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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 19 Oct 2008 07:52:59 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/19/t1224424412rp110zh2iftywmp.htm/, Retrieved Sat, 18 May 2024 13:53:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16845, Retrieved Sat, 18 May 2024 13:53:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Investigating ass...] [2007-10-22 22:08:56] [8cd6641b921d30ebe00b648d1481bba0]
-    D  [Pearson Correlation] [Verband inflatie ...] [2008-10-19 13:31:27] [e5d91604aae608e98a8ea24759233f66]
-    D    [Pearson Correlation] [Pearson correlati...] [2008-10-19 13:35:43] [e5d91604aae608e98a8ea24759233f66]
- RM D      [Central Tendency] [Central tendency ...] [2008-10-19 13:49:09] [e5d91604aae608e98a8ea24759233f66]
-    D          [Central Tendency] [Central tendency ...] [2008-10-19 13:52:59] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]
Feedback Forum

Post a new message
Dataseries X:
512238
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
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
527070
509846
514258




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16845&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16845&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean564987.0666666674719.03407159254119.725150972686
Geometric Mean563815.93710545
Harmonic Mean562637.483780112
Quadratic Mean566148.631696807
Winsorized Mean ( 1 / 20 )565012.7833333334707.96821537709120.012021637678
Winsorized Mean ( 2 / 20 )565135.8166666674644.65722558895121.674386121143
Winsorized Mean ( 3 / 20 )564989.9166666674567.70182904213123.692381379707
Winsorized Mean ( 4 / 20 )564983.254546.56972996045124.265827548391
Winsorized Mean ( 5 / 20 )564961.4166666674539.1368576007124.464503801124
Winsorized Mean ( 6 / 20 )564376.5166666674380.48662650892128.838771759121
Winsorized Mean ( 7 / 20 )564458.654340.98271371876130.030153821195
Winsorized Mean ( 8 / 20 )564622.254266.9347219353132.325026463942
Winsorized Mean ( 9 / 20 )564950.754169.79892079955135.486329372370
Winsorized Mean ( 10 / 20 )563039.5833333333708.5283585326151.822914347652
Winsorized Mean ( 11 / 20 )563959.553417.59749727019165.016374938963
Winsorized Mean ( 12 / 20 )563942.353336.02956340673169.045968952417
Winsorized Mean ( 13 / 20 )564801.653131.75870094075180.346477469781
Winsorized Mean ( 14 / 20 )565937.2833333332923.95895483218193.551719458324
Winsorized Mean ( 15 / 20 )566550.2833333332616.30168314492216.546236614546
Winsorized Mean ( 16 / 20 )566622.8166666672537.51192104201223.298583138867
Winsorized Mean ( 17 / 20 )566674.952467.29079198572229.674974608052
Winsorized Mean ( 18 / 20 )567272.252210.11618845137256.67078181871
Winsorized Mean ( 19 / 20 )566738.0333333331981.25886463171286.049462516188
Winsorized Mean ( 20 / 20 )567173.0333333331455.25416052749389.741564544126
Trimmed Mean ( 1 / 20 )565028.9310344834613.01343454417122.485862885920
Trimmed Mean ( 2 / 20 )565046.2321428574495.25885383492125.698263551790
Trimmed Mean ( 3 / 20 )564996.4629629634390.67305876375128.681059919785
Trimmed Mean ( 4 / 20 )564998.9807692314296.05218066333131.515856188225
Trimmed Mean ( 5 / 20 )565003.74183.92215288819135.041637811061
Trimmed Mean ( 6 / 20 )565014.2708333334043.08632788538139.748257893085
Trimmed Mean ( 7 / 20 )565152.9130434783913.1790903393144.422961483850
Trimmed Mean ( 8 / 20 )565288.1590909093755.99807945620150.502781719407
Trimmed Mean ( 9 / 20 )565407.0714285713571.68672717966158.302537321082
Trimmed Mean ( 10 / 20 )565483.1253355.79256223522168.509559072193
Trimmed Mean ( 11 / 20 )565868.9473684213201.87946849860176.730246386746
Trimmed Mean ( 12 / 20 )566158.253078.73228017250183.893303632194
Trimmed Mean ( 13 / 20 )566484.1176470592929.20549105892193.391730070215
Trimmed Mean ( 14 / 20 )566726.781252782.76968657069203.655654287509
Trimmed Mean ( 15 / 20 )566839.5666666672640.46681465078214.673997613424
Trimmed Mean ( 16 / 20 )566880.8928571432533.96650887366223.712859215776
Trimmed Mean ( 17 / 20 )566918.1153846152396.39153108099236.57157356456
Trimmed Mean ( 18 / 20 )566953.8752205.25018735141257.092768091286
Trimmed Mean ( 19 / 20 )566905.6363636362013.24245323842281.588357851155
Trimmed Mean ( 20 / 20 )566932.11806.1621581627313.887707943513
Median566599
Midrange563773
Midmean - Weighted Average at Xnp565866.096774194
Midmean - Weighted Average at X(n+1)p566839.566666667
Midmean - Empirical Distribution Function565866.096774194
Midmean - Empirical Distribution Function - Averaging566839.566666667
Midmean - Empirical Distribution Function - Interpolation566839.566666667
Midmean - Closest Observation565866.096774194
Midmean - True Basic - Statistics Graphics Toolkit566839.566666667
Midmean - MS Excel (old versions)566726.78125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 564987.066666667 & 4719.03407159254 & 119.725150972686 \tabularnewline
Geometric Mean & 563815.93710545 &  &  \tabularnewline
Harmonic Mean & 562637.483780112 &  &  \tabularnewline
Quadratic Mean & 566148.631696807 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 565012.783333333 & 4707.96821537709 & 120.012021637678 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 565135.816666667 & 4644.65722558895 & 121.674386121143 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 564989.916666667 & 4567.70182904213 & 123.692381379707 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 564983.25 & 4546.56972996045 & 124.265827548391 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 564961.416666667 & 4539.1368576007 & 124.464503801124 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 564376.516666667 & 4380.48662650892 & 128.838771759121 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 564458.65 & 4340.98271371876 & 130.030153821195 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 564622.25 & 4266.9347219353 & 132.325026463942 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 564950.75 & 4169.79892079955 & 135.486329372370 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 563039.583333333 & 3708.5283585326 & 151.822914347652 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 563959.55 & 3417.59749727019 & 165.016374938963 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 563942.35 & 3336.02956340673 & 169.045968952417 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 564801.65 & 3131.75870094075 & 180.346477469781 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 565937.283333333 & 2923.95895483218 & 193.551719458324 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 566550.283333333 & 2616.30168314492 & 216.546236614546 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 566622.816666667 & 2537.51192104201 & 223.298583138867 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 566674.95 & 2467.29079198572 & 229.674974608052 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 567272.25 & 2210.11618845137 & 256.67078181871 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 566738.033333333 & 1981.25886463171 & 286.049462516188 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 567173.033333333 & 1455.25416052749 & 389.741564544126 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 565028.931034483 & 4613.01343454417 & 122.485862885920 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 565046.232142857 & 4495.25885383492 & 125.698263551790 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 564996.462962963 & 4390.67305876375 & 128.681059919785 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 564998.980769231 & 4296.05218066333 & 131.515856188225 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 565003.7 & 4183.92215288819 & 135.041637811061 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 565014.270833333 & 4043.08632788538 & 139.748257893085 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 565152.913043478 & 3913.1790903393 & 144.422961483850 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 565288.159090909 & 3755.99807945620 & 150.502781719407 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 565407.071428571 & 3571.68672717966 & 158.302537321082 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 565483.125 & 3355.79256223522 & 168.509559072193 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 565868.947368421 & 3201.87946849860 & 176.730246386746 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 566158.25 & 3078.73228017250 & 183.893303632194 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 566484.117647059 & 2929.20549105892 & 193.391730070215 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 566726.78125 & 2782.76968657069 & 203.655654287509 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 566839.566666667 & 2640.46681465078 & 214.673997613424 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 566880.892857143 & 2533.96650887366 & 223.712859215776 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 566918.115384615 & 2396.39153108099 & 236.57157356456 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 566953.875 & 2205.25018735141 & 257.092768091286 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 566905.636363636 & 2013.24245323842 & 281.588357851155 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 566932.1 & 1806.1621581627 & 313.887707943513 \tabularnewline
Median & 566599 &  &  \tabularnewline
Midrange & 563773 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 565866.096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 566839.566666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 565866.096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 566839.566666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 566839.566666667 &  &  \tabularnewline
Midmean - Closest Observation & 565866.096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 566839.566666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 566726.78125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16845&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]564987.066666667[/C][C]4719.03407159254[/C][C]119.725150972686[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]563815.93710545[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]562637.483780112[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]566148.631696807[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]565012.783333333[/C][C]4707.96821537709[/C][C]120.012021637678[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]565135.816666667[/C][C]4644.65722558895[/C][C]121.674386121143[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]564989.916666667[/C][C]4567.70182904213[/C][C]123.692381379707[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]564983.25[/C][C]4546.56972996045[/C][C]124.265827548391[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]564961.416666667[/C][C]4539.1368576007[/C][C]124.464503801124[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]564376.516666667[/C][C]4380.48662650892[/C][C]128.838771759121[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]564458.65[/C][C]4340.98271371876[/C][C]130.030153821195[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]564622.25[/C][C]4266.9347219353[/C][C]132.325026463942[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]564950.75[/C][C]4169.79892079955[/C][C]135.486329372370[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]563039.583333333[/C][C]3708.5283585326[/C][C]151.822914347652[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]563959.55[/C][C]3417.59749727019[/C][C]165.016374938963[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]563942.35[/C][C]3336.02956340673[/C][C]169.045968952417[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]564801.65[/C][C]3131.75870094075[/C][C]180.346477469781[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]565937.283333333[/C][C]2923.95895483218[/C][C]193.551719458324[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]566550.283333333[/C][C]2616.30168314492[/C][C]216.546236614546[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]566622.816666667[/C][C]2537.51192104201[/C][C]223.298583138867[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]566674.95[/C][C]2467.29079198572[/C][C]229.674974608052[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]567272.25[/C][C]2210.11618845137[/C][C]256.67078181871[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]566738.033333333[/C][C]1981.25886463171[/C][C]286.049462516188[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]567173.033333333[/C][C]1455.25416052749[/C][C]389.741564544126[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]565028.931034483[/C][C]4613.01343454417[/C][C]122.485862885920[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]565046.232142857[/C][C]4495.25885383492[/C][C]125.698263551790[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]564996.462962963[/C][C]4390.67305876375[/C][C]128.681059919785[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]564998.980769231[/C][C]4296.05218066333[/C][C]131.515856188225[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]565003.7[/C][C]4183.92215288819[/C][C]135.041637811061[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]565014.270833333[/C][C]4043.08632788538[/C][C]139.748257893085[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]565152.913043478[/C][C]3913.1790903393[/C][C]144.422961483850[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]565288.159090909[/C][C]3755.99807945620[/C][C]150.502781719407[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]565407.071428571[/C][C]3571.68672717966[/C][C]158.302537321082[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]565483.125[/C][C]3355.79256223522[/C][C]168.509559072193[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]565868.947368421[/C][C]3201.87946849860[/C][C]176.730246386746[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]566158.25[/C][C]3078.73228017250[/C][C]183.893303632194[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]566484.117647059[/C][C]2929.20549105892[/C][C]193.391730070215[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]566726.78125[/C][C]2782.76968657069[/C][C]203.655654287509[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]566839.566666667[/C][C]2640.46681465078[/C][C]214.673997613424[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]566880.892857143[/C][C]2533.96650887366[/C][C]223.712859215776[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]566918.115384615[/C][C]2396.39153108099[/C][C]236.57157356456[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]566953.875[/C][C]2205.25018735141[/C][C]257.092768091286[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]566905.636363636[/C][C]2013.24245323842[/C][C]281.588357851155[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]566932.1[/C][C]1806.1621581627[/C][C]313.887707943513[/C][/ROW]
[ROW][C]Median[/C][C]566599[/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]565866.096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]566839.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]565866.096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]566839.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]566839.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]565866.096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]566839.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]566726.78125[/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=16845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16845&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 Mean564987.0666666674719.03407159254119.725150972686
Geometric Mean563815.93710545
Harmonic Mean562637.483780112
Quadratic Mean566148.631696807
Winsorized Mean ( 1 / 20 )565012.7833333334707.96821537709120.012021637678
Winsorized Mean ( 2 / 20 )565135.8166666674644.65722558895121.674386121143
Winsorized Mean ( 3 / 20 )564989.9166666674567.70182904213123.692381379707
Winsorized Mean ( 4 / 20 )564983.254546.56972996045124.265827548391
Winsorized Mean ( 5 / 20 )564961.4166666674539.1368576007124.464503801124
Winsorized Mean ( 6 / 20 )564376.5166666674380.48662650892128.838771759121
Winsorized Mean ( 7 / 20 )564458.654340.98271371876130.030153821195
Winsorized Mean ( 8 / 20 )564622.254266.9347219353132.325026463942
Winsorized Mean ( 9 / 20 )564950.754169.79892079955135.486329372370
Winsorized Mean ( 10 / 20 )563039.5833333333708.5283585326151.822914347652
Winsorized Mean ( 11 / 20 )563959.553417.59749727019165.016374938963
Winsorized Mean ( 12 / 20 )563942.353336.02956340673169.045968952417
Winsorized Mean ( 13 / 20 )564801.653131.75870094075180.346477469781
Winsorized Mean ( 14 / 20 )565937.2833333332923.95895483218193.551719458324
Winsorized Mean ( 15 / 20 )566550.2833333332616.30168314492216.546236614546
Winsorized Mean ( 16 / 20 )566622.8166666672537.51192104201223.298583138867
Winsorized Mean ( 17 / 20 )566674.952467.29079198572229.674974608052
Winsorized Mean ( 18 / 20 )567272.252210.11618845137256.67078181871
Winsorized Mean ( 19 / 20 )566738.0333333331981.25886463171286.049462516188
Winsorized Mean ( 20 / 20 )567173.0333333331455.25416052749389.741564544126
Trimmed Mean ( 1 / 20 )565028.9310344834613.01343454417122.485862885920
Trimmed Mean ( 2 / 20 )565046.2321428574495.25885383492125.698263551790
Trimmed Mean ( 3 / 20 )564996.4629629634390.67305876375128.681059919785
Trimmed Mean ( 4 / 20 )564998.9807692314296.05218066333131.515856188225
Trimmed Mean ( 5 / 20 )565003.74183.92215288819135.041637811061
Trimmed Mean ( 6 / 20 )565014.2708333334043.08632788538139.748257893085
Trimmed Mean ( 7 / 20 )565152.9130434783913.1790903393144.422961483850
Trimmed Mean ( 8 / 20 )565288.1590909093755.99807945620150.502781719407
Trimmed Mean ( 9 / 20 )565407.0714285713571.68672717966158.302537321082
Trimmed Mean ( 10 / 20 )565483.1253355.79256223522168.509559072193
Trimmed Mean ( 11 / 20 )565868.9473684213201.87946849860176.730246386746
Trimmed Mean ( 12 / 20 )566158.253078.73228017250183.893303632194
Trimmed Mean ( 13 / 20 )566484.1176470592929.20549105892193.391730070215
Trimmed Mean ( 14 / 20 )566726.781252782.76968657069203.655654287509
Trimmed Mean ( 15 / 20 )566839.5666666672640.46681465078214.673997613424
Trimmed Mean ( 16 / 20 )566880.8928571432533.96650887366223.712859215776
Trimmed Mean ( 17 / 20 )566918.1153846152396.39153108099236.57157356456
Trimmed Mean ( 18 / 20 )566953.8752205.25018735141257.092768091286
Trimmed Mean ( 19 / 20 )566905.6363636362013.24245323842281.588357851155
Trimmed Mean ( 20 / 20 )566932.11806.1621581627313.887707943513
Median566599
Midrange563773
Midmean - Weighted Average at Xnp565866.096774194
Midmean - Weighted Average at X(n+1)p566839.566666667
Midmean - Empirical Distribution Function565866.096774194
Midmean - Empirical Distribution Function - Averaging566839.566666667
Midmean - Empirical Distribution Function - Interpolation566839.566666667
Midmean - Closest Observation565866.096774194
Midmean - True Basic - Statistics Graphics Toolkit566839.566666667
Midmean - MS Excel (old versions)566726.78125
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')