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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 29 May 2012 04:37:07 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/29/t1338280673zyrmnwxbwkzebo5.htm/, Retrieved Mon, 29 Apr 2024 20:21:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167945, Retrieved Mon, 29 Apr 2024 20:21:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [Opgave 2 stap 2] [2012-05-29 06:48:13] [46972ec2bfa5b295f8450f947ab1f239]
- RMPD    [Central Tendency] [Opgave 5 Oefening...] [2012-05-29 08:37:07] [7d6606cca1b3596736d7d387043cb02b] [Current]
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Dataseries X:
26,73
26,85
27,01
27,09
27,11
27,16
27,13
27,19
27,49
27,63
27,72
27,77
27,81
27,92
28,07
28,14
28,17
28,2
28,21
28,2
28,19
28,24
28,25
28,26
28,33
28,67
28,81
28,99
29,16
29,25
29,25
29,38
29,48
29,65
29,69
29,73
29,81
30,05
30,29
30,37
30,5
30,67
30,76
30,84
30,86
31,09
31,2
31,19
31,18
31,31
31,39
31,39
31,37
31,36
31,37
31,35
31,34
31,47
31,48
31,54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167945&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167945&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167945&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean29.31850.203301399502187144.211992990656
Geometric Mean29.2768753347943
Harmonic Mean29.2352677206349
Quadratic Mean29.360057873467
Winsorized Mean ( 1 / 20 )29.31950.202696152469623144.647540877195
Winsorized Mean ( 2 / 20 )29.32450.201566243614777145.483189417586
Winsorized Mean ( 3 / 20 )29.32450.200087611460298146.558299067
Winsorized Mean ( 4 / 20 )29.32583333333330.199836132256354146.749404135352
Winsorized Mean ( 5 / 20 )29.32583333333330.19923303388012147.193629300344
Winsorized Mean ( 6 / 20 )29.32883333333330.198675286801573147.621950397009
Winsorized Mean ( 7 / 20 )29.33116666666670.197827478863774148.26639269292
Winsorized Mean ( 8 / 20 )29.36983333333330.19057547278867154.111297238662
Winsorized Mean ( 9 / 20 )29.38933333333330.186879045849923157.263930793691
Winsorized Mean ( 10 / 20 )29.39933333333330.183636349482405160.095391877468
Winsorized Mean ( 11 / 20 )29.38833333333330.178711042005915164.446096914149
Winsorized Mean ( 12 / 20 )29.39433333333330.177147097526204165.931780671626
Winsorized Mean ( 13 / 20 )29.4160.173222563475937169.816214526153
Winsorized Mean ( 14 / 20 )29.430.164599840050447178.797257585306
Winsorized Mean ( 15 / 20 )29.390.152540260500126192.670445845841
Winsorized Mean ( 16 / 20 )29.39266666666670.15056407436584195.216998413901
Winsorized Mean ( 17 / 20 )29.37566666666670.14611762282039201.041230343418
Winsorized Mean ( 18 / 20 )29.35166666666670.141402612004632207.575137761282
Winsorized Mean ( 19 / 20 )29.29783333333330.133022255405421220.24760626739
Winsorized Mean ( 20 / 20 )29.25783333333330.125991680217356232.220359970268
Trimmed Mean ( 1 / 20 )29.32482758620690.201833435574056145.292218322504
Trimmed Mean ( 2 / 20 )29.33053571428570.200570844374681146.235290606316
Trimmed Mean ( 3 / 20 )29.33388888888890.199529043099741147.015634582207
Trimmed Mean ( 4 / 20 )29.33750.198674126073429147.666435382517
Trimmed Mean ( 5 / 20 )29.3410.197435652136826148.610444377423
Trimmed Mean ( 6 / 20 )29.34479166666670.195808242601947149.86494580987
Trimmed Mean ( 7 / 20 )29.34826086956520.193645002242531151.557027187348
Trimmed Mean ( 8 / 20 )29.35159090909090.190853192636977153.7914587833
Trimmed Mean ( 9 / 20 )29.34833333333330.188915210185857155.351881431147
Trimmed Mean ( 10 / 20 )29.34150.186971665891262156.930195065301
Trimmed Mean ( 11 / 20 )29.33236842105260.184821791145671158.706223109448
Trimmed Mean ( 12 / 20 )29.32388888888890.182782843563707160.430204045208
Trimmed Mean ( 13 / 20 )29.31352941176470.179914260800481162.930549703742
Trimmed Mean ( 14 / 20 )29.298750.176450069470457166.045556615128
Trimmed Mean ( 15 / 20 )29.280.173392783792361168.865158973761
Trimmed Mean ( 16 / 20 )29.26428571428570.171954550236214170.186166484605
Trimmed Mean ( 17 / 20 )29.24576923076920.169453577102696172.588680220336
Trimmed Mean ( 18 / 20 )29.22666666666670.166202978167333175.849235609011
Trimmed Mean ( 19 / 20 )29.20772727272730.161854688474048180.456479500812
Trimmed Mean ( 20 / 20 )29.19350.157392026481649185.482712514689
Median29.25
Midrange29.135
Midmean - Weighted Average at Xnp29.2409677419355
Midmean - Weighted Average at X(n+1)p29.28
Midmean - Empirical Distribution Function29.2409677419355
Midmean - Empirical Distribution Function - Averaging29.28
Midmean - Empirical Distribution Function - Interpolation29.28
Midmean - Closest Observation29.2409677419355
Midmean - True Basic - Statistics Graphics Toolkit29.28
Midmean - MS Excel (old versions)29.29875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 29.3185 & 0.203301399502187 & 144.211992990656 \tabularnewline
Geometric Mean & 29.2768753347943 &  &  \tabularnewline
Harmonic Mean & 29.2352677206349 &  &  \tabularnewline
Quadratic Mean & 29.360057873467 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 29.3195 & 0.202696152469623 & 144.647540877195 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 29.3245 & 0.201566243614777 & 145.483189417586 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 29.3245 & 0.200087611460298 & 146.558299067 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 29.3258333333333 & 0.199836132256354 & 146.749404135352 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 29.3258333333333 & 0.19923303388012 & 147.193629300344 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 29.3288333333333 & 0.198675286801573 & 147.621950397009 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 29.3311666666667 & 0.197827478863774 & 148.26639269292 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 29.3698333333333 & 0.19057547278867 & 154.111297238662 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 29.3893333333333 & 0.186879045849923 & 157.263930793691 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 29.3993333333333 & 0.183636349482405 & 160.095391877468 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 29.3883333333333 & 0.178711042005915 & 164.446096914149 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 29.3943333333333 & 0.177147097526204 & 165.931780671626 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 29.416 & 0.173222563475937 & 169.816214526153 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 29.43 & 0.164599840050447 & 178.797257585306 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 29.39 & 0.152540260500126 & 192.670445845841 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 29.3926666666667 & 0.15056407436584 & 195.216998413901 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 29.3756666666667 & 0.14611762282039 & 201.041230343418 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 29.3516666666667 & 0.141402612004632 & 207.575137761282 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 29.2978333333333 & 0.133022255405421 & 220.24760626739 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 29.2578333333333 & 0.125991680217356 & 232.220359970268 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 29.3248275862069 & 0.201833435574056 & 145.292218322504 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 29.3305357142857 & 0.200570844374681 & 146.235290606316 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 29.3338888888889 & 0.199529043099741 & 147.015634582207 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 29.3375 & 0.198674126073429 & 147.666435382517 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 29.341 & 0.197435652136826 & 148.610444377423 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 29.3447916666667 & 0.195808242601947 & 149.86494580987 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 29.3482608695652 & 0.193645002242531 & 151.557027187348 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 29.3515909090909 & 0.190853192636977 & 153.7914587833 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 29.3483333333333 & 0.188915210185857 & 155.351881431147 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 29.3415 & 0.186971665891262 & 156.930195065301 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 29.3323684210526 & 0.184821791145671 & 158.706223109448 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 29.3238888888889 & 0.182782843563707 & 160.430204045208 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 29.3135294117647 & 0.179914260800481 & 162.930549703742 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 29.29875 & 0.176450069470457 & 166.045556615128 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 29.28 & 0.173392783792361 & 168.865158973761 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 29.2642857142857 & 0.171954550236214 & 170.186166484605 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 29.2457692307692 & 0.169453577102696 & 172.588680220336 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 29.2266666666667 & 0.166202978167333 & 175.849235609011 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 29.2077272727273 & 0.161854688474048 & 180.456479500812 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 29.1935 & 0.157392026481649 & 185.482712514689 \tabularnewline
Median & 29.25 &  &  \tabularnewline
Midrange & 29.135 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 29.2409677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 29.28 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 29.2409677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 29.28 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 29.28 &  &  \tabularnewline
Midmean - Closest Observation & 29.2409677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 29.28 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 29.29875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167945&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]29.3185[/C][C]0.203301399502187[/C][C]144.211992990656[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]29.2768753347943[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]29.2352677206349[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]29.360057873467[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]29.3195[/C][C]0.202696152469623[/C][C]144.647540877195[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]29.3245[/C][C]0.201566243614777[/C][C]145.483189417586[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]29.3245[/C][C]0.200087611460298[/C][C]146.558299067[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]29.3258333333333[/C][C]0.199836132256354[/C][C]146.749404135352[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]29.3258333333333[/C][C]0.19923303388012[/C][C]147.193629300344[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]29.3288333333333[/C][C]0.198675286801573[/C][C]147.621950397009[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]29.3311666666667[/C][C]0.197827478863774[/C][C]148.26639269292[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]29.3698333333333[/C][C]0.19057547278867[/C][C]154.111297238662[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]29.3893333333333[/C][C]0.186879045849923[/C][C]157.263930793691[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]29.3993333333333[/C][C]0.183636349482405[/C][C]160.095391877468[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]29.3883333333333[/C][C]0.178711042005915[/C][C]164.446096914149[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]29.3943333333333[/C][C]0.177147097526204[/C][C]165.931780671626[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]29.416[/C][C]0.173222563475937[/C][C]169.816214526153[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]29.43[/C][C]0.164599840050447[/C][C]178.797257585306[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]29.39[/C][C]0.152540260500126[/C][C]192.670445845841[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]29.3926666666667[/C][C]0.15056407436584[/C][C]195.216998413901[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]29.3756666666667[/C][C]0.14611762282039[/C][C]201.041230343418[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]29.3516666666667[/C][C]0.141402612004632[/C][C]207.575137761282[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]29.2978333333333[/C][C]0.133022255405421[/C][C]220.24760626739[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]29.2578333333333[/C][C]0.125991680217356[/C][C]232.220359970268[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]29.3248275862069[/C][C]0.201833435574056[/C][C]145.292218322504[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]29.3305357142857[/C][C]0.200570844374681[/C][C]146.235290606316[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]29.3338888888889[/C][C]0.199529043099741[/C][C]147.015634582207[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]29.3375[/C][C]0.198674126073429[/C][C]147.666435382517[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]29.341[/C][C]0.197435652136826[/C][C]148.610444377423[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]29.3447916666667[/C][C]0.195808242601947[/C][C]149.86494580987[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]29.3482608695652[/C][C]0.193645002242531[/C][C]151.557027187348[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]29.3515909090909[/C][C]0.190853192636977[/C][C]153.7914587833[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]29.3483333333333[/C][C]0.188915210185857[/C][C]155.351881431147[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]29.3415[/C][C]0.186971665891262[/C][C]156.930195065301[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]29.3323684210526[/C][C]0.184821791145671[/C][C]158.706223109448[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]29.3238888888889[/C][C]0.182782843563707[/C][C]160.430204045208[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]29.3135294117647[/C][C]0.179914260800481[/C][C]162.930549703742[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]29.29875[/C][C]0.176450069470457[/C][C]166.045556615128[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]29.28[/C][C]0.173392783792361[/C][C]168.865158973761[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]29.2642857142857[/C][C]0.171954550236214[/C][C]170.186166484605[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]29.2457692307692[/C][C]0.169453577102696[/C][C]172.588680220336[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]29.2266666666667[/C][C]0.166202978167333[/C][C]175.849235609011[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]29.2077272727273[/C][C]0.161854688474048[/C][C]180.456479500812[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]29.1935[/C][C]0.157392026481649[/C][C]185.482712514689[/C][/ROW]
[ROW][C]Median[/C][C]29.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]29.135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]29.2409677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]29.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]29.2409677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]29.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]29.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]29.2409677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]29.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]29.29875[/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=167945&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167945&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 Mean29.31850.203301399502187144.211992990656
Geometric Mean29.2768753347943
Harmonic Mean29.2352677206349
Quadratic Mean29.360057873467
Winsorized Mean ( 1 / 20 )29.31950.202696152469623144.647540877195
Winsorized Mean ( 2 / 20 )29.32450.201566243614777145.483189417586
Winsorized Mean ( 3 / 20 )29.32450.200087611460298146.558299067
Winsorized Mean ( 4 / 20 )29.32583333333330.199836132256354146.749404135352
Winsorized Mean ( 5 / 20 )29.32583333333330.19923303388012147.193629300344
Winsorized Mean ( 6 / 20 )29.32883333333330.198675286801573147.621950397009
Winsorized Mean ( 7 / 20 )29.33116666666670.197827478863774148.26639269292
Winsorized Mean ( 8 / 20 )29.36983333333330.19057547278867154.111297238662
Winsorized Mean ( 9 / 20 )29.38933333333330.186879045849923157.263930793691
Winsorized Mean ( 10 / 20 )29.39933333333330.183636349482405160.095391877468
Winsorized Mean ( 11 / 20 )29.38833333333330.178711042005915164.446096914149
Winsorized Mean ( 12 / 20 )29.39433333333330.177147097526204165.931780671626
Winsorized Mean ( 13 / 20 )29.4160.173222563475937169.816214526153
Winsorized Mean ( 14 / 20 )29.430.164599840050447178.797257585306
Winsorized Mean ( 15 / 20 )29.390.152540260500126192.670445845841
Winsorized Mean ( 16 / 20 )29.39266666666670.15056407436584195.216998413901
Winsorized Mean ( 17 / 20 )29.37566666666670.14611762282039201.041230343418
Winsorized Mean ( 18 / 20 )29.35166666666670.141402612004632207.575137761282
Winsorized Mean ( 19 / 20 )29.29783333333330.133022255405421220.24760626739
Winsorized Mean ( 20 / 20 )29.25783333333330.125991680217356232.220359970268
Trimmed Mean ( 1 / 20 )29.32482758620690.201833435574056145.292218322504
Trimmed Mean ( 2 / 20 )29.33053571428570.200570844374681146.235290606316
Trimmed Mean ( 3 / 20 )29.33388888888890.199529043099741147.015634582207
Trimmed Mean ( 4 / 20 )29.33750.198674126073429147.666435382517
Trimmed Mean ( 5 / 20 )29.3410.197435652136826148.610444377423
Trimmed Mean ( 6 / 20 )29.34479166666670.195808242601947149.86494580987
Trimmed Mean ( 7 / 20 )29.34826086956520.193645002242531151.557027187348
Trimmed Mean ( 8 / 20 )29.35159090909090.190853192636977153.7914587833
Trimmed Mean ( 9 / 20 )29.34833333333330.188915210185857155.351881431147
Trimmed Mean ( 10 / 20 )29.34150.186971665891262156.930195065301
Trimmed Mean ( 11 / 20 )29.33236842105260.184821791145671158.706223109448
Trimmed Mean ( 12 / 20 )29.32388888888890.182782843563707160.430204045208
Trimmed Mean ( 13 / 20 )29.31352941176470.179914260800481162.930549703742
Trimmed Mean ( 14 / 20 )29.298750.176450069470457166.045556615128
Trimmed Mean ( 15 / 20 )29.280.173392783792361168.865158973761
Trimmed Mean ( 16 / 20 )29.26428571428570.171954550236214170.186166484605
Trimmed Mean ( 17 / 20 )29.24576923076920.169453577102696172.588680220336
Trimmed Mean ( 18 / 20 )29.22666666666670.166202978167333175.849235609011
Trimmed Mean ( 19 / 20 )29.20772727272730.161854688474048180.456479500812
Trimmed Mean ( 20 / 20 )29.19350.157392026481649185.482712514689
Median29.25
Midrange29.135
Midmean - Weighted Average at Xnp29.2409677419355
Midmean - Weighted Average at X(n+1)p29.28
Midmean - Empirical Distribution Function29.2409677419355
Midmean - Empirical Distribution Function - Averaging29.28
Midmean - Empirical Distribution Function - Interpolation29.28
Midmean - Closest Observation29.2409677419355
Midmean - True Basic - Statistics Graphics Toolkit29.28
Midmean - MS Excel (old versions)29.29875
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')