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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 computationTue, 08 Mar 2016 20:52:09 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/08/t14574703597vv5trry49w2xe2.htm/, Retrieved Mon, 29 Apr 2024 05:24:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293760, Retrieved Mon, 29 Apr 2024 05:24:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten-Fail...] [2016-03-08 20:52:09] [45930f35caeb32be6f319da4f3b0c690] [Current]
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Dataseries X:
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
671
679
862
624
516
650
583
444
562
540
524
674




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293760&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293760&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293760&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean838.76666666666722.997547973773836.4720042164143
Geometric Mean819.163509159611
Harmonic Mean798.508396547573
Quadratic Mean857.166183809573
Winsorized Mean ( 1 / 20 )839.46666666666722.553733285698237.2207410645842
Winsorized Mean ( 2 / 20 )83922.320596756091137.588600751503
Winsorized Mean ( 3 / 20 )838.3521.820593924296438.4201274680489
Winsorized Mean ( 4 / 20 )839.7521.476022959265439.1017462401114
Winsorized Mean ( 5 / 20 )840.58333333333320.912790286133240.1947000774308
Winsorized Mean ( 6 / 20 )844.18333333333319.998891094493642.2115070952992
Winsorized Mean ( 7 / 20 )844.41666666666718.887644179106544.7073578186506
Winsorized Mean ( 8 / 20 )842.68333333333318.407817236296645.7785582351247
Winsorized Mean ( 9 / 20 )844.33333333333317.751528408242147.5639795016922
Winsorized Mean ( 10 / 20 )844.66666666666717.638021761980147.8889683925553
Winsorized Mean ( 11 / 20 )841.5517.06756968722449.3069614140755
Winsorized Mean ( 12 / 20 )842.5516.902368787287449.8480426384789
Winsorized Mean ( 13 / 20 )842.33333333333316.863420558090249.9503247536113
Winsorized Mean ( 14 / 20 )833.714.053917563087459.3215376607667
Winsorized Mean ( 15 / 20 )828.713.03401243769563.5798073664068
Winsorized Mean ( 16 / 20 )829.512.814815313746264.7297662659416
Winsorized Mean ( 17 / 20 )834.611.534477915838372.3569810519115
Winsorized Mean ( 18 / 20 )838.89.2374758701702490.8040260985863
Winsorized Mean ( 19 / 20 )837.858.9094574584196794.0405186185844
Winsorized Mean ( 20 / 20 )833.5166666666678.09434104012321102.975234492217
Trimmed Mean ( 1 / 20 )839.60344827586221.975223077672638.2068225340985
Trimmed Mean ( 2 / 20 )839.7521.261410229217339.4964393681667
Trimmed Mean ( 3 / 20 )840.16666666666720.532766845353540.9183366759359
Trimmed Mean ( 4 / 20 )840.86538461538519.868250608368142.3220645435804
Trimmed Mean ( 5 / 20 )841.219.170385323967543.8801821551444
Trimmed Mean ( 6 / 20 )841.35416666666718.484407114327645.5169679753764
Trimmed Mean ( 7 / 20 )840.73913043478317.899516490989846.9699352414346
Trimmed Mean ( 8 / 20 )840.02272727272717.469529154377648.0850239207638
Trimmed Mean ( 9 / 20 )839.54761904761917.032837124570349.2899458209784
Trimmed Mean ( 10 / 20 )838.7516.621107602946350.4629426652242
Trimmed Mean ( 11 / 20 )837.81578947368416.083258449885152.0924159792799
Trimmed Mean ( 12 / 20 )837.2515.505266642363653.997781483645
Trimmed Mean ( 13 / 20 )836.47058823529414.738495032342756.7541384924112
Trimmed Mean ( 14 / 20 )835.62513.650796827740861.2143752884714
Trimmed Mean ( 15 / 20 )835.913.047072160221464.0680138604996
Trimmed Mean ( 16 / 20 )836.92857142857112.47430465573167.092202293141
Trimmed Mean ( 17 / 20 )83811.663354841290171.8489672485438
Trimmed Mean ( 18 / 20 )838.510.923979738782676.7577403153846
Trimmed Mean ( 19 / 20 )838.45454545454510.685331466077578.4678087073268
Trimmed Mean ( 20 / 20 )838.5510.353609845947780.9910758157648
Median847.5
Midrange814.5
Midmean - Weighted Average at Xnp831.387096774194
Midmean - Weighted Average at X(n+1)p835.9
Midmean - Empirical Distribution Function831.387096774194
Midmean - Empirical Distribution Function - Averaging835.9
Midmean - Empirical Distribution Function - Interpolation835.9
Midmean - Closest Observation831.387096774194
Midmean - True Basic - Statistics Graphics Toolkit835.9
Midmean - MS Excel (old versions)835.625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 838.766666666667 & 22.9975479737738 & 36.4720042164143 \tabularnewline
Geometric Mean & 819.163509159611 &  &  \tabularnewline
Harmonic Mean & 798.508396547573 &  &  \tabularnewline
Quadratic Mean & 857.166183809573 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 839.466666666667 & 22.5537332856982 & 37.2207410645842 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 839 & 22.3205967560911 & 37.588600751503 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 838.35 & 21.8205939242964 & 38.4201274680489 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 839.75 & 21.4760229592654 & 39.1017462401114 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 840.583333333333 & 20.9127902861332 & 40.1947000774308 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 844.183333333333 & 19.9988910944936 & 42.2115070952992 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 844.416666666667 & 18.8876441791065 & 44.7073578186506 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 842.683333333333 & 18.4078172362966 & 45.7785582351247 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 844.333333333333 & 17.7515284082421 & 47.5639795016922 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 844.666666666667 & 17.6380217619801 & 47.8889683925553 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 841.55 & 17.067569687224 & 49.3069614140755 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 842.55 & 16.9023687872874 & 49.8480426384789 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 842.333333333333 & 16.8634205580902 & 49.9503247536113 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 833.7 & 14.0539175630874 & 59.3215376607667 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 828.7 & 13.034012437695 & 63.5798073664068 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 829.5 & 12.8148153137462 & 64.7297662659416 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 834.6 & 11.5344779158383 & 72.3569810519115 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 838.8 & 9.23747587017024 & 90.8040260985863 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 837.85 & 8.90945745841967 & 94.0405186185844 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 833.516666666667 & 8.09434104012321 & 102.975234492217 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 839.603448275862 & 21.9752230776726 & 38.2068225340985 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 839.75 & 21.2614102292173 & 39.4964393681667 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 840.166666666667 & 20.5327668453535 & 40.9183366759359 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 840.865384615385 & 19.8682506083681 & 42.3220645435804 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 841.2 & 19.1703853239675 & 43.8801821551444 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 841.354166666667 & 18.4844071143276 & 45.5169679753764 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 840.739130434783 & 17.8995164909898 & 46.9699352414346 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 840.022727272727 & 17.4695291543776 & 48.0850239207638 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 839.547619047619 & 17.0328371245703 & 49.2899458209784 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 838.75 & 16.6211076029463 & 50.4629426652242 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 837.815789473684 & 16.0832584498851 & 52.0924159792799 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 837.25 & 15.5052666423636 & 53.997781483645 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 836.470588235294 & 14.7384950323427 & 56.7541384924112 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 835.625 & 13.6507968277408 & 61.2143752884714 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 835.9 & 13.0470721602214 & 64.0680138604996 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 836.928571428571 & 12.474304655731 & 67.092202293141 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 838 & 11.6633548412901 & 71.8489672485438 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 838.5 & 10.9239797387826 & 76.7577403153846 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 838.454545454545 & 10.6853314660775 & 78.4678087073268 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 838.55 & 10.3536098459477 & 80.9910758157648 \tabularnewline
Median & 847.5 &  &  \tabularnewline
Midrange & 814.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 831.387096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 835.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 831.387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 835.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 835.9 &  &  \tabularnewline
Midmean - Closest Observation & 831.387096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 835.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 835.625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293760&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]838.766666666667[/C][C]22.9975479737738[/C][C]36.4720042164143[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]819.163509159611[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]798.508396547573[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]857.166183809573[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]839.466666666667[/C][C]22.5537332856982[/C][C]37.2207410645842[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]839[/C][C]22.3205967560911[/C][C]37.588600751503[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]838.35[/C][C]21.8205939242964[/C][C]38.4201274680489[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]839.75[/C][C]21.4760229592654[/C][C]39.1017462401114[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]840.583333333333[/C][C]20.9127902861332[/C][C]40.1947000774308[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]844.183333333333[/C][C]19.9988910944936[/C][C]42.2115070952992[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]844.416666666667[/C][C]18.8876441791065[/C][C]44.7073578186506[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]842.683333333333[/C][C]18.4078172362966[/C][C]45.7785582351247[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]844.333333333333[/C][C]17.7515284082421[/C][C]47.5639795016922[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]844.666666666667[/C][C]17.6380217619801[/C][C]47.8889683925553[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]841.55[/C][C]17.067569687224[/C][C]49.3069614140755[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]842.55[/C][C]16.9023687872874[/C][C]49.8480426384789[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]842.333333333333[/C][C]16.8634205580902[/C][C]49.9503247536113[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]833.7[/C][C]14.0539175630874[/C][C]59.3215376607667[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]828.7[/C][C]13.034012437695[/C][C]63.5798073664068[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]829.5[/C][C]12.8148153137462[/C][C]64.7297662659416[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]834.6[/C][C]11.5344779158383[/C][C]72.3569810519115[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]838.8[/C][C]9.23747587017024[/C][C]90.8040260985863[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]837.85[/C][C]8.90945745841967[/C][C]94.0405186185844[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]833.516666666667[/C][C]8.09434104012321[/C][C]102.975234492217[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]839.603448275862[/C][C]21.9752230776726[/C][C]38.2068225340985[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]839.75[/C][C]21.2614102292173[/C][C]39.4964393681667[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]840.166666666667[/C][C]20.5327668453535[/C][C]40.9183366759359[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]840.865384615385[/C][C]19.8682506083681[/C][C]42.3220645435804[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]841.2[/C][C]19.1703853239675[/C][C]43.8801821551444[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]841.354166666667[/C][C]18.4844071143276[/C][C]45.5169679753764[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]840.739130434783[/C][C]17.8995164909898[/C][C]46.9699352414346[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]840.022727272727[/C][C]17.4695291543776[/C][C]48.0850239207638[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]839.547619047619[/C][C]17.0328371245703[/C][C]49.2899458209784[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]838.75[/C][C]16.6211076029463[/C][C]50.4629426652242[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]837.815789473684[/C][C]16.0832584498851[/C][C]52.0924159792799[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]837.25[/C][C]15.5052666423636[/C][C]53.997781483645[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]836.470588235294[/C][C]14.7384950323427[/C][C]56.7541384924112[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]835.625[/C][C]13.6507968277408[/C][C]61.2143752884714[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]835.9[/C][C]13.0470721602214[/C][C]64.0680138604996[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]836.928571428571[/C][C]12.474304655731[/C][C]67.092202293141[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]838[/C][C]11.6633548412901[/C][C]71.8489672485438[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]838.5[/C][C]10.9239797387826[/C][C]76.7577403153846[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]838.454545454545[/C][C]10.6853314660775[/C][C]78.4678087073268[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]838.55[/C][C]10.3536098459477[/C][C]80.9910758157648[/C][/ROW]
[ROW][C]Median[/C][C]847.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]814.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]831.387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]835.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]831.387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]835.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]835.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]831.387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]835.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]835.625[/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=293760&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293760&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 Mean838.76666666666722.997547973773836.4720042164143
Geometric Mean819.163509159611
Harmonic Mean798.508396547573
Quadratic Mean857.166183809573
Winsorized Mean ( 1 / 20 )839.46666666666722.553733285698237.2207410645842
Winsorized Mean ( 2 / 20 )83922.320596756091137.588600751503
Winsorized Mean ( 3 / 20 )838.3521.820593924296438.4201274680489
Winsorized Mean ( 4 / 20 )839.7521.476022959265439.1017462401114
Winsorized Mean ( 5 / 20 )840.58333333333320.912790286133240.1947000774308
Winsorized Mean ( 6 / 20 )844.18333333333319.998891094493642.2115070952992
Winsorized Mean ( 7 / 20 )844.41666666666718.887644179106544.7073578186506
Winsorized Mean ( 8 / 20 )842.68333333333318.407817236296645.7785582351247
Winsorized Mean ( 9 / 20 )844.33333333333317.751528408242147.5639795016922
Winsorized Mean ( 10 / 20 )844.66666666666717.638021761980147.8889683925553
Winsorized Mean ( 11 / 20 )841.5517.06756968722449.3069614140755
Winsorized Mean ( 12 / 20 )842.5516.902368787287449.8480426384789
Winsorized Mean ( 13 / 20 )842.33333333333316.863420558090249.9503247536113
Winsorized Mean ( 14 / 20 )833.714.053917563087459.3215376607667
Winsorized Mean ( 15 / 20 )828.713.03401243769563.5798073664068
Winsorized Mean ( 16 / 20 )829.512.814815313746264.7297662659416
Winsorized Mean ( 17 / 20 )834.611.534477915838372.3569810519115
Winsorized Mean ( 18 / 20 )838.89.2374758701702490.8040260985863
Winsorized Mean ( 19 / 20 )837.858.9094574584196794.0405186185844
Winsorized Mean ( 20 / 20 )833.5166666666678.09434104012321102.975234492217
Trimmed Mean ( 1 / 20 )839.60344827586221.975223077672638.2068225340985
Trimmed Mean ( 2 / 20 )839.7521.261410229217339.4964393681667
Trimmed Mean ( 3 / 20 )840.16666666666720.532766845353540.9183366759359
Trimmed Mean ( 4 / 20 )840.86538461538519.868250608368142.3220645435804
Trimmed Mean ( 5 / 20 )841.219.170385323967543.8801821551444
Trimmed Mean ( 6 / 20 )841.35416666666718.484407114327645.5169679753764
Trimmed Mean ( 7 / 20 )840.73913043478317.899516490989846.9699352414346
Trimmed Mean ( 8 / 20 )840.02272727272717.469529154377648.0850239207638
Trimmed Mean ( 9 / 20 )839.54761904761917.032837124570349.2899458209784
Trimmed Mean ( 10 / 20 )838.7516.621107602946350.4629426652242
Trimmed Mean ( 11 / 20 )837.81578947368416.083258449885152.0924159792799
Trimmed Mean ( 12 / 20 )837.2515.505266642363653.997781483645
Trimmed Mean ( 13 / 20 )836.47058823529414.738495032342756.7541384924112
Trimmed Mean ( 14 / 20 )835.62513.650796827740861.2143752884714
Trimmed Mean ( 15 / 20 )835.913.047072160221464.0680138604996
Trimmed Mean ( 16 / 20 )836.92857142857112.47430465573167.092202293141
Trimmed Mean ( 17 / 20 )83811.663354841290171.8489672485438
Trimmed Mean ( 18 / 20 )838.510.923979738782676.7577403153846
Trimmed Mean ( 19 / 20 )838.45454545454510.685331466077578.4678087073268
Trimmed Mean ( 20 / 20 )838.5510.353609845947780.9910758157648
Median847.5
Midrange814.5
Midmean - Weighted Average at Xnp831.387096774194
Midmean - Weighted Average at X(n+1)p835.9
Midmean - Empirical Distribution Function831.387096774194
Midmean - Empirical Distribution Function - Averaging835.9
Midmean - Empirical Distribution Function - Interpolation835.9
Midmean - Closest Observation831.387096774194
Midmean - True Basic - Statistics Graphics Toolkit835.9
Midmean - MS Excel (old versions)835.625
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')