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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2007 02:41:18 -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/2007/Oct/21/7szuynb07mi80uq1192959943.htm/, Retrieved Thu, 09 May 2024 11:30:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1215, Retrieved Thu, 09 May 2024 11:30:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact201
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2Q8G6 cent tend 2] [2007-10-21 09:41:18] [fef19078983b9fa83d10cb717d6f9786] [Current]
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Dataseries X:
275964
270694
271901
274412
272433
268361
268586
264768
269974
304744
309365
308347
298427
289231
291975
294912
293488
290555
284736
281818
287854
316263
325412
326011
328282
317480
317539
313737
312276
309391
302950
300316
304035
333476
337698
335932
323931
313927
314485
313218
309664
302963
298989
298423
301631
329765
335083
327616
309119
295916
291413
291542
284678
276475
272566
264981
263290
296806
303598
286994




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1215&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1215&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean299340.2666666672654.98695878852112.74641695538
Geometric Mean298643.008570857
Harmonic Mean297943.868964388
Quadratic Mean300034.137453390
Winsorized Mean ( 1 / 20 )299335.4666666672642.36246775459113.283272192794
Winsorized Mean ( 2 / 20 )299314.2666666672634.21281779134113.625696695845
Winsorized Mean ( 3 / 20 )299402.9166666672580.05832624603116.045018680759
Winsorized Mean ( 4 / 20 )299170.5166666672523.85971752079118.536903850007
Winsorized Mean ( 5 / 20 )299162.62475.40034988351120.854228696412
Winsorized Mean ( 6 / 20 )2991682447.90851787080122.213717471851
Winsorized Mean ( 7 / 20 )299121.5666666672384.05171774073125.467733959283
Winsorized Mean ( 8 / 20 )299112.6333333332355.18583946135127.001711848668
Winsorized Mean ( 9 / 20 )298910.4333333332309.92173411163129.402840329692
Winsorized Mean ( 10 / 20 )298152.7666666672067.05791021005144.240161436197
Winsorized Mean ( 11 / 20 )298426.4833333332010.68679197408148.420173905027
Winsorized Mean ( 12 / 20 )298285.2833333331952.79348888234152.747991547254
Winsorized Mean ( 13 / 20 )299057.71681.98733885814177.800208771502
Winsorized Mean ( 14 / 20 )299594.8333333331549.09483651697193.399930250204
Winsorized Mean ( 15 / 20 )299561.8333333331539.29670788202194.609545904579
Winsorized Mean ( 16 / 20 )300025.5666666671421.59543923808211.048487062865
Winsorized Mean ( 17 / 20 )300002.3333333331342.28920062584223.500519257294
Winsorized Mean ( 18 / 20 )299631.8333333331160.86441958531258.110963070407
Winsorized Mean ( 19 / 20 )299964.651085.50309948759276.336981572505
Winsorized Mean ( 20 / 20 )300241.9833333331042.67982190711287.952233298403
Trimmed Mean ( 1 / 20 )299300.4827586212590.30920792181115.546237431147
Trimmed Mean ( 2 / 20 )2992632525.70133168653118.487089603808
Trimmed Mean ( 3 / 20 )299234.5185185192450.73494727387122.099910825272
Trimmed Mean ( 4 / 20 )299169.752383.29340760286125.527872080554
Trimmed Mean ( 5 / 20 )299169.522320.46414010259128.926586207350
Trimmed Mean ( 6 / 20 )299171.252257.00660915661132.552225937785
Trimmed Mean ( 7 / 20 )299171.9565217392183.84320364861136.993331765716
Trimmed Mean ( 8 / 20 )299181.7727272732108.09131476774141.920689408198
Trimmed Mean ( 9 / 20 )299194.1190476192016.85876899683148.346589085380
Trimmed Mean ( 10 / 20 )299241.41908.74391534301156.773990263762
Trimmed Mean ( 11 / 20 )299413.2894736841834.38184281407163.222990156926
Trimmed Mean ( 12 / 20 )299562.8055555561748.93373313228171.283108033515
Trimmed Mean ( 13 / 20 )299750.6764705881646.28515252477182.077008962199
Trimmed Mean ( 14 / 20 )299850.6251588.10632423544188.810169964128
Trimmed Mean ( 15 / 20 )299887.1666666671543.80932885824194.251427984604
Trimmed Mean ( 16 / 20 )299933.6428571431478.27114023746202.894878140531
Trimmed Mean ( 17 / 20 )299920.3846153851418.64659997524211.413035932007
Trimmed Mean ( 18 / 20 )299908.3333333331352.60113027930221.727105367274
Trimmed Mean ( 19 / 20 )299950.2272727271316.46529875334227.845145296859
Trimmed Mean ( 20 / 20 )299947.951280.71195141609234.204068813715
Median299652.5
Midrange300494
Midmean - Weighted Average at Xnp299396.548387097
Midmean - Weighted Average at X(n+1)p299887.166666667
Midmean - Empirical Distribution Function299396.548387097
Midmean - Empirical Distribution Function - Averaging299887.166666667
Midmean - Empirical Distribution Function - Interpolation299887.166666667
Midmean - Closest Observation299396.548387097
Midmean - True Basic - Statistics Graphics Toolkit299887.166666667
Midmean - MS Excel (old versions)299850.625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 299340.266666667 & 2654.98695878852 & 112.74641695538 \tabularnewline
Geometric Mean & 298643.008570857 &  &  \tabularnewline
Harmonic Mean & 297943.868964388 &  &  \tabularnewline
Quadratic Mean & 300034.137453390 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 299335.466666667 & 2642.36246775459 & 113.283272192794 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 299314.266666667 & 2634.21281779134 & 113.625696695845 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 299402.916666667 & 2580.05832624603 & 116.045018680759 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 299170.516666667 & 2523.85971752079 & 118.536903850007 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 299162.6 & 2475.40034988351 & 120.854228696412 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 299168 & 2447.90851787080 & 122.213717471851 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 299121.566666667 & 2384.05171774073 & 125.467733959283 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 299112.633333333 & 2355.18583946135 & 127.001711848668 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 298910.433333333 & 2309.92173411163 & 129.402840329692 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 298152.766666667 & 2067.05791021005 & 144.240161436197 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 298426.483333333 & 2010.68679197408 & 148.420173905027 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 298285.283333333 & 1952.79348888234 & 152.747991547254 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 299057.7 & 1681.98733885814 & 177.800208771502 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 299594.833333333 & 1549.09483651697 & 193.399930250204 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 299561.833333333 & 1539.29670788202 & 194.609545904579 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 300025.566666667 & 1421.59543923808 & 211.048487062865 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 300002.333333333 & 1342.28920062584 & 223.500519257294 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 299631.833333333 & 1160.86441958531 & 258.110963070407 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 299964.65 & 1085.50309948759 & 276.336981572505 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 300241.983333333 & 1042.67982190711 & 287.952233298403 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 299300.482758621 & 2590.30920792181 & 115.546237431147 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 299263 & 2525.70133168653 & 118.487089603808 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 299234.518518519 & 2450.73494727387 & 122.099910825272 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 299169.75 & 2383.29340760286 & 125.527872080554 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 299169.52 & 2320.46414010259 & 128.926586207350 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 299171.25 & 2257.00660915661 & 132.552225937785 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 299171.956521739 & 2183.84320364861 & 136.993331765716 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 299181.772727273 & 2108.09131476774 & 141.920689408198 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 299194.119047619 & 2016.85876899683 & 148.346589085380 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 299241.4 & 1908.74391534301 & 156.773990263762 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 299413.289473684 & 1834.38184281407 & 163.222990156926 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 299562.805555556 & 1748.93373313228 & 171.283108033515 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 299750.676470588 & 1646.28515252477 & 182.077008962199 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 299850.625 & 1588.10632423544 & 188.810169964128 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 299887.166666667 & 1543.80932885824 & 194.251427984604 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 299933.642857143 & 1478.27114023746 & 202.894878140531 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 299920.384615385 & 1418.64659997524 & 211.413035932007 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 299908.333333333 & 1352.60113027930 & 221.727105367274 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 299950.227272727 & 1316.46529875334 & 227.845145296859 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 299947.95 & 1280.71195141609 & 234.204068813715 \tabularnewline
Median & 299652.5 &  &  \tabularnewline
Midrange & 300494 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 299396.548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 299887.166666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 299396.548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 299887.166666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 299887.166666667 &  &  \tabularnewline
Midmean - Closest Observation & 299396.548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 299887.166666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 299850.625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1215&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]299340.266666667[/C][C]2654.98695878852[/C][C]112.74641695538[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]298643.008570857[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]297943.868964388[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]300034.137453390[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]299335.466666667[/C][C]2642.36246775459[/C][C]113.283272192794[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]299314.266666667[/C][C]2634.21281779134[/C][C]113.625696695845[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]299402.916666667[/C][C]2580.05832624603[/C][C]116.045018680759[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]299170.516666667[/C][C]2523.85971752079[/C][C]118.536903850007[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]299162.6[/C][C]2475.40034988351[/C][C]120.854228696412[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]299168[/C][C]2447.90851787080[/C][C]122.213717471851[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]299121.566666667[/C][C]2384.05171774073[/C][C]125.467733959283[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]299112.633333333[/C][C]2355.18583946135[/C][C]127.001711848668[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]298910.433333333[/C][C]2309.92173411163[/C][C]129.402840329692[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]298152.766666667[/C][C]2067.05791021005[/C][C]144.240161436197[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]298426.483333333[/C][C]2010.68679197408[/C][C]148.420173905027[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]298285.283333333[/C][C]1952.79348888234[/C][C]152.747991547254[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]299057.7[/C][C]1681.98733885814[/C][C]177.800208771502[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]299594.833333333[/C][C]1549.09483651697[/C][C]193.399930250204[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]299561.833333333[/C][C]1539.29670788202[/C][C]194.609545904579[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]300025.566666667[/C][C]1421.59543923808[/C][C]211.048487062865[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]300002.333333333[/C][C]1342.28920062584[/C][C]223.500519257294[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]299631.833333333[/C][C]1160.86441958531[/C][C]258.110963070407[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]299964.65[/C][C]1085.50309948759[/C][C]276.336981572505[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]300241.983333333[/C][C]1042.67982190711[/C][C]287.952233298403[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]299300.482758621[/C][C]2590.30920792181[/C][C]115.546237431147[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]299263[/C][C]2525.70133168653[/C][C]118.487089603808[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]299234.518518519[/C][C]2450.73494727387[/C][C]122.099910825272[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]299169.75[/C][C]2383.29340760286[/C][C]125.527872080554[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]299169.52[/C][C]2320.46414010259[/C][C]128.926586207350[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]299171.25[/C][C]2257.00660915661[/C][C]132.552225937785[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]299171.956521739[/C][C]2183.84320364861[/C][C]136.993331765716[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]299181.772727273[/C][C]2108.09131476774[/C][C]141.920689408198[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]299194.119047619[/C][C]2016.85876899683[/C][C]148.346589085380[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]299241.4[/C][C]1908.74391534301[/C][C]156.773990263762[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]299413.289473684[/C][C]1834.38184281407[/C][C]163.222990156926[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]299562.805555556[/C][C]1748.93373313228[/C][C]171.283108033515[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]299750.676470588[/C][C]1646.28515252477[/C][C]182.077008962199[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]299850.625[/C][C]1588.10632423544[/C][C]188.810169964128[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]299887.166666667[/C][C]1543.80932885824[/C][C]194.251427984604[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]299933.642857143[/C][C]1478.27114023746[/C][C]202.894878140531[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]299920.384615385[/C][C]1418.64659997524[/C][C]211.413035932007[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]299908.333333333[/C][C]1352.60113027930[/C][C]221.727105367274[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]299950.227272727[/C][C]1316.46529875334[/C][C]227.845145296859[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]299947.95[/C][C]1280.71195141609[/C][C]234.204068813715[/C][/ROW]
[ROW][C]Median[/C][C]299652.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]300494[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]299396.548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]299887.166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]299396.548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]299887.166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]299887.166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]299396.548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]299887.166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]299850.625[/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=1215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1215&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 Mean299340.2666666672654.98695878852112.74641695538
Geometric Mean298643.008570857
Harmonic Mean297943.868964388
Quadratic Mean300034.137453390
Winsorized Mean ( 1 / 20 )299335.4666666672642.36246775459113.283272192794
Winsorized Mean ( 2 / 20 )299314.2666666672634.21281779134113.625696695845
Winsorized Mean ( 3 / 20 )299402.9166666672580.05832624603116.045018680759
Winsorized Mean ( 4 / 20 )299170.5166666672523.85971752079118.536903850007
Winsorized Mean ( 5 / 20 )299162.62475.40034988351120.854228696412
Winsorized Mean ( 6 / 20 )2991682447.90851787080122.213717471851
Winsorized Mean ( 7 / 20 )299121.5666666672384.05171774073125.467733959283
Winsorized Mean ( 8 / 20 )299112.6333333332355.18583946135127.001711848668
Winsorized Mean ( 9 / 20 )298910.4333333332309.92173411163129.402840329692
Winsorized Mean ( 10 / 20 )298152.7666666672067.05791021005144.240161436197
Winsorized Mean ( 11 / 20 )298426.4833333332010.68679197408148.420173905027
Winsorized Mean ( 12 / 20 )298285.2833333331952.79348888234152.747991547254
Winsorized Mean ( 13 / 20 )299057.71681.98733885814177.800208771502
Winsorized Mean ( 14 / 20 )299594.8333333331549.09483651697193.399930250204
Winsorized Mean ( 15 / 20 )299561.8333333331539.29670788202194.609545904579
Winsorized Mean ( 16 / 20 )300025.5666666671421.59543923808211.048487062865
Winsorized Mean ( 17 / 20 )300002.3333333331342.28920062584223.500519257294
Winsorized Mean ( 18 / 20 )299631.8333333331160.86441958531258.110963070407
Winsorized Mean ( 19 / 20 )299964.651085.50309948759276.336981572505
Winsorized Mean ( 20 / 20 )300241.9833333331042.67982190711287.952233298403
Trimmed Mean ( 1 / 20 )299300.4827586212590.30920792181115.546237431147
Trimmed Mean ( 2 / 20 )2992632525.70133168653118.487089603808
Trimmed Mean ( 3 / 20 )299234.5185185192450.73494727387122.099910825272
Trimmed Mean ( 4 / 20 )299169.752383.29340760286125.527872080554
Trimmed Mean ( 5 / 20 )299169.522320.46414010259128.926586207350
Trimmed Mean ( 6 / 20 )299171.252257.00660915661132.552225937785
Trimmed Mean ( 7 / 20 )299171.9565217392183.84320364861136.993331765716
Trimmed Mean ( 8 / 20 )299181.7727272732108.09131476774141.920689408198
Trimmed Mean ( 9 / 20 )299194.1190476192016.85876899683148.346589085380
Trimmed Mean ( 10 / 20 )299241.41908.74391534301156.773990263762
Trimmed Mean ( 11 / 20 )299413.2894736841834.38184281407163.222990156926
Trimmed Mean ( 12 / 20 )299562.8055555561748.93373313228171.283108033515
Trimmed Mean ( 13 / 20 )299750.6764705881646.28515252477182.077008962199
Trimmed Mean ( 14 / 20 )299850.6251588.10632423544188.810169964128
Trimmed Mean ( 15 / 20 )299887.1666666671543.80932885824194.251427984604
Trimmed Mean ( 16 / 20 )299933.6428571431478.27114023746202.894878140531
Trimmed Mean ( 17 / 20 )299920.3846153851418.64659997524211.413035932007
Trimmed Mean ( 18 / 20 )299908.3333333331352.60113027930221.727105367274
Trimmed Mean ( 19 / 20 )299950.2272727271316.46529875334227.845145296859
Trimmed Mean ( 20 / 20 )299947.951280.71195141609234.204068813715
Median299652.5
Midrange300494
Midmean - Weighted Average at Xnp299396.548387097
Midmean - Weighted Average at X(n+1)p299887.166666667
Midmean - Empirical Distribution Function299396.548387097
Midmean - Empirical Distribution Function - Averaging299887.166666667
Midmean - Empirical Distribution Function - Interpolation299887.166666667
Midmean - Closest Observation299396.548387097
Midmean - True Basic - Statistics Graphics Toolkit299887.166666667
Midmean - MS Excel (old versions)299850.625
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')