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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 computationWed, 20 Oct 2010 14:46:55 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/20/t1287585950km6l5x9sch7i8tm.htm/, Retrieved Fri, 03 May 2024 21:52:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87223, Retrieved Fri, 03 May 2024 21:52:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Het aantal werklo...] [2010-10-20 14:46:55] [6b57770a9d87785617c80b642e34c9c4] [Current]
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Dataseries X:
591000
589000
584000
573000
567000
569000
621000
629000
628000
612000
595000
597000
593000
590000
580000
574000
573000
573000
620000
626000
620000
588000
566000
557000
561000
549000
532000
526000
511000
499000
555000
565000
542000
527000
510000
514000
517000
508000
493000
490000
469000
478000
528000
534000
518000
506000
502000
516000
528000
533000
536000
537000
524000
536000
587000
597000
581000
564000
558000
575000




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87223&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87223&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5553505247.96570756675105.821956724921
Geometric Mean553878.792381156
Harmonic Mean552400.58384671
Quadratic Mean556811.054128777
Winsorized Mean ( 1 / 20 )555483.3333333335204.16454632589106.738234040947
Winsorized Mean ( 2 / 20 )555816.6666666675094.16924175606109.108402231856
Winsorized Mean ( 3 / 20 )555716.6666666675004.9744557991111.032867714794
Winsorized Mean ( 4 / 20 )5560504908.33633084808113.286857810725
Winsorized Mean ( 5 / 20 )5563004860.03533966831114.464188245587
Winsorized Mean ( 6 / 20 )5559004614.01084146946120.480861250633
Winsorized Mean ( 7 / 20 )554383.3333333334240.31576392346130.741049534570
Winsorized Mean ( 8 / 20 )5546504191.51854148539132.326743758944
Winsorized Mean ( 9 / 20 )5545004113.81165437646134.789836430673
Winsorized Mean ( 10 / 20 )554666.6666666673970.48906653768139.697316217607
Winsorized Mean ( 11 / 20 )554666.6666666673848.0802071426144.141139687557
Winsorized Mean ( 12 / 20 )554666.6666666673782.33081119941146.646788542216
Winsorized Mean ( 13 / 20 )554666.6666666673711.76680383162149.434675177894
Winsorized Mean ( 14 / 20 )555833.3333333333448.01315643231161.203947930541
Winsorized Mean ( 15 / 20 )556083.3333333333331.18221550834166.932727589768
Winsorized Mean ( 16 / 20 )5555503166.51129562342175.44545025557
Winsorized Mean ( 17 / 20 )554983.3333333332995.90036895682185.247593372599
Winsorized Mean ( 18 / 20 )554683.3333333332952.01661099037187.899800857571
Winsorized Mean ( 19 / 20 )554366.6666666672535.39538438858218.650972578131
Winsorized Mean ( 20 / 20 )554366.6666666672440.01095980991227.198433038946
Trimmed Mean ( 1 / 20 )555568.9655172415059.0052601277109.817827211197
Trimmed Mean ( 2 / 20 )555660.7142857144880.00670545328113.864744010449
Trimmed Mean ( 3 / 20 )555574.0740740744732.14041806713117.404393147953
Trimmed Mean ( 4 / 20 )555519.2307692314590.837026489121.006088337247
Trimmed Mean ( 5 / 20 )5553604451.07278974315124.769920923276
Trimmed Mean ( 6 / 20 )5551254289.56603551567129.412857945026
Trimmed Mean ( 7 / 20 )554956.521739134162.28250761261133.329854646854
Trimmed Mean ( 8 / 20 )555068.1818181824105.42848580819135.203471144842
Trimmed Mean ( 9 / 20 )555142.8571428574039.52185918555137.427863122094
Trimmed Mean ( 10 / 20 )5552503967.94043327912139.934056303648
Trimmed Mean ( 11 / 20 )555342.1052631583904.49212711231142.231585359574
Trimmed Mean ( 12 / 20 )555444.4444444443843.65988875030144.509259539360
Trimmed Mean ( 13 / 20 )555558.8235294123769.46905117353147.383840001672
Trimmed Mean ( 14 / 20 )555687.53677.09713589051151.121245771884
Trimmed Mean ( 15 / 20 )555666.6666666673614.25445272495153.743095273141
Trimmed Mean ( 16 / 20 )555607.1428571433545.37454298383156.713243162607
Trimmed Mean ( 17 / 20 )555615.3846153853481.41303013454159.594790909918
Trimmed Mean ( 18 / 20 )555708.3333333333423.85026014058162.305092545290
Trimmed Mean ( 19 / 20 )555863.6363636363326.59196309697167.097029792058
Trimmed Mean ( 20 / 20 )5561003314.9581246859167.754758607303
Median559500
Midrange549000
Midmean - Weighted Average at Xnp554645.161290323
Midmean - Weighted Average at X(n+1)p555666.666666667
Midmean - Empirical Distribution Function554645.161290323
Midmean - Empirical Distribution Function - Averaging555666.666666667
Midmean - Empirical Distribution Function - Interpolation555666.666666667
Midmean - Closest Observation554645.161290323
Midmean - True Basic - Statistics Graphics Toolkit555666.666666667
Midmean - MS Excel (old versions)555687.5
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 555350 & 5247.96570756675 & 105.821956724921 \tabularnewline
Geometric Mean & 553878.792381156 &  &  \tabularnewline
Harmonic Mean & 552400.58384671 &  &  \tabularnewline
Quadratic Mean & 556811.054128777 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 555483.333333333 & 5204.16454632589 & 106.738234040947 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 555816.666666667 & 5094.16924175606 & 109.108402231856 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 555716.666666667 & 5004.9744557991 & 111.032867714794 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 556050 & 4908.33633084808 & 113.286857810725 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 556300 & 4860.03533966831 & 114.464188245587 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 555900 & 4614.01084146946 & 120.480861250633 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 554383.333333333 & 4240.31576392346 & 130.741049534570 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 554650 & 4191.51854148539 & 132.326743758944 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 554500 & 4113.81165437646 & 134.789836430673 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 554666.666666667 & 3970.48906653768 & 139.697316217607 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 554666.666666667 & 3848.0802071426 & 144.141139687557 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 554666.666666667 & 3782.33081119941 & 146.646788542216 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 554666.666666667 & 3711.76680383162 & 149.434675177894 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 555833.333333333 & 3448.01315643231 & 161.203947930541 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 556083.333333333 & 3331.18221550834 & 166.932727589768 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 555550 & 3166.51129562342 & 175.44545025557 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 554983.333333333 & 2995.90036895682 & 185.247593372599 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 554683.333333333 & 2952.01661099037 & 187.899800857571 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 554366.666666667 & 2535.39538438858 & 218.650972578131 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 554366.666666667 & 2440.01095980991 & 227.198433038946 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 555568.965517241 & 5059.0052601277 & 109.817827211197 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 555660.714285714 & 4880.00670545328 & 113.864744010449 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 555574.074074074 & 4732.14041806713 & 117.404393147953 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 555519.230769231 & 4590.837026489 & 121.006088337247 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 555360 & 4451.07278974315 & 124.769920923276 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 555125 & 4289.56603551567 & 129.412857945026 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 554956.52173913 & 4162.28250761261 & 133.329854646854 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 555068.181818182 & 4105.42848580819 & 135.203471144842 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 555142.857142857 & 4039.52185918555 & 137.427863122094 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 555250 & 3967.94043327912 & 139.934056303648 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 555342.105263158 & 3904.49212711231 & 142.231585359574 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 555444.444444444 & 3843.65988875030 & 144.509259539360 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 555558.823529412 & 3769.46905117353 & 147.383840001672 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 555687.5 & 3677.09713589051 & 151.121245771884 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 555666.666666667 & 3614.25445272495 & 153.743095273141 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 555607.142857143 & 3545.37454298383 & 156.713243162607 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 555615.384615385 & 3481.41303013454 & 159.594790909918 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 555708.333333333 & 3423.85026014058 & 162.305092545290 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 555863.636363636 & 3326.59196309697 & 167.097029792058 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 556100 & 3314.9581246859 & 167.754758607303 \tabularnewline
Median & 559500 &  &  \tabularnewline
Midrange & 549000 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 554645.161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 555666.666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 554645.161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 555666.666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 555666.666666667 &  &  \tabularnewline
Midmean - Closest Observation & 554645.161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 555666.666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 555687.5 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87223&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]555350[/C][C]5247.96570756675[/C][C]105.821956724921[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]553878.792381156[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]552400.58384671[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]556811.054128777[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]555483.333333333[/C][C]5204.16454632589[/C][C]106.738234040947[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]555816.666666667[/C][C]5094.16924175606[/C][C]109.108402231856[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]555716.666666667[/C][C]5004.9744557991[/C][C]111.032867714794[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]556050[/C][C]4908.33633084808[/C][C]113.286857810725[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]556300[/C][C]4860.03533966831[/C][C]114.464188245587[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]555900[/C][C]4614.01084146946[/C][C]120.480861250633[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]554383.333333333[/C][C]4240.31576392346[/C][C]130.741049534570[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]554650[/C][C]4191.51854148539[/C][C]132.326743758944[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]554500[/C][C]4113.81165437646[/C][C]134.789836430673[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]554666.666666667[/C][C]3970.48906653768[/C][C]139.697316217607[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]554666.666666667[/C][C]3848.0802071426[/C][C]144.141139687557[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]554666.666666667[/C][C]3782.33081119941[/C][C]146.646788542216[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]554666.666666667[/C][C]3711.76680383162[/C][C]149.434675177894[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]555833.333333333[/C][C]3448.01315643231[/C][C]161.203947930541[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]556083.333333333[/C][C]3331.18221550834[/C][C]166.932727589768[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]555550[/C][C]3166.51129562342[/C][C]175.44545025557[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]554983.333333333[/C][C]2995.90036895682[/C][C]185.247593372599[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]554683.333333333[/C][C]2952.01661099037[/C][C]187.899800857571[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]554366.666666667[/C][C]2535.39538438858[/C][C]218.650972578131[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]554366.666666667[/C][C]2440.01095980991[/C][C]227.198433038946[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]555568.965517241[/C][C]5059.0052601277[/C][C]109.817827211197[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]555660.714285714[/C][C]4880.00670545328[/C][C]113.864744010449[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]555574.074074074[/C][C]4732.14041806713[/C][C]117.404393147953[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]555519.230769231[/C][C]4590.837026489[/C][C]121.006088337247[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]555360[/C][C]4451.07278974315[/C][C]124.769920923276[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]555125[/C][C]4289.56603551567[/C][C]129.412857945026[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]554956.52173913[/C][C]4162.28250761261[/C][C]133.329854646854[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]555068.181818182[/C][C]4105.42848580819[/C][C]135.203471144842[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]555142.857142857[/C][C]4039.52185918555[/C][C]137.427863122094[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]555250[/C][C]3967.94043327912[/C][C]139.934056303648[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]555342.105263158[/C][C]3904.49212711231[/C][C]142.231585359574[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]555444.444444444[/C][C]3843.65988875030[/C][C]144.509259539360[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]555558.823529412[/C][C]3769.46905117353[/C][C]147.383840001672[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]555687.5[/C][C]3677.09713589051[/C][C]151.121245771884[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]555666.666666667[/C][C]3614.25445272495[/C][C]153.743095273141[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]555607.142857143[/C][C]3545.37454298383[/C][C]156.713243162607[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]555615.384615385[/C][C]3481.41303013454[/C][C]159.594790909918[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]555708.333333333[/C][C]3423.85026014058[/C][C]162.305092545290[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]555863.636363636[/C][C]3326.59196309697[/C][C]167.097029792058[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]556100[/C][C]3314.9581246859[/C][C]167.754758607303[/C][/ROW]
[ROW][C]Median[/C][C]559500[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]549000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]554645.161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]555666.666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]554645.161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]555666.666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]555666.666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]554645.161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]555666.666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]555687.5[/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=87223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87223&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 Mean5553505247.96570756675105.821956724921
Geometric Mean553878.792381156
Harmonic Mean552400.58384671
Quadratic Mean556811.054128777
Winsorized Mean ( 1 / 20 )555483.3333333335204.16454632589106.738234040947
Winsorized Mean ( 2 / 20 )555816.6666666675094.16924175606109.108402231856
Winsorized Mean ( 3 / 20 )555716.6666666675004.9744557991111.032867714794
Winsorized Mean ( 4 / 20 )5560504908.33633084808113.286857810725
Winsorized Mean ( 5 / 20 )5563004860.03533966831114.464188245587
Winsorized Mean ( 6 / 20 )5559004614.01084146946120.480861250633
Winsorized Mean ( 7 / 20 )554383.3333333334240.31576392346130.741049534570
Winsorized Mean ( 8 / 20 )5546504191.51854148539132.326743758944
Winsorized Mean ( 9 / 20 )5545004113.81165437646134.789836430673
Winsorized Mean ( 10 / 20 )554666.6666666673970.48906653768139.697316217607
Winsorized Mean ( 11 / 20 )554666.6666666673848.0802071426144.141139687557
Winsorized Mean ( 12 / 20 )554666.6666666673782.33081119941146.646788542216
Winsorized Mean ( 13 / 20 )554666.6666666673711.76680383162149.434675177894
Winsorized Mean ( 14 / 20 )555833.3333333333448.01315643231161.203947930541
Winsorized Mean ( 15 / 20 )556083.3333333333331.18221550834166.932727589768
Winsorized Mean ( 16 / 20 )5555503166.51129562342175.44545025557
Winsorized Mean ( 17 / 20 )554983.3333333332995.90036895682185.247593372599
Winsorized Mean ( 18 / 20 )554683.3333333332952.01661099037187.899800857571
Winsorized Mean ( 19 / 20 )554366.6666666672535.39538438858218.650972578131
Winsorized Mean ( 20 / 20 )554366.6666666672440.01095980991227.198433038946
Trimmed Mean ( 1 / 20 )555568.9655172415059.0052601277109.817827211197
Trimmed Mean ( 2 / 20 )555660.7142857144880.00670545328113.864744010449
Trimmed Mean ( 3 / 20 )555574.0740740744732.14041806713117.404393147953
Trimmed Mean ( 4 / 20 )555519.2307692314590.837026489121.006088337247
Trimmed Mean ( 5 / 20 )5553604451.07278974315124.769920923276
Trimmed Mean ( 6 / 20 )5551254289.56603551567129.412857945026
Trimmed Mean ( 7 / 20 )554956.521739134162.28250761261133.329854646854
Trimmed Mean ( 8 / 20 )555068.1818181824105.42848580819135.203471144842
Trimmed Mean ( 9 / 20 )555142.8571428574039.52185918555137.427863122094
Trimmed Mean ( 10 / 20 )5552503967.94043327912139.934056303648
Trimmed Mean ( 11 / 20 )555342.1052631583904.49212711231142.231585359574
Trimmed Mean ( 12 / 20 )555444.4444444443843.65988875030144.509259539360
Trimmed Mean ( 13 / 20 )555558.8235294123769.46905117353147.383840001672
Trimmed Mean ( 14 / 20 )555687.53677.09713589051151.121245771884
Trimmed Mean ( 15 / 20 )555666.6666666673614.25445272495153.743095273141
Trimmed Mean ( 16 / 20 )555607.1428571433545.37454298383156.713243162607
Trimmed Mean ( 17 / 20 )555615.3846153853481.41303013454159.594790909918
Trimmed Mean ( 18 / 20 )555708.3333333333423.85026014058162.305092545290
Trimmed Mean ( 19 / 20 )555863.6363636363326.59196309697167.097029792058
Trimmed Mean ( 20 / 20 )5561003314.9581246859167.754758607303
Median559500
Midrange549000
Midmean - Weighted Average at Xnp554645.161290323
Midmean - Weighted Average at X(n+1)p555666.666666667
Midmean - Empirical Distribution Function554645.161290323
Midmean - Empirical Distribution Function - Averaging555666.666666667
Midmean - Empirical Distribution Function - Interpolation555666.666666667
Midmean - Closest Observation554645.161290323
Midmean - True Basic - Statistics Graphics Toolkit555666.666666667
Midmean - MS Excel (old versions)555687.5
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')