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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 30 Nov 2010 13:27:50 +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/Nov/30/t1291123613ubqnw96kbc4eeip.htm/, Retrieved Mon, 29 Apr 2024 12:07:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103408, Retrieved Mon, 29 Apr 2024 12:07:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Mean Plot] [Colombia Coffee] [2008-01-07 13:38:24] [74be16979710d4c4e7c6647856088456]
- RM D      [Central Tendency] [Paper uitvoer cen...] [2010-11-30 13:27:50] [9d72585f2b7b60ae977d4816136e1c95] [Current]
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Dataseries X:
13768040,14
17487530,67
16198106,13
17535166,38
16571771,60
16198892,67
16554237,93
19554176,37
15903762,33
18003781,65
18329610,38
16260733,42
14851949,20
18174068,44
18406552,23
18466459,42
16016524,60
17428458,32
17167191,42
19629987,60
17183629,01
18344657,85
19301440,71
18147463,68
16192909,22
18374420,60
20515191,95
18957217,20
16471529,53
18746813,27
19009453,59
19211178,55
20547653,75
19325754,03
20605542,58
20056915,06
16141449,72
20359793,22
19711553,27
15638580,70
14384486,00
13855616,12
14308336,46
15290621,44
14423755,53
13779681,49
15686348,94
14733828,17
12522497,94
16189383,57
16059123,25
16007123,26
15806842,33
15159951,13
15692144,17
18908869,11
16969881,42
16997477,78
19858875,65
17681170,13




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=103408&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=103408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103408&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 Mean17161102.7046667256826.12743385766.8199255120036
Geometric Mean17045525.3084896
Harmonic Mean16927858.3498914
Quadratic Mean17274115.490072
Winsorized Mean ( 1 / 20 )17180896.9275251028.65667496968.4419745341895
Winsorized Mean ( 2 / 20 )17180202.9125250694.36498158068.5304710130294
Winsorized Mean ( 3 / 20 )17176229.7075248106.22140813569.2293389904363
Winsorized Mean ( 4 / 20 )17186219.1861667237305.46867081572.4223477968265
Winsorized Mean ( 5 / 20 )17176061.697232703.01399045973.8110839325193
Winsorized Mean ( 6 / 20 )17165256.412229077.96888304274.9319390934702
Winsorized Mean ( 7 / 20 )17191915.5585220192.4876168878.076757951946
Winsorized Mean ( 8 / 20 )17197556.8651667215362.44505848679.854019397376
Winsorized Mean ( 9 / 20 )17209493.8036667200852.62813488485.682193772986
Winsorized Mean ( 10 / 20 )17227219.9686667196424.49909925387.7040290170821
Winsorized Mean ( 11 / 20 )17274464.437183289.22961765794.2470240779267
Winsorized Mean ( 12 / 20 )17243673.093174774.31744889398.6625114301613
Winsorized Mean ( 13 / 20 )17233610.8416667172657.89817858599.8136258084263
Winsorized Mean ( 14 / 20 )17249092.5246667166764.454796526103.433867521186
Winsorized Mean ( 15 / 20 )17232808.5646667156502.106927378110.112310326041
Winsorized Mean ( 16 / 20 )17185610.4526667140641.424031129122.194513963843
Winsorized Mean ( 17 / 20 )17171300.4618333137661.948216983124.735271323982
Winsorized Mean ( 18 / 20 )17174440.5678333134392.080428156127.793546413731
Winsorized Mean ( 19 / 20 )17191085.7458333129339.278011192132.914656786206
Winsorized Mean ( 20 / 20 )17202047.8725126397.086268187136.095288114482
Trimmed Mean ( 1 / 20 )17181691.7544828246015.91813725669.839756242508
Trimmed Mean ( 2 / 20 )17182543.3548214239797.68962394671.654332373958
Trimmed Mean ( 3 / 20 )17183843.6005556232284.94903156473.9774301873536
Trimmed Mean ( 4 / 20 )17186772.0209615224161.52087809176.6713749694286
Trimmed Mean ( 5 / 20 )17186937.8714218282.35765811378.7371826829873
Trimmed Mean ( 6 / 20 )17189656.915212364.12731758880.944258958073
Trimmed Mean ( 7 / 20 )17194961.3721739205868.96178163683.5238164284936
Trimmed Mean ( 8 / 20 )17195554.7125200084.88691481885.9412971046664
Trimmed Mean ( 9 / 20 )17195197.1852381193819.52727306888.7175684884018
Trimmed Mean ( 10 / 20 )17192814.4155189477.92930564190.7378209087709
Trimmed Mean ( 11 / 20 )17187381.9597368184655.26158418193.0782140312933
Trimmed Mean ( 12 / 20 )17174187.645181353.75422913794.6999289758332
Trimmed Mean ( 13 / 20 )17163969.1967647178763.22181568596.0151032322617
Trimmed Mean ( 14 / 20 )17153924.72875175258.22238205697.8780025016753
Trimmed Mean ( 15 / 20 )17140329.3293333171436.51061516499.9806241262658
Trimmed Mean ( 16 / 20 )17127118.01168462.308963594101.667358801911
Trimmed Mean ( 17 / 20 )17118681.6168271.142470135101.732723440909
Trimmed Mean ( 18 / 20 )17110943.5320833167732.465904641102.013306963550
Trimmed Mean ( 19 / 20 )17101322.7690909166614.694831806102.639942931531
Trimmed Mean ( 20 / 20 )17087149.6675165068.366926327103.515591664672
Median17082334.6
Midrange16564020.26
Midmean - Weighted Average at Xnp17097313.6196774
Midmean - Weighted Average at X(n+1)p17140329.3293333
Midmean - Empirical Distribution Function17097313.6196774
Midmean - Empirical Distribution Function - Averaging17140329.3293333
Midmean - Empirical Distribution Function - Interpolation17140329.3293333
Midmean - Closest Observation17097313.6196774
Midmean - True Basic - Statistics Graphics Toolkit17140329.3293333
Midmean - MS Excel (old versions)17153924.72875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17161102.7046667 & 256826.127433857 & 66.8199255120036 \tabularnewline
Geometric Mean & 17045525.3084896 &  &  \tabularnewline
Harmonic Mean & 16927858.3498914 &  &  \tabularnewline
Quadratic Mean & 17274115.490072 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17180896.9275 & 251028.656674969 & 68.4419745341895 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17180202.9125 & 250694.364981580 & 68.5304710130294 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17176229.7075 & 248106.221408135 & 69.2293389904363 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17186219.1861667 & 237305.468670815 & 72.4223477968265 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17176061.697 & 232703.013990459 & 73.8110839325193 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 17165256.412 & 229077.968883042 & 74.9319390934702 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 17191915.5585 & 220192.48761688 & 78.076757951946 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17197556.8651667 & 215362.445058486 & 79.854019397376 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17209493.8036667 & 200852.628134884 & 85.682193772986 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17227219.9686667 & 196424.499099253 & 87.7040290170821 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17274464.437 & 183289.229617657 & 94.2470240779267 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17243673.093 & 174774.317448893 & 98.6625114301613 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17233610.8416667 & 172657.898178585 & 99.8136258084263 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17249092.5246667 & 166764.454796526 & 103.433867521186 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17232808.5646667 & 156502.106927378 & 110.112310326041 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 17185610.4526667 & 140641.424031129 & 122.194513963843 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17171300.4618333 & 137661.948216983 & 124.735271323982 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17174440.5678333 & 134392.080428156 & 127.793546413731 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17191085.7458333 & 129339.278011192 & 132.914656786206 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 17202047.8725 & 126397.086268187 & 136.095288114482 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17181691.7544828 & 246015.918137256 & 69.839756242508 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17182543.3548214 & 239797.689623946 & 71.654332373958 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17183843.6005556 & 232284.949031564 & 73.9774301873536 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17186772.0209615 & 224161.520878091 & 76.6713749694286 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17186937.8714 & 218282.357658113 & 78.7371826829873 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17189656.915 & 212364.127317588 & 80.944258958073 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17194961.3721739 & 205868.961781636 & 83.5238164284936 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17195554.7125 & 200084.886914818 & 85.9412971046664 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17195197.1852381 & 193819.527273068 & 88.7175684884018 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17192814.4155 & 189477.929305641 & 90.7378209087709 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17187381.9597368 & 184655.261584181 & 93.0782140312933 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17174187.645 & 181353.754229137 & 94.6999289758332 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17163969.1967647 & 178763.221815685 & 96.0151032322617 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17153924.72875 & 175258.222382056 & 97.8780025016753 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 17140329.3293333 & 171436.510615164 & 99.9806241262658 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 17127118.01 & 168462.308963594 & 101.667358801911 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 17118681.6 & 168271.142470135 & 101.732723440909 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 17110943.5320833 & 167732.465904641 & 102.013306963550 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17101322.7690909 & 166614.694831806 & 102.639942931531 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17087149.6675 & 165068.366926327 & 103.515591664672 \tabularnewline
Median & 17082334.6 &  &  \tabularnewline
Midrange & 16564020.26 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17097313.6196774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17140329.3293333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17097313.6196774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17140329.3293333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17140329.3293333 &  &  \tabularnewline
Midmean - Closest Observation & 17097313.6196774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17140329.3293333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17153924.72875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103408&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]17161102.7046667[/C][C]256826.127433857[/C][C]66.8199255120036[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17045525.3084896[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16927858.3498914[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17274115.490072[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17180896.9275[/C][C]251028.656674969[/C][C]68.4419745341895[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17180202.9125[/C][C]250694.364981580[/C][C]68.5304710130294[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17176229.7075[/C][C]248106.221408135[/C][C]69.2293389904363[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17186219.1861667[/C][C]237305.468670815[/C][C]72.4223477968265[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17176061.697[/C][C]232703.013990459[/C][C]73.8110839325193[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]17165256.412[/C][C]229077.968883042[/C][C]74.9319390934702[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]17191915.5585[/C][C]220192.48761688[/C][C]78.076757951946[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17197556.8651667[/C][C]215362.445058486[/C][C]79.854019397376[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17209493.8036667[/C][C]200852.628134884[/C][C]85.682193772986[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17227219.9686667[/C][C]196424.499099253[/C][C]87.7040290170821[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17274464.437[/C][C]183289.229617657[/C][C]94.2470240779267[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17243673.093[/C][C]174774.317448893[/C][C]98.6625114301613[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17233610.8416667[/C][C]172657.898178585[/C][C]99.8136258084263[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17249092.5246667[/C][C]166764.454796526[/C][C]103.433867521186[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17232808.5646667[/C][C]156502.106927378[/C][C]110.112310326041[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]17185610.4526667[/C][C]140641.424031129[/C][C]122.194513963843[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17171300.4618333[/C][C]137661.948216983[/C][C]124.735271323982[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17174440.5678333[/C][C]134392.080428156[/C][C]127.793546413731[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17191085.7458333[/C][C]129339.278011192[/C][C]132.914656786206[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]17202047.8725[/C][C]126397.086268187[/C][C]136.095288114482[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17181691.7544828[/C][C]246015.918137256[/C][C]69.839756242508[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17182543.3548214[/C][C]239797.689623946[/C][C]71.654332373958[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17183843.6005556[/C][C]232284.949031564[/C][C]73.9774301873536[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17186772.0209615[/C][C]224161.520878091[/C][C]76.6713749694286[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17186937.8714[/C][C]218282.357658113[/C][C]78.7371826829873[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17189656.915[/C][C]212364.127317588[/C][C]80.944258958073[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17194961.3721739[/C][C]205868.961781636[/C][C]83.5238164284936[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17195554.7125[/C][C]200084.886914818[/C][C]85.9412971046664[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17195197.1852381[/C][C]193819.527273068[/C][C]88.7175684884018[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17192814.4155[/C][C]189477.929305641[/C][C]90.7378209087709[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17187381.9597368[/C][C]184655.261584181[/C][C]93.0782140312933[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17174187.645[/C][C]181353.754229137[/C][C]94.6999289758332[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17163969.1967647[/C][C]178763.221815685[/C][C]96.0151032322617[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17153924.72875[/C][C]175258.222382056[/C][C]97.8780025016753[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]17140329.3293333[/C][C]171436.510615164[/C][C]99.9806241262658[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]17127118.01[/C][C]168462.308963594[/C][C]101.667358801911[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]17118681.6[/C][C]168271.142470135[/C][C]101.732723440909[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]17110943.5320833[/C][C]167732.465904641[/C][C]102.013306963550[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17101322.7690909[/C][C]166614.694831806[/C][C]102.639942931531[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17087149.6675[/C][C]165068.366926327[/C][C]103.515591664672[/C][/ROW]
[ROW][C]Median[/C][C]17082334.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16564020.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17097313.6196774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17140329.3293333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17097313.6196774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17140329.3293333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17140329.3293333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17097313.6196774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17140329.3293333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17153924.72875[/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=103408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103408&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 Mean17161102.7046667256826.12743385766.8199255120036
Geometric Mean17045525.3084896
Harmonic Mean16927858.3498914
Quadratic Mean17274115.490072
Winsorized Mean ( 1 / 20 )17180896.9275251028.65667496968.4419745341895
Winsorized Mean ( 2 / 20 )17180202.9125250694.36498158068.5304710130294
Winsorized Mean ( 3 / 20 )17176229.7075248106.22140813569.2293389904363
Winsorized Mean ( 4 / 20 )17186219.1861667237305.46867081572.4223477968265
Winsorized Mean ( 5 / 20 )17176061.697232703.01399045973.8110839325193
Winsorized Mean ( 6 / 20 )17165256.412229077.96888304274.9319390934702
Winsorized Mean ( 7 / 20 )17191915.5585220192.4876168878.076757951946
Winsorized Mean ( 8 / 20 )17197556.8651667215362.44505848679.854019397376
Winsorized Mean ( 9 / 20 )17209493.8036667200852.62813488485.682193772986
Winsorized Mean ( 10 / 20 )17227219.9686667196424.49909925387.7040290170821
Winsorized Mean ( 11 / 20 )17274464.437183289.22961765794.2470240779267
Winsorized Mean ( 12 / 20 )17243673.093174774.31744889398.6625114301613
Winsorized Mean ( 13 / 20 )17233610.8416667172657.89817858599.8136258084263
Winsorized Mean ( 14 / 20 )17249092.5246667166764.454796526103.433867521186
Winsorized Mean ( 15 / 20 )17232808.5646667156502.106927378110.112310326041
Winsorized Mean ( 16 / 20 )17185610.4526667140641.424031129122.194513963843
Winsorized Mean ( 17 / 20 )17171300.4618333137661.948216983124.735271323982
Winsorized Mean ( 18 / 20 )17174440.5678333134392.080428156127.793546413731
Winsorized Mean ( 19 / 20 )17191085.7458333129339.278011192132.914656786206
Winsorized Mean ( 20 / 20 )17202047.8725126397.086268187136.095288114482
Trimmed Mean ( 1 / 20 )17181691.7544828246015.91813725669.839756242508
Trimmed Mean ( 2 / 20 )17182543.3548214239797.68962394671.654332373958
Trimmed Mean ( 3 / 20 )17183843.6005556232284.94903156473.9774301873536
Trimmed Mean ( 4 / 20 )17186772.0209615224161.52087809176.6713749694286
Trimmed Mean ( 5 / 20 )17186937.8714218282.35765811378.7371826829873
Trimmed Mean ( 6 / 20 )17189656.915212364.12731758880.944258958073
Trimmed Mean ( 7 / 20 )17194961.3721739205868.96178163683.5238164284936
Trimmed Mean ( 8 / 20 )17195554.7125200084.88691481885.9412971046664
Trimmed Mean ( 9 / 20 )17195197.1852381193819.52727306888.7175684884018
Trimmed Mean ( 10 / 20 )17192814.4155189477.92930564190.7378209087709
Trimmed Mean ( 11 / 20 )17187381.9597368184655.26158418193.0782140312933
Trimmed Mean ( 12 / 20 )17174187.645181353.75422913794.6999289758332
Trimmed Mean ( 13 / 20 )17163969.1967647178763.22181568596.0151032322617
Trimmed Mean ( 14 / 20 )17153924.72875175258.22238205697.8780025016753
Trimmed Mean ( 15 / 20 )17140329.3293333171436.51061516499.9806241262658
Trimmed Mean ( 16 / 20 )17127118.01168462.308963594101.667358801911
Trimmed Mean ( 17 / 20 )17118681.6168271.142470135101.732723440909
Trimmed Mean ( 18 / 20 )17110943.5320833167732.465904641102.013306963550
Trimmed Mean ( 19 / 20 )17101322.7690909166614.694831806102.639942931531
Trimmed Mean ( 20 / 20 )17087149.6675165068.366926327103.515591664672
Median17082334.6
Midrange16564020.26
Midmean - Weighted Average at Xnp17097313.6196774
Midmean - Weighted Average at X(n+1)p17140329.3293333
Midmean - Empirical Distribution Function17097313.6196774
Midmean - Empirical Distribution Function - Averaging17140329.3293333
Midmean - Empirical Distribution Function - Interpolation17140329.3293333
Midmean - Closest Observation17097313.6196774
Midmean - True Basic - Statistics Graphics Toolkit17140329.3293333
Midmean - MS Excel (old versions)17153924.72875
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')