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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 02 Feb 2011 13:23:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Feb/02/t1296653294gy8v7pbzat9nbxq.htm/, Retrieved Sun, 19 May 2024 21:15:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=118025, Retrieved Sun, 19 May 2024 21:15:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact224
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-02-02 13:23:32] [ff423994c38282a6d306f7d0147a5924] [Current]
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Dataseries X:
5393
5147
4846
3995
4491
4676
5461
4758
5302
5066
3491
4944
5148
5351
5178
4025
4449
4594
4603
4911
5236
4652
3479
4556
4815
4949
4499
3865
3657
4814
4614
4539
4492
4779
3193
3894
4531
4008
3764
3290
3644
3438
3833
3922
3524
3493
2814
3899
3653
3969
3427
3067
3301
3211
3382
3613
3783
3971
2842
4161




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' @ www.yougetit.org

\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' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118025&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' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118025&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' @ www.yougetit.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4206.792.054087208289745.698133864296
Geometric Mean4145.77582775482
Harmonic Mean4083.78261572064
Quadratic Mean4265.71075359469
Winsorized Mean ( 1 / 20 )4206.0333333333391.68018277343845.8772354733124
Winsorized Mean ( 2 / 20 )4212.1333333333389.616431436581447.0017971683477
Winsorized Mean ( 3 / 20 )4215.9833333333387.790687419291748.0231270225466
Winsorized Mean ( 4 / 20 )4212.7833333333386.652895771430548.6167634194897
Winsorized Mean ( 5 / 20 )4214.5333333333384.4454340808349.9083624734434
Winsorized Mean ( 6 / 20 )4212.6333333333383.667477993680350.3497109552116
Winsorized Mean ( 7 / 20 )4221.9666666666781.951297948262551.5179963266973
Winsorized Mean ( 8 / 20 )4217.1666666666778.902035256438653.4481354373243
Winsorized Mean ( 9 / 20 )4201.2666666666775.545858661005555.612137331298
Winsorized Mean ( 10 / 20 )4207.2666666666774.252686864458656.6614737369254
Winsorized Mean ( 11 / 20 )4203.4166666666772.880981421211857.675083193148
Winsorized Mean ( 12 / 20 )4190.8166666666770.723446801575659.2563973645767
Winsorized Mean ( 13 / 20 )4190.8166666666768.562440062925861.1240886820887
Winsorized Mean ( 14 / 20 )4211.3565.196980212380764.594249400531
Winsorized Mean ( 15 / 20 )4210.3562.641409856528367.2135255199913
Winsorized Mean ( 16 / 20 )4207.1561.417497023877268.500837772083
Winsorized Mean ( 17 / 20 )4185.0557.802036135035372.4031587784038
Winsorized Mean ( 18 / 20 )4209.9551.93549576483381.0611305043261
Winsorized Mean ( 19 / 20 )4203.9333333333349.346731651350985.1917278541435
Winsorized Mean ( 20 / 20 )4216.9333333333346.457068856142190.7705422912365
Trimmed Mean ( 1 / 20 )4209.0862068965589.504565932337247.0264970624906
Trimmed Mean ( 2 / 20 )4212.3571428571486.814874049411748.5211455868683
Trimmed Mean ( 3 / 20 )4212.4814814814884.850057829004649.6461827989646
Trimmed Mean ( 4 / 20 )4211.1346153846283.247106349531850.5859578794633
Trimmed Mean ( 5 / 20 )4210.6481.636185254194451.5781082480659
Trimmed Mean ( 6 / 20 )4209.6666666666780.29349605213552.4284889019318
Trimmed Mean ( 7 / 20 )4209.0217391304378.753486168555853.4455291302519
Trimmed Mean ( 8 / 20 )4206.577.194199932192154.4924360080811
Trimmed Mean ( 9 / 20 )4204.5952380952475.929433125619655.3750379136777
Trimmed Mean ( 10 / 20 )4205.1575.046955813830856.0335852986725
Trimmed Mean ( 11 / 20 )4204.8157894736874.06502904956356.7719454570105
Trimmed Mean ( 12 / 20 )4205.0277777777872.945745071154757.6459637731577
Trimmed Mean ( 13 / 20 )4207.1176470588271.814933038462658.5827691965622
Trimmed Mean ( 14 / 20 )4209.4687570.641059184383259.5895474756782
Trimmed Mean ( 15 / 20 )4209.269.72031811904460.3726447835909
Trimmed Mean ( 16 / 20 )4209.0357142857168.861479739490961.123224917746
Trimmed Mean ( 17 / 20 )4209.3076923076967.645450565788462.226027871807
Trimmed Mean ( 18 / 20 )4212.87566.637520236431963.2207648942007
Trimmed Mean ( 19 / 20 )4213.3181818181866.723970600200663.1454954481608
Trimmed Mean ( 20 / 20 )4214.867.103635480775962.8103078142089
Median4093
Midrange4137.5
Midmean - Weighted Average at Xnp4189.96774193548
Midmean - Weighted Average at X(n+1)p4209.2
Midmean - Empirical Distribution Function4189.96774193548
Midmean - Empirical Distribution Function - Averaging4209.2
Midmean - Empirical Distribution Function - Interpolation4209.2
Midmean - Closest Observation4189.96774193548
Midmean - True Basic - Statistics Graphics Toolkit4209.2
Midmean - MS Excel (old versions)4209.46875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4206.7 & 92.0540872082897 & 45.698133864296 \tabularnewline
Geometric Mean & 4145.77582775482 &  &  \tabularnewline
Harmonic Mean & 4083.78261572064 &  &  \tabularnewline
Quadratic Mean & 4265.71075359469 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4206.03333333333 & 91.680182773438 & 45.8772354733124 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4212.13333333333 & 89.6164314365814 & 47.0017971683477 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4215.98333333333 & 87.7906874192917 & 48.0231270225466 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4212.78333333333 & 86.6528957714305 & 48.6167634194897 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4214.53333333333 & 84.44543408083 & 49.9083624734434 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4212.63333333333 & 83.6674779936803 & 50.3497109552116 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4221.96666666667 & 81.9512979482625 & 51.5179963266973 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4217.16666666667 & 78.9020352564386 & 53.4481354373243 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4201.26666666667 & 75.5458586610055 & 55.612137331298 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4207.26666666667 & 74.2526868644586 & 56.6614737369254 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4203.41666666667 & 72.8809814212118 & 57.675083193148 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4190.81666666667 & 70.7234468015756 & 59.2563973645767 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4190.81666666667 & 68.5624400629258 & 61.1240886820887 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4211.35 & 65.1969802123807 & 64.594249400531 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4210.35 & 62.6414098565283 & 67.2135255199913 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4207.15 & 61.4174970238772 & 68.500837772083 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4185.05 & 57.8020361350353 & 72.4031587784038 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4209.95 & 51.935495764833 & 81.0611305043261 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4203.93333333333 & 49.3467316513509 & 85.1917278541435 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4216.93333333333 & 46.4570688561421 & 90.7705422912365 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4209.08620689655 & 89.5045659323372 & 47.0264970624906 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4212.35714285714 & 86.8148740494117 & 48.5211455868683 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4212.48148148148 & 84.8500578290046 & 49.6461827989646 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4211.13461538462 & 83.2471063495318 & 50.5859578794633 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4210.64 & 81.6361852541944 & 51.5781082480659 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4209.66666666667 & 80.293496052135 & 52.4284889019318 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4209.02173913043 & 78.7534861685558 & 53.4455291302519 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4206.5 & 77.1941999321921 & 54.4924360080811 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4204.59523809524 & 75.9294331256196 & 55.3750379136777 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4205.15 & 75.0469558138308 & 56.0335852986725 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4204.81578947368 & 74.065029049563 & 56.7719454570105 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4205.02777777778 & 72.9457450711547 & 57.6459637731577 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4207.11764705882 & 71.8149330384626 & 58.5827691965622 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4209.46875 & 70.6410591843832 & 59.5895474756782 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4209.2 & 69.720318119044 & 60.3726447835909 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4209.03571428571 & 68.8614797394909 & 61.123224917746 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4209.30769230769 & 67.6454505657884 & 62.226027871807 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4212.875 & 66.6375202364319 & 63.2207648942007 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4213.31818181818 & 66.7239706002006 & 63.1454954481608 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4214.8 & 67.1036354807759 & 62.8103078142089 \tabularnewline
Median & 4093 &  &  \tabularnewline
Midrange & 4137.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4189.96774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4209.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4189.96774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4209.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4209.2 &  &  \tabularnewline
Midmean - Closest Observation & 4189.96774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4209.2 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4209.46875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118025&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]4206.7[/C][C]92.0540872082897[/C][C]45.698133864296[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4145.77582775482[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4083.78261572064[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4265.71075359469[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4206.03333333333[/C][C]91.680182773438[/C][C]45.8772354733124[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4212.13333333333[/C][C]89.6164314365814[/C][C]47.0017971683477[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4215.98333333333[/C][C]87.7906874192917[/C][C]48.0231270225466[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4212.78333333333[/C][C]86.6528957714305[/C][C]48.6167634194897[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4214.53333333333[/C][C]84.44543408083[/C][C]49.9083624734434[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4212.63333333333[/C][C]83.6674779936803[/C][C]50.3497109552116[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4221.96666666667[/C][C]81.9512979482625[/C][C]51.5179963266973[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4217.16666666667[/C][C]78.9020352564386[/C][C]53.4481354373243[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4201.26666666667[/C][C]75.5458586610055[/C][C]55.612137331298[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4207.26666666667[/C][C]74.2526868644586[/C][C]56.6614737369254[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4203.41666666667[/C][C]72.8809814212118[/C][C]57.675083193148[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4190.81666666667[/C][C]70.7234468015756[/C][C]59.2563973645767[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4190.81666666667[/C][C]68.5624400629258[/C][C]61.1240886820887[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4211.35[/C][C]65.1969802123807[/C][C]64.594249400531[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4210.35[/C][C]62.6414098565283[/C][C]67.2135255199913[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4207.15[/C][C]61.4174970238772[/C][C]68.500837772083[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4185.05[/C][C]57.8020361350353[/C][C]72.4031587784038[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4209.95[/C][C]51.935495764833[/C][C]81.0611305043261[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4203.93333333333[/C][C]49.3467316513509[/C][C]85.1917278541435[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4216.93333333333[/C][C]46.4570688561421[/C][C]90.7705422912365[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4209.08620689655[/C][C]89.5045659323372[/C][C]47.0264970624906[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4212.35714285714[/C][C]86.8148740494117[/C][C]48.5211455868683[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4212.48148148148[/C][C]84.8500578290046[/C][C]49.6461827989646[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4211.13461538462[/C][C]83.2471063495318[/C][C]50.5859578794633[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4210.64[/C][C]81.6361852541944[/C][C]51.5781082480659[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4209.66666666667[/C][C]80.293496052135[/C][C]52.4284889019318[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4209.02173913043[/C][C]78.7534861685558[/C][C]53.4455291302519[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4206.5[/C][C]77.1941999321921[/C][C]54.4924360080811[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4204.59523809524[/C][C]75.9294331256196[/C][C]55.3750379136777[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4205.15[/C][C]75.0469558138308[/C][C]56.0335852986725[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4204.81578947368[/C][C]74.065029049563[/C][C]56.7719454570105[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4205.02777777778[/C][C]72.9457450711547[/C][C]57.6459637731577[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4207.11764705882[/C][C]71.8149330384626[/C][C]58.5827691965622[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4209.46875[/C][C]70.6410591843832[/C][C]59.5895474756782[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4209.2[/C][C]69.720318119044[/C][C]60.3726447835909[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4209.03571428571[/C][C]68.8614797394909[/C][C]61.123224917746[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4209.30769230769[/C][C]67.6454505657884[/C][C]62.226027871807[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4212.875[/C][C]66.6375202364319[/C][C]63.2207648942007[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4213.31818181818[/C][C]66.7239706002006[/C][C]63.1454954481608[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4214.8[/C][C]67.1036354807759[/C][C]62.8103078142089[/C][/ROW]
[ROW][C]Median[/C][C]4093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4137.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4189.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4209.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4189.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4209.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4209.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4189.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4209.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4209.46875[/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=118025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118025&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 Mean4206.792.054087208289745.698133864296
Geometric Mean4145.77582775482
Harmonic Mean4083.78261572064
Quadratic Mean4265.71075359469
Winsorized Mean ( 1 / 20 )4206.0333333333391.68018277343845.8772354733124
Winsorized Mean ( 2 / 20 )4212.1333333333389.616431436581447.0017971683477
Winsorized Mean ( 3 / 20 )4215.9833333333387.790687419291748.0231270225466
Winsorized Mean ( 4 / 20 )4212.7833333333386.652895771430548.6167634194897
Winsorized Mean ( 5 / 20 )4214.5333333333384.4454340808349.9083624734434
Winsorized Mean ( 6 / 20 )4212.6333333333383.667477993680350.3497109552116
Winsorized Mean ( 7 / 20 )4221.9666666666781.951297948262551.5179963266973
Winsorized Mean ( 8 / 20 )4217.1666666666778.902035256438653.4481354373243
Winsorized Mean ( 9 / 20 )4201.2666666666775.545858661005555.612137331298
Winsorized Mean ( 10 / 20 )4207.2666666666774.252686864458656.6614737369254
Winsorized Mean ( 11 / 20 )4203.4166666666772.880981421211857.675083193148
Winsorized Mean ( 12 / 20 )4190.8166666666770.723446801575659.2563973645767
Winsorized Mean ( 13 / 20 )4190.8166666666768.562440062925861.1240886820887
Winsorized Mean ( 14 / 20 )4211.3565.196980212380764.594249400531
Winsorized Mean ( 15 / 20 )4210.3562.641409856528367.2135255199913
Winsorized Mean ( 16 / 20 )4207.1561.417497023877268.500837772083
Winsorized Mean ( 17 / 20 )4185.0557.802036135035372.4031587784038
Winsorized Mean ( 18 / 20 )4209.9551.93549576483381.0611305043261
Winsorized Mean ( 19 / 20 )4203.9333333333349.346731651350985.1917278541435
Winsorized Mean ( 20 / 20 )4216.9333333333346.457068856142190.7705422912365
Trimmed Mean ( 1 / 20 )4209.0862068965589.504565932337247.0264970624906
Trimmed Mean ( 2 / 20 )4212.3571428571486.814874049411748.5211455868683
Trimmed Mean ( 3 / 20 )4212.4814814814884.850057829004649.6461827989646
Trimmed Mean ( 4 / 20 )4211.1346153846283.247106349531850.5859578794633
Trimmed Mean ( 5 / 20 )4210.6481.636185254194451.5781082480659
Trimmed Mean ( 6 / 20 )4209.6666666666780.29349605213552.4284889019318
Trimmed Mean ( 7 / 20 )4209.0217391304378.753486168555853.4455291302519
Trimmed Mean ( 8 / 20 )4206.577.194199932192154.4924360080811
Trimmed Mean ( 9 / 20 )4204.5952380952475.929433125619655.3750379136777
Trimmed Mean ( 10 / 20 )4205.1575.046955813830856.0335852986725
Trimmed Mean ( 11 / 20 )4204.8157894736874.06502904956356.7719454570105
Trimmed Mean ( 12 / 20 )4205.0277777777872.945745071154757.6459637731577
Trimmed Mean ( 13 / 20 )4207.1176470588271.814933038462658.5827691965622
Trimmed Mean ( 14 / 20 )4209.4687570.641059184383259.5895474756782
Trimmed Mean ( 15 / 20 )4209.269.72031811904460.3726447835909
Trimmed Mean ( 16 / 20 )4209.0357142857168.861479739490961.123224917746
Trimmed Mean ( 17 / 20 )4209.3076923076967.645450565788462.226027871807
Trimmed Mean ( 18 / 20 )4212.87566.637520236431963.2207648942007
Trimmed Mean ( 19 / 20 )4213.3181818181866.723970600200663.1454954481608
Trimmed Mean ( 20 / 20 )4214.867.103635480775962.8103078142089
Median4093
Midrange4137.5
Midmean - Weighted Average at Xnp4189.96774193548
Midmean - Weighted Average at X(n+1)p4209.2
Midmean - Empirical Distribution Function4189.96774193548
Midmean - Empirical Distribution Function - Averaging4209.2
Midmean - Empirical Distribution Function - Interpolation4209.2
Midmean - Closest Observation4189.96774193548
Midmean - True Basic - Statistics Graphics Toolkit4209.2
Midmean - MS Excel (old versions)4209.46875
Number of observations60



Parameters (Session):
par4 = 12 ;
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')