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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 13:44:42 +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/t1291124636thyfp8wqq2harfu.htm/, Retrieved Mon, 29 Apr 2024 10:21:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103436, Retrieved Mon, 29 Apr 2024 10:21:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
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 invoer cent...] [2010-11-30 13:44:42] [9d72585f2b7b60ae977d4816136e1c95] [Current]
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Dataseries X:
14731798,37
16471559,62
15213975,95
17637387,4
17972385,83
16896235,55
16697955,94
19691579,52
15930700,75
17444615,98
17699369,88
15189796,81
15672722,75
17180794,3
17664893,45
17862884,98
16162288,88
17463628,82
16772112,17
19106861,48
16721314,25
18161267,85
18509941,2
17802737,97
16409869,75
17967742,04
20286602,27
19537280,81
18021889,62
20194317,23
19049596,62
20244720,94
21473302,24
19673603,19
21053177,29
20159479,84
18203628,31
21289464,94
20432335,71
17180395,07
15816786,32
15071819,75
14521120,61
15668789,39
14346884,11
13881008,13
15465943,69
14238232,92
13557713,21
16127590,29
16793894,2
16014007,43
16867867,15
16014583,21
15878594,85
18664899,14
17962530,06
17332692,2
19542066,35
17203555,19




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=103436&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=103436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103436&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 Mean17380113.2295250529.22151746669.3735969170699
Geometric Mean17273958.7921661
Harmonic Mean17168260.3231621
Quadratic Mean17486322.2099290
Winsorized Mean ( 1 / 20 )17382437.5231667248355.73318082869.990079554598
Winsorized Mean ( 2 / 20 )17386468.7611667243572.28851391771.3811446583065
Winsorized Mean ( 3 / 20 )17360859.2416667234978.40778633973.8827852534117
Winsorized Mean ( 4 / 20 )17362759.4456667230379.6030870175.3658709929675
Winsorized Mean ( 5 / 20 )17376825.8148333226051.98799869376.870926766341
Winsorized Mean ( 6 / 20 )17405787.5818333218510.50517824179.6565252898722
Winsorized Mean ( 7 / 20 )17415487.21215179.00886305480.9348797636843
Winsorized Mean ( 8 / 20 )17356324.386201723.87299535186.0400116668393
Winsorized Mean ( 9 / 20 )17391423.0975194616.69611800089.3624413753032
Winsorized Mean ( 10 / 20 )17403307.9075184758.59918649894.1948465951123
Winsorized Mean ( 11 / 20 )17403151.6745184471.81658540394.340436369276
Winsorized Mean ( 12 / 20 )17345880.5225163569.265523457106.046086757127
Winsorized Mean ( 13 / 20 )17346864.9843333159204.777226839108.959450127662
Winsorized Mean ( 14 / 20 )17269260.2823333141611.76972541121.947916587859
Winsorized Mean ( 15 / 20 )17251347.4673333131916.042396430130.775204849537
Winsorized Mean ( 16 / 20 )17169817.5713333119255.448385686143.975120665382
Winsorized Mean ( 17 / 20 )17189834.1136667112296.666908024153.075194366595
Winsorized Mean ( 18 / 20 )17158430.2216667104627.813040899163.994923748998
Winsorized Mean ( 19 / 20 )17221154.630333390089.9971115463191.155013680494
Winsorized Mean ( 20 / 20 )17240169.990333386756.9485392933198.718031011949
Trimmed Mean ( 1 / 20 )17375444.4537931240249.36072383672.3225418849959
Trimmed Mean ( 2 / 20 )17367951.8794643230250.94001391175.4305362593307
Trimmed Mean ( 3 / 20 )17357664.7229630221097.24477071378.506924593129
Trimmed Mean ( 4 / 20 )17356436.0619231213944.05889387181.1260483308533
Trimmed Mean ( 5 / 20 )17354539.0468206785.3430629283.9253826685358
Trimmed Mean ( 6 / 20 )17348967.3547917199210.57213459187.0885875628647
Trimmed Mean ( 7 / 20 )17336615.1315217191914.57255311690.3350636738308
Trimmed Mean ( 8 / 20 )17321250.4409091183420.64725755394.434572660662
Trimmed Mean ( 9 / 20 )17314987.2364286176414.30478477798.149564784741
Trimmed Mean ( 10 / 20 )17302247.92625169091.791723553102.324588023393
Trimmed Mean ( 11 / 20 )17286291.0871053162021.643304042106.691246518631
Trimmed Mean ( 12 / 20 )17268584.9375152302.644471533113.383355866337
Trimmed Mean ( 13 / 20 )17257217.9397059145446.964258277118.649557436355
Trimmed Mean ( 14 / 20 )17244288.0775136993.696215602125.876507853039
Trimmed Mean ( 15 / 20 )17240720.6196667130749.850486112131.860346727494
Trimmed Mean ( 16 / 20 )17239202.4985714124707.566381383138.237021207279
Trimmed Mean ( 17 / 20 )17249209.94119774.668431238144.013840037492
Trimmed Mean ( 18 / 20 )17257941.6791667114470.830168823150.762789557081
Trimmed Mean ( 19 / 20 )17273019.1727273108553.041069733159.120546071403
Trimmed Mean ( 20 / 20 )17281208.311105239.282392215164.208724329712
Median17268123.695
Midrange17515507.725
Midmean - Weighted Average at Xnp17198461.9141935
Midmean - Weighted Average at X(n+1)p17240720.6196667
Midmean - Empirical Distribution Function17198461.9141935
Midmean - Empirical Distribution Function - Averaging17240720.6196667
Midmean - Empirical Distribution Function - Interpolation17240720.6196667
Midmean - Closest Observation17198461.9141935
Midmean - True Basic - Statistics Graphics Toolkit17240720.6196667
Midmean - MS Excel (old versions)17244288.0775
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17380113.2295 & 250529.221517466 & 69.3735969170699 \tabularnewline
Geometric Mean & 17273958.7921661 &  &  \tabularnewline
Harmonic Mean & 17168260.3231621 &  &  \tabularnewline
Quadratic Mean & 17486322.2099290 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17382437.5231667 & 248355.733180828 & 69.990079554598 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17386468.7611667 & 243572.288513917 & 71.3811446583065 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17360859.2416667 & 234978.407786339 & 73.8827852534117 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17362759.4456667 & 230379.60308701 & 75.3658709929675 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17376825.8148333 & 226051.987998693 & 76.870926766341 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 17405787.5818333 & 218510.505178241 & 79.6565252898722 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 17415487.21 & 215179.008863054 & 80.9348797636843 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17356324.386 & 201723.872995351 & 86.0400116668393 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17391423.0975 & 194616.696118000 & 89.3624413753032 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17403307.9075 & 184758.599186498 & 94.1948465951123 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17403151.6745 & 184471.816585403 & 94.340436369276 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17345880.5225 & 163569.265523457 & 106.046086757127 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17346864.9843333 & 159204.777226839 & 108.959450127662 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17269260.2823333 & 141611.76972541 & 121.947916587859 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17251347.4673333 & 131916.042396430 & 130.775204849537 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 17169817.5713333 & 119255.448385686 & 143.975120665382 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17189834.1136667 & 112296.666908024 & 153.075194366595 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17158430.2216667 & 104627.813040899 & 163.994923748998 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17221154.6303333 & 90089.9971115463 & 191.155013680494 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 17240169.9903333 & 86756.9485392933 & 198.718031011949 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17375444.4537931 & 240249.360723836 & 72.3225418849959 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17367951.8794643 & 230250.940013911 & 75.4305362593307 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17357664.7229630 & 221097.244770713 & 78.506924593129 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17356436.0619231 & 213944.058893871 & 81.1260483308533 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17354539.0468 & 206785.34306292 & 83.9253826685358 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17348967.3547917 & 199210.572134591 & 87.0885875628647 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17336615.1315217 & 191914.572553116 & 90.3350636738308 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17321250.4409091 & 183420.647257553 & 94.434572660662 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17314987.2364286 & 176414.304784777 & 98.149564784741 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17302247.92625 & 169091.791723553 & 102.324588023393 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17286291.0871053 & 162021.643304042 & 106.691246518631 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17268584.9375 & 152302.644471533 & 113.383355866337 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17257217.9397059 & 145446.964258277 & 118.649557436355 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17244288.0775 & 136993.696215602 & 125.876507853039 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 17240720.6196667 & 130749.850486112 & 131.860346727494 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 17239202.4985714 & 124707.566381383 & 138.237021207279 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 17249209.94 & 119774.668431238 & 144.013840037492 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 17257941.6791667 & 114470.830168823 & 150.762789557081 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17273019.1727273 & 108553.041069733 & 159.120546071403 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17281208.311 & 105239.282392215 & 164.208724329712 \tabularnewline
Median & 17268123.695 &  &  \tabularnewline
Midrange & 17515507.725 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17198461.9141935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17240720.6196667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17198461.9141935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17240720.6196667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17240720.6196667 &  &  \tabularnewline
Midmean - Closest Observation & 17198461.9141935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17240720.6196667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17244288.0775 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103436&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]17380113.2295[/C][C]250529.221517466[/C][C]69.3735969170699[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17273958.7921661[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17168260.3231621[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17486322.2099290[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17382437.5231667[/C][C]248355.733180828[/C][C]69.990079554598[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17386468.7611667[/C][C]243572.288513917[/C][C]71.3811446583065[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17360859.2416667[/C][C]234978.407786339[/C][C]73.8827852534117[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17362759.4456667[/C][C]230379.60308701[/C][C]75.3658709929675[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17376825.8148333[/C][C]226051.987998693[/C][C]76.870926766341[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]17405787.5818333[/C][C]218510.505178241[/C][C]79.6565252898722[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]17415487.21[/C][C]215179.008863054[/C][C]80.9348797636843[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17356324.386[/C][C]201723.872995351[/C][C]86.0400116668393[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17391423.0975[/C][C]194616.696118000[/C][C]89.3624413753032[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17403307.9075[/C][C]184758.599186498[/C][C]94.1948465951123[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17403151.6745[/C][C]184471.816585403[/C][C]94.340436369276[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17345880.5225[/C][C]163569.265523457[/C][C]106.046086757127[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17346864.9843333[/C][C]159204.777226839[/C][C]108.959450127662[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17269260.2823333[/C][C]141611.76972541[/C][C]121.947916587859[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17251347.4673333[/C][C]131916.042396430[/C][C]130.775204849537[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]17169817.5713333[/C][C]119255.448385686[/C][C]143.975120665382[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17189834.1136667[/C][C]112296.666908024[/C][C]153.075194366595[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17158430.2216667[/C][C]104627.813040899[/C][C]163.994923748998[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17221154.6303333[/C][C]90089.9971115463[/C][C]191.155013680494[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]17240169.9903333[/C][C]86756.9485392933[/C][C]198.718031011949[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17375444.4537931[/C][C]240249.360723836[/C][C]72.3225418849959[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17367951.8794643[/C][C]230250.940013911[/C][C]75.4305362593307[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17357664.7229630[/C][C]221097.244770713[/C][C]78.506924593129[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17356436.0619231[/C][C]213944.058893871[/C][C]81.1260483308533[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17354539.0468[/C][C]206785.34306292[/C][C]83.9253826685358[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17348967.3547917[/C][C]199210.572134591[/C][C]87.0885875628647[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17336615.1315217[/C][C]191914.572553116[/C][C]90.3350636738308[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17321250.4409091[/C][C]183420.647257553[/C][C]94.434572660662[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17314987.2364286[/C][C]176414.304784777[/C][C]98.149564784741[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17302247.92625[/C][C]169091.791723553[/C][C]102.324588023393[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17286291.0871053[/C][C]162021.643304042[/C][C]106.691246518631[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17268584.9375[/C][C]152302.644471533[/C][C]113.383355866337[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17257217.9397059[/C][C]145446.964258277[/C][C]118.649557436355[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17244288.0775[/C][C]136993.696215602[/C][C]125.876507853039[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]17240720.6196667[/C][C]130749.850486112[/C][C]131.860346727494[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]17239202.4985714[/C][C]124707.566381383[/C][C]138.237021207279[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]17249209.94[/C][C]119774.668431238[/C][C]144.013840037492[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]17257941.6791667[/C][C]114470.830168823[/C][C]150.762789557081[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17273019.1727273[/C][C]108553.041069733[/C][C]159.120546071403[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17281208.311[/C][C]105239.282392215[/C][C]164.208724329712[/C][/ROW]
[ROW][C]Median[/C][C]17268123.695[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17515507.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17198461.9141935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17240720.6196667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17198461.9141935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17240720.6196667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17240720.6196667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17198461.9141935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17240720.6196667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17244288.0775[/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=103436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103436&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 Mean17380113.2295250529.22151746669.3735969170699
Geometric Mean17273958.7921661
Harmonic Mean17168260.3231621
Quadratic Mean17486322.2099290
Winsorized Mean ( 1 / 20 )17382437.5231667248355.73318082869.990079554598
Winsorized Mean ( 2 / 20 )17386468.7611667243572.28851391771.3811446583065
Winsorized Mean ( 3 / 20 )17360859.2416667234978.40778633973.8827852534117
Winsorized Mean ( 4 / 20 )17362759.4456667230379.6030870175.3658709929675
Winsorized Mean ( 5 / 20 )17376825.8148333226051.98799869376.870926766341
Winsorized Mean ( 6 / 20 )17405787.5818333218510.50517824179.6565252898722
Winsorized Mean ( 7 / 20 )17415487.21215179.00886305480.9348797636843
Winsorized Mean ( 8 / 20 )17356324.386201723.87299535186.0400116668393
Winsorized Mean ( 9 / 20 )17391423.0975194616.69611800089.3624413753032
Winsorized Mean ( 10 / 20 )17403307.9075184758.59918649894.1948465951123
Winsorized Mean ( 11 / 20 )17403151.6745184471.81658540394.340436369276
Winsorized Mean ( 12 / 20 )17345880.5225163569.265523457106.046086757127
Winsorized Mean ( 13 / 20 )17346864.9843333159204.777226839108.959450127662
Winsorized Mean ( 14 / 20 )17269260.2823333141611.76972541121.947916587859
Winsorized Mean ( 15 / 20 )17251347.4673333131916.042396430130.775204849537
Winsorized Mean ( 16 / 20 )17169817.5713333119255.448385686143.975120665382
Winsorized Mean ( 17 / 20 )17189834.1136667112296.666908024153.075194366595
Winsorized Mean ( 18 / 20 )17158430.2216667104627.813040899163.994923748998
Winsorized Mean ( 19 / 20 )17221154.630333390089.9971115463191.155013680494
Winsorized Mean ( 20 / 20 )17240169.990333386756.9485392933198.718031011949
Trimmed Mean ( 1 / 20 )17375444.4537931240249.36072383672.3225418849959
Trimmed Mean ( 2 / 20 )17367951.8794643230250.94001391175.4305362593307
Trimmed Mean ( 3 / 20 )17357664.7229630221097.24477071378.506924593129
Trimmed Mean ( 4 / 20 )17356436.0619231213944.05889387181.1260483308533
Trimmed Mean ( 5 / 20 )17354539.0468206785.3430629283.9253826685358
Trimmed Mean ( 6 / 20 )17348967.3547917199210.57213459187.0885875628647
Trimmed Mean ( 7 / 20 )17336615.1315217191914.57255311690.3350636738308
Trimmed Mean ( 8 / 20 )17321250.4409091183420.64725755394.434572660662
Trimmed Mean ( 9 / 20 )17314987.2364286176414.30478477798.149564784741
Trimmed Mean ( 10 / 20 )17302247.92625169091.791723553102.324588023393
Trimmed Mean ( 11 / 20 )17286291.0871053162021.643304042106.691246518631
Trimmed Mean ( 12 / 20 )17268584.9375152302.644471533113.383355866337
Trimmed Mean ( 13 / 20 )17257217.9397059145446.964258277118.649557436355
Trimmed Mean ( 14 / 20 )17244288.0775136993.696215602125.876507853039
Trimmed Mean ( 15 / 20 )17240720.6196667130749.850486112131.860346727494
Trimmed Mean ( 16 / 20 )17239202.4985714124707.566381383138.237021207279
Trimmed Mean ( 17 / 20 )17249209.94119774.668431238144.013840037492
Trimmed Mean ( 18 / 20 )17257941.6791667114470.830168823150.762789557081
Trimmed Mean ( 19 / 20 )17273019.1727273108553.041069733159.120546071403
Trimmed Mean ( 20 / 20 )17281208.311105239.282392215164.208724329712
Median17268123.695
Midrange17515507.725
Midmean - Weighted Average at Xnp17198461.9141935
Midmean - Weighted Average at X(n+1)p17240720.6196667
Midmean - Empirical Distribution Function17198461.9141935
Midmean - Empirical Distribution Function - Averaging17240720.6196667
Midmean - Empirical Distribution Function - Interpolation17240720.6196667
Midmean - Closest Observation17198461.9141935
Midmean - True Basic - Statistics Graphics Toolkit17240720.6196667
Midmean - MS Excel (old versions)17244288.0775
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')