][C]82.5757424604115[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4508.72285714286[/C][C]53.2441172172785[/C][C]84.6802068056395[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4503.59696969697[/C][C]51.9979156205295[/C][C]86.611105771303[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4499.67419354839[/C][C]50.9257621113136[/C][C]88.3575229313798[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4495.7[/C][C]49.7441389472761[/C][C]90.376476407904[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4492.37407407407[/C][C]48.7126008469107[/C][C]92.222012291897[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4489.624[/C][C]47.5034115546803[/C][C]94.5116119677442[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4487.3347826087[/C][C]45.8792023669753[/C][C]97.807602379739[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4487.46190476190[/C][C]44.8019884104811[/C][C]100.162114762569[/C][/ROW]
[ROW][C]Median[/C][C]4481.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4623.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4482.93[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4499.67419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4499.67419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4499.67419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4499.67419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4487.115625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4499.67419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4499.67419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47160&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47160&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 Mean4570.1459016393481.661239629215655.9646892747426
Geometric Mean4527.00081521529
Harmonic Mean4484.48946516694
Quadratic Mean4613.71293490803
Winsorized Mean ( 1 / 20 )4571.3655737704978.319670877548158.3680386108589
Winsorized Mean ( 2 / 20 )4576.2639344262377.037749813672759.402876453357
Winsorized Mean ( 3 / 20 )457876.71617985383659.6745042404648
Winsorized Mean ( 4 / 20 )4569.8622950819774.350551835698361.4637306953761
Winsorized Mean ( 5 / 20 )4570.4852459016473.79878080486561.9317175169422
Winsorized Mean ( 6 / 20 )4571.4688524590272.89985032782762.708892156861
Winsorized Mean ( 7 / 20 )4568.313114754172.04982832846163.4049132487596
Winsorized Mean ( 8 / 20 )4552.8508196721366.776739578683368.1801904135719
Winsorized Mean ( 9 / 20 )4544.1016393442664.524875556090670.4240279455345
Winsorized Mean ( 10 / 20 )4531.8885245901661.919218442736773.1903379688373
Winsorized Mean ( 11 / 20 )4543.4475409836159.344842222357476.5601081886763
Winsorized Mean ( 12 / 20 )4530.8770491803355.266604872850881.9821854373775
Winsorized Mean ( 13 / 20 )4544.7721311475452.328182239156386.8513282264707
Winsorized Mean ( 14 / 20 )4531.5065573770549.608388143001991.3455713238345
Winsorized Mean ( 15 / 20 )4528.0147540983647.893504347322894.5434003171137
Winsorized Mean ( 16 / 20 )4519.2540983606645.1666093343719100.057413318416
Winsorized Mean ( 17 / 20 )4511.5344262295143.5498611219888103.594691463932
Winsorized Mean ( 18 / 20 )4505.160655737742.2606096407275106.604251430296
Winsorized Mean ( 19 / 20 )4486.5032786885237.9960835605600118.078045373748
Winsorized Mean ( 20 / 20 )4481.2573770491835.5349288228176126.108522670564
Trimmed Mean ( 1 / 20 )4568.3237288135676.61077204652859.6303053314628
Trimmed Mean ( 2 / 20 )4565.0684210526374.502052466971161.2743980855622
Trimmed Mean ( 3 / 20 )4558.8672.728004906247162.6836939343624
Trimmed Mean ( 4 / 20 )4551.5169811320870.647573456123664.4256661406614
Trimmed Mean ( 5 / 20 )4546.0313725490268.968529594539865.9145758112397
Trimmed Mean ( 6 / 20 )4539.9428571428667.00466852198867.7556199782265
Trimmed Mean ( 7 / 20 )4533.1234042553264.754091174939570.0052046442694
Trimmed Mean ( 8 / 20 )4526.3088888888962.09070839434372.8983290082945
Trimmed Mean ( 9 / 20 )4521.6023255814060.182471840351975.1315488931063
Trimmed Mean ( 10 / 20 )4517.8829268292758.282677309986377.5167362816939
Trimmed Mean ( 11 / 20 )4515.6923076923156.454694599320179.9878971933486
Trimmed Mean ( 12 / 20 )4511.5324324324354.635081659669682.5757424604115
Trimmed Mean ( 13 / 20 )4508.7228571428653.244117217278584.6802068056395
Trimmed Mean ( 14 / 20 )4503.5969696969751.997915620529586.611105771303
Trimmed Mean ( 15 / 20 )4499.6741935483950.925762111313688.3575229313798
Trimmed Mean ( 16 / 20 )4495.749.744138947276190.376476407904
Trimmed Mean ( 17 / 20 )4492.3740740740748.712600846910792.222012291897
Trimmed Mean ( 18 / 20 )4489.62447.503411554680394.5116119677442
Trimmed Mean ( 19 / 20 )4487.334782608745.879202366975397.807602379739
Trimmed Mean ( 20 / 20 )4487.4619047619044.8019884104811100.162114762569
Median4481.6
Midrange4623.9
Midmean - Weighted Average at Xnp4482.93
Midmean - Weighted Average at X(n+1)p4499.67419354839
Midmean - Empirical Distribution Function4499.67419354839
Midmean - Empirical Distribution Function - Averaging4499.67419354839
Midmean - Empirical Distribution Function - Interpolation4499.67419354839
Midmean - Closest Observation4487.115625
Midmean - True Basic - Statistics Graphics Toolkit4499.67419354839
Midmean - MS Excel (old versions)4499.67419354839
Number of observations61



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')