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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 17:14:04 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444407273usn7vrbufmobz52.htm/, Retrieved Tue, 14 May 2024 09:46:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281958, Retrieved Tue, 14 May 2024 09:46:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
789
811
996
778
603
990
735
800
706
766
870
647
726
784
884
696
893
674
703
799
793
799
1022
758
1021
944
915
864
1022
891
1087
822
890
1092
967
833
1104
1063
1103
1039
1185
1047
1155
878
879
1133
920
943
938
900
781
1040
792
653
866
679
799
760
699
762




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' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281958&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281958&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281958&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean874.818.594145849890647.0470656228151
Geometric Mean863.254779883847
Harmonic Mean851.874463316075
Quadratic Mean886.382441913948
Winsorized Mean ( 1 / 20 )875.03333333333318.290112896184647.841877100489
Winsorized Mean ( 2 / 20 )874.518.064096487809848.4109460215814
Winsorized Mean ( 3 / 20 )874.117.515863673424449.9033342744161
Winsorized Mean ( 4 / 20 )874.36666666666717.437118125201850.1439894131902
Winsorized Mean ( 5 / 20 )874.86666666666716.974731414409451.5393525416264
Winsorized Mean ( 6 / 20 )874.66666666666716.813662501202252.0211861397913
Winsorized Mean ( 7 / 20 )872.33333333333316.150696870915454.0121172668565
Winsorized Mean ( 8 / 20 )870.615.662330208836255.5855985917624
Winsorized Mean ( 9 / 20 )872.5514.94550222385258.3821130217673
Winsorized Mean ( 10 / 20 )873.88333333333314.668735569281659.5745508674496
Winsorized Mean ( 11 / 20 )874.98333333333313.43119086109965.1456257588866
Winsorized Mean ( 12 / 20 )875.38333333333313.372416412736765.4618661515478
Winsorized Mean ( 13 / 20 )875.613.26903706501665.9882096726168
Winsorized Mean ( 14 / 20 )870.712.076832656191372.0967181369052
Winsorized Mean ( 15 / 20 )872.211.38225896775576.6280228266524
Winsorized Mean ( 16 / 20 )866.86666666666710.220519591274784.8163010622973
Winsorized Mean ( 17 / 20 )861.29.0501053463294695.1591132968729
Winsorized Mean ( 18 / 20 )862.48.7888990074247598.1237808366503
Winsorized Mean ( 19 / 20 )861.7666666666678.41015550574929102.467387918993
Winsorized Mean ( 20 / 20 )856.17.46519986601484114.678778246431
Trimmed Mean ( 1 / 20 )874.13793103448317.853701497285748.9611597442345
Trimmed Mean ( 2 / 20 )873.17857142857117.313723014944550.4327446312315
Trimmed Mean ( 3 / 20 )872.44444444444416.794700394243551.9476039443659
Trimmed Mean ( 4 / 20 )871.80769230769216.411034401335753.1232627381937
Trimmed Mean ( 5 / 20 )871.0415.953861025866254.5974418723951
Trimmed Mean ( 6 / 20 )870.08333333333315.529679698456256.0271267809746
Trimmed Mean ( 7 / 20 )869.08695652173915.031587548845457.8173764878542
Trimmed Mean ( 8 / 20 )868.45454545454514.585696842236659.5415189858954
Trimmed Mean ( 9 / 20 )868.07142857142914.138702037473761.3968259795462
Trimmed Mean ( 10 / 20 )867.32513.739023007664363.1285790493375
Trimmed Mean ( 11 / 20 )866.28947368421113.266172550208965.3006336534172
Trimmed Mean ( 12 / 20 )864.97222222222212.953181022014166.776818817879
Trimmed Mean ( 13 / 20 )863.44117647058812.512111150731369.0084323955293
Trimmed Mean ( 14 / 20 )861.687511.898379997822472.4205732341463
Trimmed Mean ( 15 / 20 )860.411.406451088606975.4309989422909
Trimmed Mean ( 16 / 20 )858.71428571428610.882228746646178.9097808644153
Trimmed Mean ( 17 / 20 )857.53846153846210.504684781889681.6339070941834
Trimmed Mean ( 18 / 20 )85710.324095917887483.0096898378456
Trimmed Mean ( 19 / 20 )856.18181818181810.064862449116685.0664201831157
Trimmed Mean ( 20 / 20 )855.39.7295264124481687.9076702958236
Median868
Midrange894
Midmean - Weighted Average at Xnp857.354838709677
Midmean - Weighted Average at X(n+1)p860.4
Midmean - Empirical Distribution Function857.354838709677
Midmean - Empirical Distribution Function - Averaging860.4
Midmean - Empirical Distribution Function - Interpolation860.4
Midmean - Closest Observation857.354838709677
Midmean - True Basic - Statistics Graphics Toolkit860.4
Midmean - MS Excel (old versions)861.6875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 874.8 & 18.5941458498906 & 47.0470656228151 \tabularnewline
Geometric Mean & 863.254779883847 &  &  \tabularnewline
Harmonic Mean & 851.874463316075 &  &  \tabularnewline
Quadratic Mean & 886.382441913948 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 875.033333333333 & 18.2901128961846 & 47.841877100489 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 874.5 & 18.0640964878098 & 48.4109460215814 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 874.1 & 17.5158636734244 & 49.9033342744161 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 874.366666666667 & 17.4371181252018 & 50.1439894131902 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 874.866666666667 & 16.9747314144094 & 51.5393525416264 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 874.666666666667 & 16.8136625012022 & 52.0211861397913 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 872.333333333333 & 16.1506968709154 & 54.0121172668565 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 870.6 & 15.6623302088362 & 55.5855985917624 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 872.55 & 14.945502223852 & 58.3821130217673 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 873.883333333333 & 14.6687355692816 & 59.5745508674496 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 874.983333333333 & 13.431190861099 & 65.1456257588866 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 875.383333333333 & 13.3724164127367 & 65.4618661515478 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 875.6 & 13.269037065016 & 65.9882096726168 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 870.7 & 12.0768326561913 & 72.0967181369052 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 872.2 & 11.382258967755 & 76.6280228266524 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 866.866666666667 & 10.2205195912747 & 84.8163010622973 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 861.2 & 9.05010534632946 & 95.1591132968729 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 862.4 & 8.78889900742475 & 98.1237808366503 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 861.766666666667 & 8.41015550574929 & 102.467387918993 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 856.1 & 7.46519986601484 & 114.678778246431 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 874.137931034483 & 17.8537014972857 & 48.9611597442345 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 873.178571428571 & 17.3137230149445 & 50.4327446312315 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 872.444444444444 & 16.7947003942435 & 51.9476039443659 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 871.807692307692 & 16.4110344013357 & 53.1232627381937 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 871.04 & 15.9538610258662 & 54.5974418723951 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 870.083333333333 & 15.5296796984562 & 56.0271267809746 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 869.086956521739 & 15.0315875488454 & 57.8173764878542 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 868.454545454545 & 14.5856968422366 & 59.5415189858954 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 868.071428571429 & 14.1387020374737 & 61.3968259795462 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 867.325 & 13.7390230076643 & 63.1285790493375 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 866.289473684211 & 13.2661725502089 & 65.3006336534172 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 864.972222222222 & 12.9531810220141 & 66.776818817879 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 863.441176470588 & 12.5121111507313 & 69.0084323955293 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 861.6875 & 11.8983799978224 & 72.4205732341463 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 860.4 & 11.4064510886069 & 75.4309989422909 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 858.714285714286 & 10.8822287466461 & 78.9097808644153 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 857.538461538462 & 10.5046847818896 & 81.6339070941834 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 857 & 10.3240959178874 & 83.0096898378456 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 856.181818181818 & 10.0648624491166 & 85.0664201831157 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 855.3 & 9.72952641244816 & 87.9076702958236 \tabularnewline
Median & 868 &  &  \tabularnewline
Midrange & 894 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 857.354838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 860.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 857.354838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 860.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 860.4 &  &  \tabularnewline
Midmean - Closest Observation & 857.354838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 860.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 861.6875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281958&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]874.8[/C][C]18.5941458498906[/C][C]47.0470656228151[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]863.254779883847[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]851.874463316075[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]886.382441913948[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]875.033333333333[/C][C]18.2901128961846[/C][C]47.841877100489[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]874.5[/C][C]18.0640964878098[/C][C]48.4109460215814[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]874.1[/C][C]17.5158636734244[/C][C]49.9033342744161[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]874.366666666667[/C][C]17.4371181252018[/C][C]50.1439894131902[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]874.866666666667[/C][C]16.9747314144094[/C][C]51.5393525416264[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]874.666666666667[/C][C]16.8136625012022[/C][C]52.0211861397913[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]872.333333333333[/C][C]16.1506968709154[/C][C]54.0121172668565[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]870.6[/C][C]15.6623302088362[/C][C]55.5855985917624[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]872.55[/C][C]14.945502223852[/C][C]58.3821130217673[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]873.883333333333[/C][C]14.6687355692816[/C][C]59.5745508674496[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]874.983333333333[/C][C]13.431190861099[/C][C]65.1456257588866[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]875.383333333333[/C][C]13.3724164127367[/C][C]65.4618661515478[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]875.6[/C][C]13.269037065016[/C][C]65.9882096726168[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]870.7[/C][C]12.0768326561913[/C][C]72.0967181369052[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]872.2[/C][C]11.382258967755[/C][C]76.6280228266524[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]866.866666666667[/C][C]10.2205195912747[/C][C]84.8163010622973[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]861.2[/C][C]9.05010534632946[/C][C]95.1591132968729[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]862.4[/C][C]8.78889900742475[/C][C]98.1237808366503[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]861.766666666667[/C][C]8.41015550574929[/C][C]102.467387918993[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]856.1[/C][C]7.46519986601484[/C][C]114.678778246431[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]874.137931034483[/C][C]17.8537014972857[/C][C]48.9611597442345[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]873.178571428571[/C][C]17.3137230149445[/C][C]50.4327446312315[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]872.444444444444[/C][C]16.7947003942435[/C][C]51.9476039443659[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]871.807692307692[/C][C]16.4110344013357[/C][C]53.1232627381937[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]871.04[/C][C]15.9538610258662[/C][C]54.5974418723951[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]870.083333333333[/C][C]15.5296796984562[/C][C]56.0271267809746[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]869.086956521739[/C][C]15.0315875488454[/C][C]57.8173764878542[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]868.454545454545[/C][C]14.5856968422366[/C][C]59.5415189858954[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]868.071428571429[/C][C]14.1387020374737[/C][C]61.3968259795462[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]867.325[/C][C]13.7390230076643[/C][C]63.1285790493375[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]866.289473684211[/C][C]13.2661725502089[/C][C]65.3006336534172[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]864.972222222222[/C][C]12.9531810220141[/C][C]66.776818817879[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]863.441176470588[/C][C]12.5121111507313[/C][C]69.0084323955293[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]861.6875[/C][C]11.8983799978224[/C][C]72.4205732341463[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]860.4[/C][C]11.4064510886069[/C][C]75.4309989422909[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]858.714285714286[/C][C]10.8822287466461[/C][C]78.9097808644153[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]857.538461538462[/C][C]10.5046847818896[/C][C]81.6339070941834[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]857[/C][C]10.3240959178874[/C][C]83.0096898378456[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]856.181818181818[/C][C]10.0648624491166[/C][C]85.0664201831157[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]855.3[/C][C]9.72952641244816[/C][C]87.9076702958236[/C][/ROW]
[ROW][C]Median[/C][C]868[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]894[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]857.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]860.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]857.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]860.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]860.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]857.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]860.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]861.6875[/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=281958&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281958&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 Mean874.818.594145849890647.0470656228151
Geometric Mean863.254779883847
Harmonic Mean851.874463316075
Quadratic Mean886.382441913948
Winsorized Mean ( 1 / 20 )875.03333333333318.290112896184647.841877100489
Winsorized Mean ( 2 / 20 )874.518.064096487809848.4109460215814
Winsorized Mean ( 3 / 20 )874.117.515863673424449.9033342744161
Winsorized Mean ( 4 / 20 )874.36666666666717.437118125201850.1439894131902
Winsorized Mean ( 5 / 20 )874.86666666666716.974731414409451.5393525416264
Winsorized Mean ( 6 / 20 )874.66666666666716.813662501202252.0211861397913
Winsorized Mean ( 7 / 20 )872.33333333333316.150696870915454.0121172668565
Winsorized Mean ( 8 / 20 )870.615.662330208836255.5855985917624
Winsorized Mean ( 9 / 20 )872.5514.94550222385258.3821130217673
Winsorized Mean ( 10 / 20 )873.88333333333314.668735569281659.5745508674496
Winsorized Mean ( 11 / 20 )874.98333333333313.43119086109965.1456257588866
Winsorized Mean ( 12 / 20 )875.38333333333313.372416412736765.4618661515478
Winsorized Mean ( 13 / 20 )875.613.26903706501665.9882096726168
Winsorized Mean ( 14 / 20 )870.712.076832656191372.0967181369052
Winsorized Mean ( 15 / 20 )872.211.38225896775576.6280228266524
Winsorized Mean ( 16 / 20 )866.86666666666710.220519591274784.8163010622973
Winsorized Mean ( 17 / 20 )861.29.0501053463294695.1591132968729
Winsorized Mean ( 18 / 20 )862.48.7888990074247598.1237808366503
Winsorized Mean ( 19 / 20 )861.7666666666678.41015550574929102.467387918993
Winsorized Mean ( 20 / 20 )856.17.46519986601484114.678778246431
Trimmed Mean ( 1 / 20 )874.13793103448317.853701497285748.9611597442345
Trimmed Mean ( 2 / 20 )873.17857142857117.313723014944550.4327446312315
Trimmed Mean ( 3 / 20 )872.44444444444416.794700394243551.9476039443659
Trimmed Mean ( 4 / 20 )871.80769230769216.411034401335753.1232627381937
Trimmed Mean ( 5 / 20 )871.0415.953861025866254.5974418723951
Trimmed Mean ( 6 / 20 )870.08333333333315.529679698456256.0271267809746
Trimmed Mean ( 7 / 20 )869.08695652173915.031587548845457.8173764878542
Trimmed Mean ( 8 / 20 )868.45454545454514.585696842236659.5415189858954
Trimmed Mean ( 9 / 20 )868.07142857142914.138702037473761.3968259795462
Trimmed Mean ( 10 / 20 )867.32513.739023007664363.1285790493375
Trimmed Mean ( 11 / 20 )866.28947368421113.266172550208965.3006336534172
Trimmed Mean ( 12 / 20 )864.97222222222212.953181022014166.776818817879
Trimmed Mean ( 13 / 20 )863.44117647058812.512111150731369.0084323955293
Trimmed Mean ( 14 / 20 )861.687511.898379997822472.4205732341463
Trimmed Mean ( 15 / 20 )860.411.406451088606975.4309989422909
Trimmed Mean ( 16 / 20 )858.71428571428610.882228746646178.9097808644153
Trimmed Mean ( 17 / 20 )857.53846153846210.504684781889681.6339070941834
Trimmed Mean ( 18 / 20 )85710.324095917887483.0096898378456
Trimmed Mean ( 19 / 20 )856.18181818181810.064862449116685.0664201831157
Trimmed Mean ( 20 / 20 )855.39.7295264124481687.9076702958236
Median868
Midrange894
Midmean - Weighted Average at Xnp857.354838709677
Midmean - Weighted Average at X(n+1)p860.4
Midmean - Empirical Distribution Function857.354838709677
Midmean - Empirical Distribution Function - Averaging860.4
Midmean - Empirical Distribution Function - Interpolation860.4
Midmean - Closest Observation857.354838709677
Midmean - True Basic - Statistics Graphics Toolkit860.4
Midmean - MS Excel (old versions)861.6875
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')