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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 11 Mar 2013 10:18:05 -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/2013/Mar/11/t1363011509e7tmvqpunteb66b.htm/, Retrieved Thu, 02 May 2024 13:29:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207687, Retrieved Thu, 02 May 2024 13:29:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid aanta...] [2013-03-11 14:18:05] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3169889
3051720
3695426
3905501
4296458
4246247
4921849
4821446
4425064
4379099
3472889
3359160
3200944
3153170
3741498
3918719
4403449
4400407
4847473
4716136
4297440
4272253
3271834
3168388
2911748
2720999
3199918
3672623
3892013
3850845
4532467
4484739
4014972
3983758
3158459
3100569
2935404
2855719
3465611
3006985
4095110
4104793
4730788
4642726
4246919
4308117
3508154
3236641
3257275
3045631
3657692
4125747
4472507
4513455
5150896
5057815
4681742
4603682
3580181
3534002
3422762
3295209
3868093
4189245
4544332
4612845
5221595
5137505
4760439
4643697
3692267
3587603




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207687&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207687&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207687&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3950732.6805555678143.03485562350.5577072589377
Geometric Mean3894906.59140634
Harmonic Mean3838625.22484867
Quadratic Mean4005226.38809062
Winsorized Mean ( 1 / 24 )3951621.8611111177529.883362590350.9690159422817
Winsorized Mean ( 2 / 24 )3952806.2577146.287319219651.2378027168552
Winsorized Mean ( 3 / 24 )3950471.576261.488171287251.8016576220889
Winsorized Mean ( 4 / 24 )3946894.5555555674059.307198312453.293700749681
Winsorized Mean ( 5 / 24 )3944413.3055555672654.392911365754.2900869100581
Winsorized Mean ( 6 / 24 )3942751.8055555672190.306033109554.6160838235988
Winsorized Mean ( 7 / 24 )3941569.7777777870383.039253098656.0016989832426
Winsorized Mean ( 8 / 24 )3944119.7777777868883.476752627957.2578499767335
Winsorized Mean ( 9 / 24 )3942949.4027777868483.763084936757.5749524436552
Winsorized Mean ( 10 / 24 )3939551.4861111167511.884196167658.3534518850645
Winsorized Mean ( 11 / 24 )3933968.37566588.544233299759.0787562679993
Winsorized Mean ( 12 / 24 )3938811.37565763.717802451659.8933805237691
Winsorized Mean ( 13 / 24 )3933601.4444444464930.139512276460.5820574850407
Winsorized Mean ( 14 / 24 )3938760.8333333363576.142077672861.9534420399595
Winsorized Mean ( 15 / 24 )393069561122.688197684464.3082808676094
Winsorized Mean ( 16 / 24 )3931293.6666666760250.584002919765.2490549548227
Winsorized Mean ( 17 / 24 )3932323.8194444458775.799134547466.9037916514365
Winsorized Mean ( 18 / 24 )3941132.5694444455374.685110268271.1720989762096
Winsorized Mean ( 19 / 24 )3954688.5416666752486.023457818675.3474597831731
Winsorized Mean ( 20 / 24 )3953412.4305555648991.579594963480.6957534996889
Winsorized Mean ( 21 / 24 )3949230.8055555647844.930060739782.5423049117631
Winsorized Mean ( 22 / 24 )3959076.7222222246224.296497782285.6492585541497
Winsorized Mean ( 23 / 24 )396052744183.75121497189.6376358071208
Winsorized Mean ( 24 / 24 )3952259.3333333338999.828739512101.340427921653
Trimmed Mean ( 1 / 24 )3950145.1285714376258.548383255351.7993747890275
Trimmed Mean ( 2 / 24 )3948581.5294117674737.587900603152.8326059259921
Trimmed Mean ( 3 / 24 )3946277.1363636473156.548996946353.9429099714417
Trimmed Mean ( 4 / 24 )3944704.2571654.949177073255.0513857773016
Trimmed Mean ( 5 / 24 )3944068.3548387170631.873611493355.8397810106644
Trimmed Mean ( 6 / 24 )3943985.5666666769794.987137565856.5081494877717
Trimmed Mean ( 7 / 24 )3944240.8275862168865.286618906557.274731889424
Trimmed Mean ( 8 / 24 )3944731.4285714368139.683910002957.8918363311096
Trimmed Mean ( 9 / 24 )3944833.3703703767541.523584613458.4060465474759
Trimmed Mean ( 10 / 24 )3945123.2115384666825.054506584259.0365880083159
Trimmed Mean ( 11 / 24 )3945925.5466075.967788180559.7180135544808
Trimmed Mean ( 12 / 24 )3947556.062565258.408832662560.491147931946
Trimmed Mean ( 13 / 24 )3948696.6739130464325.759961527661.3859311771008
Trimmed Mean ( 14 / 24 )3950596.7727272763232.461113432962.4773526629034
Trimmed Mean ( 15 / 24 )3952046.0714285762042.872905149263.6986310654962
Trimmed Mean ( 16 / 24 )3954608.260947.401071430464.8855920101531
Trimmed Mean ( 17 / 24 )3957369.1315789559600.153123045266.3986403425662
Trimmed Mean ( 18 / 24 )3960315.6388888958052.812171047468.2191868194115
Trimmed Mean ( 19 / 24 )3962572.4705882456721.018855246669.8607421122108
Trimmed Mean ( 20 / 24 )3963506.0937555524.668887452271.3827956684257
Trimmed Mean ( 21 / 24 )3964717.3333333354639.31583080372.5616211156549
Trimmed Mean ( 22 / 24 )3966613.6428571453487.678864285474.1593901077976
Trimmed Mean ( 23 / 24 )3967562.3461538552101.662628747576.1503980098461
Trimmed Mean ( 24 / 24 )396848050488.948250790678.6009639235821
Median3951238.5
Midrange3971297
Midmean - Weighted Average at Xnp3942339.78378378
Midmean - Weighted Average at X(n+1)p3960315.63888889
Midmean - Empirical Distribution Function3942339.78378378
Midmean - Empirical Distribution Function - Averaging3960315.63888889
Midmean - Empirical Distribution Function - Interpolation3960315.63888889
Midmean - Closest Observation3942339.78378378
Midmean - True Basic - Statistics Graphics Toolkit3960315.63888889
Midmean - MS Excel (old versions)3957369.13157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3950732.68055556 & 78143.034855623 & 50.5577072589377 \tabularnewline
Geometric Mean & 3894906.59140634 &  &  \tabularnewline
Harmonic Mean & 3838625.22484867 &  &  \tabularnewline
Quadratic Mean & 4005226.38809062 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3951621.86111111 & 77529.8833625903 & 50.9690159422817 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3952806.25 & 77146.2873192196 & 51.2378027168552 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3950471.5 & 76261.4881712872 & 51.8016576220889 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3946894.55555556 & 74059.3071983124 & 53.293700749681 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3944413.30555556 & 72654.3929113657 & 54.2900869100581 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3942751.80555556 & 72190.3060331095 & 54.6160838235988 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3941569.77777778 & 70383.0392530986 & 56.0016989832426 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3944119.77777778 & 68883.4767526279 & 57.2578499767335 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3942949.40277778 & 68483.7630849367 & 57.5749524436552 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3939551.48611111 & 67511.8841961676 & 58.3534518850645 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3933968.375 & 66588.5442332997 & 59.0787562679993 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3938811.375 & 65763.7178024516 & 59.8933805237691 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3933601.44444444 & 64930.1395122764 & 60.5820574850407 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3938760.83333333 & 63576.1420776728 & 61.9534420399595 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3930695 & 61122.6881976844 & 64.3082808676094 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3931293.66666667 & 60250.5840029197 & 65.2490549548227 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3932323.81944444 & 58775.7991345474 & 66.9037916514365 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3941132.56944444 & 55374.6851102682 & 71.1720989762096 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3954688.54166667 & 52486.0234578186 & 75.3474597831731 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3953412.43055556 & 48991.5795949634 & 80.6957534996889 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3949230.80555556 & 47844.9300607397 & 82.5423049117631 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3959076.72222222 & 46224.2964977822 & 85.6492585541497 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3960527 & 44183.751214971 & 89.6376358071208 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3952259.33333333 & 38999.828739512 & 101.340427921653 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3950145.12857143 & 76258.5483832553 & 51.7993747890275 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3948581.52941176 & 74737.5879006031 & 52.8326059259921 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3946277.13636364 & 73156.5489969463 & 53.9429099714417 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3944704.25 & 71654.9491770732 & 55.0513857773016 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3944068.35483871 & 70631.8736114933 & 55.8397810106644 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3943985.56666667 & 69794.9871375658 & 56.5081494877717 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3944240.82758621 & 68865.2866189065 & 57.274731889424 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3944731.42857143 & 68139.6839100029 & 57.8918363311096 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3944833.37037037 & 67541.5235846134 & 58.4060465474759 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3945123.21153846 & 66825.0545065842 & 59.0365880083159 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3945925.54 & 66075.9677881805 & 59.7180135544808 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3947556.0625 & 65258.4088326625 & 60.491147931946 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3948696.67391304 & 64325.7599615276 & 61.3859311771008 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3950596.77272727 & 63232.4611134329 & 62.4773526629034 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3952046.07142857 & 62042.8729051492 & 63.6986310654962 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3954608.2 & 60947.4010714304 & 64.8855920101531 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3957369.13157895 & 59600.1531230452 & 66.3986403425662 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3960315.63888889 & 58052.8121710474 & 68.2191868194115 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3962572.47058824 & 56721.0188552466 & 69.8607421122108 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3963506.09375 & 55524.6688874522 & 71.3827956684257 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3964717.33333333 & 54639.315830803 & 72.5616211156549 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3966613.64285714 & 53487.6788642854 & 74.1593901077976 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3967562.34615385 & 52101.6626287475 & 76.1503980098461 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3968480 & 50488.9482507906 & 78.6009639235821 \tabularnewline
Median & 3951238.5 &  &  \tabularnewline
Midrange & 3971297 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3942339.78378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3960315.63888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3942339.78378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3960315.63888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3960315.63888889 &  &  \tabularnewline
Midmean - Closest Observation & 3942339.78378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3960315.63888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3957369.13157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207687&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]3950732.68055556[/C][C]78143.034855623[/C][C]50.5577072589377[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3894906.59140634[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3838625.22484867[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4005226.38809062[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3951621.86111111[/C][C]77529.8833625903[/C][C]50.9690159422817[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3952806.25[/C][C]77146.2873192196[/C][C]51.2378027168552[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3950471.5[/C][C]76261.4881712872[/C][C]51.8016576220889[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3946894.55555556[/C][C]74059.3071983124[/C][C]53.293700749681[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3944413.30555556[/C][C]72654.3929113657[/C][C]54.2900869100581[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3942751.80555556[/C][C]72190.3060331095[/C][C]54.6160838235988[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3941569.77777778[/C][C]70383.0392530986[/C][C]56.0016989832426[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3944119.77777778[/C][C]68883.4767526279[/C][C]57.2578499767335[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3942949.40277778[/C][C]68483.7630849367[/C][C]57.5749524436552[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3939551.48611111[/C][C]67511.8841961676[/C][C]58.3534518850645[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3933968.375[/C][C]66588.5442332997[/C][C]59.0787562679993[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3938811.375[/C][C]65763.7178024516[/C][C]59.8933805237691[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3933601.44444444[/C][C]64930.1395122764[/C][C]60.5820574850407[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3938760.83333333[/C][C]63576.1420776728[/C][C]61.9534420399595[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3930695[/C][C]61122.6881976844[/C][C]64.3082808676094[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3931293.66666667[/C][C]60250.5840029197[/C][C]65.2490549548227[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3932323.81944444[/C][C]58775.7991345474[/C][C]66.9037916514365[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3941132.56944444[/C][C]55374.6851102682[/C][C]71.1720989762096[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3954688.54166667[/C][C]52486.0234578186[/C][C]75.3474597831731[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3953412.43055556[/C][C]48991.5795949634[/C][C]80.6957534996889[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3949230.80555556[/C][C]47844.9300607397[/C][C]82.5423049117631[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3959076.72222222[/C][C]46224.2964977822[/C][C]85.6492585541497[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3960527[/C][C]44183.751214971[/C][C]89.6376358071208[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3952259.33333333[/C][C]38999.828739512[/C][C]101.340427921653[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3950145.12857143[/C][C]76258.5483832553[/C][C]51.7993747890275[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3948581.52941176[/C][C]74737.5879006031[/C][C]52.8326059259921[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3946277.13636364[/C][C]73156.5489969463[/C][C]53.9429099714417[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3944704.25[/C][C]71654.9491770732[/C][C]55.0513857773016[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3944068.35483871[/C][C]70631.8736114933[/C][C]55.8397810106644[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3943985.56666667[/C][C]69794.9871375658[/C][C]56.5081494877717[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3944240.82758621[/C][C]68865.2866189065[/C][C]57.274731889424[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3944731.42857143[/C][C]68139.6839100029[/C][C]57.8918363311096[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3944833.37037037[/C][C]67541.5235846134[/C][C]58.4060465474759[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3945123.21153846[/C][C]66825.0545065842[/C][C]59.0365880083159[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3945925.54[/C][C]66075.9677881805[/C][C]59.7180135544808[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3947556.0625[/C][C]65258.4088326625[/C][C]60.491147931946[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3948696.67391304[/C][C]64325.7599615276[/C][C]61.3859311771008[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3950596.77272727[/C][C]63232.4611134329[/C][C]62.4773526629034[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3952046.07142857[/C][C]62042.8729051492[/C][C]63.6986310654962[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3954608.2[/C][C]60947.4010714304[/C][C]64.8855920101531[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3957369.13157895[/C][C]59600.1531230452[/C][C]66.3986403425662[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3960315.63888889[/C][C]58052.8121710474[/C][C]68.2191868194115[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3962572.47058824[/C][C]56721.0188552466[/C][C]69.8607421122108[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3963506.09375[/C][C]55524.6688874522[/C][C]71.3827956684257[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3964717.33333333[/C][C]54639.315830803[/C][C]72.5616211156549[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3966613.64285714[/C][C]53487.6788642854[/C][C]74.1593901077976[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3967562.34615385[/C][C]52101.6626287475[/C][C]76.1503980098461[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3968480[/C][C]50488.9482507906[/C][C]78.6009639235821[/C][/ROW]
[ROW][C]Median[/C][C]3951238.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3971297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3942339.78378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3960315.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3942339.78378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3960315.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3960315.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3942339.78378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3960315.63888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3957369.13157895[/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=207687&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207687&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 Mean3950732.6805555678143.03485562350.5577072589377
Geometric Mean3894906.59140634
Harmonic Mean3838625.22484867
Quadratic Mean4005226.38809062
Winsorized Mean ( 1 / 24 )3951621.8611111177529.883362590350.9690159422817
Winsorized Mean ( 2 / 24 )3952806.2577146.287319219651.2378027168552
Winsorized Mean ( 3 / 24 )3950471.576261.488171287251.8016576220889
Winsorized Mean ( 4 / 24 )3946894.5555555674059.307198312453.293700749681
Winsorized Mean ( 5 / 24 )3944413.3055555672654.392911365754.2900869100581
Winsorized Mean ( 6 / 24 )3942751.8055555672190.306033109554.6160838235988
Winsorized Mean ( 7 / 24 )3941569.7777777870383.039253098656.0016989832426
Winsorized Mean ( 8 / 24 )3944119.7777777868883.476752627957.2578499767335
Winsorized Mean ( 9 / 24 )3942949.4027777868483.763084936757.5749524436552
Winsorized Mean ( 10 / 24 )3939551.4861111167511.884196167658.3534518850645
Winsorized Mean ( 11 / 24 )3933968.37566588.544233299759.0787562679993
Winsorized Mean ( 12 / 24 )3938811.37565763.717802451659.8933805237691
Winsorized Mean ( 13 / 24 )3933601.4444444464930.139512276460.5820574850407
Winsorized Mean ( 14 / 24 )3938760.8333333363576.142077672861.9534420399595
Winsorized Mean ( 15 / 24 )393069561122.688197684464.3082808676094
Winsorized Mean ( 16 / 24 )3931293.6666666760250.584002919765.2490549548227
Winsorized Mean ( 17 / 24 )3932323.8194444458775.799134547466.9037916514365
Winsorized Mean ( 18 / 24 )3941132.5694444455374.685110268271.1720989762096
Winsorized Mean ( 19 / 24 )3954688.5416666752486.023457818675.3474597831731
Winsorized Mean ( 20 / 24 )3953412.4305555648991.579594963480.6957534996889
Winsorized Mean ( 21 / 24 )3949230.8055555647844.930060739782.5423049117631
Winsorized Mean ( 22 / 24 )3959076.7222222246224.296497782285.6492585541497
Winsorized Mean ( 23 / 24 )396052744183.75121497189.6376358071208
Winsorized Mean ( 24 / 24 )3952259.3333333338999.828739512101.340427921653
Trimmed Mean ( 1 / 24 )3950145.1285714376258.548383255351.7993747890275
Trimmed Mean ( 2 / 24 )3948581.5294117674737.587900603152.8326059259921
Trimmed Mean ( 3 / 24 )3946277.1363636473156.548996946353.9429099714417
Trimmed Mean ( 4 / 24 )3944704.2571654.949177073255.0513857773016
Trimmed Mean ( 5 / 24 )3944068.3548387170631.873611493355.8397810106644
Trimmed Mean ( 6 / 24 )3943985.5666666769794.987137565856.5081494877717
Trimmed Mean ( 7 / 24 )3944240.8275862168865.286618906557.274731889424
Trimmed Mean ( 8 / 24 )3944731.4285714368139.683910002957.8918363311096
Trimmed Mean ( 9 / 24 )3944833.3703703767541.523584613458.4060465474759
Trimmed Mean ( 10 / 24 )3945123.2115384666825.054506584259.0365880083159
Trimmed Mean ( 11 / 24 )3945925.5466075.967788180559.7180135544808
Trimmed Mean ( 12 / 24 )3947556.062565258.408832662560.491147931946
Trimmed Mean ( 13 / 24 )3948696.6739130464325.759961527661.3859311771008
Trimmed Mean ( 14 / 24 )3950596.7727272763232.461113432962.4773526629034
Trimmed Mean ( 15 / 24 )3952046.0714285762042.872905149263.6986310654962
Trimmed Mean ( 16 / 24 )3954608.260947.401071430464.8855920101531
Trimmed Mean ( 17 / 24 )3957369.1315789559600.153123045266.3986403425662
Trimmed Mean ( 18 / 24 )3960315.6388888958052.812171047468.2191868194115
Trimmed Mean ( 19 / 24 )3962572.4705882456721.018855246669.8607421122108
Trimmed Mean ( 20 / 24 )3963506.0937555524.668887452271.3827956684257
Trimmed Mean ( 21 / 24 )3964717.3333333354639.31583080372.5616211156549
Trimmed Mean ( 22 / 24 )3966613.6428571453487.678864285474.1593901077976
Trimmed Mean ( 23 / 24 )3967562.3461538552101.662628747576.1503980098461
Trimmed Mean ( 24 / 24 )396848050488.948250790678.6009639235821
Median3951238.5
Midrange3971297
Midmean - Weighted Average at Xnp3942339.78378378
Midmean - Weighted Average at X(n+1)p3960315.63888889
Midmean - Empirical Distribution Function3942339.78378378
Midmean - Empirical Distribution Function - Averaging3960315.63888889
Midmean - Empirical Distribution Function - Interpolation3960315.63888889
Midmean - Closest Observation3942339.78378378
Midmean - True Basic - Statistics Graphics Toolkit3960315.63888889
Midmean - MS Excel (old versions)3957369.13157895
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')