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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 03:38:51 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t1255858901za2gnfar2gcxkeu.htm/, Retrieved Thu, 31 Oct 2024 23:22:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47233, Retrieved Thu, 31 Oct 2024 23:22:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS3 Part2 Vraag3] [2009-10-18 09:38:51] [37de18e38c1490dd77c2b362ed87f3bb] [Current]
-               [Central Tendency] [WS3 part 2 vraag3a] [2009-10-21 06:23:03] [f5d341d4bbba73282fc6e80153a6d315]
-               [Central Tendency] [BDM 10] [2009-10-21 08:40:55] [f5d341d4bbba73282fc6e80153a6d315]
-               [Central Tendency] [TG 10] [2009-10-21 09:03:50] [a21bac9c8d3d56fdec8be4e719e2c7ed]
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Dataseries X:
1.134378499
1.177187154
1.03183315
1.140954495
1.176470588
1.235017626
1.107913669
0.992682927
1.315920398
1.468864469
1.073560768
0.936708861
1.021668472
1.141714286
1.242788462
1.259756098
1.230386052
1.273838631
1.071680376
0.887173397
1.285545024
1.355029586
1.038585209
0.961373391
0.968095713
0.900359066
1.067014795
1.053881279
0.991810737
1.220226843
0.927797834
0.884191176
1.099913867
1.173952641
1.111599297
1.052724077
0.964224872
0.954811715
1.093800979
1.077050539
1.023529412
1.047581285
0.786407767
0.74583635
0.834045584
0.852226721
0.931848853
0.766516998
0.80654588
0.788248982
0.945974576
0.75476966
0.774179431
0.931363636
0.586512866
0.645672859
0.747837961
0.753554502
0.784787472
0.653266332




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47233&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47233&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.004386569083330.024752024932461640.5779556146984
Geometric Mean0.985702319870748
Harmonic Mean0.96629194972673
Quadratic Mean1.02222281412232
Winsorized Mean ( 1 / 20 )1.003475320916670.023946999923629741.9040098599779
Winsorized Mean ( 2 / 20 )1.002424797083330.023573951876286842.5225605933166
Winsorized Mean ( 3 / 20 )1.005534529283330.022196598154815245.3012899665979
Winsorized Mean ( 4 / 20 )1.004887543816670.022005881343097745.6644988741547
Winsorized Mean ( 5 / 20 )1.004190377816670.021673179489484746.3333207895905
Winsorized Mean ( 6 / 20 )1.002615130016670.021317674096218647.0321070437282
Winsorized Mean ( 7 / 20 )1.003079055250.020879088343199248.0422822472863
Winsorized Mean ( 8 / 20 )1.003483169783330.020568584594140848.7871766377735
Winsorized Mean ( 9 / 20 )1.003550494583330.019988134173726450.2073122914324
Winsorized Mean ( 10 / 20 )0.996647262250.018688711936798153.3288364452555
Winsorized Mean ( 11 / 20 )0.99685344790.018602948538457253.5857767836771
Winsorized Mean ( 12 / 20 )1.00000923810.017835759087051856.067657856288
Winsorized Mean ( 13 / 20 )0.9989825303833330.015634235392769763.897114587729
Winsorized Mean ( 14 / 20 )1.003047511116670.014862105524461167.4902697646563
Winsorized Mean ( 15 / 20 )1.009394625866670.013272959162659676.0489513677075
Winsorized Mean ( 16 / 20 )1.004115430933330.012205467193071282.2676768574125
Winsorized Mean ( 17 / 20 )1.006807109216670.011451472859198287.9194424678713
Winsorized Mean ( 18 / 20 )1.012638799016670.00983793460127732102.932052311589
Winsorized Mean ( 19 / 20 )1.011832221783330.0093844772771644107.819774282523
Winsorized Mean ( 20 / 20 )1.006410480783330.00855577286691443117.629406067472
Trimmed Mean ( 1 / 20 )1.003583048448280.023193539155273643.269940035007
Trimmed Mean ( 2 / 20 )1.003698470803570.022264754164367645.0801506000854
Trimmed Mean ( 3 / 20 )1.004406067314810.021365861625761647.0098554838418
Trimmed Mean ( 4 / 20 )1.003972043480770.020919618443797247.991890778412
Trimmed Mean ( 5 / 20 )1.003697393380.020425669133800049.1390214345097
Trimmed Mean ( 6 / 20 )1.003574147270830.019906933794048650.4132960732939
Trimmed Mean ( 7 / 20 )1.003782629282610.019347971530746851.8805099380804
Trimmed Mean ( 8 / 20 )1.003919689159090.018749582868103553.5435746075688
Trimmed Mean ( 9 / 20 )1.003997639047620.018050432637782855.621804706557
Trimmed Mean ( 10 / 20 )1.0040721631250.017288101951466858.078796963585
Trimmed Mean ( 11 / 20 )1.005244515894740.016630269296110460.4466769596961
Trimmed Mean ( 12 / 20 )1.006515889833330.015745696694728863.9232362560548
Trimmed Mean ( 13 / 20 )1.007472750382350.01475690644318768.2712704225001
Trimmed Mean ( 14 / 20 )1.008697301343750.01406307859580571.7266347103146
Trimmed Mean ( 15 / 20 )1.009504414233330.013312921189996675.8289183738189
Trimmed Mean ( 16 / 20 )1.009520098285710.012749961916173079.1782834272757
Trimmed Mean ( 17 / 20 )1.010299617615380.012246936118280982.49407099522
Trimmed Mean ( 18 / 20 )1.010813221791670.011723727946679786.219436888071
Trimmed Mean ( 19 / 20 )1.010536619181820.011494203050634587.917066953679
Trimmed Mean ( 20 / 20 )1.010332050350.011219785776569190.0491391252703
Median1.022598942
Midrange1.0276886675
Midmean - Weighted Average at Xnp1.00443094025806
Midmean - Weighted Average at X(n+1)p1.00950441423333
Midmean - Empirical Distribution Function1.00443094025806
Midmean - Empirical Distribution Function - Averaging1.00950441423333
Midmean - Empirical Distribution Function - Interpolation1.00950441423333
Midmean - Closest Observation1.00443094025806
Midmean - True Basic - Statistics Graphics Toolkit1.00950441423333
Midmean - MS Excel (old versions)1.00869730134375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.00438656908333 & 0.0247520249324616 & 40.5779556146984 \tabularnewline
Geometric Mean & 0.985702319870748 &  &  \tabularnewline
Harmonic Mean & 0.96629194972673 &  &  \tabularnewline
Quadratic Mean & 1.02222281412232 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.00347532091667 & 0.0239469999236297 & 41.9040098599779 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.00242479708333 & 0.0235739518762868 & 42.5225605933166 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.00553452928333 & 0.0221965981548152 & 45.3012899665979 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.00488754381667 & 0.0220058813430977 & 45.6644988741547 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.00419037781667 & 0.0216731794894847 & 46.3333207895905 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.00261513001667 & 0.0213176740962186 & 47.0321070437282 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.00307905525 & 0.0208790883431992 & 48.0422822472863 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.00348316978333 & 0.0205685845941408 & 48.7871766377735 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.00355049458333 & 0.0199881341737264 & 50.2073122914324 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.99664726225 & 0.0186887119367981 & 53.3288364452555 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.9968534479 & 0.0186029485384572 & 53.5857767836771 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.0000092381 & 0.0178357590870518 & 56.067657856288 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.998982530383333 & 0.0156342353927697 & 63.897114587729 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.00304751111667 & 0.0148621055244611 & 67.4902697646563 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.00939462586667 & 0.0132729591626596 & 76.0489513677075 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.00411543093333 & 0.0122054671930712 & 82.2676768574125 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.00680710921667 & 0.0114514728591982 & 87.9194424678713 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.01263879901667 & 0.00983793460127732 & 102.932052311589 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.01183222178333 & 0.0093844772771644 & 107.819774282523 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.00641048078333 & 0.00855577286691443 & 117.629406067472 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.00358304844828 & 0.0231935391552736 & 43.269940035007 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.00369847080357 & 0.0222647541643676 & 45.0801506000854 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.00440606731481 & 0.0213658616257616 & 47.0098554838418 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.00397204348077 & 0.0209196184437972 & 47.991890778412 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.00369739338 & 0.0204256691338000 & 49.1390214345097 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.00357414727083 & 0.0199069337940486 & 50.4132960732939 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.00378262928261 & 0.0193479715307468 & 51.8805099380804 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.00391968915909 & 0.0187495828681035 & 53.5435746075688 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.00399763904762 & 0.0180504326377828 & 55.621804706557 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.004072163125 & 0.0172881019514668 & 58.078796963585 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.00524451589474 & 0.0166302692961104 & 60.4466769596961 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.00651588983333 & 0.0157456966947288 & 63.9232362560548 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.00747275038235 & 0.014756906443187 & 68.2712704225001 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.00869730134375 & 0.014063078595805 & 71.7266347103146 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.00950441423333 & 0.0133129211899966 & 75.8289183738189 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.00952009828571 & 0.0127499619161730 & 79.1782834272757 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.01029961761538 & 0.0122469361182809 & 82.49407099522 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.01081322179167 & 0.0117237279466797 & 86.219436888071 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.01053661918182 & 0.0114942030506345 & 87.917066953679 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.01033205035 & 0.0112197857765691 & 90.0491391252703 \tabularnewline
Median & 1.022598942 &  &  \tabularnewline
Midrange & 1.0276886675 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.00443094025806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.00950441423333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.00443094025806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.00950441423333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.00950441423333 &  &  \tabularnewline
Midmean - Closest Observation & 1.00443094025806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.00950441423333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.00869730134375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47233&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]1.00438656908333[/C][C]0.0247520249324616[/C][C]40.5779556146984[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.985702319870748[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.96629194972673[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.02222281412232[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.00347532091667[/C][C]0.0239469999236297[/C][C]41.9040098599779[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.00242479708333[/C][C]0.0235739518762868[/C][C]42.5225605933166[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.00553452928333[/C][C]0.0221965981548152[/C][C]45.3012899665979[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.00488754381667[/C][C]0.0220058813430977[/C][C]45.6644988741547[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.00419037781667[/C][C]0.0216731794894847[/C][C]46.3333207895905[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.00261513001667[/C][C]0.0213176740962186[/C][C]47.0321070437282[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.00307905525[/C][C]0.0208790883431992[/C][C]48.0422822472863[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.00348316978333[/C][C]0.0205685845941408[/C][C]48.7871766377735[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.00355049458333[/C][C]0.0199881341737264[/C][C]50.2073122914324[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.99664726225[/C][C]0.0186887119367981[/C][C]53.3288364452555[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.9968534479[/C][C]0.0186029485384572[/C][C]53.5857767836771[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.0000092381[/C][C]0.0178357590870518[/C][C]56.067657856288[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.998982530383333[/C][C]0.0156342353927697[/C][C]63.897114587729[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.00304751111667[/C][C]0.0148621055244611[/C][C]67.4902697646563[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.00939462586667[/C][C]0.0132729591626596[/C][C]76.0489513677075[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.00411543093333[/C][C]0.0122054671930712[/C][C]82.2676768574125[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.00680710921667[/C][C]0.0114514728591982[/C][C]87.9194424678713[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.01263879901667[/C][C]0.00983793460127732[/C][C]102.932052311589[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.01183222178333[/C][C]0.0093844772771644[/C][C]107.819774282523[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.00641048078333[/C][C]0.00855577286691443[/C][C]117.629406067472[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.00358304844828[/C][C]0.0231935391552736[/C][C]43.269940035007[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.00369847080357[/C][C]0.0222647541643676[/C][C]45.0801506000854[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.00440606731481[/C][C]0.0213658616257616[/C][C]47.0098554838418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.00397204348077[/C][C]0.0209196184437972[/C][C]47.991890778412[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.00369739338[/C][C]0.0204256691338000[/C][C]49.1390214345097[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.00357414727083[/C][C]0.0199069337940486[/C][C]50.4132960732939[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.00378262928261[/C][C]0.0193479715307468[/C][C]51.8805099380804[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.00391968915909[/C][C]0.0187495828681035[/C][C]53.5435746075688[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.00399763904762[/C][C]0.0180504326377828[/C][C]55.621804706557[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.004072163125[/C][C]0.0172881019514668[/C][C]58.078796963585[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.00524451589474[/C][C]0.0166302692961104[/C][C]60.4466769596961[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.00651588983333[/C][C]0.0157456966947288[/C][C]63.9232362560548[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.00747275038235[/C][C]0.014756906443187[/C][C]68.2712704225001[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.00869730134375[/C][C]0.014063078595805[/C][C]71.7266347103146[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.00950441423333[/C][C]0.0133129211899966[/C][C]75.8289183738189[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.00952009828571[/C][C]0.0127499619161730[/C][C]79.1782834272757[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.01029961761538[/C][C]0.0122469361182809[/C][C]82.49407099522[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.01081322179167[/C][C]0.0117237279466797[/C][C]86.219436888071[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.01053661918182[/C][C]0.0114942030506345[/C][C]87.917066953679[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.01033205035[/C][C]0.0112197857765691[/C][C]90.0491391252703[/C][/ROW]
[ROW][C]Median[/C][C]1.022598942[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.0276886675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.00443094025806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.00950441423333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.00443094025806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.00950441423333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.00950441423333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.00443094025806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.00950441423333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.00869730134375[/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=47233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47233&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 Mean1.004386569083330.024752024932461640.5779556146984
Geometric Mean0.985702319870748
Harmonic Mean0.96629194972673
Quadratic Mean1.02222281412232
Winsorized Mean ( 1 / 20 )1.003475320916670.023946999923629741.9040098599779
Winsorized Mean ( 2 / 20 )1.002424797083330.023573951876286842.5225605933166
Winsorized Mean ( 3 / 20 )1.005534529283330.022196598154815245.3012899665979
Winsorized Mean ( 4 / 20 )1.004887543816670.022005881343097745.6644988741547
Winsorized Mean ( 5 / 20 )1.004190377816670.021673179489484746.3333207895905
Winsorized Mean ( 6 / 20 )1.002615130016670.021317674096218647.0321070437282
Winsorized Mean ( 7 / 20 )1.003079055250.020879088343199248.0422822472863
Winsorized Mean ( 8 / 20 )1.003483169783330.020568584594140848.7871766377735
Winsorized Mean ( 9 / 20 )1.003550494583330.019988134173726450.2073122914324
Winsorized Mean ( 10 / 20 )0.996647262250.018688711936798153.3288364452555
Winsorized Mean ( 11 / 20 )0.99685344790.018602948538457253.5857767836771
Winsorized Mean ( 12 / 20 )1.00000923810.017835759087051856.067657856288
Winsorized Mean ( 13 / 20 )0.9989825303833330.015634235392769763.897114587729
Winsorized Mean ( 14 / 20 )1.003047511116670.014862105524461167.4902697646563
Winsorized Mean ( 15 / 20 )1.009394625866670.013272959162659676.0489513677075
Winsorized Mean ( 16 / 20 )1.004115430933330.012205467193071282.2676768574125
Winsorized Mean ( 17 / 20 )1.006807109216670.011451472859198287.9194424678713
Winsorized Mean ( 18 / 20 )1.012638799016670.00983793460127732102.932052311589
Winsorized Mean ( 19 / 20 )1.011832221783330.0093844772771644107.819774282523
Winsorized Mean ( 20 / 20 )1.006410480783330.00855577286691443117.629406067472
Trimmed Mean ( 1 / 20 )1.003583048448280.023193539155273643.269940035007
Trimmed Mean ( 2 / 20 )1.003698470803570.022264754164367645.0801506000854
Trimmed Mean ( 3 / 20 )1.004406067314810.021365861625761647.0098554838418
Trimmed Mean ( 4 / 20 )1.003972043480770.020919618443797247.991890778412
Trimmed Mean ( 5 / 20 )1.003697393380.020425669133800049.1390214345097
Trimmed Mean ( 6 / 20 )1.003574147270830.019906933794048650.4132960732939
Trimmed Mean ( 7 / 20 )1.003782629282610.019347971530746851.8805099380804
Trimmed Mean ( 8 / 20 )1.003919689159090.018749582868103553.5435746075688
Trimmed Mean ( 9 / 20 )1.003997639047620.018050432637782855.621804706557
Trimmed Mean ( 10 / 20 )1.0040721631250.017288101951466858.078796963585
Trimmed Mean ( 11 / 20 )1.005244515894740.016630269296110460.4466769596961
Trimmed Mean ( 12 / 20 )1.006515889833330.015745696694728863.9232362560548
Trimmed Mean ( 13 / 20 )1.007472750382350.01475690644318768.2712704225001
Trimmed Mean ( 14 / 20 )1.008697301343750.01406307859580571.7266347103146
Trimmed Mean ( 15 / 20 )1.009504414233330.013312921189996675.8289183738189
Trimmed Mean ( 16 / 20 )1.009520098285710.012749961916173079.1782834272757
Trimmed Mean ( 17 / 20 )1.010299617615380.012246936118280982.49407099522
Trimmed Mean ( 18 / 20 )1.010813221791670.011723727946679786.219436888071
Trimmed Mean ( 19 / 20 )1.010536619181820.011494203050634587.917066953679
Trimmed Mean ( 20 / 20 )1.010332050350.011219785776569190.0491391252703
Median1.022598942
Midrange1.0276886675
Midmean - Weighted Average at Xnp1.00443094025806
Midmean - Weighted Average at X(n+1)p1.00950441423333
Midmean - Empirical Distribution Function1.00443094025806
Midmean - Empirical Distribution Function - Averaging1.00950441423333
Midmean - Empirical Distribution Function - Interpolation1.00950441423333
Midmean - Closest Observation1.00443094025806
Midmean - True Basic - Statistics Graphics Toolkit1.00950441423333
Midmean - MS Excel (old versions)1.00869730134375
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')