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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 computationSun, 18 Oct 2009 09:11:51 -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/18/t1255878768n4jwv2to8mto0vf.htm/, Retrieved Mon, 29 Apr 2024 08:16:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47354, Retrieved Mon, 29 Apr 2024 08:16:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws3p2c2
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-18 15:11:51] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataseries X:
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6
2070.83
2293.41
2443.27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time17 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 17 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47354&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]17 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47354&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47354&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 time17 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3370.7225109.64027903731330.7434688200023
Geometric Mean3251.11558032461
Harmonic Mean3117.5947618858
Quadratic Mean3474.33571038575
Winsorized Mean ( 1 / 20 )3371.81183333333108.79420140343330.9925693634158
Winsorized Mean ( 2 / 20 )3372.5355108.18609416876531.1734657389424
Winsorized Mean ( 3 / 20 )3371.1945107.89829227832031.244187732871
Winsorized Mean ( 4 / 20 )3369.9125106.51939189984731.6366103851634
Winsorized Mean ( 5 / 20 )3374.105103.57955521319832.5750095475414
Winsorized Mean ( 6 / 20 )3374.752103.09185167151732.7353902881967
Winsorized Mean ( 7 / 20 )3368.2385100.9597115925433.3622040601083
Winsorized Mean ( 8 / 20 )3362.6811666666799.091798777582733.9350098408689
Winsorized Mean ( 9 / 20 )3380.8896666666794.83612639616135.6498076750162
Winsorized Mean ( 10 / 20 )3382.09389.154260191849137.9352931954362
Winsorized Mean ( 11 / 20 )3409.059583.533917099320940.8104829556438
Winsorized Mean ( 12 / 20 )3459.511569.998170130975849.422884820086
Winsorized Mean ( 13 / 20 )3474.8233333333365.897999097160952.7303314355571
Winsorized Mean ( 14 / 20 )3488.9796666666762.807636924977655.5502457580784
Winsorized Mean ( 15 / 20 )3465.4346666666755.836366025976462.0641154378575
Winsorized Mean ( 16 / 20 )3456.7333333333352.951277665622465.2813961385779
Winsorized Mean ( 17 / 20 )3464.7516666666749.865965299627569.481291414859
Winsorized Mean ( 18 / 20 )3459.1086666666747.788328337373472.3839646000221
Winsorized Mean ( 19 / 20 )3462.1423333333346.922294492236873.7845915422175
Winsorized Mean ( 20 / 20 )3464.2056666666745.370960304442276.3529280275668
Trimmed Mean ( 1 / 20 )3377.17793103448107.07117446811631.5414297808057
Trimmed Mean ( 2 / 20 )3382.92732142857104.90855827396932.2464380131318
Trimmed Mean ( 3 / 20 )3388.70055555556102.59609447453033.0295278091391
Trimmed Mean ( 4 / 20 )3395.4336538461599.813102951549734.0179150175737
Trimmed Mean ( 5 / 20 )3403.0996.83133890872935.1445104276382
Trimmed Mean ( 6 / 20 )3410.3362594.056078047605536.25854193361
Trimmed Mean ( 7 / 20 )3418.0719565217490.618419816346137.7193948366022
Trimmed Mean ( 8 / 20 )3427.7797727272786.774543183243239.5021356146903
Trimmed Mean ( 9 / 20 )3439.4045238095282.23354244493741.8248371838356
Trimmed Mean ( 10 / 20 )3449.15777.519278407175844.4941835227496
Trimmed Mean ( 11 / 20 )3459.7460526315872.874550207385947.4753675019037
Trimmed Mean ( 12 / 20 )3467.4258333333368.33560764319250.7411282773422
Trimmed Mean ( 13 / 20 )3468.5897058823566.276256217688352.3353294804336
Trimmed Mean ( 14 / 20 )3467.69062564.483278688594553.7765866674727
Trimmed Mean ( 15 / 20 )3464.6493333333362.695840779266755.2612308929922
Trimmed Mean ( 16 / 20 )3464.5371428571462.06300303292555.8229053308809
Trimmed Mean ( 17 / 20 )3465.6626923076961.686066915926956.1822606883189
Trimmed Mean ( 18 / 20 )3465.7966666666761.694793125451656.176485746848
Trimmed Mean ( 19 / 20 )3466.8161.869668270874556.0340809461237
Trimmed Mean ( 20 / 20 )3467.54761.798809425169556.1102557193882
Median3499.27
Midrange3183.515
Midmean - Weighted Average at Xnp3447.1264516129
Midmean - Weighted Average at X(n+1)p3464.64933333333
Midmean - Empirical Distribution Function3447.1264516129
Midmean - Empirical Distribution Function - Averaging3464.64933333333
Midmean - Empirical Distribution Function - Interpolation3464.64933333333
Midmean - Closest Observation3447.1264516129
Midmean - True Basic - Statistics Graphics Toolkit3464.64933333333
Midmean - MS Excel (old versions)3467.690625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3370.7225 & 109.640279037313 & 30.7434688200023 \tabularnewline
Geometric Mean & 3251.11558032461 &  &  \tabularnewline
Harmonic Mean & 3117.5947618858 &  &  \tabularnewline
Quadratic Mean & 3474.33571038575 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3371.81183333333 & 108.794201403433 & 30.9925693634158 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3372.5355 & 108.186094168765 & 31.1734657389424 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3371.1945 & 107.898292278320 & 31.244187732871 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3369.9125 & 106.519391899847 & 31.6366103851634 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3374.105 & 103.579555213198 & 32.5750095475414 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3374.752 & 103.091851671517 & 32.7353902881967 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3368.2385 & 100.95971159254 & 33.3622040601083 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3362.68116666667 & 99.0917987775827 & 33.9350098408689 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3380.88966666667 & 94.836126396161 & 35.6498076750162 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3382.093 & 89.1542601918491 & 37.9352931954362 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3409.0595 & 83.5339170993209 & 40.8104829556438 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3459.5115 & 69.9981701309758 & 49.422884820086 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3474.82333333333 & 65.8979990971609 & 52.7303314355571 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3488.97966666667 & 62.8076369249776 & 55.5502457580784 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3465.43466666667 & 55.8363660259764 & 62.0641154378575 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3456.73333333333 & 52.9512776656224 & 65.2813961385779 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3464.75166666667 & 49.8659652996275 & 69.481291414859 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3459.10866666667 & 47.7883283373734 & 72.3839646000221 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3462.14233333333 & 46.9222944922368 & 73.7845915422175 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3464.20566666667 & 45.3709603044422 & 76.3529280275668 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3377.17793103448 & 107.071174468116 & 31.5414297808057 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3382.92732142857 & 104.908558273969 & 32.2464380131318 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3388.70055555556 & 102.596094474530 & 33.0295278091391 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3395.43365384615 & 99.8131029515497 & 34.0179150175737 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3403.09 & 96.831338908729 & 35.1445104276382 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3410.33625 & 94.0560780476055 & 36.25854193361 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3418.07195652174 & 90.6184198163461 & 37.7193948366022 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3427.77977272727 & 86.7745431832432 & 39.5021356146903 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3439.40452380952 & 82.233542444937 & 41.8248371838356 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3449.157 & 77.5192784071758 & 44.4941835227496 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3459.74605263158 & 72.8745502073859 & 47.4753675019037 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3467.42583333333 & 68.335607643192 & 50.7411282773422 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3468.58970588235 & 66.2762562176883 & 52.3353294804336 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3467.690625 & 64.4832786885945 & 53.7765866674727 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3464.64933333333 & 62.6958407792667 & 55.2612308929922 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3464.53714285714 & 62.063003032925 & 55.8229053308809 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3465.66269230769 & 61.6860669159269 & 56.1822606883189 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3465.79666666667 & 61.6947931254516 & 56.176485746848 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3466.81 & 61.8696682708745 & 56.0340809461237 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3467.547 & 61.7988094251695 & 56.1102557193882 \tabularnewline
Median & 3499.27 &  &  \tabularnewline
Midrange & 3183.515 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3447.1264516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3464.64933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3447.1264516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3464.64933333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3464.64933333333 &  &  \tabularnewline
Midmean - Closest Observation & 3447.1264516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3464.64933333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3467.690625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47354&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]3370.7225[/C][C]109.640279037313[/C][C]30.7434688200023[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3251.11558032461[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3117.5947618858[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3474.33571038575[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3371.81183333333[/C][C]108.794201403433[/C][C]30.9925693634158[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3372.5355[/C][C]108.186094168765[/C][C]31.1734657389424[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3371.1945[/C][C]107.898292278320[/C][C]31.244187732871[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3369.9125[/C][C]106.519391899847[/C][C]31.6366103851634[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3374.105[/C][C]103.579555213198[/C][C]32.5750095475414[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3374.752[/C][C]103.091851671517[/C][C]32.7353902881967[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3368.2385[/C][C]100.95971159254[/C][C]33.3622040601083[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3362.68116666667[/C][C]99.0917987775827[/C][C]33.9350098408689[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3380.88966666667[/C][C]94.836126396161[/C][C]35.6498076750162[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3382.093[/C][C]89.1542601918491[/C][C]37.9352931954362[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3409.0595[/C][C]83.5339170993209[/C][C]40.8104829556438[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3459.5115[/C][C]69.9981701309758[/C][C]49.422884820086[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3474.82333333333[/C][C]65.8979990971609[/C][C]52.7303314355571[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3488.97966666667[/C][C]62.8076369249776[/C][C]55.5502457580784[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3465.43466666667[/C][C]55.8363660259764[/C][C]62.0641154378575[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3456.73333333333[/C][C]52.9512776656224[/C][C]65.2813961385779[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3464.75166666667[/C][C]49.8659652996275[/C][C]69.481291414859[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3459.10866666667[/C][C]47.7883283373734[/C][C]72.3839646000221[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3462.14233333333[/C][C]46.9222944922368[/C][C]73.7845915422175[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3464.20566666667[/C][C]45.3709603044422[/C][C]76.3529280275668[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3377.17793103448[/C][C]107.071174468116[/C][C]31.5414297808057[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3382.92732142857[/C][C]104.908558273969[/C][C]32.2464380131318[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3388.70055555556[/C][C]102.596094474530[/C][C]33.0295278091391[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3395.43365384615[/C][C]99.8131029515497[/C][C]34.0179150175737[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3403.09[/C][C]96.831338908729[/C][C]35.1445104276382[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3410.33625[/C][C]94.0560780476055[/C][C]36.25854193361[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3418.07195652174[/C][C]90.6184198163461[/C][C]37.7193948366022[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3427.77977272727[/C][C]86.7745431832432[/C][C]39.5021356146903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3439.40452380952[/C][C]82.233542444937[/C][C]41.8248371838356[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3449.157[/C][C]77.5192784071758[/C][C]44.4941835227496[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3459.74605263158[/C][C]72.8745502073859[/C][C]47.4753675019037[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3467.42583333333[/C][C]68.335607643192[/C][C]50.7411282773422[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3468.58970588235[/C][C]66.2762562176883[/C][C]52.3353294804336[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3467.690625[/C][C]64.4832786885945[/C][C]53.7765866674727[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3464.64933333333[/C][C]62.6958407792667[/C][C]55.2612308929922[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3464.53714285714[/C][C]62.063003032925[/C][C]55.8229053308809[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3465.66269230769[/C][C]61.6860669159269[/C][C]56.1822606883189[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3465.79666666667[/C][C]61.6947931254516[/C][C]56.176485746848[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3466.81[/C][C]61.8696682708745[/C][C]56.0340809461237[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3467.547[/C][C]61.7988094251695[/C][C]56.1102557193882[/C][/ROW]
[ROW][C]Median[/C][C]3499.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3183.515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3447.1264516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3447.1264516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3447.1264516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3464.64933333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3467.690625[/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=47354&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47354&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 Mean3370.7225109.64027903731330.7434688200023
Geometric Mean3251.11558032461
Harmonic Mean3117.5947618858
Quadratic Mean3474.33571038575
Winsorized Mean ( 1 / 20 )3371.81183333333108.79420140343330.9925693634158
Winsorized Mean ( 2 / 20 )3372.5355108.18609416876531.1734657389424
Winsorized Mean ( 3 / 20 )3371.1945107.89829227832031.244187732871
Winsorized Mean ( 4 / 20 )3369.9125106.51939189984731.6366103851634
Winsorized Mean ( 5 / 20 )3374.105103.57955521319832.5750095475414
Winsorized Mean ( 6 / 20 )3374.752103.09185167151732.7353902881967
Winsorized Mean ( 7 / 20 )3368.2385100.9597115925433.3622040601083
Winsorized Mean ( 8 / 20 )3362.6811666666799.091798777582733.9350098408689
Winsorized Mean ( 9 / 20 )3380.8896666666794.83612639616135.6498076750162
Winsorized Mean ( 10 / 20 )3382.09389.154260191849137.9352931954362
Winsorized Mean ( 11 / 20 )3409.059583.533917099320940.8104829556438
Winsorized Mean ( 12 / 20 )3459.511569.998170130975849.422884820086
Winsorized Mean ( 13 / 20 )3474.8233333333365.897999097160952.7303314355571
Winsorized Mean ( 14 / 20 )3488.9796666666762.807636924977655.5502457580784
Winsorized Mean ( 15 / 20 )3465.4346666666755.836366025976462.0641154378575
Winsorized Mean ( 16 / 20 )3456.7333333333352.951277665622465.2813961385779
Winsorized Mean ( 17 / 20 )3464.7516666666749.865965299627569.481291414859
Winsorized Mean ( 18 / 20 )3459.1086666666747.788328337373472.3839646000221
Winsorized Mean ( 19 / 20 )3462.1423333333346.922294492236873.7845915422175
Winsorized Mean ( 20 / 20 )3464.2056666666745.370960304442276.3529280275668
Trimmed Mean ( 1 / 20 )3377.17793103448107.07117446811631.5414297808057
Trimmed Mean ( 2 / 20 )3382.92732142857104.90855827396932.2464380131318
Trimmed Mean ( 3 / 20 )3388.70055555556102.59609447453033.0295278091391
Trimmed Mean ( 4 / 20 )3395.4336538461599.813102951549734.0179150175737
Trimmed Mean ( 5 / 20 )3403.0996.83133890872935.1445104276382
Trimmed Mean ( 6 / 20 )3410.3362594.056078047605536.25854193361
Trimmed Mean ( 7 / 20 )3418.0719565217490.618419816346137.7193948366022
Trimmed Mean ( 8 / 20 )3427.7797727272786.774543183243239.5021356146903
Trimmed Mean ( 9 / 20 )3439.4045238095282.23354244493741.8248371838356
Trimmed Mean ( 10 / 20 )3449.15777.519278407175844.4941835227496
Trimmed Mean ( 11 / 20 )3459.7460526315872.874550207385947.4753675019037
Trimmed Mean ( 12 / 20 )3467.4258333333368.33560764319250.7411282773422
Trimmed Mean ( 13 / 20 )3468.5897058823566.276256217688352.3353294804336
Trimmed Mean ( 14 / 20 )3467.69062564.483278688594553.7765866674727
Trimmed Mean ( 15 / 20 )3464.6493333333362.695840779266755.2612308929922
Trimmed Mean ( 16 / 20 )3464.5371428571462.06300303292555.8229053308809
Trimmed Mean ( 17 / 20 )3465.6626923076961.686066915926956.1822606883189
Trimmed Mean ( 18 / 20 )3465.7966666666761.694793125451656.176485746848
Trimmed Mean ( 19 / 20 )3466.8161.869668270874556.0340809461237
Trimmed Mean ( 20 / 20 )3467.54761.798809425169556.1102557193882
Median3499.27
Midrange3183.515
Midmean - Weighted Average at Xnp3447.1264516129
Midmean - Weighted Average at X(n+1)p3464.64933333333
Midmean - Empirical Distribution Function3447.1264516129
Midmean - Empirical Distribution Function - Averaging3464.64933333333
Midmean - Empirical Distribution Function - Interpolation3464.64933333333
Midmean - Closest Observation3447.1264516129
Midmean - True Basic - Statistics Graphics Toolkit3464.64933333333
Midmean - MS Excel (old versions)3467.690625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')