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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 computationSun, 21 Oct 2007 02:20:29 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/21/vef4ikihdebojh91192958642.htm/, Retrieved Thu, 09 May 2024 14:07:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1304, Retrieved Thu, 09 May 2024 14:07:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2Q8G6 central t...] [2007-10-21 09:20:29] [fef19078983b9fa83d10cb717d6f9786] [Current]
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Dataseries X:
518585
509239
512238
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1304&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1304&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1304&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean566188.84690.54114563235120.708630927844
Geometric Mean565031.125179333
Harmonic Mean563863.00898776
Quadratic Mean567333.963943226
Winsorized Mean ( 1 / 20 )566214.5166666674679.29596993918121.004210954843
Winsorized Mean ( 2 / 20 )566337.554615.04873491752122.715399669581
Winsorized Mean ( 3 / 20 )566191.654538.24608955846124.760014954387
Winsorized Mean ( 4 / 20 )566144.5166666674525.59577396361125.098339521125
Winsorized Mean ( 5 / 20 )566173.2666666674507.46967601011125.607781607491
Winsorized Mean ( 6 / 20 )565588.3666666674350.42642126882130.007569810067
Winsorized Mean ( 7 / 20 )565670.54310.25566215785131.238270844660
Winsorized Mean ( 8 / 20 )566200.94160.25416397485136.097670402674
Winsorized Mean ( 9 / 20 )566353.154097.74558577968138.210910888515
Winsorized Mean ( 10 / 20 )564179.3166666673696.28039912807152.634339321160
Winsorized Mean ( 11 / 20 )565108.453400.46452446736166.185662556946
Winsorized Mean ( 12 / 20 )566249.253180.29369016768178.049358067350
Winsorized Mean ( 13 / 20 )567062.1833333332944.19000472008192.603800170583
Winsorized Mean ( 14 / 20 )568079.052722.75153859438208.641531167133
Winsorized Mean ( 15 / 20 )568314.82674.41940515867212.500252916121
Winsorized Mean ( 16 / 20 )567870.5333333332530.24811209064224.432746583151
Winsorized Mean ( 17 / 20 )568706.9333333332326.48114001380244.449406252208
Winsorized Mean ( 18 / 20 )568952.0333333332224.16609231322255.804652044489
Winsorized Mean ( 19 / 20 )570275.71859.54534421055306.674801867821
Winsorized Mean ( 20 / 20 )569391.3666666671667.97424395949341.36700175599
Trimmed Mean ( 1 / 20 )566272.1034482764581.493209517123.599900196725
Trimmed Mean ( 2 / 20 )566333.8035714294460.31661449848126.971659754048
Trimmed Mean ( 3 / 20 )566331.7222222224352.30427161154130.122272451444
Trimmed Mean ( 4 / 20 )566385.5961538464253.52916085183133.156627058463
Trimmed Mean ( 5 / 20 )566457.924132.98519626219137.057814896675
Trimmed Mean ( 6 / 20 )566529.0833333333985.45417113368142.149190282166
Trimmed Mean ( 7 / 20 )566733.5869565223846.63996067088147.332111336378
Trimmed Mean ( 8 / 20 )566940.6818181823678.24100528968154.133641869270
Trimmed Mean ( 9 / 20 )567072.7857142863503.27105309738161.869514838971
Trimmed Mean ( 10 / 20 )567192.7253288.8186732273172.460929396091
Trimmed Mean ( 11 / 20 )567668.526315793117.1087325061182.113803216417
Trimmed Mean ( 12 / 20 )568056.4166666672973.52601537086191.037984443468
Trimmed Mean ( 13 / 20 )568322.1764705882842.68067400932199.924733603309
Trimmed Mean ( 14 / 20 )568503.906252730.37657487825208.214468099643
Trimmed Mean ( 15 / 20 )568564.62636.64370753042215.639526256863
Trimmed Mean ( 16 / 20 )568600.2857142862510.05232447050226.529256052156
Trimmed Mean ( 17 / 20 )568705.5384615382367.08335898894240.255813679689
Trimmed Mean ( 18 / 20 )568705.3333333332223.54143421296255.765565949362
Trimmed Mean ( 19 / 20 )568667.9545454552032.02535122969279.852785400203
Trimmed Mean ( 20 / 20 )568414.11887.87344426975301.086972606825
Median568242
Midrange563773
Midmean - Weighted Average at Xnp567696.612903226
Midmean - Weighted Average at X(n+1)p568564.6
Midmean - Empirical Distribution Function567696.612903226
Midmean - Empirical Distribution Function - Averaging568564.6
Midmean - Empirical Distribution Function - Interpolation568564.6
Midmean - Closest Observation567696.612903226
Midmean - True Basic - Statistics Graphics Toolkit568564.6
Midmean - MS Excel (old versions)568503.90625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 566188.8 & 4690.54114563235 & 120.708630927844 \tabularnewline
Geometric Mean & 565031.125179333 &  &  \tabularnewline
Harmonic Mean & 563863.00898776 &  &  \tabularnewline
Quadratic Mean & 567333.963943226 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 566214.516666667 & 4679.29596993918 & 121.004210954843 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 566337.55 & 4615.04873491752 & 122.715399669581 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 566191.65 & 4538.24608955846 & 124.760014954387 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 566144.516666667 & 4525.59577396361 & 125.098339521125 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 566173.266666667 & 4507.46967601011 & 125.607781607491 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 565588.366666667 & 4350.42642126882 & 130.007569810067 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 565670.5 & 4310.25566215785 & 131.238270844660 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 566200.9 & 4160.25416397485 & 136.097670402674 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 566353.15 & 4097.74558577968 & 138.210910888515 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 564179.316666667 & 3696.28039912807 & 152.634339321160 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 565108.45 & 3400.46452446736 & 166.185662556946 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 566249.25 & 3180.29369016768 & 178.049358067350 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 567062.183333333 & 2944.19000472008 & 192.603800170583 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 568079.05 & 2722.75153859438 & 208.641531167133 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 568314.8 & 2674.41940515867 & 212.500252916121 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 567870.533333333 & 2530.24811209064 & 224.432746583151 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 568706.933333333 & 2326.48114001380 & 244.449406252208 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 568952.033333333 & 2224.16609231322 & 255.804652044489 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 570275.7 & 1859.54534421055 & 306.674801867821 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 569391.366666667 & 1667.97424395949 & 341.36700175599 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 566272.103448276 & 4581.493209517 & 123.599900196725 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 566333.803571429 & 4460.31661449848 & 126.971659754048 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 566331.722222222 & 4352.30427161154 & 130.122272451444 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 566385.596153846 & 4253.52916085183 & 133.156627058463 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 566457.92 & 4132.98519626219 & 137.057814896675 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 566529.083333333 & 3985.45417113368 & 142.149190282166 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 566733.586956522 & 3846.63996067088 & 147.332111336378 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 566940.681818182 & 3678.24100528968 & 154.133641869270 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 567072.785714286 & 3503.27105309738 & 161.869514838971 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 567192.725 & 3288.8186732273 & 172.460929396091 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 567668.52631579 & 3117.1087325061 & 182.113803216417 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 568056.416666667 & 2973.52601537086 & 191.037984443468 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 568322.176470588 & 2842.68067400932 & 199.924733603309 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 568503.90625 & 2730.37657487825 & 208.214468099643 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 568564.6 & 2636.64370753042 & 215.639526256863 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 568600.285714286 & 2510.05232447050 & 226.529256052156 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 568705.538461538 & 2367.08335898894 & 240.255813679689 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 568705.333333333 & 2223.54143421296 & 255.765565949362 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 568667.954545455 & 2032.02535122969 & 279.852785400203 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 568414.1 & 1887.87344426975 & 301.086972606825 \tabularnewline
Median & 568242 &  &  \tabularnewline
Midrange & 563773 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 567696.612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 568564.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 567696.612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 568564.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 568564.6 &  &  \tabularnewline
Midmean - Closest Observation & 567696.612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 568564.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 568503.90625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1304&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]566188.8[/C][C]4690.54114563235[/C][C]120.708630927844[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]565031.125179333[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]563863.00898776[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]567333.963943226[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]566214.516666667[/C][C]4679.29596993918[/C][C]121.004210954843[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]566337.55[/C][C]4615.04873491752[/C][C]122.715399669581[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]566191.65[/C][C]4538.24608955846[/C][C]124.760014954387[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]566144.516666667[/C][C]4525.59577396361[/C][C]125.098339521125[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]566173.266666667[/C][C]4507.46967601011[/C][C]125.607781607491[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]565588.366666667[/C][C]4350.42642126882[/C][C]130.007569810067[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]565670.5[/C][C]4310.25566215785[/C][C]131.238270844660[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]566200.9[/C][C]4160.25416397485[/C][C]136.097670402674[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]566353.15[/C][C]4097.74558577968[/C][C]138.210910888515[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]564179.316666667[/C][C]3696.28039912807[/C][C]152.634339321160[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]565108.45[/C][C]3400.46452446736[/C][C]166.185662556946[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]566249.25[/C][C]3180.29369016768[/C][C]178.049358067350[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]567062.183333333[/C][C]2944.19000472008[/C][C]192.603800170583[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]568079.05[/C][C]2722.75153859438[/C][C]208.641531167133[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]568314.8[/C][C]2674.41940515867[/C][C]212.500252916121[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]567870.533333333[/C][C]2530.24811209064[/C][C]224.432746583151[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]568706.933333333[/C][C]2326.48114001380[/C][C]244.449406252208[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]568952.033333333[/C][C]2224.16609231322[/C][C]255.804652044489[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]570275.7[/C][C]1859.54534421055[/C][C]306.674801867821[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]569391.366666667[/C][C]1667.97424395949[/C][C]341.36700175599[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]566272.103448276[/C][C]4581.493209517[/C][C]123.599900196725[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]566333.803571429[/C][C]4460.31661449848[/C][C]126.971659754048[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]566331.722222222[/C][C]4352.30427161154[/C][C]130.122272451444[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]566385.596153846[/C][C]4253.52916085183[/C][C]133.156627058463[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]566457.92[/C][C]4132.98519626219[/C][C]137.057814896675[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]566529.083333333[/C][C]3985.45417113368[/C][C]142.149190282166[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]566733.586956522[/C][C]3846.63996067088[/C][C]147.332111336378[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]566940.681818182[/C][C]3678.24100528968[/C][C]154.133641869270[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]567072.785714286[/C][C]3503.27105309738[/C][C]161.869514838971[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]567192.725[/C][C]3288.8186732273[/C][C]172.460929396091[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]567668.52631579[/C][C]3117.1087325061[/C][C]182.113803216417[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]568056.416666667[/C][C]2973.52601537086[/C][C]191.037984443468[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]568322.176470588[/C][C]2842.68067400932[/C][C]199.924733603309[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]568503.90625[/C][C]2730.37657487825[/C][C]208.214468099643[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]568564.6[/C][C]2636.64370753042[/C][C]215.639526256863[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]568600.285714286[/C][C]2510.05232447050[/C][C]226.529256052156[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]568705.538461538[/C][C]2367.08335898894[/C][C]240.255813679689[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]568705.333333333[/C][C]2223.54143421296[/C][C]255.765565949362[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]568667.954545455[/C][C]2032.02535122969[/C][C]279.852785400203[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]568414.1[/C][C]1887.87344426975[/C][C]301.086972606825[/C][/ROW]
[ROW][C]Median[/C][C]568242[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]563773[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]567696.612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]568564.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]567696.612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]568564.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]568564.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]567696.612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]568564.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]568503.90625[/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=1304&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1304&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 Mean566188.84690.54114563235120.708630927844
Geometric Mean565031.125179333
Harmonic Mean563863.00898776
Quadratic Mean567333.963943226
Winsorized Mean ( 1 / 20 )566214.5166666674679.29596993918121.004210954843
Winsorized Mean ( 2 / 20 )566337.554615.04873491752122.715399669581
Winsorized Mean ( 3 / 20 )566191.654538.24608955846124.760014954387
Winsorized Mean ( 4 / 20 )566144.5166666674525.59577396361125.098339521125
Winsorized Mean ( 5 / 20 )566173.2666666674507.46967601011125.607781607491
Winsorized Mean ( 6 / 20 )565588.3666666674350.42642126882130.007569810067
Winsorized Mean ( 7 / 20 )565670.54310.25566215785131.238270844660
Winsorized Mean ( 8 / 20 )566200.94160.25416397485136.097670402674
Winsorized Mean ( 9 / 20 )566353.154097.74558577968138.210910888515
Winsorized Mean ( 10 / 20 )564179.3166666673696.28039912807152.634339321160
Winsorized Mean ( 11 / 20 )565108.453400.46452446736166.185662556946
Winsorized Mean ( 12 / 20 )566249.253180.29369016768178.049358067350
Winsorized Mean ( 13 / 20 )567062.1833333332944.19000472008192.603800170583
Winsorized Mean ( 14 / 20 )568079.052722.75153859438208.641531167133
Winsorized Mean ( 15 / 20 )568314.82674.41940515867212.500252916121
Winsorized Mean ( 16 / 20 )567870.5333333332530.24811209064224.432746583151
Winsorized Mean ( 17 / 20 )568706.9333333332326.48114001380244.449406252208
Winsorized Mean ( 18 / 20 )568952.0333333332224.16609231322255.804652044489
Winsorized Mean ( 19 / 20 )570275.71859.54534421055306.674801867821
Winsorized Mean ( 20 / 20 )569391.3666666671667.97424395949341.36700175599
Trimmed Mean ( 1 / 20 )566272.1034482764581.493209517123.599900196725
Trimmed Mean ( 2 / 20 )566333.8035714294460.31661449848126.971659754048
Trimmed Mean ( 3 / 20 )566331.7222222224352.30427161154130.122272451444
Trimmed Mean ( 4 / 20 )566385.5961538464253.52916085183133.156627058463
Trimmed Mean ( 5 / 20 )566457.924132.98519626219137.057814896675
Trimmed Mean ( 6 / 20 )566529.0833333333985.45417113368142.149190282166
Trimmed Mean ( 7 / 20 )566733.5869565223846.63996067088147.332111336378
Trimmed Mean ( 8 / 20 )566940.6818181823678.24100528968154.133641869270
Trimmed Mean ( 9 / 20 )567072.7857142863503.27105309738161.869514838971
Trimmed Mean ( 10 / 20 )567192.7253288.8186732273172.460929396091
Trimmed Mean ( 11 / 20 )567668.526315793117.1087325061182.113803216417
Trimmed Mean ( 12 / 20 )568056.4166666672973.52601537086191.037984443468
Trimmed Mean ( 13 / 20 )568322.1764705882842.68067400932199.924733603309
Trimmed Mean ( 14 / 20 )568503.906252730.37657487825208.214468099643
Trimmed Mean ( 15 / 20 )568564.62636.64370753042215.639526256863
Trimmed Mean ( 16 / 20 )568600.2857142862510.05232447050226.529256052156
Trimmed Mean ( 17 / 20 )568705.5384615382367.08335898894240.255813679689
Trimmed Mean ( 18 / 20 )568705.3333333332223.54143421296255.765565949362
Trimmed Mean ( 19 / 20 )568667.9545454552032.02535122969279.852785400203
Trimmed Mean ( 20 / 20 )568414.11887.87344426975301.086972606825
Median568242
Midrange563773
Midmean - Weighted Average at Xnp567696.612903226
Midmean - Weighted Average at X(n+1)p568564.6
Midmean - Empirical Distribution Function567696.612903226
Midmean - Empirical Distribution Function - Averaging568564.6
Midmean - Empirical Distribution Function - Interpolation568564.6
Midmean - Closest Observation567696.612903226
Midmean - True Basic - Statistics Graphics Toolkit568564.6
Midmean - MS Excel (old versions)568503.90625
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')