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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Oct 2009 14:05:36 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t1256242004h28vv6z7sy3fdfg.htm/, Retrieved Thu, 02 May 2024 21:45:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49815, Retrieved Thu, 02 May 2024 21:45:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsRobustness of central tendency maandelijkse bezoekers VS
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [KDGP1W52 ] [2009-10-22 20:05:36] [923770d86edf74ed976a539eae527e37] [Current]
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Dataseries X:
 2357402 
 2199181 
 2603060 
 2629720 
 2638792 
 2717481 
 3810804 
 3871664 
 2998364 
 2923432 
 2712359 
 2996099 
 2395029 
 2483862 
 3120231 
 3360606 
 3177203 
 3062783 
 4242509 
 4026394 
 3192481 
 3118695 
 2782482 
 3209833 
 2630190 
 2592882 
 3785309 
 3231539 
 3421369 
 3312134 
 4647303 
 4289177 
 3463853 
 3304422 
 3006121 
 3464238 
 2921118 
 2624018 
 3500718 
 3939351 
 3467672 
 3343628 
 4852445 
 4597807 
 3653145 
 3572079 
 3334861 
 3695369 
 3075704 
 2852998 
 3942704 
 4004560 
 3822145 
 3760085 
 5267816 
 5271333 
 4144142 
 4109749 
 3896808 
 4211074 
 3402318 
 3279817 
 4706628 
 4079499 
 4344530 
 4048625 
 5394915 
 5611967 
 4145481 
 4025610 
 3552218 
 3910443 




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=49815&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=49815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49815&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 Mean3557533.0972222289456.14417547339.7684600651234
Geometric Mean3480484.75860473
Harmonic Mean3406034.53921403
Quadratic Mean3636511.00104404
Winsorized Mean ( 1 / 24 )355671688079.289000627340.3808436734164
Winsorized Mean ( 2 / 24 )3554328.3611111186898.48461139940.9020753009180
Winsorized Mean ( 3 / 24 )3557883.1944444486184.952166411941.2819535778663
Winsorized Mean ( 4 / 24 )3540863.6944444479204.273595760144.7054626435459
Winsorized Mean ( 5 / 24 )3531444.3194444476811.260058189745.9756071801079
Winsorized Mean ( 6 / 24 )3528247.0694444475466.160715379346.7527039403956
Winsorized Mean ( 7 / 24 )3523989.3194444474380.603947666747.3777992166329
Winsorized Mean ( 8 / 24 )3495899.6527777869059.317480466250.6216942234712
Winsorized Mean ( 9 / 24 )3490055.7777777867694.973260078951.5556120299989
Winsorized Mean ( 10 / 24 )3493791.7564856.329972835253.8697109667377
Winsorized Mean ( 11 / 24 )3489771.7083333363951.421755940654.5691028051172
Winsorized Mean ( 12 / 24 )3489673.0416666760431.770880798257.7456690546112
Winsorized Mean ( 13 / 24 )3502163.3333333358346.821424703260.0232068828786
Winsorized Mean ( 14 / 24 )3508721.3611111155286.02118713563.464891952246
Winsorized Mean ( 15 / 24 )3502901.3611111154259.485430743364.5583225366597
Winsorized Mean ( 16 / 24 )3512188.6944444450866.129408999369.0476892040278
Winsorized Mean ( 17 / 24 )3507474.550016.18964775270.126783441562
Winsorized Mean ( 18 / 24 )3509217.7549710.304581973170.5933664963417
Winsorized Mean ( 19 / 24 )3518615.3611111146805.398447912875.1754173191536
Winsorized Mean ( 20 / 24 )3505022.3055555643846.083515851779.9392334389086
Winsorized Mean ( 21 / 24 )3516583.3888888942006.396065604283.7154271315446
Winsorized Mean ( 22 / 24 )3508219.7222222240702.660430427986.191410711807
Winsorized Mean ( 23 / 24 )3522063.4861111137698.690177342393.426680596663
Winsorized Mean ( 24 / 24 )3518774.8194444435876.955689815598.078968847497
Trimmed Mean ( 1 / 24 )3547589.0714285784925.41693301341.7729956418915
Trimmed Mean ( 2 / 24 )3537925.2647058881146.346588973243.5993167089379
Trimmed Mean ( 3 / 24 )3528978.1212121277375.10465203345.6087023995954
Trimmed Mean ( 4 / 24 )3518138.7187573125.527152785448.1109518896096
Trimmed Mean ( 5 / 24 )3511541.1451612970731.82808715249.6458417677903
Trimmed Mean ( 6 / 24 )3506764.3833333368614.978848600151.107854905429
Trimmed Mean ( 7 / 24 )3502319.6896551766420.808572040952.7292540538182
Trimmed Mean ( 8 / 24 )3498339.5535714364017.928525221354.6462472960708
Trimmed Mean ( 9 / 24 )3498746.2037037062425.408411545656.0468292115588
Trimmed Mean ( 10 / 24 )3500083.1923076960753.883907532657.6108549312636
Trimmed Mean ( 11 / 24 )3500989.1659305.080255162959.0335456075066
Trimmed Mean ( 12 / 24 )3502518.812557653.045259299160.7516705621905
Trimmed Mean ( 13 / 24 )3504194.3478260956323.240571135762.2157800632995
Trimmed Mean ( 14 / 24 )350445055046.990401877963.6628810115738
Trimmed Mean ( 15 / 24 )3503926.9761904854027.186070090164.8548856800499
Trimmed Mean ( 16 / 24 )3504050.0552855.336262449466.2951046721354
Trimmed Mean ( 17 / 24 )3503086.2631578952011.7314183167.3518486624477
Trimmed Mean ( 18 / 24 )350257050981.902041367168.7022229409563
Trimmed Mean ( 19 / 24 )3501787.9117647149551.295154255270.6699572809045
Trimmed Mean ( 20 / 24 )3499795.187548248.026239097372.5375825770873
Trimmed Mean ( 21 / 24 )3499167.9333333347139.017988760474.2308194491379
Trimmed Mean ( 22 / 24 )3497035.4285714345926.205868487376.1446621257027
Trimmed Mean ( 23 / 24 )3495627.6153846244404.238528219478.722836631082
Trimmed Mean ( 24 / 24 )3492179.4583333342965.341778222781.278987057968
Median3464045.5
Midrange3905574
Midmean - Weighted Average at Xnp3488942.81081081
Midmean - Weighted Average at X(n+1)p3502570
Midmean - Empirical Distribution Function3488942.81081081
Midmean - Empirical Distribution Function - Averaging3502570
Midmean - Empirical Distribution Function - Interpolation3502570
Midmean - Closest Observation3488942.81081081
Midmean - True Basic - Statistics Graphics Toolkit3502570
Midmean - MS Excel (old versions)3503086.26315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3557533.09722222 & 89456.144175473 & 39.7684600651234 \tabularnewline
Geometric Mean & 3480484.75860473 &  &  \tabularnewline
Harmonic Mean & 3406034.53921403 &  &  \tabularnewline
Quadratic Mean & 3636511.00104404 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3556716 & 88079.2890006273 & 40.3808436734164 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3554328.36111111 & 86898.484611399 & 40.9020753009180 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3557883.19444444 & 86184.9521664119 & 41.2819535778663 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3540863.69444444 & 79204.2735957601 & 44.7054626435459 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3531444.31944444 & 76811.2600581897 & 45.9756071801079 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3528247.06944444 & 75466.1607153793 & 46.7527039403956 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3523989.31944444 & 74380.6039476667 & 47.3777992166329 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3495899.65277778 & 69059.3174804662 & 50.6216942234712 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3490055.77777778 & 67694.9732600789 & 51.5556120299989 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3493791.75 & 64856.3299728352 & 53.8697109667377 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3489771.70833333 & 63951.4217559406 & 54.5691028051172 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3489673.04166667 & 60431.7708807982 & 57.7456690546112 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3502163.33333333 & 58346.8214247032 & 60.0232068828786 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3508721.36111111 & 55286.021187135 & 63.464891952246 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3502901.36111111 & 54259.4854307433 & 64.5583225366597 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3512188.69444444 & 50866.1294089993 & 69.0476892040278 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3507474.5 & 50016.189647752 & 70.126783441562 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3509217.75 & 49710.3045819731 & 70.5933664963417 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3518615.36111111 & 46805.3984479128 & 75.1754173191536 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3505022.30555556 & 43846.0835158517 & 79.9392334389086 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3516583.38888889 & 42006.3960656042 & 83.7154271315446 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3508219.72222222 & 40702.6604304279 & 86.191410711807 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3522063.48611111 & 37698.6901773423 & 93.426680596663 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3518774.81944444 & 35876.9556898155 & 98.078968847497 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3547589.07142857 & 84925.416933013 & 41.7729956418915 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3537925.26470588 & 81146.3465889732 & 43.5993167089379 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3528978.12121212 & 77375.104652033 & 45.6087023995954 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3518138.71875 & 73125.5271527854 & 48.1109518896096 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3511541.14516129 & 70731.828087152 & 49.6458417677903 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3506764.38333333 & 68614.9788486001 & 51.107854905429 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3502319.68965517 & 66420.8085720409 & 52.7292540538182 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3498339.55357143 & 64017.9285252213 & 54.6462472960708 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3498746.20370370 & 62425.4084115456 & 56.0468292115588 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3500083.19230769 & 60753.8839075326 & 57.6108549312636 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3500989.16 & 59305.0802551629 & 59.0335456075066 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3502518.8125 & 57653.0452592991 & 60.7516705621905 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3504194.34782609 & 56323.2405711357 & 62.2157800632995 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3504450 & 55046.9904018779 & 63.6628810115738 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3503926.97619048 & 54027.1860700901 & 64.8548856800499 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3504050.05 & 52855.3362624494 & 66.2951046721354 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3503086.26315789 & 52011.73141831 & 67.3518486624477 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3502570 & 50981.9020413671 & 68.7022229409563 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3501787.91176471 & 49551.2951542552 & 70.6699572809045 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3499795.1875 & 48248.0262390973 & 72.5375825770873 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3499167.93333333 & 47139.0179887604 & 74.2308194491379 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3497035.42857143 & 45926.2058684873 & 76.1446621257027 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3495627.61538462 & 44404.2385282194 & 78.722836631082 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3492179.45833333 & 42965.3417782227 & 81.278987057968 \tabularnewline
Median & 3464045.5 &  &  \tabularnewline
Midrange & 3905574 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3488942.81081081 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3502570 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3488942.81081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3502570 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3502570 &  &  \tabularnewline
Midmean - Closest Observation & 3488942.81081081 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3502570 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3503086.26315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49815&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]3557533.09722222[/C][C]89456.144175473[/C][C]39.7684600651234[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3480484.75860473[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3406034.53921403[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3636511.00104404[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3556716[/C][C]88079.2890006273[/C][C]40.3808436734164[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3554328.36111111[/C][C]86898.484611399[/C][C]40.9020753009180[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3557883.19444444[/C][C]86184.9521664119[/C][C]41.2819535778663[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3540863.69444444[/C][C]79204.2735957601[/C][C]44.7054626435459[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3531444.31944444[/C][C]76811.2600581897[/C][C]45.9756071801079[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3528247.06944444[/C][C]75466.1607153793[/C][C]46.7527039403956[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3523989.31944444[/C][C]74380.6039476667[/C][C]47.3777992166329[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3495899.65277778[/C][C]69059.3174804662[/C][C]50.6216942234712[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3490055.77777778[/C][C]67694.9732600789[/C][C]51.5556120299989[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3493791.75[/C][C]64856.3299728352[/C][C]53.8697109667377[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3489771.70833333[/C][C]63951.4217559406[/C][C]54.5691028051172[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3489673.04166667[/C][C]60431.7708807982[/C][C]57.7456690546112[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3502163.33333333[/C][C]58346.8214247032[/C][C]60.0232068828786[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3508721.36111111[/C][C]55286.021187135[/C][C]63.464891952246[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3502901.36111111[/C][C]54259.4854307433[/C][C]64.5583225366597[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3512188.69444444[/C][C]50866.1294089993[/C][C]69.0476892040278[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3507474.5[/C][C]50016.189647752[/C][C]70.126783441562[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3509217.75[/C][C]49710.3045819731[/C][C]70.5933664963417[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3518615.36111111[/C][C]46805.3984479128[/C][C]75.1754173191536[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3505022.30555556[/C][C]43846.0835158517[/C][C]79.9392334389086[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3516583.38888889[/C][C]42006.3960656042[/C][C]83.7154271315446[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3508219.72222222[/C][C]40702.6604304279[/C][C]86.191410711807[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3522063.48611111[/C][C]37698.6901773423[/C][C]93.426680596663[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3518774.81944444[/C][C]35876.9556898155[/C][C]98.078968847497[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3547589.07142857[/C][C]84925.416933013[/C][C]41.7729956418915[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3537925.26470588[/C][C]81146.3465889732[/C][C]43.5993167089379[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3528978.12121212[/C][C]77375.104652033[/C][C]45.6087023995954[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3518138.71875[/C][C]73125.5271527854[/C][C]48.1109518896096[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3511541.14516129[/C][C]70731.828087152[/C][C]49.6458417677903[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3506764.38333333[/C][C]68614.9788486001[/C][C]51.107854905429[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3502319.68965517[/C][C]66420.8085720409[/C][C]52.7292540538182[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3498339.55357143[/C][C]64017.9285252213[/C][C]54.6462472960708[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3498746.20370370[/C][C]62425.4084115456[/C][C]56.0468292115588[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3500083.19230769[/C][C]60753.8839075326[/C][C]57.6108549312636[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3500989.16[/C][C]59305.0802551629[/C][C]59.0335456075066[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3502518.8125[/C][C]57653.0452592991[/C][C]60.7516705621905[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3504194.34782609[/C][C]56323.2405711357[/C][C]62.2157800632995[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3504450[/C][C]55046.9904018779[/C][C]63.6628810115738[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3503926.97619048[/C][C]54027.1860700901[/C][C]64.8548856800499[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3504050.05[/C][C]52855.3362624494[/C][C]66.2951046721354[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3503086.26315789[/C][C]52011.73141831[/C][C]67.3518486624477[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3502570[/C][C]50981.9020413671[/C][C]68.7022229409563[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3501787.91176471[/C][C]49551.2951542552[/C][C]70.6699572809045[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3499795.1875[/C][C]48248.0262390973[/C][C]72.5375825770873[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3499167.93333333[/C][C]47139.0179887604[/C][C]74.2308194491379[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3497035.42857143[/C][C]45926.2058684873[/C][C]76.1446621257027[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3495627.61538462[/C][C]44404.2385282194[/C][C]78.722836631082[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3492179.45833333[/C][C]42965.3417782227[/C][C]81.278987057968[/C][/ROW]
[ROW][C]Median[/C][C]3464045.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3905574[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3488942.81081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3502570[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3488942.81081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3502570[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3502570[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3488942.81081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3502570[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3503086.26315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49815&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 Mean3557533.0972222289456.14417547339.7684600651234
Geometric Mean3480484.75860473
Harmonic Mean3406034.53921403
Quadratic Mean3636511.00104404
Winsorized Mean ( 1 / 24 )355671688079.289000627340.3808436734164
Winsorized Mean ( 2 / 24 )3554328.3611111186898.48461139940.9020753009180
Winsorized Mean ( 3 / 24 )3557883.1944444486184.952166411941.2819535778663
Winsorized Mean ( 4 / 24 )3540863.6944444479204.273595760144.7054626435459
Winsorized Mean ( 5 / 24 )3531444.3194444476811.260058189745.9756071801079
Winsorized Mean ( 6 / 24 )3528247.0694444475466.160715379346.7527039403956
Winsorized Mean ( 7 / 24 )3523989.3194444474380.603947666747.3777992166329
Winsorized Mean ( 8 / 24 )3495899.6527777869059.317480466250.6216942234712
Winsorized Mean ( 9 / 24 )3490055.7777777867694.973260078951.5556120299989
Winsorized Mean ( 10 / 24 )3493791.7564856.329972835253.8697109667377
Winsorized Mean ( 11 / 24 )3489771.7083333363951.421755940654.5691028051172
Winsorized Mean ( 12 / 24 )3489673.0416666760431.770880798257.7456690546112
Winsorized Mean ( 13 / 24 )3502163.3333333358346.821424703260.0232068828786
Winsorized Mean ( 14 / 24 )3508721.3611111155286.02118713563.464891952246
Winsorized Mean ( 15 / 24 )3502901.3611111154259.485430743364.5583225366597
Winsorized Mean ( 16 / 24 )3512188.6944444450866.129408999369.0476892040278
Winsorized Mean ( 17 / 24 )3507474.550016.18964775270.126783441562
Winsorized Mean ( 18 / 24 )3509217.7549710.304581973170.5933664963417
Winsorized Mean ( 19 / 24 )3518615.3611111146805.398447912875.1754173191536
Winsorized Mean ( 20 / 24 )3505022.3055555643846.083515851779.9392334389086
Winsorized Mean ( 21 / 24 )3516583.3888888942006.396065604283.7154271315446
Winsorized Mean ( 22 / 24 )3508219.7222222240702.660430427986.191410711807
Winsorized Mean ( 23 / 24 )3522063.4861111137698.690177342393.426680596663
Winsorized Mean ( 24 / 24 )3518774.8194444435876.955689815598.078968847497
Trimmed Mean ( 1 / 24 )3547589.0714285784925.41693301341.7729956418915
Trimmed Mean ( 2 / 24 )3537925.2647058881146.346588973243.5993167089379
Trimmed Mean ( 3 / 24 )3528978.1212121277375.10465203345.6087023995954
Trimmed Mean ( 4 / 24 )3518138.7187573125.527152785448.1109518896096
Trimmed Mean ( 5 / 24 )3511541.1451612970731.82808715249.6458417677903
Trimmed Mean ( 6 / 24 )3506764.3833333368614.978848600151.107854905429
Trimmed Mean ( 7 / 24 )3502319.6896551766420.808572040952.7292540538182
Trimmed Mean ( 8 / 24 )3498339.5535714364017.928525221354.6462472960708
Trimmed Mean ( 9 / 24 )3498746.2037037062425.408411545656.0468292115588
Trimmed Mean ( 10 / 24 )3500083.1923076960753.883907532657.6108549312636
Trimmed Mean ( 11 / 24 )3500989.1659305.080255162959.0335456075066
Trimmed Mean ( 12 / 24 )3502518.812557653.045259299160.7516705621905
Trimmed Mean ( 13 / 24 )3504194.3478260956323.240571135762.2157800632995
Trimmed Mean ( 14 / 24 )350445055046.990401877963.6628810115738
Trimmed Mean ( 15 / 24 )3503926.9761904854027.186070090164.8548856800499
Trimmed Mean ( 16 / 24 )3504050.0552855.336262449466.2951046721354
Trimmed Mean ( 17 / 24 )3503086.2631578952011.7314183167.3518486624477
Trimmed Mean ( 18 / 24 )350257050981.902041367168.7022229409563
Trimmed Mean ( 19 / 24 )3501787.9117647149551.295154255270.6699572809045
Trimmed Mean ( 20 / 24 )3499795.187548248.026239097372.5375825770873
Trimmed Mean ( 21 / 24 )3499167.9333333347139.017988760474.2308194491379
Trimmed Mean ( 22 / 24 )3497035.4285714345926.205868487376.1446621257027
Trimmed Mean ( 23 / 24 )3495627.6153846244404.238528219478.722836631082
Trimmed Mean ( 24 / 24 )3492179.4583333342965.341778222781.278987057968
Median3464045.5
Midrange3905574
Midmean - Weighted Average at Xnp3488942.81081081
Midmean - Weighted Average at X(n+1)p3502570
Midmean - Empirical Distribution Function3488942.81081081
Midmean - Empirical Distribution Function - Averaging3502570
Midmean - Empirical Distribution Function - Interpolation3502570
Midmean - Closest Observation3488942.81081081
Midmean - True Basic - Statistics Graphics Toolkit3502570
Midmean - MS Excel (old versions)3503086.26315789
Number of observations72



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')