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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 12 Mar 2013 12:32:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/12/t13631059593cxig4ybgrcnb8d.htm/, Retrieved Mon, 29 Apr 2024 04:43:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207732, Retrieved Mon, 29 Apr 2024 04:43:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-12 16:32:29] [f5344c9d857de7b42142f71fd8a100cb] [Current]
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Dataseries X:
530,3
527,76
521,41
1601,93
1577,49
1551,43
1551,43
1516,88
1485,95
1438,22
1385,06
1329,49
1329,49
1276,16
1242,34
1181,59
1160,21
1135,18
1135,18
1084,96
1077,35
1061,13
1029,98
1013,08
1013,08
996,04
975,02
951,89
944,4
932,47
932,47
920,44
900,18
886,9
867,74
859,03
859,03
844,99
834,82
825,62
816,92
813,21
813,21
811,03
804,16
788,62
778,76
765,91
765,91
753,85
742,22
732,11
729,94
731,22
731,22
729,11
726,94
720,52
709,36
703,21
703,21
695,88
681,63
672,1
665,49
658,93
658,93
656
650,66
645,93
638,74
634,67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207732&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207732&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207732&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean922.46833333333333.083856657915527.882732743996
Geometric Mean884.942786619682
Harmonic Mean851.919340998649
Quadratic Mean963.670212038042
Winsorized Mean ( 1 / 24 )922.21708333333332.972293808232827.9694548610102
Winsorized Mean ( 2 / 24 )921.5637532.76108313786528.129831548056
Winsorized Mean ( 3 / 24 )925.912532.11674112598628.8295906601444
Winsorized Mean ( 4 / 24 )924.21916666666731.570803611545829.2744897481377
Winsorized Mean ( 5 / 24 )922.57055555555630.948176311608929.8101751219987
Winsorized Mean ( 6 / 24 )918.98722222222229.901755698071730.7335539592241
Winsorized Mean ( 7 / 24 )914.33805555555528.604225413183631.965139497682
Winsorized Mean ( 8 / 24 )908.48916666666727.172137760063733.4345856291779
Winsorized Mean ( 9 / 24 )908.48916666666727.172137760063733.4345856291779
Winsorized Mean ( 10 / 24 )901.99333333333325.478093755697335.40270092348
Winsorized Mean ( 11 / 24 )897.8362524.295230409182636.9552473830689
Winsorized Mean ( 12 / 24 )889.29958333333322.130343643920840.1846260339308
Winsorized Mean ( 13 / 24 )888.01222222222221.084892740695442.1160417149429
Winsorized Mean ( 14 / 24 )884.57055555555620.030911735528444.1602742418665
Winsorized Mean ( 15 / 24 )884.57055555555620.030911735528444.1602742418665
Winsorized Mean ( 16 / 24 )874.77722222222217.9480809685848.7393177996919
Winsorized Mean ( 17 / 24 )875.61541666666717.315140381228650.5693512953509
Winsorized Mean ( 18 / 24 )873.16541666666716.454354309449653.0659180084151
Winsorized Mean ( 19 / 24 )865.51791666666715.088521470371957.3626725697553
Winsorized Mean ( 20 / 24 )861.05402777777814.34813273753760.0115738771447
Winsorized Mean ( 21 / 24 )861.42736111111114.300168836611660.2389643754183
Winsorized Mean ( 22 / 24 )856.22069444444413.532191969386863.2728752578612
Winsorized Mean ( 23 / 24 )849.79027777777812.533228757261867.8029815170654
Winsorized Mean ( 24 / 24 )845.45027777777811.019936766467576.7200661577656
Trimmed Mean ( 1 / 24 )918.49114285714332.083203510829528.6284112042337
Trimmed Mean ( 2 / 24 )914.54602941176531.018929337148129.4834815048406
Trimmed Mean ( 3 / 24 )910.71818181818229.877104055709130.4821437887705
Trimmed Mean ( 4 / 24 )905.020312528.784224536042431.441538797294
Trimmed Mean ( 5 / 24 )899.44645161290327.65961631849132.5183994331695
Trimmed Mean ( 6 / 24 )893.89666666666726.485955320635633.749836690626
Trimmed Mean ( 7 / 24 )888.70551724137925.360770650193435.0425280642882
Trimmed Mean ( 8 / 24 )883.997524.339020486925736.3201756814685
Trimmed Mean ( 9 / 24 )879.91555555555623.455327080650237.5145293233388
Trimmed Mean ( 10 / 24 )875.51961538461522.331820078223639.2050272802601
Trimmed Mean ( 11 / 24 )871.707421.354420391811240.8209346826511
Trimmed Mean ( 12 / 24 )868.14437520.40597063992942.5436452065295
Trimmed Mean ( 13 / 24 )865.38519.732762721259443.8552377193317
Trimmed Mean ( 14 / 24 )862.53681818181819.097085940362945.1658866109405
Trimmed Mean ( 15 / 24 )859.8388095238118.509890880780346.452937786717
Trimmed Mean ( 16 / 24 )856.87117.710043238592648.3833375478587
Trimmed Mean ( 17 / 24 )854.75052631578917.187201120421649.731804517036
Trimmed Mean ( 18 / 24 )852.29583333333316.608158161573551.3179020239161
Trimmed Mean ( 19 / 24 )849.84058823529416.021826750766753.0426774334349
Trimmed Mean ( 20 / 24 )847.984062515.58275985858654.4180921862034
Trimmed Mean ( 21 / 24 )846.41566666666715.147358949519755.8787620658786
Trimmed Mean ( 22 / 24 )844.577514.478286548562158.3340782189365
Trimmed Mean ( 23 / 24 )843.11192307692313.735224408227961.3831924414624
Trimmed Mean ( 24 / 24 )842.24083333333312.97204871236264.9273566580658
Median830.22
Midrange1061.67
Midmean - Weighted Average at Xnp848.734324324325
Midmean - Weighted Average at X(n+1)p852.295833333334
Midmean - Empirical Distribution Function848.734324324325
Midmean - Empirical Distribution Function - Averaging852.295833333334
Midmean - Empirical Distribution Function - Interpolation852.295833333334
Midmean - Closest Observation848.734324324325
Midmean - True Basic - Statistics Graphics Toolkit852.295833333334
Midmean - MS Excel (old versions)854.75052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 922.468333333333 & 33.0838566579155 & 27.882732743996 \tabularnewline
Geometric Mean & 884.942786619682 &  &  \tabularnewline
Harmonic Mean & 851.919340998649 &  &  \tabularnewline
Quadratic Mean & 963.670212038042 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 922.217083333333 & 32.9722938082328 & 27.9694548610102 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 921.56375 & 32.761083137865 & 28.129831548056 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 925.9125 & 32.116741125986 & 28.8295906601444 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 924.219166666667 & 31.5708036115458 & 29.2744897481377 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 922.570555555556 & 30.9481763116089 & 29.8101751219987 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 918.987222222222 & 29.9017556980717 & 30.7335539592241 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 914.338055555555 & 28.6042254131836 & 31.965139497682 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 908.489166666667 & 27.1721377600637 & 33.4345856291779 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 908.489166666667 & 27.1721377600637 & 33.4345856291779 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 901.993333333333 & 25.4780937556973 & 35.40270092348 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 897.83625 & 24.2952304091826 & 36.9552473830689 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 889.299583333333 & 22.1303436439208 & 40.1846260339308 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 888.012222222222 & 21.0848927406954 & 42.1160417149429 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 884.570555555556 & 20.0309117355284 & 44.1602742418665 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 884.570555555556 & 20.0309117355284 & 44.1602742418665 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 874.777222222222 & 17.94808096858 & 48.7393177996919 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 875.615416666667 & 17.3151403812286 & 50.5693512953509 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 873.165416666667 & 16.4543543094496 & 53.0659180084151 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 865.517916666667 & 15.0885214703719 & 57.3626725697553 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 861.054027777778 & 14.348132737537 & 60.0115738771447 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 861.427361111111 & 14.3001688366116 & 60.2389643754183 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 856.220694444444 & 13.5321919693868 & 63.2728752578612 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 849.790277777778 & 12.5332287572618 & 67.8029815170654 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 845.450277777778 & 11.0199367664675 & 76.7200661577656 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 918.491142857143 & 32.0832035108295 & 28.6284112042337 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 914.546029411765 & 31.0189293371481 & 29.4834815048406 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 910.718181818182 & 29.8771040557091 & 30.4821437887705 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 905.0203125 & 28.7842245360424 & 31.441538797294 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 899.446451612903 & 27.659616318491 & 32.5183994331695 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 893.896666666667 & 26.4859553206356 & 33.749836690626 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 888.705517241379 & 25.3607706501934 & 35.0425280642882 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 883.9975 & 24.3390204869257 & 36.3201756814685 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 879.915555555556 & 23.4553270806502 & 37.5145293233388 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 875.519615384615 & 22.3318200782236 & 39.2050272802601 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 871.7074 & 21.3544203918112 & 40.8209346826511 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 868.144375 & 20.405970639929 & 42.5436452065295 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 865.385 & 19.7327627212594 & 43.8552377193317 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 862.536818181818 & 19.0970859403629 & 45.1658866109405 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 859.83880952381 & 18.5098908807803 & 46.452937786717 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 856.871 & 17.7100432385926 & 48.3833375478587 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 854.750526315789 & 17.1872011204216 & 49.731804517036 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 852.295833333333 & 16.6081581615735 & 51.3179020239161 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 849.840588235294 & 16.0218267507667 & 53.0426774334349 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 847.9840625 & 15.582759858586 & 54.4180921862034 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 846.415666666667 & 15.1473589495197 & 55.8787620658786 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 844.5775 & 14.4782865485621 & 58.3340782189365 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 843.111923076923 & 13.7352244082279 & 61.3831924414624 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 842.240833333333 & 12.972048712362 & 64.9273566580658 \tabularnewline
Median & 830.22 &  &  \tabularnewline
Midrange & 1061.67 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 848.734324324325 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 852.295833333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 848.734324324325 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 852.295833333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 852.295833333334 &  &  \tabularnewline
Midmean - Closest Observation & 848.734324324325 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 852.295833333334 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 854.75052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207732&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]922.468333333333[/C][C]33.0838566579155[/C][C]27.882732743996[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]884.942786619682[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]851.919340998649[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]963.670212038042[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]922.217083333333[/C][C]32.9722938082328[/C][C]27.9694548610102[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]921.56375[/C][C]32.761083137865[/C][C]28.129831548056[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]925.9125[/C][C]32.116741125986[/C][C]28.8295906601444[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]924.219166666667[/C][C]31.5708036115458[/C][C]29.2744897481377[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]922.570555555556[/C][C]30.9481763116089[/C][C]29.8101751219987[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]918.987222222222[/C][C]29.9017556980717[/C][C]30.7335539592241[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]914.338055555555[/C][C]28.6042254131836[/C][C]31.965139497682[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]908.489166666667[/C][C]27.1721377600637[/C][C]33.4345856291779[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]908.489166666667[/C][C]27.1721377600637[/C][C]33.4345856291779[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]901.993333333333[/C][C]25.4780937556973[/C][C]35.40270092348[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]897.83625[/C][C]24.2952304091826[/C][C]36.9552473830689[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]889.299583333333[/C][C]22.1303436439208[/C][C]40.1846260339308[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]888.012222222222[/C][C]21.0848927406954[/C][C]42.1160417149429[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]884.570555555556[/C][C]20.0309117355284[/C][C]44.1602742418665[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]884.570555555556[/C][C]20.0309117355284[/C][C]44.1602742418665[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]874.777222222222[/C][C]17.94808096858[/C][C]48.7393177996919[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]875.615416666667[/C][C]17.3151403812286[/C][C]50.5693512953509[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]873.165416666667[/C][C]16.4543543094496[/C][C]53.0659180084151[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]865.517916666667[/C][C]15.0885214703719[/C][C]57.3626725697553[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]861.054027777778[/C][C]14.348132737537[/C][C]60.0115738771447[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]861.427361111111[/C][C]14.3001688366116[/C][C]60.2389643754183[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]856.220694444444[/C][C]13.5321919693868[/C][C]63.2728752578612[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]849.790277777778[/C][C]12.5332287572618[/C][C]67.8029815170654[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]845.450277777778[/C][C]11.0199367664675[/C][C]76.7200661577656[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]918.491142857143[/C][C]32.0832035108295[/C][C]28.6284112042337[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]914.546029411765[/C][C]31.0189293371481[/C][C]29.4834815048406[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]910.718181818182[/C][C]29.8771040557091[/C][C]30.4821437887705[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]905.0203125[/C][C]28.7842245360424[/C][C]31.441538797294[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]899.446451612903[/C][C]27.659616318491[/C][C]32.5183994331695[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]893.896666666667[/C][C]26.4859553206356[/C][C]33.749836690626[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]888.705517241379[/C][C]25.3607706501934[/C][C]35.0425280642882[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]883.9975[/C][C]24.3390204869257[/C][C]36.3201756814685[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]879.915555555556[/C][C]23.4553270806502[/C][C]37.5145293233388[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]875.519615384615[/C][C]22.3318200782236[/C][C]39.2050272802601[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]871.7074[/C][C]21.3544203918112[/C][C]40.8209346826511[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]868.144375[/C][C]20.405970639929[/C][C]42.5436452065295[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]865.385[/C][C]19.7327627212594[/C][C]43.8552377193317[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]862.536818181818[/C][C]19.0970859403629[/C][C]45.1658866109405[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]859.83880952381[/C][C]18.5098908807803[/C][C]46.452937786717[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]856.871[/C][C]17.7100432385926[/C][C]48.3833375478587[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]854.750526315789[/C][C]17.1872011204216[/C][C]49.731804517036[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]852.295833333333[/C][C]16.6081581615735[/C][C]51.3179020239161[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]849.840588235294[/C][C]16.0218267507667[/C][C]53.0426774334349[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]847.9840625[/C][C]15.582759858586[/C][C]54.4180921862034[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]846.415666666667[/C][C]15.1473589495197[/C][C]55.8787620658786[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]844.5775[/C][C]14.4782865485621[/C][C]58.3340782189365[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]843.111923076923[/C][C]13.7352244082279[/C][C]61.3831924414624[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]842.240833333333[/C][C]12.972048712362[/C][C]64.9273566580658[/C][/ROW]
[ROW][C]Median[/C][C]830.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1061.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]848.734324324325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]852.295833333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]848.734324324325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]852.295833333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]852.295833333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]848.734324324325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]852.295833333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]854.75052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207732&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207732&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 Mean922.46833333333333.083856657915527.882732743996
Geometric Mean884.942786619682
Harmonic Mean851.919340998649
Quadratic Mean963.670212038042
Winsorized Mean ( 1 / 24 )922.21708333333332.972293808232827.9694548610102
Winsorized Mean ( 2 / 24 )921.5637532.76108313786528.129831548056
Winsorized Mean ( 3 / 24 )925.912532.11674112598628.8295906601444
Winsorized Mean ( 4 / 24 )924.21916666666731.570803611545829.2744897481377
Winsorized Mean ( 5 / 24 )922.57055555555630.948176311608929.8101751219987
Winsorized Mean ( 6 / 24 )918.98722222222229.901755698071730.7335539592241
Winsorized Mean ( 7 / 24 )914.33805555555528.604225413183631.965139497682
Winsorized Mean ( 8 / 24 )908.48916666666727.172137760063733.4345856291779
Winsorized Mean ( 9 / 24 )908.48916666666727.172137760063733.4345856291779
Winsorized Mean ( 10 / 24 )901.99333333333325.478093755697335.40270092348
Winsorized Mean ( 11 / 24 )897.8362524.295230409182636.9552473830689
Winsorized Mean ( 12 / 24 )889.29958333333322.130343643920840.1846260339308
Winsorized Mean ( 13 / 24 )888.01222222222221.084892740695442.1160417149429
Winsorized Mean ( 14 / 24 )884.57055555555620.030911735528444.1602742418665
Winsorized Mean ( 15 / 24 )884.57055555555620.030911735528444.1602742418665
Winsorized Mean ( 16 / 24 )874.77722222222217.9480809685848.7393177996919
Winsorized Mean ( 17 / 24 )875.61541666666717.315140381228650.5693512953509
Winsorized Mean ( 18 / 24 )873.16541666666716.454354309449653.0659180084151
Winsorized Mean ( 19 / 24 )865.51791666666715.088521470371957.3626725697553
Winsorized Mean ( 20 / 24 )861.05402777777814.34813273753760.0115738771447
Winsorized Mean ( 21 / 24 )861.42736111111114.300168836611660.2389643754183
Winsorized Mean ( 22 / 24 )856.22069444444413.532191969386863.2728752578612
Winsorized Mean ( 23 / 24 )849.79027777777812.533228757261867.8029815170654
Winsorized Mean ( 24 / 24 )845.45027777777811.019936766467576.7200661577656
Trimmed Mean ( 1 / 24 )918.49114285714332.083203510829528.6284112042337
Trimmed Mean ( 2 / 24 )914.54602941176531.018929337148129.4834815048406
Trimmed Mean ( 3 / 24 )910.71818181818229.877104055709130.4821437887705
Trimmed Mean ( 4 / 24 )905.020312528.784224536042431.441538797294
Trimmed Mean ( 5 / 24 )899.44645161290327.65961631849132.5183994331695
Trimmed Mean ( 6 / 24 )893.89666666666726.485955320635633.749836690626
Trimmed Mean ( 7 / 24 )888.70551724137925.360770650193435.0425280642882
Trimmed Mean ( 8 / 24 )883.997524.339020486925736.3201756814685
Trimmed Mean ( 9 / 24 )879.91555555555623.455327080650237.5145293233388
Trimmed Mean ( 10 / 24 )875.51961538461522.331820078223639.2050272802601
Trimmed Mean ( 11 / 24 )871.707421.354420391811240.8209346826511
Trimmed Mean ( 12 / 24 )868.14437520.40597063992942.5436452065295
Trimmed Mean ( 13 / 24 )865.38519.732762721259443.8552377193317
Trimmed Mean ( 14 / 24 )862.53681818181819.097085940362945.1658866109405
Trimmed Mean ( 15 / 24 )859.8388095238118.509890880780346.452937786717
Trimmed Mean ( 16 / 24 )856.87117.710043238592648.3833375478587
Trimmed Mean ( 17 / 24 )854.75052631578917.187201120421649.731804517036
Trimmed Mean ( 18 / 24 )852.29583333333316.608158161573551.3179020239161
Trimmed Mean ( 19 / 24 )849.84058823529416.021826750766753.0426774334349
Trimmed Mean ( 20 / 24 )847.984062515.58275985858654.4180921862034
Trimmed Mean ( 21 / 24 )846.41566666666715.147358949519755.8787620658786
Trimmed Mean ( 22 / 24 )844.577514.478286548562158.3340782189365
Trimmed Mean ( 23 / 24 )843.11192307692313.735224408227961.3831924414624
Trimmed Mean ( 24 / 24 )842.24083333333312.97204871236264.9273566580658
Median830.22
Midrange1061.67
Midmean - Weighted Average at Xnp848.734324324325
Midmean - Weighted Average at X(n+1)p852.295833333334
Midmean - Empirical Distribution Function848.734324324325
Midmean - Empirical Distribution Function - Averaging852.295833333334
Midmean - Empirical Distribution Function - Interpolation852.295833333334
Midmean - Closest Observation848.734324324325
Midmean - True Basic - Statistics Graphics Toolkit852.295833333334
Midmean - MS Excel (old versions)854.75052631579
Number of observations72



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')