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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 computationMon, 20 Oct 2008 14:52:18 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224536035zt8uh6b4kh05ata.htm/, Retrieved Fri, 17 May 2024 05:03:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18133, Retrieved Fri, 17 May 2024 05:03:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
F RM D  [Pearson Correlation] [Pearson Correlation] [2008-10-20 11:08:13] [8af599f2ccf50a86f2698320831f9f94]
F RM D      [Central Tendency] [Goudprijs] [2008-10-20 20:52:18] [6d5cd2fe15d123a10639b4bf141c23b5] [Current]
Feedback Forum
2008-10-27 22:55:49 [Jeroen Michel] [reply
Hier maakt de student gebruik van 'Central Tendecy'. De student geeft dit grafisch weer, maar trekt hieruit geen enkele conclusie.

Post a new message
Dataseries X:
13812
13031
12574
11964
11451
11346
11353
10702
10646
10556
10463
10407
10625
10872
10805
10653
10574
10431
10383
10296
10872
10635
10297
10570
10662
10709
10413
10846
10371
9924
9828
9897
9721
10171
10738
10812
10511
10244
10368
10457
10186
10166
10827
10997
10940
10756
10893
10236
9960
10018
10063
10002
9728
10002
10177
9948
9394
9308
9155
9103
9732




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18133&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18133&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10534.1147540984103.601082073280101.679582329529
Geometric Mean10505.5797476984
Harmonic Mean10478.7717114973
Quadratic Mean10564.6374620674
Winsorized Mean ( 1 / 20 )10522.163934426297.2553879281425108.191064357283
Winsorized Mean ( 2 / 20 )10512.196721311590.0123149427393116.786205620850
Winsorized Mean ( 3 / 20 )10486.426229508278.5533909102989133.494252864052
Winsorized Mean ( 4 / 20 )10474.229508196764.3039503390236162.886252757015
Winsorized Mean ( 5 / 20 )10466.770491803362.2198701128015168.222313431827
Winsorized Mean ( 6 / 20 )10466.475409836161.9789388102304168.871484584187
Winsorized Mean ( 7 / 20 )10437.442622950851.3231832520189203.367015870752
Winsorized Mean ( 8 / 20 )10439.016393442648.2521864042312216.342867989236
Winsorized Mean ( 9 / 20 )10436.065573770546.341980571695225.196796619968
Winsorized Mean ( 10 / 20 )10436.557377049245.063983198817231.594205310354
Winsorized Mean ( 11 / 20 )10438.721311475444.6752405796057233.657864536284
Winsorized Mean ( 12 / 20 )10441.868852459042.4027944963333246.254261694049
Winsorized Mean ( 13 / 20 )10437.819672131141.7667247231162249.907545811324
Winsorized Mean ( 14 / 20 )10438.049180327940.5991629986505257.100107720813
Winsorized Mean ( 15 / 20 )10447.393442623038.4570463580329271.663958416315
Winsorized Mean ( 16 / 20 )10461.557377049232.1419794667090325.479561328347
Winsorized Mean ( 17 / 20 )10457.934426229531.1696386957261335.516703556254
Winsorized Mean ( 18 / 20 )10451.147540983629.6356272452875352.654845280709
Winsorized Mean ( 19 / 20 )10451.770491803328.8891266008683361.789078507107
Winsorized Mean ( 20 / 20 )10455.049180327924.5395011798977426.049784128964
Trimmed Mean ( 1 / 20 )10502.813559322087.8887821799017119.501184324338
Trimmed Mean ( 2 / 20 )10482.105263157975.5104919107477138.816540561643
Trimmed Mean ( 3 / 20 )10465.418181818264.6940309223024161.767910155222
Trimmed Mean ( 4 / 20 )10457.358490566057.2509631581831182.658210686737
Trimmed Mean ( 5 / 20 )10452.313725490254.2413668214914192.700043121863
Trimmed Mean ( 6 / 20 )10448.714285714351.2012170348551204.071600067657
Trimmed Mean ( 7 / 20 )10444.872340425547.3459585786286220.607474301729
Trimmed Mean ( 8 / 20 )10446.311111111145.8420412909309227.876220537713
Trimmed Mean ( 9 / 20 )10447.604651162844.7424788378167233.505271110111
Trimmed Mean ( 10 / 20 )10449.512195122043.7755099418867238.706806819475
Trimmed Mean ( 11 / 20 )10451.538461538542.7823927067397244.295323386436
Trimmed Mean ( 12 / 20 )10453.459459459541.4998388975236251.891567224451
Trimmed Mean ( 13 / 20 )10455.142857142940.3349035176324259.208326916473
Trimmed Mean ( 14 / 20 )10457.606060606138.8299502540365269.318039095839
Trimmed Mean ( 15 / 20 )10460.354838709736.9992312732435282.718166803488
Trimmed Mean ( 16 / 20 )10462.172413793135.0290192493344298.67157682389
Trimmed Mean ( 17 / 20 )10462.259259259334.2251882633216305.688873900847
Trimmed Mean ( 18 / 20 )10462.8833.2019738369072315.128252657362
Trimmed Mean ( 19 / 20 )10464.608695652232.0280101676355326.733026525224
Trimmed Mean ( 20 / 20 )10466.571428571430.2762339159951345.702555265365
Median10457
Midrange11457.5
Midmean - Weighted Average at Xnp10448.8666666667
Midmean - Weighted Average at X(n+1)p10460.3548387097
Midmean - Empirical Distribution Function10460.3548387097
Midmean - Empirical Distribution Function - Averaging10460.3548387097
Midmean - Empirical Distribution Function - Interpolation10460.3548387097
Midmean - Closest Observation10446.53125
Midmean - True Basic - Statistics Graphics Toolkit10460.3548387097
Midmean - MS Excel (old versions)10460.3548387097
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10534.1147540984 & 103.601082073280 & 101.679582329529 \tabularnewline
Geometric Mean & 10505.5797476984 &  &  \tabularnewline
Harmonic Mean & 10478.7717114973 &  &  \tabularnewline
Quadratic Mean & 10564.6374620674 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 10522.1639344262 & 97.2553879281425 & 108.191064357283 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 10512.1967213115 & 90.0123149427393 & 116.786205620850 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 10486.4262295082 & 78.5533909102989 & 133.494252864052 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 10474.2295081967 & 64.3039503390236 & 162.886252757015 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 10466.7704918033 & 62.2198701128015 & 168.222313431827 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 10466.4754098361 & 61.9789388102304 & 168.871484584187 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 10437.4426229508 & 51.3231832520189 & 203.367015870752 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 10439.0163934426 & 48.2521864042312 & 216.342867989236 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 10436.0655737705 & 46.341980571695 & 225.196796619968 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 10436.5573770492 & 45.063983198817 & 231.594205310354 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 10438.7213114754 & 44.6752405796057 & 233.657864536284 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 10441.8688524590 & 42.4027944963333 & 246.254261694049 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 10437.8196721311 & 41.7667247231162 & 249.907545811324 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 10438.0491803279 & 40.5991629986505 & 257.100107720813 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 10447.3934426230 & 38.4570463580329 & 271.663958416315 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 10461.5573770492 & 32.1419794667090 & 325.479561328347 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 10457.9344262295 & 31.1696386957261 & 335.516703556254 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 10451.1475409836 & 29.6356272452875 & 352.654845280709 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 10451.7704918033 & 28.8891266008683 & 361.789078507107 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 10455.0491803279 & 24.5395011798977 & 426.049784128964 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 10502.8135593220 & 87.8887821799017 & 119.501184324338 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 10482.1052631579 & 75.5104919107477 & 138.816540561643 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 10465.4181818182 & 64.6940309223024 & 161.767910155222 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 10457.3584905660 & 57.2509631581831 & 182.658210686737 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 10452.3137254902 & 54.2413668214914 & 192.700043121863 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 10448.7142857143 & 51.2012170348551 & 204.071600067657 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 10444.8723404255 & 47.3459585786286 & 220.607474301729 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 10446.3111111111 & 45.8420412909309 & 227.876220537713 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 10447.6046511628 & 44.7424788378167 & 233.505271110111 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 10449.5121951220 & 43.7755099418867 & 238.706806819475 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 10451.5384615385 & 42.7823927067397 & 244.295323386436 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 10453.4594594595 & 41.4998388975236 & 251.891567224451 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 10455.1428571429 & 40.3349035176324 & 259.208326916473 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 10457.6060606061 & 38.8299502540365 & 269.318039095839 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 10460.3548387097 & 36.9992312732435 & 282.718166803488 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 10462.1724137931 & 35.0290192493344 & 298.67157682389 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 10462.2592592593 & 34.2251882633216 & 305.688873900847 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 10462.88 & 33.2019738369072 & 315.128252657362 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 10464.6086956522 & 32.0280101676355 & 326.733026525224 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 10466.5714285714 & 30.2762339159951 & 345.702555265365 \tabularnewline
Median & 10457 &  &  \tabularnewline
Midrange & 11457.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10448.8666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10460.3548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10460.3548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10460.3548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10460.3548387097 &  &  \tabularnewline
Midmean - Closest Observation & 10446.53125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10460.3548387097 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10460.3548387097 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18133&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]10534.1147540984[/C][C]103.601082073280[/C][C]101.679582329529[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10505.5797476984[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10478.7717114973[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10564.6374620674[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]10522.1639344262[/C][C]97.2553879281425[/C][C]108.191064357283[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]10512.1967213115[/C][C]90.0123149427393[/C][C]116.786205620850[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]10486.4262295082[/C][C]78.5533909102989[/C][C]133.494252864052[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]10474.2295081967[/C][C]64.3039503390236[/C][C]162.886252757015[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]10466.7704918033[/C][C]62.2198701128015[/C][C]168.222313431827[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]10466.4754098361[/C][C]61.9789388102304[/C][C]168.871484584187[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]10437.4426229508[/C][C]51.3231832520189[/C][C]203.367015870752[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]10439.0163934426[/C][C]48.2521864042312[/C][C]216.342867989236[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]10436.0655737705[/C][C]46.341980571695[/C][C]225.196796619968[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]10436.5573770492[/C][C]45.063983198817[/C][C]231.594205310354[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]10438.7213114754[/C][C]44.6752405796057[/C][C]233.657864536284[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]10441.8688524590[/C][C]42.4027944963333[/C][C]246.254261694049[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]10437.8196721311[/C][C]41.7667247231162[/C][C]249.907545811324[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]10438.0491803279[/C][C]40.5991629986505[/C][C]257.100107720813[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]10447.3934426230[/C][C]38.4570463580329[/C][C]271.663958416315[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]10461.5573770492[/C][C]32.1419794667090[/C][C]325.479561328347[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]10457.9344262295[/C][C]31.1696386957261[/C][C]335.516703556254[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]10451.1475409836[/C][C]29.6356272452875[/C][C]352.654845280709[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]10451.7704918033[/C][C]28.8891266008683[/C][C]361.789078507107[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]10455.0491803279[/C][C]24.5395011798977[/C][C]426.049784128964[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]10502.8135593220[/C][C]87.8887821799017[/C][C]119.501184324338[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]10482.1052631579[/C][C]75.5104919107477[/C][C]138.816540561643[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]10465.4181818182[/C][C]64.6940309223024[/C][C]161.767910155222[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]10457.3584905660[/C][C]57.2509631581831[/C][C]182.658210686737[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]10452.3137254902[/C][C]54.2413668214914[/C][C]192.700043121863[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]10448.7142857143[/C][C]51.2012170348551[/C][C]204.071600067657[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]10444.8723404255[/C][C]47.3459585786286[/C][C]220.607474301729[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]10446.3111111111[/C][C]45.8420412909309[/C][C]227.876220537713[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]10447.6046511628[/C][C]44.7424788378167[/C][C]233.505271110111[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]10449.5121951220[/C][C]43.7755099418867[/C][C]238.706806819475[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]10451.5384615385[/C][C]42.7823927067397[/C][C]244.295323386436[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]10453.4594594595[/C][C]41.4998388975236[/C][C]251.891567224451[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]10455.1428571429[/C][C]40.3349035176324[/C][C]259.208326916473[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]10457.6060606061[/C][C]38.8299502540365[/C][C]269.318039095839[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]10460.3548387097[/C][C]36.9992312732435[/C][C]282.718166803488[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]10462.1724137931[/C][C]35.0290192493344[/C][C]298.67157682389[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]10462.2592592593[/C][C]34.2251882633216[/C][C]305.688873900847[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]10462.88[/C][C]33.2019738369072[/C][C]315.128252657362[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]10464.6086956522[/C][C]32.0280101676355[/C][C]326.733026525224[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]10466.5714285714[/C][C]30.2762339159951[/C][C]345.702555265365[/C][/ROW]
[ROW][C]Median[/C][C]10457[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11457.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10448.8666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10460.3548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10460.3548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10460.3548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10460.3548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10446.53125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10460.3548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10460.3548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18133&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 Mean10534.1147540984103.601082073280101.679582329529
Geometric Mean10505.5797476984
Harmonic Mean10478.7717114973
Quadratic Mean10564.6374620674
Winsorized Mean ( 1 / 20 )10522.163934426297.2553879281425108.191064357283
Winsorized Mean ( 2 / 20 )10512.196721311590.0123149427393116.786205620850
Winsorized Mean ( 3 / 20 )10486.426229508278.5533909102989133.494252864052
Winsorized Mean ( 4 / 20 )10474.229508196764.3039503390236162.886252757015
Winsorized Mean ( 5 / 20 )10466.770491803362.2198701128015168.222313431827
Winsorized Mean ( 6 / 20 )10466.475409836161.9789388102304168.871484584187
Winsorized Mean ( 7 / 20 )10437.442622950851.3231832520189203.367015870752
Winsorized Mean ( 8 / 20 )10439.016393442648.2521864042312216.342867989236
Winsorized Mean ( 9 / 20 )10436.065573770546.341980571695225.196796619968
Winsorized Mean ( 10 / 20 )10436.557377049245.063983198817231.594205310354
Winsorized Mean ( 11 / 20 )10438.721311475444.6752405796057233.657864536284
Winsorized Mean ( 12 / 20 )10441.868852459042.4027944963333246.254261694049
Winsorized Mean ( 13 / 20 )10437.819672131141.7667247231162249.907545811324
Winsorized Mean ( 14 / 20 )10438.049180327940.5991629986505257.100107720813
Winsorized Mean ( 15 / 20 )10447.393442623038.4570463580329271.663958416315
Winsorized Mean ( 16 / 20 )10461.557377049232.1419794667090325.479561328347
Winsorized Mean ( 17 / 20 )10457.934426229531.1696386957261335.516703556254
Winsorized Mean ( 18 / 20 )10451.147540983629.6356272452875352.654845280709
Winsorized Mean ( 19 / 20 )10451.770491803328.8891266008683361.789078507107
Winsorized Mean ( 20 / 20 )10455.049180327924.5395011798977426.049784128964
Trimmed Mean ( 1 / 20 )10502.813559322087.8887821799017119.501184324338
Trimmed Mean ( 2 / 20 )10482.105263157975.5104919107477138.816540561643
Trimmed Mean ( 3 / 20 )10465.418181818264.6940309223024161.767910155222
Trimmed Mean ( 4 / 20 )10457.358490566057.2509631581831182.658210686737
Trimmed Mean ( 5 / 20 )10452.313725490254.2413668214914192.700043121863
Trimmed Mean ( 6 / 20 )10448.714285714351.2012170348551204.071600067657
Trimmed Mean ( 7 / 20 )10444.872340425547.3459585786286220.607474301729
Trimmed Mean ( 8 / 20 )10446.311111111145.8420412909309227.876220537713
Trimmed Mean ( 9 / 20 )10447.604651162844.7424788378167233.505271110111
Trimmed Mean ( 10 / 20 )10449.512195122043.7755099418867238.706806819475
Trimmed Mean ( 11 / 20 )10451.538461538542.7823927067397244.295323386436
Trimmed Mean ( 12 / 20 )10453.459459459541.4998388975236251.891567224451
Trimmed Mean ( 13 / 20 )10455.142857142940.3349035176324259.208326916473
Trimmed Mean ( 14 / 20 )10457.606060606138.8299502540365269.318039095839
Trimmed Mean ( 15 / 20 )10460.354838709736.9992312732435282.718166803488
Trimmed Mean ( 16 / 20 )10462.172413793135.0290192493344298.67157682389
Trimmed Mean ( 17 / 20 )10462.259259259334.2251882633216305.688873900847
Trimmed Mean ( 18 / 20 )10462.8833.2019738369072315.128252657362
Trimmed Mean ( 19 / 20 )10464.608695652232.0280101676355326.733026525224
Trimmed Mean ( 20 / 20 )10466.571428571430.2762339159951345.702555265365
Median10457
Midrange11457.5
Midmean - Weighted Average at Xnp10448.8666666667
Midmean - Weighted Average at X(n+1)p10460.3548387097
Midmean - Empirical Distribution Function10460.3548387097
Midmean - Empirical Distribution Function - Averaging10460.3548387097
Midmean - Empirical Distribution Function - Interpolation10460.3548387097
Midmean - Closest Observation10446.53125
Midmean - True Basic - Statistics Graphics Toolkit10460.3548387097
Midmean - MS Excel (old versions)10460.3548387097
Number of observations61



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')