Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 19:32:32 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/13/t1476383564gb4z3p4fif9v3g1.htm/, Retrieved Tue, 30 Apr 2024 19:59:30 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 19:59:30 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
94,94
96,24
95,77
94,41
95,09
95,37
95,17
95,05
95,33
95,42
95,95
96,12
96,94
98,73
98,03
97,42
98,39
98,77
98,46
98,3
98,25
98,33
98,61
98,99
98,8
100,26
100,85
98,87
99,81
100,44
100,07
99,8
99,77
99,9
100,58
100,86
101,05
101,3
101,45
101,13
101,38
101,03
100,79
100,84
101,17
101,36
101,14
101,24
100,98
102,23
99,96
101,43
101,72
101,51
101,29
101,55
101,6
101,88
102,11
102,24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.27450.300139273227169330.76144595333
Geometric Mean99.2474399144643
Harmonic Mean99.2200911247287
Quadratic Mean99.3012652571288
Winsorized Mean ( 1 / 20 )99.28316666666660.297805864385716333.382174563479
Winsorized Mean ( 2 / 20 )99.28283333333330.296249731618431335.132230469695
Winsorized Mean ( 3 / 20 )99.27333333333330.293971890991353337.696685892507
Winsorized Mean ( 4 / 20 )99.2680.291129380832957340.975547421501
Winsorized Mean ( 5 / 20 )99.27133333333330.28658198723035346.397672417355
Winsorized Mean ( 6 / 20 )99.27033333333330.284968525040316348.355430899918
Winsorized Mean ( 7 / 20 )99.27150.282989870753624350.795241312463
Winsorized Mean ( 8 / 20 )99.31016666666670.27137258267046365.955048551325
Winsorized Mean ( 9 / 20 )99.33416666666670.265064035719701374.755354482379
Winsorized Mean ( 10 / 20 )99.35416666666670.257873013428342385.283304157282
Winsorized Mean ( 11 / 20 )99.37250.252735164864967393.188261131344
Winsorized Mean ( 12 / 20 )99.50050.222701622607166446.78839262664
Winsorized Mean ( 13 / 20 )99.60233333333330.202750349768996491.256037026893
Winsorized Mean ( 14 / 20 )99.7330.176360138084219565.507608938102
Winsorized Mean ( 15 / 20 )99.77050.165032854972393604.549318477764
Winsorized Mean ( 16 / 20 )99.77583333333330.161814620107711616.605800309752
Winsorized Mean ( 17 / 20 )99.78150.160099867314512623.245363495411
Winsorized Mean ( 18 / 20 )99.77550.153946286215511648.118915063163
Winsorized Mean ( 19 / 20 )99.79133333333330.149696202086161666.625685506009
Winsorized Mean ( 20 / 20 )99.82466666666670.139910880970481713.487514153587
Trimmed Mean ( 1 / 20 )99.30724137931030.294318122917231337.414632829925
Trimmed Mean ( 2 / 20 )99.33303571428570.289829542340274342.729160430664
Trimmed Mean ( 3 / 20 )99.36092592592590.285097880444346348.515133718513
Trimmed Mean ( 4 / 20 )99.39461538461540.280042614395938354.926751412506
Trimmed Mean ( 5 / 20 )99.43260.274533490763915362.1875047861
Trimmed Mean ( 6 / 20 )99.47291666666670.26883498298993370.014778435262
Trimmed Mean ( 7 / 20 )99.51695652173910.261737758193716380.216279105153
Trimmed Mean ( 8 / 20 )99.56477272727270.252838952293067393.787317279604
Trimmed Mean ( 9 / 20 )99.61023809523810.244462122144127407.466961431805
Trimmed Mean ( 10 / 20 )99.656250.234952446770809424.154978463419
Trimmed Mean ( 11 / 20 )99.70394736842110.224009290180776445.088448286943
Trimmed Mean ( 12 / 20 )99.75416666666670.210292832490376474.358376770791
Trimmed Mean ( 13 / 20 )99.79147058823530.201076927817944496.285037130601
Trimmed Mean ( 14 / 20 )99.818750.19435415690551513.592050663106
Trimmed Mean ( 15 / 20 )99.8310.192524875240076518.53559118276
Trimmed Mean ( 16 / 20 )99.83964285714290.192287457145179519.220776744491
Trimmed Mean ( 17 / 20 )99.84884615384620.19170917631669520.834985952383
Trimmed Mean ( 18 / 20 )99.858750.190053684730684525.423909257561
Trimmed Mean ( 19 / 20 )99.87136363636360.188171073788257530.747694774519
Trimmed Mean ( 20 / 20 )99.8840.185110777644091539.590407815396
Median99.93
Midrange98.325
Midmean - Weighted Average at Xnp99.7729032258065
Midmean - Weighted Average at X(n+1)p99.831
Midmean - Empirical Distribution Function99.7729032258065
Midmean - Empirical Distribution Function - Averaging99.831
Midmean - Empirical Distribution Function - Interpolation99.831
Midmean - Closest Observation99.7729032258065
Midmean - True Basic - Statistics Graphics Toolkit99.831
Midmean - MS Excel (old versions)99.81875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.2745 & 0.300139273227169 & 330.76144595333 \tabularnewline
Geometric Mean & 99.2474399144643 &  &  \tabularnewline
Harmonic Mean & 99.2200911247287 &  &  \tabularnewline
Quadratic Mean & 99.3012652571288 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.2831666666666 & 0.297805864385716 & 333.382174563479 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 99.2828333333333 & 0.296249731618431 & 335.132230469695 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 99.2733333333333 & 0.293971890991353 & 337.696685892507 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.268 & 0.291129380832957 & 340.975547421501 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.2713333333333 & 0.28658198723035 & 346.397672417355 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.2703333333333 & 0.284968525040316 & 348.355430899918 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.2715 & 0.282989870753624 & 350.795241312463 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.3101666666667 & 0.27137258267046 & 365.955048551325 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.3341666666667 & 0.265064035719701 & 374.755354482379 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.3541666666667 & 0.257873013428342 & 385.283304157282 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.3725 & 0.252735164864967 & 393.188261131344 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 99.5005 & 0.222701622607166 & 446.78839262664 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 99.6023333333333 & 0.202750349768996 & 491.256037026893 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 99.733 & 0.176360138084219 & 565.507608938102 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.7705 & 0.165032854972393 & 604.549318477764 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.7758333333333 & 0.161814620107711 & 616.605800309752 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.7815 & 0.160099867314512 & 623.245363495411 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.7755 & 0.153946286215511 & 648.118915063163 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.7913333333333 & 0.149696202086161 & 666.625685506009 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 99.8246666666667 & 0.139910880970481 & 713.487514153587 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.3072413793103 & 0.294318122917231 & 337.414632829925 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.3330357142857 & 0.289829542340274 & 342.729160430664 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.3609259259259 & 0.285097880444346 & 348.515133718513 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.3946153846154 & 0.280042614395938 & 354.926751412506 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.4326 & 0.274533490763915 & 362.1875047861 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.4729166666667 & 0.26883498298993 & 370.014778435262 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.5169565217391 & 0.261737758193716 & 380.216279105153 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.5647727272727 & 0.252838952293067 & 393.787317279604 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.6102380952381 & 0.244462122144127 & 407.466961431805 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.65625 & 0.234952446770809 & 424.154978463419 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.7039473684211 & 0.224009290180776 & 445.088448286943 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.7541666666667 & 0.210292832490376 & 474.358376770791 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.7914705882353 & 0.201076927817944 & 496.285037130601 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.81875 & 0.19435415690551 & 513.592050663106 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.831 & 0.192524875240076 & 518.53559118276 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.8396428571429 & 0.192287457145179 & 519.220776744491 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.8488461538462 & 0.19170917631669 & 520.834985952383 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.85875 & 0.190053684730684 & 525.423909257561 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.8713636363636 & 0.188171073788257 & 530.747694774519 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.884 & 0.185110777644091 & 539.590407815396 \tabularnewline
Median & 99.93 &  &  \tabularnewline
Midrange & 98.325 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.7729032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.831 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.7729032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.831 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.831 &  &  \tabularnewline
Midmean - Closest Observation & 99.7729032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.831 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.81875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]99.2745[/C][C]0.300139273227169[/C][C]330.76144595333[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.2474399144643[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.2200911247287[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.3012652571288[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.2831666666666[/C][C]0.297805864385716[/C][C]333.382174563479[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]99.2828333333333[/C][C]0.296249731618431[/C][C]335.132230469695[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]99.2733333333333[/C][C]0.293971890991353[/C][C]337.696685892507[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.268[/C][C]0.291129380832957[/C][C]340.975547421501[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.2713333333333[/C][C]0.28658198723035[/C][C]346.397672417355[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.2703333333333[/C][C]0.284968525040316[/C][C]348.355430899918[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.2715[/C][C]0.282989870753624[/C][C]350.795241312463[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.3101666666667[/C][C]0.27137258267046[/C][C]365.955048551325[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.3341666666667[/C][C]0.265064035719701[/C][C]374.755354482379[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.3541666666667[/C][C]0.257873013428342[/C][C]385.283304157282[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.3725[/C][C]0.252735164864967[/C][C]393.188261131344[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]99.5005[/C][C]0.222701622607166[/C][C]446.78839262664[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]99.6023333333333[/C][C]0.202750349768996[/C][C]491.256037026893[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]99.733[/C][C]0.176360138084219[/C][C]565.507608938102[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.7705[/C][C]0.165032854972393[/C][C]604.549318477764[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.7758333333333[/C][C]0.161814620107711[/C][C]616.605800309752[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.7815[/C][C]0.160099867314512[/C][C]623.245363495411[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.7755[/C][C]0.153946286215511[/C][C]648.118915063163[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.7913333333333[/C][C]0.149696202086161[/C][C]666.625685506009[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]99.8246666666667[/C][C]0.139910880970481[/C][C]713.487514153587[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.3072413793103[/C][C]0.294318122917231[/C][C]337.414632829925[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.3330357142857[/C][C]0.289829542340274[/C][C]342.729160430664[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.3609259259259[/C][C]0.285097880444346[/C][C]348.515133718513[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.3946153846154[/C][C]0.280042614395938[/C][C]354.926751412506[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.4326[/C][C]0.274533490763915[/C][C]362.1875047861[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.4729166666667[/C][C]0.26883498298993[/C][C]370.014778435262[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.5169565217391[/C][C]0.261737758193716[/C][C]380.216279105153[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.5647727272727[/C][C]0.252838952293067[/C][C]393.787317279604[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.6102380952381[/C][C]0.244462122144127[/C][C]407.466961431805[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.65625[/C][C]0.234952446770809[/C][C]424.154978463419[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.7039473684211[/C][C]0.224009290180776[/C][C]445.088448286943[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.7541666666667[/C][C]0.210292832490376[/C][C]474.358376770791[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.7914705882353[/C][C]0.201076927817944[/C][C]496.285037130601[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.81875[/C][C]0.19435415690551[/C][C]513.592050663106[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.831[/C][C]0.192524875240076[/C][C]518.53559118276[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.8396428571429[/C][C]0.192287457145179[/C][C]519.220776744491[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.8488461538462[/C][C]0.19170917631669[/C][C]520.834985952383[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.85875[/C][C]0.190053684730684[/C][C]525.423909257561[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.8713636363636[/C][C]0.188171073788257[/C][C]530.747694774519[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.884[/C][C]0.185110777644091[/C][C]539.590407815396[/C][/ROW]
[ROW][C]Median[/C][C]99.93[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.7729032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.831[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.7729032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.831[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.831[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.7729032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.831[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.81875[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean99.27450.300139273227169330.76144595333
Geometric Mean99.2474399144643
Harmonic Mean99.2200911247287
Quadratic Mean99.3012652571288
Winsorized Mean ( 1 / 20 )99.28316666666660.297805864385716333.382174563479
Winsorized Mean ( 2 / 20 )99.28283333333330.296249731618431335.132230469695
Winsorized Mean ( 3 / 20 )99.27333333333330.293971890991353337.696685892507
Winsorized Mean ( 4 / 20 )99.2680.291129380832957340.975547421501
Winsorized Mean ( 5 / 20 )99.27133333333330.28658198723035346.397672417355
Winsorized Mean ( 6 / 20 )99.27033333333330.284968525040316348.355430899918
Winsorized Mean ( 7 / 20 )99.27150.282989870753624350.795241312463
Winsorized Mean ( 8 / 20 )99.31016666666670.27137258267046365.955048551325
Winsorized Mean ( 9 / 20 )99.33416666666670.265064035719701374.755354482379
Winsorized Mean ( 10 / 20 )99.35416666666670.257873013428342385.283304157282
Winsorized Mean ( 11 / 20 )99.37250.252735164864967393.188261131344
Winsorized Mean ( 12 / 20 )99.50050.222701622607166446.78839262664
Winsorized Mean ( 13 / 20 )99.60233333333330.202750349768996491.256037026893
Winsorized Mean ( 14 / 20 )99.7330.176360138084219565.507608938102
Winsorized Mean ( 15 / 20 )99.77050.165032854972393604.549318477764
Winsorized Mean ( 16 / 20 )99.77583333333330.161814620107711616.605800309752
Winsorized Mean ( 17 / 20 )99.78150.160099867314512623.245363495411
Winsorized Mean ( 18 / 20 )99.77550.153946286215511648.118915063163
Winsorized Mean ( 19 / 20 )99.79133333333330.149696202086161666.625685506009
Winsorized Mean ( 20 / 20 )99.82466666666670.139910880970481713.487514153587
Trimmed Mean ( 1 / 20 )99.30724137931030.294318122917231337.414632829925
Trimmed Mean ( 2 / 20 )99.33303571428570.289829542340274342.729160430664
Trimmed Mean ( 3 / 20 )99.36092592592590.285097880444346348.515133718513
Trimmed Mean ( 4 / 20 )99.39461538461540.280042614395938354.926751412506
Trimmed Mean ( 5 / 20 )99.43260.274533490763915362.1875047861
Trimmed Mean ( 6 / 20 )99.47291666666670.26883498298993370.014778435262
Trimmed Mean ( 7 / 20 )99.51695652173910.261737758193716380.216279105153
Trimmed Mean ( 8 / 20 )99.56477272727270.252838952293067393.787317279604
Trimmed Mean ( 9 / 20 )99.61023809523810.244462122144127407.466961431805
Trimmed Mean ( 10 / 20 )99.656250.234952446770809424.154978463419
Trimmed Mean ( 11 / 20 )99.70394736842110.224009290180776445.088448286943
Trimmed Mean ( 12 / 20 )99.75416666666670.210292832490376474.358376770791
Trimmed Mean ( 13 / 20 )99.79147058823530.201076927817944496.285037130601
Trimmed Mean ( 14 / 20 )99.818750.19435415690551513.592050663106
Trimmed Mean ( 15 / 20 )99.8310.192524875240076518.53559118276
Trimmed Mean ( 16 / 20 )99.83964285714290.192287457145179519.220776744491
Trimmed Mean ( 17 / 20 )99.84884615384620.19170917631669520.834985952383
Trimmed Mean ( 18 / 20 )99.858750.190053684730684525.423909257561
Trimmed Mean ( 19 / 20 )99.87136363636360.188171073788257530.747694774519
Trimmed Mean ( 20 / 20 )99.8840.185110777644091539.590407815396
Median99.93
Midrange98.325
Midmean - Weighted Average at Xnp99.7729032258065
Midmean - Weighted Average at X(n+1)p99.831
Midmean - Empirical Distribution Function99.7729032258065
Midmean - Empirical Distribution Function - Averaging99.831
Midmean - Empirical Distribution Function - Interpolation99.831
Midmean - Closest Observation99.7729032258065
Midmean - True Basic - Statistics Graphics Toolkit99.831
Midmean - MS Excel (old versions)99.81875
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')