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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 24 Dec 2009 02:16:01 -0700
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/Dec/24/t12616463019co2cn4k52992n7.htm/, Retrieved Sun, 05 May 2024 22:00:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70619, Retrieved Sun, 05 May 2024 22:00:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-12-24 09:16:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
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
2513.17
2466.92




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70619&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70619&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70619&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3360.29016666667110.78962856155630.3303676553051
Geometric Mean3238.32039844188
Harmonic Mean3103.15480692867
Quadratic Mean3466.3721915294
Winsorized Mean ( 1 / 20 )3361.3795109.95414725491330.5707386571524
Winsorized Mean ( 2 / 20 )3362.10316666667109.35366078633330.7452273887374
Winsorized Mean ( 3 / 20 )3360.76216666667109.06676580580630.8138060374003
Winsorized Mean ( 4 / 20 )3359.48016666667107.70072150650731.192735941548
Winsorized Mean ( 5 / 20 )3363.67266666667104.80110423817332.0957750504451
Winsorized Mean ( 6 / 20 )3364.31966666667104.32020838023332.2499323851441
Winsorized Mean ( 7 / 20 )3357.80616666667102.20242627475132.8544662691263
Winsorized Mean ( 8 / 20 )3352.24883333333100.34785433682833.4062831286972
Winsorized Mean ( 9 / 20 )3370.4573333333396.181273541123735.0427605004860
Winsorized Mean ( 10 / 20 )3371.6606666666790.586169835224937.2204793822244
Winsorized Mean ( 11 / 20 )3398.6271666666785.116530423987639.9291083616451
Winsorized Mean ( 12 / 20 )3391.1111666666782.296592483258241.2059729855344
Winsorized Mean ( 13 / 20 )3396.479.674555100078742.6284150031814
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 )3366.38586206897108.34157124024131.0719682531112
Trimmed Mean ( 2 / 20 )3371.74982142857106.30994315339831.71622259795
Trimmed Mean ( 3 / 20 )3377.10907407407104.14863475232632.425860234319
Trimmed Mean ( 4 / 20 )3383.39634615385101.5486342187433.3179896724742
Trimmed Mean ( 5 / 20 )3390.571298.784514761290834.3229018049357
Trimmed Mean ( 6 / 20 )3397.2958333333396.256686918324435.2941280455248
Trimmed Mean ( 7 / 20 )3404.4645652173993.12701288799236.5572185732199
Trimmed Mean ( 8 / 20 )3413.5538636363689.667988922711738.0688125678679
Trimmed Mean ( 9 / 20 )3424.5011904761985.624107017700839.9945915905232
Trimmed Mean ( 10 / 20 )3433.508581.516870389013542.1202198221628
Trimmed Mean ( 11 / 20 )3443.2739473684277.621895782782644.3595703589113
Trimmed Mean ( 12 / 20 )3450.0386111111173.987675088117846.6299097383745
Trimmed Mean ( 13 / 20 )3458.7044117647169.723030794759549.6063405784229
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 & 3360.29016666667 & 110.789628561556 & 30.3303676553051 \tabularnewline
Geometric Mean & 3238.32039844188 &  &  \tabularnewline
Harmonic Mean & 3103.15480692867 &  &  \tabularnewline
Quadratic Mean & 3466.3721915294 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3361.3795 & 109.954147254913 & 30.5707386571524 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3362.10316666667 & 109.353660786333 & 30.7452273887374 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3360.76216666667 & 109.066765805806 & 30.8138060374003 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3359.48016666667 & 107.700721506507 & 31.192735941548 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3363.67266666667 & 104.801104238173 & 32.0957750504451 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3364.31966666667 & 104.320208380233 & 32.2499323851441 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3357.80616666667 & 102.202426274751 & 32.8544662691263 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3352.24883333333 & 100.347854336828 & 33.4062831286972 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3370.45733333333 & 96.1812735411237 & 35.0427605004860 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3371.66066666667 & 90.5861698352249 & 37.2204793822244 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3398.62716666667 & 85.1165304239876 & 39.9291083616451 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3391.11116666667 & 82.2965924832582 & 41.2059729855344 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3396.4 & 79.6745551000787 & 42.6284150031814 \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 ) & 3366.38586206897 & 108.341571240241 & 31.0719682531112 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3371.74982142857 & 106.309943153398 & 31.71622259795 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3377.10907407407 & 104.148634752326 & 32.425860234319 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3383.39634615385 & 101.54863421874 & 33.3179896724742 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3390.5712 & 98.7845147612908 & 34.3229018049357 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3397.29583333333 & 96.2566869183244 & 35.2941280455248 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3404.46456521739 & 93.127012887992 & 36.5572185732199 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3413.55386363636 & 89.6679889227117 & 38.0688125678679 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3424.50119047619 & 85.6241070177008 & 39.9945915905232 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3433.5085 & 81.5168703890135 & 42.1202198221628 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3443.27394736842 & 77.6218957827826 & 44.3595703589113 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3450.03861111111 & 73.9876750881178 & 46.6299097383745 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3458.70441176471 & 69.7230307947595 & 49.6063405784229 \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=70619&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]3360.29016666667[/C][C]110.789628561556[/C][C]30.3303676553051[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3238.32039844188[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3103.15480692867[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3466.3721915294[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3361.3795[/C][C]109.954147254913[/C][C]30.5707386571524[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3362.10316666667[/C][C]109.353660786333[/C][C]30.7452273887374[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3360.76216666667[/C][C]109.066765805806[/C][C]30.8138060374003[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3359.48016666667[/C][C]107.700721506507[/C][C]31.192735941548[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3363.67266666667[/C][C]104.801104238173[/C][C]32.0957750504451[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3364.31966666667[/C][C]104.320208380233[/C][C]32.2499323851441[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3357.80616666667[/C][C]102.202426274751[/C][C]32.8544662691263[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3352.24883333333[/C][C]100.347854336828[/C][C]33.4062831286972[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3370.45733333333[/C][C]96.1812735411237[/C][C]35.0427605004860[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3371.66066666667[/C][C]90.5861698352249[/C][C]37.2204793822244[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3398.62716666667[/C][C]85.1165304239876[/C][C]39.9291083616451[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3391.11116666667[/C][C]82.2965924832582[/C][C]41.2059729855344[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3396.4[/C][C]79.6745551000787[/C][C]42.6284150031814[/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]3366.38586206897[/C][C]108.341571240241[/C][C]31.0719682531112[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3371.74982142857[/C][C]106.309943153398[/C][C]31.71622259795[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3377.10907407407[/C][C]104.148634752326[/C][C]32.425860234319[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3383.39634615385[/C][C]101.54863421874[/C][C]33.3179896724742[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3390.5712[/C][C]98.7845147612908[/C][C]34.3229018049357[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3397.29583333333[/C][C]96.2566869183244[/C][C]35.2941280455248[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3404.46456521739[/C][C]93.127012887992[/C][C]36.5572185732199[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3413.55386363636[/C][C]89.6679889227117[/C][C]38.0688125678679[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3424.50119047619[/C][C]85.6241070177008[/C][C]39.9945915905232[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3433.5085[/C][C]81.5168703890135[/C][C]42.1202198221628[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3443.27394736842[/C][C]77.6218957827826[/C][C]44.3595703589113[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3450.03861111111[/C][C]73.9876750881178[/C][C]46.6299097383745[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3458.70441176471[/C][C]69.7230307947595[/C][C]49.6063405784229[/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=70619&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70619&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 Mean3360.29016666667110.78962856155630.3303676553051
Geometric Mean3238.32039844188
Harmonic Mean3103.15480692867
Quadratic Mean3466.3721915294
Winsorized Mean ( 1 / 20 )3361.3795109.95414725491330.5707386571524
Winsorized Mean ( 2 / 20 )3362.10316666667109.35366078633330.7452273887374
Winsorized Mean ( 3 / 20 )3360.76216666667109.06676580580630.8138060374003
Winsorized Mean ( 4 / 20 )3359.48016666667107.70072150650731.192735941548
Winsorized Mean ( 5 / 20 )3363.67266666667104.80110423817332.0957750504451
Winsorized Mean ( 6 / 20 )3364.31966666667104.32020838023332.2499323851441
Winsorized Mean ( 7 / 20 )3357.80616666667102.20242627475132.8544662691263
Winsorized Mean ( 8 / 20 )3352.24883333333100.34785433682833.4062831286972
Winsorized Mean ( 9 / 20 )3370.4573333333396.181273541123735.0427605004860
Winsorized Mean ( 10 / 20 )3371.6606666666790.586169835224937.2204793822244
Winsorized Mean ( 11 / 20 )3398.6271666666785.116530423987639.9291083616451
Winsorized Mean ( 12 / 20 )3391.1111666666782.296592483258241.2059729855344
Winsorized Mean ( 13 / 20 )3396.479.674555100078742.6284150031814
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 )3366.38586206897108.34157124024131.0719682531112
Trimmed Mean ( 2 / 20 )3371.74982142857106.30994315339831.71622259795
Trimmed Mean ( 3 / 20 )3377.10907407407104.14863475232632.425860234319
Trimmed Mean ( 4 / 20 )3383.39634615385101.5486342187433.3179896724742
Trimmed Mean ( 5 / 20 )3390.571298.784514761290834.3229018049357
Trimmed Mean ( 6 / 20 )3397.2958333333396.256686918324435.2941280455248
Trimmed Mean ( 7 / 20 )3404.4645652173993.12701288799236.5572185732199
Trimmed Mean ( 8 / 20 )3413.5538636363689.667988922711738.0688125678679
Trimmed Mean ( 9 / 20 )3424.5011904761985.624107017700839.9945915905232
Trimmed Mean ( 10 / 20 )3433.508581.516870389013542.1202198221628
Trimmed Mean ( 11 / 20 )3443.2739473684277.621895782782644.3595703589113
Trimmed Mean ( 12 / 20 )3450.0386111111173.987675088117846.6299097383745
Trimmed Mean ( 13 / 20 )3458.7044117647169.723030794759549.6063405784229
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')