Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 17:19:28 +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/2016/Oct/11/t1476202805wykihrj55ofq7eq.htm/, Retrieved Mon, 29 Apr 2024 05:57:17 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 05:57:17 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
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
683




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean838.91666666666722.979815408219836.5066756091778
Geometric Mean819.344629147453
Harmonic Mean798.716214301628
Quadratic Mean857.284909855916
Winsorized Mean ( 1 / 20 )839.61666666666722.535572528564937.2573923117513
Winsorized Mean ( 2 / 20 )839.1522.302299354487537.626165206645
Winsorized Mean ( 3 / 20 )838.521.801952693346938.4598577840175
Winsorized Mean ( 4 / 20 )839.921.456916496475539.14355541897
Winsorized Mean ( 5 / 20 )840.73333333333320.893067358659540.2398230427796
Winsorized Mean ( 6 / 20 )844.33333333333319.977807838358242.2635626573693
Winsorized Mean ( 7 / 20 )844.56666666666718.865287626029144.7682899624276
Winsorized Mean ( 8 / 20 )842.83333333333318.385116903095545.8432403653318
Winsorized Mean ( 9 / 20 )844.48333333333317.727751101978847.6362358922713
Winsorized Mean ( 10 / 20 )844.81666666666717.614043120928147.9626773289149
Winsorized Mean ( 11 / 20 )842.61666666666716.891563294915649.8838770547837
Winsorized Mean ( 12 / 20 )842.61666666666716.891563294915649.8838770547837
Winsorized Mean ( 13 / 20 )843.26666666666716.710950208585550.461922041598
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 )839.75862068965521.95524665365938.2486534511195
Trimmed Mean ( 2 / 20 )839.91071428571421.239226096671439.5452598160977
Trimmed Mean ( 3 / 20 )840.33333333333320.507979391645640.9759205080761
Trimmed Mean ( 4 / 20 )841.03846153846219.840483042869842.3900194224711
Trimmed Mean ( 5 / 20 )841.3819.139165742166643.9611637902434
Trimmed Mean ( 6 / 20 )841.54166666666718.449205674278245.6139782668225
Trimmed Mean ( 7 / 20 )840.93478260869617.860041010656547.0847061385211
Trimmed Mean ( 8 / 20 )840.22727272727317.425463847865948.2183590671061
Trimmed Mean ( 9 / 20 )839.76190476190516.983315222965549.4462885330153
Trimmed Mean ( 10 / 20 )838.97516.565351834786350.6463737303908
Trimmed Mean ( 11 / 20 )838.05263157894716.01967794948352.3139500195755
Trimmed Mean ( 12 / 20 )837.36111111111115.473230995013454.1167588967662
Trimmed Mean ( 13 / 20 )836.58823529411814.700826225283656.9075657703706
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 & 838.916666666667 & 22.9798154082198 & 36.5066756091778 \tabularnewline
Geometric Mean & 819.344629147453 &  &  \tabularnewline
Harmonic Mean & 798.716214301628 &  &  \tabularnewline
Quadratic Mean & 857.284909855916 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 839.616666666667 & 22.5355725285649 & 37.2573923117513 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 839.15 & 22.3022993544875 & 37.626165206645 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 838.5 & 21.8019526933469 & 38.4598577840175 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 839.9 & 21.4569164964755 & 39.14355541897 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 840.733333333333 & 20.8930673586595 & 40.2398230427796 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 844.333333333333 & 19.9778078383582 & 42.2635626573693 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 844.566666666667 & 18.8652876260291 & 44.7682899624276 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 842.833333333333 & 18.3851169030955 & 45.8432403653318 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 844.483333333333 & 17.7277511019788 & 47.6362358922713 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 844.816666666667 & 17.6140431209281 & 47.9626773289149 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 842.616666666667 & 16.8915632949156 & 49.8838770547837 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 842.616666666667 & 16.8915632949156 & 49.8838770547837 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 843.266666666667 & 16.7109502085855 & 50.461922041598 \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 ) & 839.758620689655 & 21.955246653659 & 38.2486534511195 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 839.910714285714 & 21.2392260966714 & 39.5452598160977 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 840.333333333333 & 20.5079793916456 & 40.9759205080761 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 841.038461538462 & 19.8404830428698 & 42.3900194224711 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 841.38 & 19.1391657421666 & 43.9611637902434 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 841.541666666667 & 18.4492056742782 & 45.6139782668225 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 840.934782608696 & 17.8600410106565 & 47.0847061385211 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 840.227272727273 & 17.4254638478659 & 48.2183590671061 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 839.761904761905 & 16.9833152229655 & 49.4462885330153 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 838.975 & 16.5653518347863 & 50.6463737303908 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 838.052631578947 & 16.019677949483 & 52.3139500195755 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 837.361111111111 & 15.4732309950134 & 54.1167588967662 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 836.588235294118 & 14.7008262252836 & 56.9075657703706 \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=&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]838.916666666667[/C][C]22.9798154082198[/C][C]36.5066756091778[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]819.344629147453[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]798.716214301628[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]857.284909855916[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]839.616666666667[/C][C]22.5355725285649[/C][C]37.2573923117513[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]839.15[/C][C]22.3022993544875[/C][C]37.626165206645[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]838.5[/C][C]21.8019526933469[/C][C]38.4598577840175[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]839.9[/C][C]21.4569164964755[/C][C]39.14355541897[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]840.733333333333[/C][C]20.8930673586595[/C][C]40.2398230427796[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]844.333333333333[/C][C]19.9778078383582[/C][C]42.2635626573693[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]844.566666666667[/C][C]18.8652876260291[/C][C]44.7682899624276[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]842.833333333333[/C][C]18.3851169030955[/C][C]45.8432403653318[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]844.483333333333[/C][C]17.7277511019788[/C][C]47.6362358922713[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]844.816666666667[/C][C]17.6140431209281[/C][C]47.9626773289149[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]842.616666666667[/C][C]16.8915632949156[/C][C]49.8838770547837[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]842.616666666667[/C][C]16.8915632949156[/C][C]49.8838770547837[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]843.266666666667[/C][C]16.7109502085855[/C][C]50.461922041598[/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]839.758620689655[/C][C]21.955246653659[/C][C]38.2486534511195[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]839.910714285714[/C][C]21.2392260966714[/C][C]39.5452598160977[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]840.333333333333[/C][C]20.5079793916456[/C][C]40.9759205080761[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]841.038461538462[/C][C]19.8404830428698[/C][C]42.3900194224711[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]841.38[/C][C]19.1391657421666[/C][C]43.9611637902434[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]841.541666666667[/C][C]18.4492056742782[/C][C]45.6139782668225[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]840.934782608696[/C][C]17.8600410106565[/C][C]47.0847061385211[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]840.227272727273[/C][C]17.4254638478659[/C][C]48.2183590671061[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]839.761904761905[/C][C]16.9833152229655[/C][C]49.4462885330153[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]838.975[/C][C]16.5653518347863[/C][C]50.6463737303908[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]838.052631578947[/C][C]16.019677949483[/C][C]52.3139500195755[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]837.361111111111[/C][C]15.4732309950134[/C][C]54.1167588967662[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]836.588235294118[/C][C]14.7008262252836[/C][C]56.9075657703706[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean838.91666666666722.979815408219836.5066756091778
Geometric Mean819.344629147453
Harmonic Mean798.716214301628
Quadratic Mean857.284909855916
Winsorized Mean ( 1 / 20 )839.61666666666722.535572528564937.2573923117513
Winsorized Mean ( 2 / 20 )839.1522.302299354487537.626165206645
Winsorized Mean ( 3 / 20 )838.521.801952693346938.4598577840175
Winsorized Mean ( 4 / 20 )839.921.456916496475539.14355541897
Winsorized Mean ( 5 / 20 )840.73333333333320.893067358659540.2398230427796
Winsorized Mean ( 6 / 20 )844.33333333333319.977807838358242.2635626573693
Winsorized Mean ( 7 / 20 )844.56666666666718.865287626029144.7682899624276
Winsorized Mean ( 8 / 20 )842.83333333333318.385116903095545.8432403653318
Winsorized Mean ( 9 / 20 )844.48333333333317.727751101978847.6362358922713
Winsorized Mean ( 10 / 20 )844.81666666666717.614043120928147.9626773289149
Winsorized Mean ( 11 / 20 )842.61666666666716.891563294915649.8838770547837
Winsorized Mean ( 12 / 20 )842.61666666666716.891563294915649.8838770547837
Winsorized Mean ( 13 / 20 )843.26666666666716.710950208585550.461922041598
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 )839.75862068965521.95524665365938.2486534511195
Trimmed Mean ( 2 / 20 )839.91071428571421.239226096671439.5452598160977
Trimmed Mean ( 3 / 20 )840.33333333333320.507979391645640.9759205080761
Trimmed Mean ( 4 / 20 )841.03846153846219.840483042869842.3900194224711
Trimmed Mean ( 5 / 20 )841.3819.139165742166643.9611637902434
Trimmed Mean ( 6 / 20 )841.54166666666718.449205674278245.6139782668225
Trimmed Mean ( 7 / 20 )840.93478260869617.860041010656547.0847061385211
Trimmed Mean ( 8 / 20 )840.22727272727317.425463847865948.2183590671061
Trimmed Mean ( 9 / 20 )839.76190476190516.983315222965549.4462885330153
Trimmed Mean ( 10 / 20 )838.97516.565351834786350.6463737303908
Trimmed Mean ( 11 / 20 )838.05263157894716.01967794948352.3139500195755
Trimmed Mean ( 12 / 20 )837.36111111111115.473230995013454.1167588967662
Trimmed Mean ( 13 / 20 )836.58823529411814.700826225283656.9075657703706
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')