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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Dec 2008 09:37:44 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/15/t1229359187pbafiwgkb66vlmr.htm/, Retrieved Thu, 25 Apr 2024 19:35:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33734, Retrieved Thu, 25 Apr 2024 19:35:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- R  D  [Central Tendency] [Central Tendency ...] [2008-12-15 16:12:30] [74be16979710d4c4e7c6647856088456]
-    D      [Central Tendency] [central Tendency ...] [2008-12-15 16:37:44] [ee28d11f695cd3bc1f8bbd77ba77987a] [Current]
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Dataseries X:
3796
3711
3949
3740
3243
4407
4814
3908
5250
3937
4004
5560
3922
3759
4138
4634
3996
4308
4142
4429
5219
4929
5754
5592
4163
4962
5208
4755
4491
5732
5730
5024
6056
4901
5353
5578
4618
4724
5011
5298
4143
4617
4736
4214
5112
4197
4119
5104
4194
4583
3790
5557
4304
3838
4277
4951
4479
4677
4274
4782




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33734&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33734&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4611.5582.275444864695956.0501375299011
Geometric Mean4568.6028547909
Harmonic Mean4526.09284125354
Quadratic Mean4654.65133853582
Winsorized Mean ( 1 / 20 )4614.3166666666779.047112790345758.3742593977478
Winsorized Mean ( 2 / 20 )4614.5578.684575280074158.6461829853529
Winsorized Mean ( 3 / 20 )4615.478.483170314398458.8075122540413
Winsorized Mean ( 4 / 20 )4608.2666666666775.985193572067460.6469030350762
Winsorized Mean ( 5 / 20 )4607.675.639250116537360.9154637691552
Winsorized Mean ( 6 / 20 )461074.498166663067661.8807174255659
Winsorized Mean ( 7 / 20 )4617.8166666666773.031908093734463.2301248481667
Winsorized Mean ( 8 / 20 )4592.4833333333367.129714604357768.4120789191499
Winsorized Mean ( 9 / 20 )4586.4833333333365.193755080579570.3515747430783
Winsorized Mean ( 10 / 20 )4580.4833333333363.399876542264672.2475118745669
Winsorized Mean ( 11 / 20 )4583.4166666666760.957465450607175.1904074879973
Winsorized Mean ( 12 / 20 )4582.8166666666760.308990118200675.9889472147474
Winsorized Mean ( 13 / 20 )4586.9333333333352.816690066012286.8462852859659
Winsorized Mean ( 14 / 20 )4589.551.842310338592588.5280761992484
Winsorized Mean ( 15 / 20 )4570.548.420804348805694.3912448681316
Winsorized Mean ( 16 / 20 )4567.347.833074272414195.4841408266752
Winsorized Mean ( 17 / 20 )4559.0833333333344.8329245670568101.690518237647
Winsorized Mean ( 18 / 20 )4565.0833333333342.9528074473402106.281372618777
Winsorized Mean ( 19 / 20 )4559.0666666666741.7598925433891109.173333286951
Winsorized Mean ( 20 / 20 )4555.439.5364681829849115.220205783593
Trimmed Mean ( 1 / 20 )4610.2413793103577.786366935545759.2679869356853
Trimmed Mean ( 2 / 20 )4605.87576.204164688743260.4412504068872
Trimmed Mean ( 3 / 20 )4601.0555555555674.457363392943561.79450017957
Trimmed Mean ( 4 / 20 )4595.5384615384672.348773269619163.519231271724
Trimmed Mean ( 5 / 20 )4591.7270.678709896637664.9660980897225
Trimmed Mean ( 6 / 20 )4587.7568.650398515318666.8277256828494
Trimmed Mean ( 7 / 20 )4582.9130434782666.389931618987869.0302419616822
Trimmed Mean ( 8 / 20 )4576.1136363636463.866736718737471.6509699957957
Trimmed Mean ( 9 / 20 )4573.1904761904862.309484199829773.3947734429003
Trimmed Mean ( 10 / 20 )4570.97560.739739953471975.2550966385678
Trimmed Mean ( 11 / 20 )4569.4736842105359.078506209405177.3457891439219
Trimmed Mean ( 12 / 20 )4567.3611111111157.434588781814779.5228312413244
Trimmed Mean ( 13 / 20 )4565.0882352941255.277881192240882.5843562892368
Trimmed Mean ( 14 / 20 )4561.937554.347373172639483.940349527264
Trimmed Mean ( 15 / 20 )455853.131673346918885.7868708602292
Trimmed Mean ( 16 / 20 )4556.2142857142952.2722663915787.1631287532822
Trimmed Mean ( 17 / 20 )4554.6153846153850.960680979723689.37508873611
Trimmed Mean ( 18 / 20 )4553.9583333333349.795032025012191.454069776396
Trimmed Mean ( 19 / 20 )4552.2727272727348.381473942594394.0912369200265
Trimmed Mean ( 20 / 20 )4551.246.262102257281498.3785815588108
Median4600
Midrange4649.5
Midmean - Weighted Average at Xnp4544.45161290323
Midmean - Weighted Average at X(n+1)p4558
Midmean - Empirical Distribution Function4544.45161290323
Midmean - Empirical Distribution Function - Averaging4558
Midmean - Empirical Distribution Function - Interpolation4558
Midmean - Closest Observation4544.45161290323
Midmean - True Basic - Statistics Graphics Toolkit4558
Midmean - MS Excel (old versions)4561.9375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4611.55 & 82.2754448646959 & 56.0501375299011 \tabularnewline
Geometric Mean & 4568.6028547909 &  &  \tabularnewline
Harmonic Mean & 4526.09284125354 &  &  \tabularnewline
Quadratic Mean & 4654.65133853582 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4614.31666666667 & 79.0471127903457 & 58.3742593977478 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4614.55 & 78.6845752800741 & 58.6461829853529 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4615.4 & 78.4831703143984 & 58.8075122540413 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4608.26666666667 & 75.9851935720674 & 60.6469030350762 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4607.6 & 75.6392501165373 & 60.9154637691552 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4610 & 74.4981666630676 & 61.8807174255659 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4617.81666666667 & 73.0319080937344 & 63.2301248481667 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4592.48333333333 & 67.1297146043577 & 68.4120789191499 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4586.48333333333 & 65.1937550805795 & 70.3515747430783 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4580.48333333333 & 63.3998765422646 & 72.2475118745669 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4583.41666666667 & 60.9574654506071 & 75.1904074879973 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4582.81666666667 & 60.3089901182006 & 75.9889472147474 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4586.93333333333 & 52.8166900660122 & 86.8462852859659 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4589.5 & 51.8423103385925 & 88.5280761992484 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4570.5 & 48.4208043488056 & 94.3912448681316 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4567.3 & 47.8330742724141 & 95.4841408266752 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4559.08333333333 & 44.8329245670568 & 101.690518237647 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4565.08333333333 & 42.9528074473402 & 106.281372618777 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4559.06666666667 & 41.7598925433891 & 109.173333286951 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4555.4 & 39.5364681829849 & 115.220205783593 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4610.24137931035 & 77.7863669355457 & 59.2679869356853 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4605.875 & 76.2041646887432 & 60.4412504068872 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4601.05555555556 & 74.4573633929435 & 61.79450017957 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4595.53846153846 & 72.3487732696191 & 63.519231271724 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4591.72 & 70.6787098966376 & 64.9660980897225 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4587.75 & 68.6503985153186 & 66.8277256828494 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4582.91304347826 & 66.3899316189878 & 69.0302419616822 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4576.11363636364 & 63.8667367187374 & 71.6509699957957 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4573.19047619048 & 62.3094841998297 & 73.3947734429003 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4570.975 & 60.7397399534719 & 75.2550966385678 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4569.47368421053 & 59.0785062094051 & 77.3457891439219 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4567.36111111111 & 57.4345887818147 & 79.5228312413244 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4565.08823529412 & 55.2778811922408 & 82.5843562892368 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4561.9375 & 54.3473731726394 & 83.940349527264 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4558 & 53.1316733469188 & 85.7868708602292 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4556.21428571429 & 52.27226639157 & 87.1631287532822 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4554.61538461538 & 50.9606809797236 & 89.37508873611 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4553.95833333333 & 49.7950320250121 & 91.454069776396 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4552.27272727273 & 48.3814739425943 & 94.0912369200265 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4551.2 & 46.2621022572814 & 98.3785815588108 \tabularnewline
Median & 4600 &  &  \tabularnewline
Midrange & 4649.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4544.45161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4558 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4544.45161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4558 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4558 &  &  \tabularnewline
Midmean - Closest Observation & 4544.45161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4558 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4561.9375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33734&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]4611.55[/C][C]82.2754448646959[/C][C]56.0501375299011[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4568.6028547909[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4526.09284125354[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4654.65133853582[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4614.31666666667[/C][C]79.0471127903457[/C][C]58.3742593977478[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4614.55[/C][C]78.6845752800741[/C][C]58.6461829853529[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4615.4[/C][C]78.4831703143984[/C][C]58.8075122540413[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4608.26666666667[/C][C]75.9851935720674[/C][C]60.6469030350762[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4607.6[/C][C]75.6392501165373[/C][C]60.9154637691552[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4610[/C][C]74.4981666630676[/C][C]61.8807174255659[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4617.81666666667[/C][C]73.0319080937344[/C][C]63.2301248481667[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4592.48333333333[/C][C]67.1297146043577[/C][C]68.4120789191499[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4586.48333333333[/C][C]65.1937550805795[/C][C]70.3515747430783[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4580.48333333333[/C][C]63.3998765422646[/C][C]72.2475118745669[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4583.41666666667[/C][C]60.9574654506071[/C][C]75.1904074879973[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4582.81666666667[/C][C]60.3089901182006[/C][C]75.9889472147474[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4586.93333333333[/C][C]52.8166900660122[/C][C]86.8462852859659[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4589.5[/C][C]51.8423103385925[/C][C]88.5280761992484[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4570.5[/C][C]48.4208043488056[/C][C]94.3912448681316[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4567.3[/C][C]47.8330742724141[/C][C]95.4841408266752[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4559.08333333333[/C][C]44.8329245670568[/C][C]101.690518237647[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4565.08333333333[/C][C]42.9528074473402[/C][C]106.281372618777[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4559.06666666667[/C][C]41.7598925433891[/C][C]109.173333286951[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4555.4[/C][C]39.5364681829849[/C][C]115.220205783593[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4610.24137931035[/C][C]77.7863669355457[/C][C]59.2679869356853[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4605.875[/C][C]76.2041646887432[/C][C]60.4412504068872[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4601.05555555556[/C][C]74.4573633929435[/C][C]61.79450017957[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4595.53846153846[/C][C]72.3487732696191[/C][C]63.519231271724[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4591.72[/C][C]70.6787098966376[/C][C]64.9660980897225[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4587.75[/C][C]68.6503985153186[/C][C]66.8277256828494[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4582.91304347826[/C][C]66.3899316189878[/C][C]69.0302419616822[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4576.11363636364[/C][C]63.8667367187374[/C][C]71.6509699957957[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4573.19047619048[/C][C]62.3094841998297[/C][C]73.3947734429003[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4570.975[/C][C]60.7397399534719[/C][C]75.2550966385678[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4569.47368421053[/C][C]59.0785062094051[/C][C]77.3457891439219[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4567.36111111111[/C][C]57.4345887818147[/C][C]79.5228312413244[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4565.08823529412[/C][C]55.2778811922408[/C][C]82.5843562892368[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4561.9375[/C][C]54.3473731726394[/C][C]83.940349527264[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4558[/C][C]53.1316733469188[/C][C]85.7868708602292[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4556.21428571429[/C][C]52.27226639157[/C][C]87.1631287532822[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4554.61538461538[/C][C]50.9606809797236[/C][C]89.37508873611[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4553.95833333333[/C][C]49.7950320250121[/C][C]91.454069776396[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4552.27272727273[/C][C]48.3814739425943[/C][C]94.0912369200265[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4551.2[/C][C]46.2621022572814[/C][C]98.3785815588108[/C][/ROW]
[ROW][C]Median[/C][C]4600[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4649.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4544.45161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4544.45161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4544.45161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4561.9375[/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=33734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33734&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 Mean4611.5582.275444864695956.0501375299011
Geometric Mean4568.6028547909
Harmonic Mean4526.09284125354
Quadratic Mean4654.65133853582
Winsorized Mean ( 1 / 20 )4614.3166666666779.047112790345758.3742593977478
Winsorized Mean ( 2 / 20 )4614.5578.684575280074158.6461829853529
Winsorized Mean ( 3 / 20 )4615.478.483170314398458.8075122540413
Winsorized Mean ( 4 / 20 )4608.2666666666775.985193572067460.6469030350762
Winsorized Mean ( 5 / 20 )4607.675.639250116537360.9154637691552
Winsorized Mean ( 6 / 20 )461074.498166663067661.8807174255659
Winsorized Mean ( 7 / 20 )4617.8166666666773.031908093734463.2301248481667
Winsorized Mean ( 8 / 20 )4592.4833333333367.129714604357768.4120789191499
Winsorized Mean ( 9 / 20 )4586.4833333333365.193755080579570.3515747430783
Winsorized Mean ( 10 / 20 )4580.4833333333363.399876542264672.2475118745669
Winsorized Mean ( 11 / 20 )4583.4166666666760.957465450607175.1904074879973
Winsorized Mean ( 12 / 20 )4582.8166666666760.308990118200675.9889472147474
Winsorized Mean ( 13 / 20 )4586.9333333333352.816690066012286.8462852859659
Winsorized Mean ( 14 / 20 )4589.551.842310338592588.5280761992484
Winsorized Mean ( 15 / 20 )4570.548.420804348805694.3912448681316
Winsorized Mean ( 16 / 20 )4567.347.833074272414195.4841408266752
Winsorized Mean ( 17 / 20 )4559.0833333333344.8329245670568101.690518237647
Winsorized Mean ( 18 / 20 )4565.0833333333342.9528074473402106.281372618777
Winsorized Mean ( 19 / 20 )4559.0666666666741.7598925433891109.173333286951
Winsorized Mean ( 20 / 20 )4555.439.5364681829849115.220205783593
Trimmed Mean ( 1 / 20 )4610.2413793103577.786366935545759.2679869356853
Trimmed Mean ( 2 / 20 )4605.87576.204164688743260.4412504068872
Trimmed Mean ( 3 / 20 )4601.0555555555674.457363392943561.79450017957
Trimmed Mean ( 4 / 20 )4595.5384615384672.348773269619163.519231271724
Trimmed Mean ( 5 / 20 )4591.7270.678709896637664.9660980897225
Trimmed Mean ( 6 / 20 )4587.7568.650398515318666.8277256828494
Trimmed Mean ( 7 / 20 )4582.9130434782666.389931618987869.0302419616822
Trimmed Mean ( 8 / 20 )4576.1136363636463.866736718737471.6509699957957
Trimmed Mean ( 9 / 20 )4573.1904761904862.309484199829773.3947734429003
Trimmed Mean ( 10 / 20 )4570.97560.739739953471975.2550966385678
Trimmed Mean ( 11 / 20 )4569.4736842105359.078506209405177.3457891439219
Trimmed Mean ( 12 / 20 )4567.3611111111157.434588781814779.5228312413244
Trimmed Mean ( 13 / 20 )4565.0882352941255.277881192240882.5843562892368
Trimmed Mean ( 14 / 20 )4561.937554.347373172639483.940349527264
Trimmed Mean ( 15 / 20 )455853.131673346918885.7868708602292
Trimmed Mean ( 16 / 20 )4556.2142857142952.2722663915787.1631287532822
Trimmed Mean ( 17 / 20 )4554.6153846153850.960680979723689.37508873611
Trimmed Mean ( 18 / 20 )4553.9583333333349.795032025012191.454069776396
Trimmed Mean ( 19 / 20 )4552.2727272727348.381473942594394.0912369200265
Trimmed Mean ( 20 / 20 )4551.246.262102257281498.3785815588108
Median4600
Midrange4649.5
Midmean - Weighted Average at Xnp4544.45161290323
Midmean - Weighted Average at X(n+1)p4558
Midmean - Empirical Distribution Function4544.45161290323
Midmean - Empirical Distribution Function - Averaging4558
Midmean - Empirical Distribution Function - Interpolation4558
Midmean - Closest Observation4544.45161290323
Midmean - True Basic - Statistics Graphics Toolkit4558
Midmean - MS Excel (old versions)4561.9375
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')