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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 computationThu, 31 Mar 2011 14:18:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Mar/31/t1301580965ezdmh7u4yssh4hq.htm/, Retrieved Tue, 14 May 2024 04:53:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=119886, Retrieved Tue, 14 May 2024 04:53:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-03-31 14:18:01] [60509181c3aa3f51e201bae3996eda3b] [Current]
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Dataseries X:
31.900
31.815
31.075
31.070
31.300
31.410
30.310
31.440
31.355
31.380
31.975
31.905
32.565
32.780
32.850
32.910
32.910
33.755
34.130
34.330
34.120
33.600
33.715
33.535
33.745
34.295
33.940
34.245
34.395
33.640
33.890
33.905
33.930
33.975
33.880
33.800
33.165
33.660
33.545
33.590
33.810
33.720
33.660
33.915
34.265
34.175
33.735
33.855
34.210
33.950
33.130
32.195
33.160
33.255
32.260
31.795
31.875
31.985
31.835
32.200
32.275
32.515
32.700
32.680
32.135
31.460
30.755
31.090
31.270
31.110
30.835
31.025
30.800
30.790




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119886&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119886&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean32.75891891891890.137032645219631239.059231954649
Geometric Mean32.7378165525563
Harmonic Mean32.7165446109395
Quadratic Mean32.7798346363093
Winsorized Mean ( 1 / 24 )32.76405405405410.135544026889539241.72259601491
Winsorized Mean ( 2 / 24 )32.76405405405410.135205175296062242.328401870045
Winsorized Mean ( 3 / 24 )32.76324324324320.134937197687708242.803643507322
Winsorized Mean ( 4 / 24 )32.76405405405410.134398666068186243.782583656236
Winsorized Mean ( 5 / 24 )32.7745270270270.131611567399846249.024669142154
Winsorized Mean ( 6 / 24 )32.77533783783780.130532413409079251.089648784186
Winsorized Mean ( 7 / 24 )32.77155405405410.129830041752813252.418882499081
Winsorized Mean ( 8 / 24 )32.77209459459460.129385884887189253.289565729433
Winsorized Mean ( 9 / 24 )32.75689189189190.126530200868374258.885955029567
Winsorized Mean ( 10 / 24 )32.77513513513510.122333800734079267.915612352955
Winsorized Mean ( 11 / 24 )32.77810810810810.121390831665443270.02128297832
Winsorized Mean ( 12 / 24 )32.78540540540540.119704404100047273.886375792856
Winsorized Mean ( 13 / 24 )32.78716216216220.118643998503843276.349099622599
Winsorized Mean ( 14 / 24 )32.79094594594590.11747988853524279.119654902547
Winsorized Mean ( 15 / 24 )32.79398648648650.116110488325407282.437762164769
Winsorized Mean ( 16 / 24 )32.79614864864860.115142192218536284.831719951994
Winsorized Mean ( 17 / 24 )32.86736486486490.1027404586405319.906736837446
Winsorized Mean ( 18 / 24 )32.86128378378380.100618416425156326.593132264483
Winsorized Mean ( 19 / 24 )32.86385135135140.099558008189229330.097517508459
Winsorized Mean ( 20 / 24 )32.86250.0964807075765344340.612137135618
Winsorized Mean ( 21 / 24 )32.86675675675680.0951302441440737345.492193912384
Winsorized Mean ( 22 / 24 )32.86527027027030.0945480633427124347.603844101408
Winsorized Mean ( 23 / 24 )32.88236486486490.0909597120933832361.504715748291
Winsorized Mean ( 24 / 24 )32.88398648648650.0903125091699204364.11330820868
Trimmed Mean ( 1 / 24 )32.77020833333330.134701985063063243.279327457509
Trimmed Mean ( 2 / 24 )32.77671428571430.133637084869915245.266606328773
Trimmed Mean ( 3 / 24 )32.78360294117650.132513762831046247.397721118035
Trimmed Mean ( 4 / 24 )32.79121212121210.131221491991379249.892084166871
Trimmed Mean ( 5 / 24 )32.79906250.129794598635003252.699749026034
Trimmed Mean ( 6 / 24 )32.80491935483870.128845373404297254.60688644133
Trimmed Mean ( 7 / 24 )32.8110.127886105313296256.56422892557
Trimmed Mean ( 8 / 24 )32.81818965517240.126782195198285258.854877878122
Trimmed Mean ( 9 / 24 )32.82580357142860.125428018938485261.710292877444
Trimmed Mean ( 10 / 24 )32.83629629629630.124251159128656264.273561120633
Trimmed Mean ( 11 / 24 )32.8450.123558048106489265.826471875733
Trimmed Mean ( 12 / 24 )32.8540.122719025353339267.717250079236
Trimmed Mean ( 13 / 24 )32.86281250.121836557971644269.728668037787
Trimmed Mean ( 14 / 24 )32.87217391304350.120743535066021272.247900436818
Trimmed Mean ( 15 / 24 )32.88193181818180.11939253572753275.410281034845
Trimmed Mean ( 16 / 24 )32.89226190476190.117735629060204279.373900384416
Trimmed Mean ( 17 / 24 )32.9033750.115575120911544284.692542309195
Trimmed Mean ( 18 / 24 )32.90750.115335917022124285.318752819103
Trimmed Mean ( 19 / 24 )32.91277777777780.115105445867823285.935887130587
Trimmed Mean ( 20 / 24 )32.91838235294120.114634333117282287.159888820241
Trimmed Mean ( 21 / 24 )32.924843750.114275082915537288.119184952467
Trimmed Mean ( 22 / 24 )32.93166666666670.113613413217081289.857207297734
Trimmed Mean ( 23 / 24 )32.93964285714290.112268553389277293.400439060872
Trimmed Mean ( 24 / 24 )32.94673076923080.110856782974074297.200855782871
Median32.91
Midrange32.3525
Midmean - Weighted Average at Xnp32.8831081081081
Midmean - Weighted Average at X(n+1)p32.9075
Midmean - Empirical Distribution Function32.9075
Midmean - Empirical Distribution Function - Averaging32.9075
Midmean - Empirical Distribution Function - Interpolation32.9127777777778
Midmean - Closest Observation32.9075
Midmean - True Basic - Statistics Graphics Toolkit32.9075
Midmean - MS Excel (old versions)32.9075
Number of observations74

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 32.7589189189189 & 0.137032645219631 & 239.059231954649 \tabularnewline
Geometric Mean & 32.7378165525563 &  &  \tabularnewline
Harmonic Mean & 32.7165446109395 &  &  \tabularnewline
Quadratic Mean & 32.7798346363093 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 32.7640540540541 & 0.135544026889539 & 241.72259601491 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 32.7640540540541 & 0.135205175296062 & 242.328401870045 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 32.7632432432432 & 0.134937197687708 & 242.803643507322 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 32.7640540540541 & 0.134398666068186 & 243.782583656236 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 32.774527027027 & 0.131611567399846 & 249.024669142154 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 32.7753378378378 & 0.130532413409079 & 251.089648784186 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 32.7715540540541 & 0.129830041752813 & 252.418882499081 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 32.7720945945946 & 0.129385884887189 & 253.289565729433 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 32.7568918918919 & 0.126530200868374 & 258.885955029567 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 32.7751351351351 & 0.122333800734079 & 267.915612352955 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 32.7781081081081 & 0.121390831665443 & 270.02128297832 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 32.7854054054054 & 0.119704404100047 & 273.886375792856 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 32.7871621621622 & 0.118643998503843 & 276.349099622599 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 32.7909459459459 & 0.11747988853524 & 279.119654902547 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 32.7939864864865 & 0.116110488325407 & 282.437762164769 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 32.7961486486486 & 0.115142192218536 & 284.831719951994 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 32.8673648648649 & 0.1027404586405 & 319.906736837446 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 32.8612837837838 & 0.100618416425156 & 326.593132264483 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 32.8638513513514 & 0.099558008189229 & 330.097517508459 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 32.8625 & 0.0964807075765344 & 340.612137135618 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 32.8667567567568 & 0.0951302441440737 & 345.492193912384 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 32.8652702702703 & 0.0945480633427124 & 347.603844101408 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 32.8823648648649 & 0.0909597120933832 & 361.504715748291 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 32.8839864864865 & 0.0903125091699204 & 364.11330820868 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 32.7702083333333 & 0.134701985063063 & 243.279327457509 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 32.7767142857143 & 0.133637084869915 & 245.266606328773 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 32.7836029411765 & 0.132513762831046 & 247.397721118035 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 32.7912121212121 & 0.131221491991379 & 249.892084166871 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 32.7990625 & 0.129794598635003 & 252.699749026034 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 32.8049193548387 & 0.128845373404297 & 254.60688644133 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 32.811 & 0.127886105313296 & 256.56422892557 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 32.8181896551724 & 0.126782195198285 & 258.854877878122 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 32.8258035714286 & 0.125428018938485 & 261.710292877444 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 32.8362962962963 & 0.124251159128656 & 264.273561120633 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 32.845 & 0.123558048106489 & 265.826471875733 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 32.854 & 0.122719025353339 & 267.717250079236 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 32.8628125 & 0.121836557971644 & 269.728668037787 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 32.8721739130435 & 0.120743535066021 & 272.247900436818 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 32.8819318181818 & 0.11939253572753 & 275.410281034845 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 32.8922619047619 & 0.117735629060204 & 279.373900384416 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 32.903375 & 0.115575120911544 & 284.692542309195 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 32.9075 & 0.115335917022124 & 285.318752819103 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 32.9127777777778 & 0.115105445867823 & 285.935887130587 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 32.9183823529412 & 0.114634333117282 & 287.159888820241 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 32.92484375 & 0.114275082915537 & 288.119184952467 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 32.9316666666667 & 0.113613413217081 & 289.857207297734 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 32.9396428571429 & 0.112268553389277 & 293.400439060872 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 32.9467307692308 & 0.110856782974074 & 297.200855782871 \tabularnewline
Median & 32.91 &  &  \tabularnewline
Midrange & 32.3525 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 32.8831081081081 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 32.9075 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 32.9075 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 32.9075 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 32.9127777777778 &  &  \tabularnewline
Midmean - Closest Observation & 32.9075 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 32.9075 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 32.9075 &  &  \tabularnewline
Number of observations & 74 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=119886&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]32.7589189189189[/C][C]0.137032645219631[/C][C]239.059231954649[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]32.7378165525563[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]32.7165446109395[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]32.7798346363093[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]32.7640540540541[/C][C]0.135544026889539[/C][C]241.72259601491[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]32.7640540540541[/C][C]0.135205175296062[/C][C]242.328401870045[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]32.7632432432432[/C][C]0.134937197687708[/C][C]242.803643507322[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]32.7640540540541[/C][C]0.134398666068186[/C][C]243.782583656236[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]32.774527027027[/C][C]0.131611567399846[/C][C]249.024669142154[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]32.7753378378378[/C][C]0.130532413409079[/C][C]251.089648784186[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]32.7715540540541[/C][C]0.129830041752813[/C][C]252.418882499081[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]32.7720945945946[/C][C]0.129385884887189[/C][C]253.289565729433[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]32.7568918918919[/C][C]0.126530200868374[/C][C]258.885955029567[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]32.7751351351351[/C][C]0.122333800734079[/C][C]267.915612352955[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]32.7781081081081[/C][C]0.121390831665443[/C][C]270.02128297832[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]32.7854054054054[/C][C]0.119704404100047[/C][C]273.886375792856[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]32.7871621621622[/C][C]0.118643998503843[/C][C]276.349099622599[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]32.7909459459459[/C][C]0.11747988853524[/C][C]279.119654902547[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]32.7939864864865[/C][C]0.116110488325407[/C][C]282.437762164769[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]32.7961486486486[/C][C]0.115142192218536[/C][C]284.831719951994[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]32.8673648648649[/C][C]0.1027404586405[/C][C]319.906736837446[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]32.8612837837838[/C][C]0.100618416425156[/C][C]326.593132264483[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]32.8638513513514[/C][C]0.099558008189229[/C][C]330.097517508459[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]32.8625[/C][C]0.0964807075765344[/C][C]340.612137135618[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]32.8667567567568[/C][C]0.0951302441440737[/C][C]345.492193912384[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]32.8652702702703[/C][C]0.0945480633427124[/C][C]347.603844101408[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]32.8823648648649[/C][C]0.0909597120933832[/C][C]361.504715748291[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]32.8839864864865[/C][C]0.0903125091699204[/C][C]364.11330820868[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]32.7702083333333[/C][C]0.134701985063063[/C][C]243.279327457509[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]32.7767142857143[/C][C]0.133637084869915[/C][C]245.266606328773[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]32.7836029411765[/C][C]0.132513762831046[/C][C]247.397721118035[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]32.7912121212121[/C][C]0.131221491991379[/C][C]249.892084166871[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]32.7990625[/C][C]0.129794598635003[/C][C]252.699749026034[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]32.8049193548387[/C][C]0.128845373404297[/C][C]254.60688644133[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]32.811[/C][C]0.127886105313296[/C][C]256.56422892557[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]32.8181896551724[/C][C]0.126782195198285[/C][C]258.854877878122[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]32.8258035714286[/C][C]0.125428018938485[/C][C]261.710292877444[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]32.8362962962963[/C][C]0.124251159128656[/C][C]264.273561120633[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]32.845[/C][C]0.123558048106489[/C][C]265.826471875733[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]32.854[/C][C]0.122719025353339[/C][C]267.717250079236[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]32.8628125[/C][C]0.121836557971644[/C][C]269.728668037787[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]32.8721739130435[/C][C]0.120743535066021[/C][C]272.247900436818[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]32.8819318181818[/C][C]0.11939253572753[/C][C]275.410281034845[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]32.8922619047619[/C][C]0.117735629060204[/C][C]279.373900384416[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]32.903375[/C][C]0.115575120911544[/C][C]284.692542309195[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]32.9075[/C][C]0.115335917022124[/C][C]285.318752819103[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]32.9127777777778[/C][C]0.115105445867823[/C][C]285.935887130587[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]32.9183823529412[/C][C]0.114634333117282[/C][C]287.159888820241[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]32.92484375[/C][C]0.114275082915537[/C][C]288.119184952467[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]32.9316666666667[/C][C]0.113613413217081[/C][C]289.857207297734[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]32.9396428571429[/C][C]0.112268553389277[/C][C]293.400439060872[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]32.9467307692308[/C][C]0.110856782974074[/C][C]297.200855782871[/C][/ROW]
[ROW][C]Median[/C][C]32.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]32.3525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]32.8831081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]32.9075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]32.9075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]32.9075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]32.9127777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]32.9075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]32.9075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]32.9075[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]74[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=119886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=119886&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 Mean32.75891891891890.137032645219631239.059231954649
Geometric Mean32.7378165525563
Harmonic Mean32.7165446109395
Quadratic Mean32.7798346363093
Winsorized Mean ( 1 / 24 )32.76405405405410.135544026889539241.72259601491
Winsorized Mean ( 2 / 24 )32.76405405405410.135205175296062242.328401870045
Winsorized Mean ( 3 / 24 )32.76324324324320.134937197687708242.803643507322
Winsorized Mean ( 4 / 24 )32.76405405405410.134398666068186243.782583656236
Winsorized Mean ( 5 / 24 )32.7745270270270.131611567399846249.024669142154
Winsorized Mean ( 6 / 24 )32.77533783783780.130532413409079251.089648784186
Winsorized Mean ( 7 / 24 )32.77155405405410.129830041752813252.418882499081
Winsorized Mean ( 8 / 24 )32.77209459459460.129385884887189253.289565729433
Winsorized Mean ( 9 / 24 )32.75689189189190.126530200868374258.885955029567
Winsorized Mean ( 10 / 24 )32.77513513513510.122333800734079267.915612352955
Winsorized Mean ( 11 / 24 )32.77810810810810.121390831665443270.02128297832
Winsorized Mean ( 12 / 24 )32.78540540540540.119704404100047273.886375792856
Winsorized Mean ( 13 / 24 )32.78716216216220.118643998503843276.349099622599
Winsorized Mean ( 14 / 24 )32.79094594594590.11747988853524279.119654902547
Winsorized Mean ( 15 / 24 )32.79398648648650.116110488325407282.437762164769
Winsorized Mean ( 16 / 24 )32.79614864864860.115142192218536284.831719951994
Winsorized Mean ( 17 / 24 )32.86736486486490.1027404586405319.906736837446
Winsorized Mean ( 18 / 24 )32.86128378378380.100618416425156326.593132264483
Winsorized Mean ( 19 / 24 )32.86385135135140.099558008189229330.097517508459
Winsorized Mean ( 20 / 24 )32.86250.0964807075765344340.612137135618
Winsorized Mean ( 21 / 24 )32.86675675675680.0951302441440737345.492193912384
Winsorized Mean ( 22 / 24 )32.86527027027030.0945480633427124347.603844101408
Winsorized Mean ( 23 / 24 )32.88236486486490.0909597120933832361.504715748291
Winsorized Mean ( 24 / 24 )32.88398648648650.0903125091699204364.11330820868
Trimmed Mean ( 1 / 24 )32.77020833333330.134701985063063243.279327457509
Trimmed Mean ( 2 / 24 )32.77671428571430.133637084869915245.266606328773
Trimmed Mean ( 3 / 24 )32.78360294117650.132513762831046247.397721118035
Trimmed Mean ( 4 / 24 )32.79121212121210.131221491991379249.892084166871
Trimmed Mean ( 5 / 24 )32.79906250.129794598635003252.699749026034
Trimmed Mean ( 6 / 24 )32.80491935483870.128845373404297254.60688644133
Trimmed Mean ( 7 / 24 )32.8110.127886105313296256.56422892557
Trimmed Mean ( 8 / 24 )32.81818965517240.126782195198285258.854877878122
Trimmed Mean ( 9 / 24 )32.82580357142860.125428018938485261.710292877444
Trimmed Mean ( 10 / 24 )32.83629629629630.124251159128656264.273561120633
Trimmed Mean ( 11 / 24 )32.8450.123558048106489265.826471875733
Trimmed Mean ( 12 / 24 )32.8540.122719025353339267.717250079236
Trimmed Mean ( 13 / 24 )32.86281250.121836557971644269.728668037787
Trimmed Mean ( 14 / 24 )32.87217391304350.120743535066021272.247900436818
Trimmed Mean ( 15 / 24 )32.88193181818180.11939253572753275.410281034845
Trimmed Mean ( 16 / 24 )32.89226190476190.117735629060204279.373900384416
Trimmed Mean ( 17 / 24 )32.9033750.115575120911544284.692542309195
Trimmed Mean ( 18 / 24 )32.90750.115335917022124285.318752819103
Trimmed Mean ( 19 / 24 )32.91277777777780.115105445867823285.935887130587
Trimmed Mean ( 20 / 24 )32.91838235294120.114634333117282287.159888820241
Trimmed Mean ( 21 / 24 )32.924843750.114275082915537288.119184952467
Trimmed Mean ( 22 / 24 )32.93166666666670.113613413217081289.857207297734
Trimmed Mean ( 23 / 24 )32.93964285714290.112268553389277293.400439060872
Trimmed Mean ( 24 / 24 )32.94673076923080.110856782974074297.200855782871
Median32.91
Midrange32.3525
Midmean - Weighted Average at Xnp32.8831081081081
Midmean - Weighted Average at X(n+1)p32.9075
Midmean - Empirical Distribution Function32.9075
Midmean - Empirical Distribution Function - Averaging32.9075
Midmean - Empirical Distribution Function - Interpolation32.9127777777778
Midmean - Closest Observation32.9075
Midmean - True Basic - Statistics Graphics Toolkit32.9075
Midmean - MS Excel (old versions)32.9075
Number of observations74



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')