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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 computationSun, 26 Oct 2008 13:20:42 -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/2008/Oct/26/t12250488962kpeplrhfszb9wy.htm/, Retrieved Sun, 19 May 2024 14:45:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19035, Retrieved Sun, 19 May 2024 14:45:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Harrell-Davis Quantiles] [Q7 95% confidence...] [2007-10-20 15:02:46] [b731da8b544846036771bbf9bf2f34ce]
F RMPD    [Central Tendency] [Q9 Prediction Uiv...] [2008-10-26 19:20:42] [db9a5fd0f9c3e1245d8075d8bb09236d] [Current]
Feedback Forum
2008-10-26 19:27:06 [Stijn Van de Velde] [reply
De mediaan, het gemiddelde en de midrange liggen relatief gezien dicht bij elkaar. Ook de beide grafieken kennen (in het begin) een zeer rustig verloop.
Daaruit leid ik af dat in de datareeks zo goed als geen outliers aanwezig zijn.

Aangezien de grafieken vrij constant zijn vermoed ik dat de uitvoer extra-Eu in de toekomst niet sterk zal wijzigen.

Post a new message
Dataseries X:
3219,2
3552,3
3787,7
3392,7
3550
3681,9
3519,1
4283,2
4046,2
3824,9
4793,1
3977,7
3983,4
4152,9
4286,1
4348,1
3949,3
4166,7
4217,9
4528,2
4232,2
4470,9
5121,2
4170,8
4398,6
4491,4
4251,8
4901,9
4745,2
4666,9
4210,4
5273,6
4095,3
4610,1
4718,1
4185,5
4314,7
4422,6
5059,2
5043,6
4436,6
4922,6
4454,8
5058,7
4768,9
5171,8
4989,3
5202,1
4838,4
4876,5
5845,3
5686,3
4753,8
6620,4
5597,2
5643,5
6357,3
5909,1
6165,8
6321,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19035&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19035&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19035&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4637.7433333333398.080232703992447.2851991219282
Geometric Mean4578.89633532407
Harmonic Mean4522.13582886144
Quadratic Mean4698.53460311475
Winsorized Mean ( 1 / 20 )4636.2595.989543083379348.2995319185218
Winsorized Mean ( 2 / 20 )4639.2733333333394.74465039730648.9660715816547
Winsorized Mean ( 3 / 20 )4633.0283333333392.164813257434550.2689493916987
Winsorized Mean ( 4 / 20 )4616.0683333333387.573574442470352.7107447962601
Winsorized Mean ( 5 / 20 )4621.5516666666784.116637057697654.9421830011658
Winsorized Mean ( 6 / 20 )4616.2316666666778.360514583019658.9101755039646
Winsorized Mean ( 7 / 20 )4615.5783333333376.444120468419360.3784608293077
Winsorized Mean ( 8 / 20 )4625.9916666666772.263458281331864.015641884409
Winsorized Mean ( 9 / 20 )4581.7116666666761.329331656409374.7066948704935
Winsorized Mean ( 10 / 20 )4570.74558.94776340380377.5389045499412
Winsorized Mean ( 11 / 20 )4576.7033333333356.04664980722781.6588208050784
Winsorized Mean ( 12 / 20 )4576.4033333333352.700415256174886.8380886770552
Winsorized Mean ( 13 / 20 )4575.4548.497473025205294.3440908276197
Winsorized Mean ( 14 / 20 )4578.5533333333348.005835654364295.3749324623432
Winsorized Mean ( 15 / 20 )4575.8033333333347.219877132642496.9041770371348
Winsorized Mean ( 16 / 20 )4565.2433333333344.2571545090215103.152662749765
Winsorized Mean ( 17 / 20 )4553.440.2266596536757113.193589505112
Winsorized Mean ( 18 / 20 )4549.4438.9422956560146116.825162034261
Winsorized Mean ( 19 / 20 )4545.92537.0656284371475122.645296779699
Winsorized Mean ( 20 / 20 )4539.7583333333334.2314501122736132.619515633830
Trimmed Mean ( 1 / 20 )4628.0172413793192.202288492500450.1941688980501
Trimmed Mean ( 2 / 20 )4619.1964285714387.5058206956152.7873047970072
Trimmed Mean ( 3 / 20 )4608.0425925925982.478380268728555.8697027945846
Trimmed Mean ( 4 / 20 )4598.4326923076977.475279165410759.3535478909341
Trimmed Mean ( 5 / 20 )4593.14273.136084791940362.802678227399
Trimmed Mean ( 6 / 20 )4586.0395833333368.881933159402966.5782647638614
Trimmed Mean ( 7 / 20 )4579.4760869565265.401728484359470.0207195296328
Trimmed Mean ( 8 / 20 )4572.4431818181861.476206435438774.3774453067478
Trimmed Mean ( 9 / 20 )4562.8809523809557.574910274575279.2512038771844
Trimmed Mean ( 10 / 20 )4559.742555.817091042115881.6907942508062
Trimmed Mean ( 11 / 20 )4558.0052631578954.101649618359384.2489146876428
Trimmed Mean ( 12 / 20 )4555.1722222222252.526397537539286.7215806864875
Trimmed Mean ( 13 / 20 )4552.0551.225332527113788.8632591616773
Trimmed Mean ( 14 / 20 )4548.67550.474368495306690.1185123380585
Trimmed Mean ( 15 / 20 )4544.4066666666749.371959311774692.0442844483768
Trimmed Mean ( 16 / 20 )4539.9214285714347.85566382062694.8669617370285
Trimmed Mean ( 17 / 20 )4536.2692307692346.466894011255597.6236808440526
Trimmed Mean ( 18 / 20 )4533.7545.601205727130999.4217132575203
Trimmed Mean ( 19 / 20 )4531.3727272727344.440909832556101.963995434522
Trimmed Mean ( 20 / 20 )4529.07543.033790196591105.244622407412
Median4481.15
Midrange4919.8
Midmean - Weighted Average at Xnp4532.22258064516
Midmean - Weighted Average at X(n+1)p4544.40666666667
Midmean - Empirical Distribution Function4532.22258064516
Midmean - Empirical Distribution Function - Averaging4544.40666666667
Midmean - Empirical Distribution Function - Interpolation4544.40666666667
Midmean - Closest Observation4532.22258064516
Midmean - True Basic - Statistics Graphics Toolkit4544.40666666667
Midmean - MS Excel (old versions)4548.675
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4637.74333333333 & 98.0802327039924 & 47.2851991219282 \tabularnewline
Geometric Mean & 4578.89633532407 &  &  \tabularnewline
Harmonic Mean & 4522.13582886144 &  &  \tabularnewline
Quadratic Mean & 4698.53460311475 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4636.25 & 95.9895430833793 & 48.2995319185218 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4639.27333333333 & 94.744650397306 & 48.9660715816547 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4633.02833333333 & 92.1648132574345 & 50.2689493916987 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4616.06833333333 & 87.5735744424703 & 52.7107447962601 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4621.55166666667 & 84.1166370576976 & 54.9421830011658 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4616.23166666667 & 78.3605145830196 & 58.9101755039646 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4615.57833333333 & 76.4441204684193 & 60.3784608293077 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4625.99166666667 & 72.2634582813318 & 64.015641884409 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4581.71166666667 & 61.3293316564093 & 74.7066948704935 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4570.745 & 58.947763403803 & 77.5389045499412 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4576.70333333333 & 56.046649807227 & 81.6588208050784 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4576.40333333333 & 52.7004152561748 & 86.8380886770552 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4575.45 & 48.4974730252052 & 94.3440908276197 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4578.55333333333 & 48.0058356543642 & 95.3749324623432 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4575.80333333333 & 47.2198771326424 & 96.9041770371348 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4565.24333333333 & 44.2571545090215 & 103.152662749765 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4553.4 & 40.2266596536757 & 113.193589505112 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4549.44 & 38.9422956560146 & 116.825162034261 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4545.925 & 37.0656284371475 & 122.645296779699 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4539.75833333333 & 34.2314501122736 & 132.619515633830 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4628.01724137931 & 92.2022884925004 & 50.1941688980501 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4619.19642857143 & 87.50582069561 & 52.7873047970072 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4608.04259259259 & 82.4783802687285 & 55.8697027945846 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4598.43269230769 & 77.4752791654107 & 59.3535478909341 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4593.142 & 73.1360847919403 & 62.802678227399 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4586.03958333333 & 68.8819331594029 & 66.5782647638614 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4579.47608695652 & 65.4017284843594 & 70.0207195296328 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4572.44318181818 & 61.4762064354387 & 74.3774453067478 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4562.88095238095 & 57.5749102745752 & 79.2512038771844 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4559.7425 & 55.8170910421158 & 81.6907942508062 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4558.00526315789 & 54.1016496183593 & 84.2489146876428 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4555.17222222222 & 52.5263975375392 & 86.7215806864875 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4552.05 & 51.2253325271137 & 88.8632591616773 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4548.675 & 50.4743684953066 & 90.1185123380585 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4544.40666666667 & 49.3719593117746 & 92.0442844483768 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4539.92142857143 & 47.855663820626 & 94.8669617370285 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4536.26923076923 & 46.4668940112555 & 97.6236808440526 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4533.75 & 45.6012057271309 & 99.4217132575203 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4531.37272727273 & 44.440909832556 & 101.963995434522 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4529.075 & 43.033790196591 & 105.244622407412 \tabularnewline
Median & 4481.15 &  &  \tabularnewline
Midrange & 4919.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4532.22258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4544.40666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4532.22258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4544.40666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4544.40666666667 &  &  \tabularnewline
Midmean - Closest Observation & 4532.22258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4544.40666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4548.675 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19035&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]4637.74333333333[/C][C]98.0802327039924[/C][C]47.2851991219282[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4578.89633532407[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4522.13582886144[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4698.53460311475[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4636.25[/C][C]95.9895430833793[/C][C]48.2995319185218[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4639.27333333333[/C][C]94.744650397306[/C][C]48.9660715816547[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4633.02833333333[/C][C]92.1648132574345[/C][C]50.2689493916987[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4616.06833333333[/C][C]87.5735744424703[/C][C]52.7107447962601[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4621.55166666667[/C][C]84.1166370576976[/C][C]54.9421830011658[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4616.23166666667[/C][C]78.3605145830196[/C][C]58.9101755039646[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4615.57833333333[/C][C]76.4441204684193[/C][C]60.3784608293077[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4625.99166666667[/C][C]72.2634582813318[/C][C]64.015641884409[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4581.71166666667[/C][C]61.3293316564093[/C][C]74.7066948704935[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4570.745[/C][C]58.947763403803[/C][C]77.5389045499412[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4576.70333333333[/C][C]56.046649807227[/C][C]81.6588208050784[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4576.40333333333[/C][C]52.7004152561748[/C][C]86.8380886770552[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4575.45[/C][C]48.4974730252052[/C][C]94.3440908276197[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4578.55333333333[/C][C]48.0058356543642[/C][C]95.3749324623432[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4575.80333333333[/C][C]47.2198771326424[/C][C]96.9041770371348[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4565.24333333333[/C][C]44.2571545090215[/C][C]103.152662749765[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4553.4[/C][C]40.2266596536757[/C][C]113.193589505112[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4549.44[/C][C]38.9422956560146[/C][C]116.825162034261[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4545.925[/C][C]37.0656284371475[/C][C]122.645296779699[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4539.75833333333[/C][C]34.2314501122736[/C][C]132.619515633830[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4628.01724137931[/C][C]92.2022884925004[/C][C]50.1941688980501[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4619.19642857143[/C][C]87.50582069561[/C][C]52.7873047970072[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4608.04259259259[/C][C]82.4783802687285[/C][C]55.8697027945846[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4598.43269230769[/C][C]77.4752791654107[/C][C]59.3535478909341[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4593.142[/C][C]73.1360847919403[/C][C]62.802678227399[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4586.03958333333[/C][C]68.8819331594029[/C][C]66.5782647638614[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4579.47608695652[/C][C]65.4017284843594[/C][C]70.0207195296328[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4572.44318181818[/C][C]61.4762064354387[/C][C]74.3774453067478[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4562.88095238095[/C][C]57.5749102745752[/C][C]79.2512038771844[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4559.7425[/C][C]55.8170910421158[/C][C]81.6907942508062[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4558.00526315789[/C][C]54.1016496183593[/C][C]84.2489146876428[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4555.17222222222[/C][C]52.5263975375392[/C][C]86.7215806864875[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4552.05[/C][C]51.2253325271137[/C][C]88.8632591616773[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4548.675[/C][C]50.4743684953066[/C][C]90.1185123380585[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4544.40666666667[/C][C]49.3719593117746[/C][C]92.0442844483768[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4539.92142857143[/C][C]47.855663820626[/C][C]94.8669617370285[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4536.26923076923[/C][C]46.4668940112555[/C][C]97.6236808440526[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4533.75[/C][C]45.6012057271309[/C][C]99.4217132575203[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4531.37272727273[/C][C]44.440909832556[/C][C]101.963995434522[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4529.075[/C][C]43.033790196591[/C][C]105.244622407412[/C][/ROW]
[ROW][C]Median[/C][C]4481.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4919.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4532.22258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4544.40666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4532.22258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4544.40666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4544.40666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4532.22258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4544.40666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4548.675[/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=19035&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19035&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 Mean4637.7433333333398.080232703992447.2851991219282
Geometric Mean4578.89633532407
Harmonic Mean4522.13582886144
Quadratic Mean4698.53460311475
Winsorized Mean ( 1 / 20 )4636.2595.989543083379348.2995319185218
Winsorized Mean ( 2 / 20 )4639.2733333333394.74465039730648.9660715816547
Winsorized Mean ( 3 / 20 )4633.0283333333392.164813257434550.2689493916987
Winsorized Mean ( 4 / 20 )4616.0683333333387.573574442470352.7107447962601
Winsorized Mean ( 5 / 20 )4621.5516666666784.116637057697654.9421830011658
Winsorized Mean ( 6 / 20 )4616.2316666666778.360514583019658.9101755039646
Winsorized Mean ( 7 / 20 )4615.5783333333376.444120468419360.3784608293077
Winsorized Mean ( 8 / 20 )4625.9916666666772.263458281331864.015641884409
Winsorized Mean ( 9 / 20 )4581.7116666666761.329331656409374.7066948704935
Winsorized Mean ( 10 / 20 )4570.74558.94776340380377.5389045499412
Winsorized Mean ( 11 / 20 )4576.7033333333356.04664980722781.6588208050784
Winsorized Mean ( 12 / 20 )4576.4033333333352.700415256174886.8380886770552
Winsorized Mean ( 13 / 20 )4575.4548.497473025205294.3440908276197
Winsorized Mean ( 14 / 20 )4578.5533333333348.005835654364295.3749324623432
Winsorized Mean ( 15 / 20 )4575.8033333333347.219877132642496.9041770371348
Winsorized Mean ( 16 / 20 )4565.2433333333344.2571545090215103.152662749765
Winsorized Mean ( 17 / 20 )4553.440.2266596536757113.193589505112
Winsorized Mean ( 18 / 20 )4549.4438.9422956560146116.825162034261
Winsorized Mean ( 19 / 20 )4545.92537.0656284371475122.645296779699
Winsorized Mean ( 20 / 20 )4539.7583333333334.2314501122736132.619515633830
Trimmed Mean ( 1 / 20 )4628.0172413793192.202288492500450.1941688980501
Trimmed Mean ( 2 / 20 )4619.1964285714387.5058206956152.7873047970072
Trimmed Mean ( 3 / 20 )4608.0425925925982.478380268728555.8697027945846
Trimmed Mean ( 4 / 20 )4598.4326923076977.475279165410759.3535478909341
Trimmed Mean ( 5 / 20 )4593.14273.136084791940362.802678227399
Trimmed Mean ( 6 / 20 )4586.0395833333368.881933159402966.5782647638614
Trimmed Mean ( 7 / 20 )4579.4760869565265.401728484359470.0207195296328
Trimmed Mean ( 8 / 20 )4572.4431818181861.476206435438774.3774453067478
Trimmed Mean ( 9 / 20 )4562.8809523809557.574910274575279.2512038771844
Trimmed Mean ( 10 / 20 )4559.742555.817091042115881.6907942508062
Trimmed Mean ( 11 / 20 )4558.0052631578954.101649618359384.2489146876428
Trimmed Mean ( 12 / 20 )4555.1722222222252.526397537539286.7215806864875
Trimmed Mean ( 13 / 20 )4552.0551.225332527113788.8632591616773
Trimmed Mean ( 14 / 20 )4548.67550.474368495306690.1185123380585
Trimmed Mean ( 15 / 20 )4544.4066666666749.371959311774692.0442844483768
Trimmed Mean ( 16 / 20 )4539.9214285714347.85566382062694.8669617370285
Trimmed Mean ( 17 / 20 )4536.2692307692346.466894011255597.6236808440526
Trimmed Mean ( 18 / 20 )4533.7545.601205727130999.4217132575203
Trimmed Mean ( 19 / 20 )4531.3727272727344.440909832556101.963995434522
Trimmed Mean ( 20 / 20 )4529.07543.033790196591105.244622407412
Median4481.15
Midrange4919.8
Midmean - Weighted Average at Xnp4532.22258064516
Midmean - Weighted Average at X(n+1)p4544.40666666667
Midmean - Empirical Distribution Function4532.22258064516
Midmean - Empirical Distribution Function - Averaging4544.40666666667
Midmean - Empirical Distribution Function - Interpolation4544.40666666667
Midmean - Closest Observation4532.22258064516
Midmean - True Basic - Statistics Graphics Toolkit4544.40666666667
Midmean - MS Excel (old versions)4548.675
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')