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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 29 Nov 2011 05:41:52 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322563331mlom3rn92699tjo.htm/, Retrieved Thu, 28 Mar 2024 18:45:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148181, Retrieved Thu, 28 Mar 2024 18:45:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Central Tendency] [Workshop 8, Robus...] [2010-11-28 19:41:12] [d946de7cca328fbcf207448a112523ab]
-         [Central Tendency] [Workshop 8, Centr...] [2010-11-29 20:08:54] [3635fb7041b1998c5a1332cf9de22bce]
- R           [Central Tendency] [] [2011-11-29 10:41:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
9.911
8.915
9.452
9.112
8.472
8.230
8.384
8.625
8.221
8.649
8.625
10.443
10.357
8.586
8.892
8.329
8.101
7.922
8.120
7.838
7.735
8.406
8.209
9.451
10.041
9.411
10.405
8.467
8.464
8.102
7.627
7.513
7.510
8.291
8.064
9.383
9.706
8.579
9.474
8.318
8.213
8.059
9.111
7.708
7.680
8.014
8.007
8.718
9.486
9.113
9.025
8.476
7.952
7.759
7.835
7.600
7.651
8.319
8.812
8.630




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'AstonUniversity' @ aston.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 & 12 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148181&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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148181&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 time12 seconds
R Server'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.575133333333330.097473361467925587.9741213824359
Geometric Mean8.54367550118092
Harmonic Mean8.5134183895635
Quadratic Mean8.60775661830654
Winsorized Mean ( 1 / 20 )8.574550.097260240989836888.160896094181
Winsorized Mean ( 2 / 20 )8.575850.096236528369717189.1122128497164
Winsorized Mean ( 3 / 20 )8.56140.091348467342784293.7224263202297
Winsorized Mean ( 4 / 20 )8.554333333333330.088758542730946696.377577528104
Winsorized Mean ( 5 / 20 )8.539666666666670.0841150163161618101.523687929498
Winsorized Mean ( 6 / 20 )8.520466666666670.0787467279085858108.200897903437
Winsorized Mean ( 7 / 20 )8.522216666666670.0779111332516569109.383810900805
Winsorized Mean ( 8 / 20 )8.522483333333330.076762656041356111.023820342301
Winsorized Mean ( 9 / 20 )8.533733333333330.074868418913846113.983084685593
Winsorized Mean ( 10 / 20 )8.527566666666670.0734169324465969116.152587454802
Winsorized Mean ( 11 / 20 )8.537833333333330.0699922601316942121.982535172731
Winsorized Mean ( 12 / 20 )8.489833333333330.058631869656013144.798952909779
Winsorized Mean ( 13 / 20 )8.501533333333330.0567860115795353149.711752892276
Winsorized Mean ( 14 / 20 )8.502933333333330.0565031515878513150.486001123547
Winsorized Mean ( 15 / 20 )8.492683333333330.0510011769647435166.519359723879
Winsorized Mean ( 16 / 20 )8.464683333333330.0457572228355216184.991195024234
Winsorized Mean ( 17 / 20 )8.468650.0431358897656661196.324917510815
Winsorized Mean ( 18 / 20 )8.444950.0391863894926405215.50722353704
Winsorized Mean ( 19 / 20 )8.420883333333330.033738510006205249.592626698233
Winsorized Mean ( 20 / 20 )8.427550.0259797990297677324.388575536851
Trimmed Mean ( 1 / 20 )8.561293103448280.093657279645650291.4108666815831
Trimmed Mean ( 2 / 20 )8.547089285714290.089169549854697795.8521075820369
Trimmed Mean ( 3 / 20 )8.531111111111110.084226204803423101.288086421821
Trimmed Mean ( 4 / 20 )8.519461538461540.0805311902024843105.790831068566
Trimmed Mean ( 5 / 20 )8.5090.0769385283382594110.594785002779
Trimmed Mean ( 6 / 20 )8.501333333333330.074078244366454114.761539046181
Trimmed Mean ( 7 / 20 )8.497173913043480.0721654453446062117.745742057955
Trimmed Mean ( 8 / 20 )8.492295454545450.0698991540230261121.493536985411
Trimmed Mean ( 9 / 20 )8.486904761904760.0672339321851518126.229486898567
Trimmed Mean ( 10 / 20 )8.47910.0641874039084992132.099126677365
Trimmed Mean ( 11 / 20 )8.471447368421050.060495602480205140.034102002588
Trimmed Mean ( 12 / 20 )8.461388888888890.0564076753442517150.004211966717
Trimmed Mean ( 13 / 20 )8.457205882352940.0544329999031134155.369094068049
Trimmed Mean ( 14 / 20 )8.45081250.0520902101642879162.234179385088
Trimmed Mean ( 15 / 20 )8.443366666666670.0486999606630475173.375225599993
Trimmed Mean ( 16 / 20 )8.436321428571430.0456571955643655184.775287318694
Trimmed Mean ( 17 / 20 )8.432230769230770.0431054273824362195.618771956929
Trimmed Mean ( 18 / 20 )8.4268750.040062465379035210.343395501812
Trimmed Mean ( 19 / 20 )8.424136363636360.0369839848020445227.777953314827
Trimmed Mean ( 20 / 20 )8.424650.0345295658972515243.98366388587
Median8.435
Midrange8.9765
Midmean - Weighted Average at Xnp8.42951612903226
Midmean - Weighted Average at X(n+1)p8.44336666666667
Midmean - Empirical Distribution Function8.42951612903226
Midmean - Empirical Distribution Function - Averaging8.44336666666667
Midmean - Empirical Distribution Function - Interpolation8.44336666666667
Midmean - Closest Observation8.42951612903226
Midmean - True Basic - Statistics Graphics Toolkit8.44336666666667
Midmean - MS Excel (old versions)8.4508125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.57513333333333 & 0.0974733614679255 & 87.9741213824359 \tabularnewline
Geometric Mean & 8.54367550118092 &  &  \tabularnewline
Harmonic Mean & 8.5134183895635 &  &  \tabularnewline
Quadratic Mean & 8.60775661830654 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.57455 & 0.0972602409898368 & 88.160896094181 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.57585 & 0.0962365283697171 & 89.1122128497164 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.5614 & 0.0913484673427842 & 93.7224263202297 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.55433333333333 & 0.0887585427309466 & 96.377577528104 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.53966666666667 & 0.0841150163161618 & 101.523687929498 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.52046666666667 & 0.0787467279085858 & 108.200897903437 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.52221666666667 & 0.0779111332516569 & 109.383810900805 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.52248333333333 & 0.076762656041356 & 111.023820342301 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.53373333333333 & 0.074868418913846 & 113.983084685593 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.52756666666667 & 0.0734169324465969 & 116.152587454802 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.53783333333333 & 0.0699922601316942 & 121.982535172731 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.48983333333333 & 0.058631869656013 & 144.798952909779 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.50153333333333 & 0.0567860115795353 & 149.711752892276 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.50293333333333 & 0.0565031515878513 & 150.486001123547 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.49268333333333 & 0.0510011769647435 & 166.519359723879 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.46468333333333 & 0.0457572228355216 & 184.991195024234 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.46865 & 0.0431358897656661 & 196.324917510815 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.44495 & 0.0391863894926405 & 215.50722353704 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.42088333333333 & 0.033738510006205 & 249.592626698233 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.42755 & 0.0259797990297677 & 324.388575536851 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.56129310344828 & 0.0936572796456502 & 91.4108666815831 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.54708928571429 & 0.0891695498546977 & 95.8521075820369 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.53111111111111 & 0.084226204803423 & 101.288086421821 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.51946153846154 & 0.0805311902024843 & 105.790831068566 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.509 & 0.0769385283382594 & 110.594785002779 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.50133333333333 & 0.074078244366454 & 114.761539046181 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.49717391304348 & 0.0721654453446062 & 117.745742057955 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.49229545454545 & 0.0698991540230261 & 121.493536985411 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.48690476190476 & 0.0672339321851518 & 126.229486898567 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.4791 & 0.0641874039084992 & 132.099126677365 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.47144736842105 & 0.060495602480205 & 140.034102002588 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.46138888888889 & 0.0564076753442517 & 150.004211966717 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.45720588235294 & 0.0544329999031134 & 155.369094068049 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.4508125 & 0.0520902101642879 & 162.234179385088 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.44336666666667 & 0.0486999606630475 & 173.375225599993 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.43632142857143 & 0.0456571955643655 & 184.775287318694 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.43223076923077 & 0.0431054273824362 & 195.618771956929 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.426875 & 0.040062465379035 & 210.343395501812 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.42413636363636 & 0.0369839848020445 & 227.777953314827 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.42465 & 0.0345295658972515 & 243.98366388587 \tabularnewline
Median & 8.435 &  &  \tabularnewline
Midrange & 8.9765 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.42951612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.44336666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.42951612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.44336666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.44336666666667 &  &  \tabularnewline
Midmean - Closest Observation & 8.42951612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.44336666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.4508125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148181&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]8.57513333333333[/C][C]0.0974733614679255[/C][C]87.9741213824359[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.54367550118092[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.5134183895635[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.60775661830654[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.57455[/C][C]0.0972602409898368[/C][C]88.160896094181[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.57585[/C][C]0.0962365283697171[/C][C]89.1122128497164[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.5614[/C][C]0.0913484673427842[/C][C]93.7224263202297[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.55433333333333[/C][C]0.0887585427309466[/C][C]96.377577528104[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.53966666666667[/C][C]0.0841150163161618[/C][C]101.523687929498[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.52046666666667[/C][C]0.0787467279085858[/C][C]108.200897903437[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.52221666666667[/C][C]0.0779111332516569[/C][C]109.383810900805[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.52248333333333[/C][C]0.076762656041356[/C][C]111.023820342301[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.53373333333333[/C][C]0.074868418913846[/C][C]113.983084685593[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.52756666666667[/C][C]0.0734169324465969[/C][C]116.152587454802[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.53783333333333[/C][C]0.0699922601316942[/C][C]121.982535172731[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.48983333333333[/C][C]0.058631869656013[/C][C]144.798952909779[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.50153333333333[/C][C]0.0567860115795353[/C][C]149.711752892276[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.50293333333333[/C][C]0.0565031515878513[/C][C]150.486001123547[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.49268333333333[/C][C]0.0510011769647435[/C][C]166.519359723879[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.46468333333333[/C][C]0.0457572228355216[/C][C]184.991195024234[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.46865[/C][C]0.0431358897656661[/C][C]196.324917510815[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.44495[/C][C]0.0391863894926405[/C][C]215.50722353704[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.42088333333333[/C][C]0.033738510006205[/C][C]249.592626698233[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.42755[/C][C]0.0259797990297677[/C][C]324.388575536851[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.56129310344828[/C][C]0.0936572796456502[/C][C]91.4108666815831[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.54708928571429[/C][C]0.0891695498546977[/C][C]95.8521075820369[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.53111111111111[/C][C]0.084226204803423[/C][C]101.288086421821[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.51946153846154[/C][C]0.0805311902024843[/C][C]105.790831068566[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.509[/C][C]0.0769385283382594[/C][C]110.594785002779[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.50133333333333[/C][C]0.074078244366454[/C][C]114.761539046181[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.49717391304348[/C][C]0.0721654453446062[/C][C]117.745742057955[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.49229545454545[/C][C]0.0698991540230261[/C][C]121.493536985411[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.48690476190476[/C][C]0.0672339321851518[/C][C]126.229486898567[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.4791[/C][C]0.0641874039084992[/C][C]132.099126677365[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.47144736842105[/C][C]0.060495602480205[/C][C]140.034102002588[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.46138888888889[/C][C]0.0564076753442517[/C][C]150.004211966717[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.45720588235294[/C][C]0.0544329999031134[/C][C]155.369094068049[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.4508125[/C][C]0.0520902101642879[/C][C]162.234179385088[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.44336666666667[/C][C]0.0486999606630475[/C][C]173.375225599993[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.43632142857143[/C][C]0.0456571955643655[/C][C]184.775287318694[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.43223076923077[/C][C]0.0431054273824362[/C][C]195.618771956929[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.426875[/C][C]0.040062465379035[/C][C]210.343395501812[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.42413636363636[/C][C]0.0369839848020445[/C][C]227.777953314827[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.42465[/C][C]0.0345295658972515[/C][C]243.98366388587[/C][/ROW]
[ROW][C]Median[/C][C]8.435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.9765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.42951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.44336666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.42951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.44336666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.44336666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.42951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.44336666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.4508125[/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=148181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148181&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 Mean8.575133333333330.097473361467925587.9741213824359
Geometric Mean8.54367550118092
Harmonic Mean8.5134183895635
Quadratic Mean8.60775661830654
Winsorized Mean ( 1 / 20 )8.574550.097260240989836888.160896094181
Winsorized Mean ( 2 / 20 )8.575850.096236528369717189.1122128497164
Winsorized Mean ( 3 / 20 )8.56140.091348467342784293.7224263202297
Winsorized Mean ( 4 / 20 )8.554333333333330.088758542730946696.377577528104
Winsorized Mean ( 5 / 20 )8.539666666666670.0841150163161618101.523687929498
Winsorized Mean ( 6 / 20 )8.520466666666670.0787467279085858108.200897903437
Winsorized Mean ( 7 / 20 )8.522216666666670.0779111332516569109.383810900805
Winsorized Mean ( 8 / 20 )8.522483333333330.076762656041356111.023820342301
Winsorized Mean ( 9 / 20 )8.533733333333330.074868418913846113.983084685593
Winsorized Mean ( 10 / 20 )8.527566666666670.0734169324465969116.152587454802
Winsorized Mean ( 11 / 20 )8.537833333333330.0699922601316942121.982535172731
Winsorized Mean ( 12 / 20 )8.489833333333330.058631869656013144.798952909779
Winsorized Mean ( 13 / 20 )8.501533333333330.0567860115795353149.711752892276
Winsorized Mean ( 14 / 20 )8.502933333333330.0565031515878513150.486001123547
Winsorized Mean ( 15 / 20 )8.492683333333330.0510011769647435166.519359723879
Winsorized Mean ( 16 / 20 )8.464683333333330.0457572228355216184.991195024234
Winsorized Mean ( 17 / 20 )8.468650.0431358897656661196.324917510815
Winsorized Mean ( 18 / 20 )8.444950.0391863894926405215.50722353704
Winsorized Mean ( 19 / 20 )8.420883333333330.033738510006205249.592626698233
Winsorized Mean ( 20 / 20 )8.427550.0259797990297677324.388575536851
Trimmed Mean ( 1 / 20 )8.561293103448280.093657279645650291.4108666815831
Trimmed Mean ( 2 / 20 )8.547089285714290.089169549854697795.8521075820369
Trimmed Mean ( 3 / 20 )8.531111111111110.084226204803423101.288086421821
Trimmed Mean ( 4 / 20 )8.519461538461540.0805311902024843105.790831068566
Trimmed Mean ( 5 / 20 )8.5090.0769385283382594110.594785002779
Trimmed Mean ( 6 / 20 )8.501333333333330.074078244366454114.761539046181
Trimmed Mean ( 7 / 20 )8.497173913043480.0721654453446062117.745742057955
Trimmed Mean ( 8 / 20 )8.492295454545450.0698991540230261121.493536985411
Trimmed Mean ( 9 / 20 )8.486904761904760.0672339321851518126.229486898567
Trimmed Mean ( 10 / 20 )8.47910.0641874039084992132.099126677365
Trimmed Mean ( 11 / 20 )8.471447368421050.060495602480205140.034102002588
Trimmed Mean ( 12 / 20 )8.461388888888890.0564076753442517150.004211966717
Trimmed Mean ( 13 / 20 )8.457205882352940.0544329999031134155.369094068049
Trimmed Mean ( 14 / 20 )8.45081250.0520902101642879162.234179385088
Trimmed Mean ( 15 / 20 )8.443366666666670.0486999606630475173.375225599993
Trimmed Mean ( 16 / 20 )8.436321428571430.0456571955643655184.775287318694
Trimmed Mean ( 17 / 20 )8.432230769230770.0431054273824362195.618771956929
Trimmed Mean ( 18 / 20 )8.4268750.040062465379035210.343395501812
Trimmed Mean ( 19 / 20 )8.424136363636360.0369839848020445227.777953314827
Trimmed Mean ( 20 / 20 )8.424650.0345295658972515243.98366388587
Median8.435
Midrange8.9765
Midmean - Weighted Average at Xnp8.42951612903226
Midmean - Weighted Average at X(n+1)p8.44336666666667
Midmean - Empirical Distribution Function8.42951612903226
Midmean - Empirical Distribution Function - Averaging8.44336666666667
Midmean - Empirical Distribution Function - Interpolation8.44336666666667
Midmean - Closest Observation8.42951612903226
Midmean - True Basic - Statistics Graphics Toolkit8.44336666666667
Midmean - MS Excel (old versions)8.4508125
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')