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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 computationFri, 25 Dec 2009 11:14:18 -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/2009/Dec/25/t1261764912ni4m04mzxhzl8cp.htm/, Retrieved Sat, 04 May 2024 11:39:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70721, Retrieved Sat, 04 May 2024 11:39:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Paper: aantal nie...] [2009-12-24 09:31:37] [005293453b571dbccb80b45226e44173]
- RM D    [Central Tendency] [central tendency ...] [2009-12-25 18:14:18] [a315839f8c359622c3a1e6ed387dd5cd] [Current]
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Dataseries X:
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
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570
596594




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=70721&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=70721&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70721&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 Mean557567.3166666675463.30285289262102.056820147075
Geometric Mean555975.01708392
Harmonic Mean554371.837126678
Quadratic Mean559144.279788813
Winsorized Mean ( 1 / 20 )557693.55424.99353060095102.800767752846
Winsorized Mean ( 2 / 20 )558034.8333333335308.77246396052105.115605749096
Winsorized Mean ( 3 / 20 )557900.0833333335230.02519413035106.672542220153
Winsorized Mean ( 4 / 20 )558248.155136.70759926561108.678202761592
Winsorized Mean ( 5 / 20 )558486.0666666675079.3085226521109.953168659867
Winsorized Mean ( 6 / 20 )558221.4666666674862.60305951328114.798896770846
Winsorized Mean ( 7 / 20 )558325.4166666674822.53314429755115.774303661731
Winsorized Mean ( 8 / 20 )558524.354748.92599293164117.610666249867
Winsorized Mean ( 9 / 20 )556575.74347.43348108811128.023971481375
Winsorized Mean ( 10 / 20 )557021.24239.47634550162131.389151537793
Winsorized Mean ( 11 / 20 )557157.4166666674148.14559394030134.314817078883
Winsorized Mean ( 12 / 20 )557303.6166666674120.51761140849135.250876036462
Winsorized Mean ( 13 / 20 )557257.254042.09449465781137.863489024439
Winsorized Mean ( 14 / 20 )558398.953803.42067243942146.814932685807
Winsorized Mean ( 15 / 20 )558343.73616.19949751382154.400690665398
Winsorized Mean ( 16 / 20 )558439.1666666673537.66681866286157.85521794213
Winsorized Mean ( 17 / 20 )558569.2166666673459.16926778896161.474959282260
Winsorized Mean ( 18 / 20 )558090.1166666673373.38324934248165.439286145577
Winsorized Mean ( 19 / 20 )558799.1333333333170.23050762087176.2645119937
Winsorized Mean ( 20 / 20 )558406.83018.44402144904184.998229561975
Trimmed Mean ( 1 / 20 )557858.5862068975297.80771847379105.299893059842
Trimmed Mean ( 2 / 20 )558035.4642857145140.55399232697108.555510771536
Trimmed Mean ( 3 / 20 )558035.8148148155022.68923642208111.102994540895
Trimmed Mean ( 4 / 20 )558088.0192307694912.14452929569113.613924814787
Trimmed Mean ( 5 / 20 )558039.984807.99827859065116.064929241942
Trimmed Mean ( 6 / 20 )557928.4583333334693.37228135772118.875815700674
Trimmed Mean ( 7 / 20 )557864.7608695654611.76186649116120.965647624389
Trimmed Mean ( 8 / 20 )557775.0227272734513.9759019554123.566238465219
Trimmed Mean ( 9 / 20 )557641.2142857144403.16609712866126.645509613947
Trimmed Mean ( 10 / 20 )557818.84359.82245804127127.945301756762
Trimmed Mean ( 11 / 20 )557944.7368421054320.95186646041129.125422843267
Trimmed Mean ( 12 / 20 )558064.0277777784281.36319958998130.347275333058
Trimmed Mean ( 13 / 20 )558175.8529411774222.90293559353132.178234132849
Trimmed Mean ( 14 / 20 )558308.343754151.13643218913134.495300954388
Trimmed Mean ( 15 / 20 )558295.44104.55451111477136.018512724873
Trimmed Mean ( 16 / 20 )558288.54074.08224400936137.034175198825
Trimmed Mean ( 17 / 20 )558266.769230774031.30072206428138.483037540524
Trimmed Mean ( 18 / 20 )558222.2916666673968.32888452987140.669361816970
Trimmed Mean ( 19 / 20 )558242.3181818183875.09081160808144.059157661433
Trimmed Mean ( 20 / 20 )558154.43779.79499820044147.667902694653
Median562583.5
Midrange549120.5
Midmean - Weighted Average at Xnp557176.096774194
Midmean - Weighted Average at X(n+1)p558295.4
Midmean - Empirical Distribution Function557176.096774194
Midmean - Empirical Distribution Function - Averaging558295.4
Midmean - Empirical Distribution Function - Interpolation558295.4
Midmean - Closest Observation557176.096774194
Midmean - True Basic - Statistics Graphics Toolkit558295.4
Midmean - MS Excel (old versions)558308.34375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 557567.316666667 & 5463.30285289262 & 102.056820147075 \tabularnewline
Geometric Mean & 555975.01708392 &  &  \tabularnewline
Harmonic Mean & 554371.837126678 &  &  \tabularnewline
Quadratic Mean & 559144.279788813 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 557693.5 & 5424.99353060095 & 102.800767752846 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 558034.833333333 & 5308.77246396052 & 105.115605749096 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 557900.083333333 & 5230.02519413035 & 106.672542220153 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 558248.15 & 5136.70759926561 & 108.678202761592 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 558486.066666667 & 5079.3085226521 & 109.953168659867 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 558221.466666667 & 4862.60305951328 & 114.798896770846 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 558325.416666667 & 4822.53314429755 & 115.774303661731 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 558524.35 & 4748.92599293164 & 117.610666249867 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 556575.7 & 4347.43348108811 & 128.023971481375 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 557021.2 & 4239.47634550162 & 131.389151537793 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 557157.416666667 & 4148.14559394030 & 134.314817078883 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 557303.616666667 & 4120.51761140849 & 135.250876036462 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 557257.25 & 4042.09449465781 & 137.863489024439 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 558398.95 & 3803.42067243942 & 146.814932685807 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 558343.7 & 3616.19949751382 & 154.400690665398 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 558439.166666667 & 3537.66681866286 & 157.85521794213 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 558569.216666667 & 3459.16926778896 & 161.474959282260 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 558090.116666667 & 3373.38324934248 & 165.439286145577 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 558799.133333333 & 3170.23050762087 & 176.2645119937 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 558406.8 & 3018.44402144904 & 184.998229561975 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 557858.586206897 & 5297.80771847379 & 105.299893059842 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 558035.464285714 & 5140.55399232697 & 108.555510771536 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 558035.814814815 & 5022.68923642208 & 111.102994540895 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 558088.019230769 & 4912.14452929569 & 113.613924814787 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 558039.98 & 4807.99827859065 & 116.064929241942 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 557928.458333333 & 4693.37228135772 & 118.875815700674 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 557864.760869565 & 4611.76186649116 & 120.965647624389 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 557775.022727273 & 4513.9759019554 & 123.566238465219 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 557641.214285714 & 4403.16609712866 & 126.645509613947 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 557818.8 & 4359.82245804127 & 127.945301756762 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 557944.736842105 & 4320.95186646041 & 129.125422843267 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 558064.027777778 & 4281.36319958998 & 130.347275333058 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 558175.852941177 & 4222.90293559353 & 132.178234132849 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 558308.34375 & 4151.13643218913 & 134.495300954388 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 558295.4 & 4104.55451111477 & 136.018512724873 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 558288.5 & 4074.08224400936 & 137.034175198825 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 558266.76923077 & 4031.30072206428 & 138.483037540524 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 558222.291666667 & 3968.32888452987 & 140.669361816970 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 558242.318181818 & 3875.09081160808 & 144.059157661433 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 558154.4 & 3779.79499820044 & 147.667902694653 \tabularnewline
Median & 562583.5 &  &  \tabularnewline
Midrange & 549120.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 557176.096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 558295.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 557176.096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 558295.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 558295.4 &  &  \tabularnewline
Midmean - Closest Observation & 557176.096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 558295.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 558308.34375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70721&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]557567.316666667[/C][C]5463.30285289262[/C][C]102.056820147075[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]555975.01708392[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]554371.837126678[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]559144.279788813[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]557693.5[/C][C]5424.99353060095[/C][C]102.800767752846[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]558034.833333333[/C][C]5308.77246396052[/C][C]105.115605749096[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]557900.083333333[/C][C]5230.02519413035[/C][C]106.672542220153[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]558248.15[/C][C]5136.70759926561[/C][C]108.678202761592[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]558486.066666667[/C][C]5079.3085226521[/C][C]109.953168659867[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]558221.466666667[/C][C]4862.60305951328[/C][C]114.798896770846[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]558325.416666667[/C][C]4822.53314429755[/C][C]115.774303661731[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]558524.35[/C][C]4748.92599293164[/C][C]117.610666249867[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]556575.7[/C][C]4347.43348108811[/C][C]128.023971481375[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]557021.2[/C][C]4239.47634550162[/C][C]131.389151537793[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]557157.416666667[/C][C]4148.14559394030[/C][C]134.314817078883[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]557303.616666667[/C][C]4120.51761140849[/C][C]135.250876036462[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]557257.25[/C][C]4042.09449465781[/C][C]137.863489024439[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]558398.95[/C][C]3803.42067243942[/C][C]146.814932685807[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]558343.7[/C][C]3616.19949751382[/C][C]154.400690665398[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]558439.166666667[/C][C]3537.66681866286[/C][C]157.85521794213[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]558569.216666667[/C][C]3459.16926778896[/C][C]161.474959282260[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]558090.116666667[/C][C]3373.38324934248[/C][C]165.439286145577[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]558799.133333333[/C][C]3170.23050762087[/C][C]176.2645119937[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]558406.8[/C][C]3018.44402144904[/C][C]184.998229561975[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]557858.586206897[/C][C]5297.80771847379[/C][C]105.299893059842[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]558035.464285714[/C][C]5140.55399232697[/C][C]108.555510771536[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]558035.814814815[/C][C]5022.68923642208[/C][C]111.102994540895[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]558088.019230769[/C][C]4912.14452929569[/C][C]113.613924814787[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]558039.98[/C][C]4807.99827859065[/C][C]116.064929241942[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]557928.458333333[/C][C]4693.37228135772[/C][C]118.875815700674[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]557864.760869565[/C][C]4611.76186649116[/C][C]120.965647624389[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]557775.022727273[/C][C]4513.9759019554[/C][C]123.566238465219[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]557641.214285714[/C][C]4403.16609712866[/C][C]126.645509613947[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]557818.8[/C][C]4359.82245804127[/C][C]127.945301756762[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]557944.736842105[/C][C]4320.95186646041[/C][C]129.125422843267[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]558064.027777778[/C][C]4281.36319958998[/C][C]130.347275333058[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]558175.852941177[/C][C]4222.90293559353[/C][C]132.178234132849[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]558308.34375[/C][C]4151.13643218913[/C][C]134.495300954388[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]558295.4[/C][C]4104.55451111477[/C][C]136.018512724873[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]558288.5[/C][C]4074.08224400936[/C][C]137.034175198825[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]558266.76923077[/C][C]4031.30072206428[/C][C]138.483037540524[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]558222.291666667[/C][C]3968.32888452987[/C][C]140.669361816970[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]558242.318181818[/C][C]3875.09081160808[/C][C]144.059157661433[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]558154.4[/C][C]3779.79499820044[/C][C]147.667902694653[/C][/ROW]
[ROW][C]Median[/C][C]562583.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]549120.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]557176.096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]558295.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]557176.096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]558295.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]558295.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]557176.096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]558295.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]558308.34375[/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=70721&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70721&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 Mean557567.3166666675463.30285289262102.056820147075
Geometric Mean555975.01708392
Harmonic Mean554371.837126678
Quadratic Mean559144.279788813
Winsorized Mean ( 1 / 20 )557693.55424.99353060095102.800767752846
Winsorized Mean ( 2 / 20 )558034.8333333335308.77246396052105.115605749096
Winsorized Mean ( 3 / 20 )557900.0833333335230.02519413035106.672542220153
Winsorized Mean ( 4 / 20 )558248.155136.70759926561108.678202761592
Winsorized Mean ( 5 / 20 )558486.0666666675079.3085226521109.953168659867
Winsorized Mean ( 6 / 20 )558221.4666666674862.60305951328114.798896770846
Winsorized Mean ( 7 / 20 )558325.4166666674822.53314429755115.774303661731
Winsorized Mean ( 8 / 20 )558524.354748.92599293164117.610666249867
Winsorized Mean ( 9 / 20 )556575.74347.43348108811128.023971481375
Winsorized Mean ( 10 / 20 )557021.24239.47634550162131.389151537793
Winsorized Mean ( 11 / 20 )557157.4166666674148.14559394030134.314817078883
Winsorized Mean ( 12 / 20 )557303.6166666674120.51761140849135.250876036462
Winsorized Mean ( 13 / 20 )557257.254042.09449465781137.863489024439
Winsorized Mean ( 14 / 20 )558398.953803.42067243942146.814932685807
Winsorized Mean ( 15 / 20 )558343.73616.19949751382154.400690665398
Winsorized Mean ( 16 / 20 )558439.1666666673537.66681866286157.85521794213
Winsorized Mean ( 17 / 20 )558569.2166666673459.16926778896161.474959282260
Winsorized Mean ( 18 / 20 )558090.1166666673373.38324934248165.439286145577
Winsorized Mean ( 19 / 20 )558799.1333333333170.23050762087176.2645119937
Winsorized Mean ( 20 / 20 )558406.83018.44402144904184.998229561975
Trimmed Mean ( 1 / 20 )557858.5862068975297.80771847379105.299893059842
Trimmed Mean ( 2 / 20 )558035.4642857145140.55399232697108.555510771536
Trimmed Mean ( 3 / 20 )558035.8148148155022.68923642208111.102994540895
Trimmed Mean ( 4 / 20 )558088.0192307694912.14452929569113.613924814787
Trimmed Mean ( 5 / 20 )558039.984807.99827859065116.064929241942
Trimmed Mean ( 6 / 20 )557928.4583333334693.37228135772118.875815700674
Trimmed Mean ( 7 / 20 )557864.7608695654611.76186649116120.965647624389
Trimmed Mean ( 8 / 20 )557775.0227272734513.9759019554123.566238465219
Trimmed Mean ( 9 / 20 )557641.2142857144403.16609712866126.645509613947
Trimmed Mean ( 10 / 20 )557818.84359.82245804127127.945301756762
Trimmed Mean ( 11 / 20 )557944.7368421054320.95186646041129.125422843267
Trimmed Mean ( 12 / 20 )558064.0277777784281.36319958998130.347275333058
Trimmed Mean ( 13 / 20 )558175.8529411774222.90293559353132.178234132849
Trimmed Mean ( 14 / 20 )558308.343754151.13643218913134.495300954388
Trimmed Mean ( 15 / 20 )558295.44104.55451111477136.018512724873
Trimmed Mean ( 16 / 20 )558288.54074.08224400936137.034175198825
Trimmed Mean ( 17 / 20 )558266.769230774031.30072206428138.483037540524
Trimmed Mean ( 18 / 20 )558222.2916666673968.32888452987140.669361816970
Trimmed Mean ( 19 / 20 )558242.3181818183875.09081160808144.059157661433
Trimmed Mean ( 20 / 20 )558154.43779.79499820044147.667902694653
Median562583.5
Midrange549120.5
Midmean - Weighted Average at Xnp557176.096774194
Midmean - Weighted Average at X(n+1)p558295.4
Midmean - Empirical Distribution Function557176.096774194
Midmean - Empirical Distribution Function - Averaging558295.4
Midmean - Empirical Distribution Function - Interpolation558295.4
Midmean - Closest Observation557176.096774194
Midmean - True Basic - Statistics Graphics Toolkit558295.4
Midmean - MS Excel (old versions)558308.34375
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')