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 16:52:57 +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/t147637406097a926wpbadam9i.htm/, Retrieved Tue, 30 Apr 2024 18:52:07 +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 18:52:07 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
272 567
266 674
301 601
322 421
313 776
300 156
315 745
299 214
295 184
340 003
332 748
316 337
293 572
308 713
354 188
334 540
313 285
337 881
356 955
323 661
296 034
377 623
342 590
300 905
309 470
271 492
307 759
326 106
335 576
310 485
335 173
298 344
288 269
319 410
327 692
315 401
277 720
260 573
318 025
300 264
317 640
303 273
315 089
275 840
292 823
339 759
328 032
344 675
260 952
275 466
331 940
347 644
338 063
384 283
398 482
347 062
350 731
368 799
387 710
362 988




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.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]'George Udny Yule' @ yule.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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean319823.054056.8396768318378.8355161843035
Geometric Mean318316.520084859
Harmonic Mean316819.864682112
Quadratic Mean321337.520767417
Winsorized Mean ( 1 / 20 )319649.8333333333999.857904479479.9152972347744
Winsorized Mean ( 2 / 20 )319726.3333333333921.8405990755781.5245610463355
Winsorized Mean ( 3 / 20 )319634.2333333333778.3589545558984.5960474316298
Winsorized Mean ( 4 / 20 )319117.6333333333617.6561248734388.2111572571033
Winsorized Mean ( 5 / 20 )318874.9666666673456.7694240184292.2465248769707
Winsorized Mean ( 6 / 20 )318309.0666666673323.939140467195.7626037105889
Winsorized Mean ( 7 / 20 )318205.5833333333214.321021368898.9962051761175
Winsorized Mean ( 8 / 20 )319151.1833333332846.51702104963112.11989282806
Winsorized Mean ( 9 / 20 )319371.2333333332639.69513384447120.987923657759
Winsorized Mean ( 10 / 20 )319399.0666666672601.00204743713122.798467990974
Winsorized Mean ( 11 / 20 )319256.9833333332474.17594870222129.035682971857
Winsorized Mean ( 12 / 20 )319009.9833333332374.79971198187134.331321384196
Winsorized Mean ( 13 / 20 )318949.9666666672201.34940228525144.888388156628
Winsorized Mean ( 14 / 20 )319096.0333333332160.18014523515147.717325352325
Winsorized Mean ( 15 / 20 )318907.5333333332055.72823769809155.131173218903
Winsorized Mean ( 16 / 20 )318887.82043.62259399006156.040455286506
Winsorized Mean ( 17 / 20 )318416.3333333331914.41289825612166.325839960327
Winsorized Mean ( 18 / 20 )318504.2333333331863.83061373729170.886898726639
Winsorized Mean ( 19 / 20 )318833.251752.86692148061181.89244493854
Winsorized Mean ( 20 / 20 )319731.251443.58449360736221.484264631457
Trimmed Mean ( 1 / 20 )319488.4137931033832.4261560270483.3645322273626
Trimmed Mean ( 2 / 20 )319315.4642857143625.0602828811488.0855597887955
Trimmed Mean ( 3 / 20 )319087.2037037043420.2378489896793.2938636995555
Trimmed Mean ( 4 / 20 )318876.8076923083236.860455421698.5142276239319
Trimmed Mean ( 5 / 20 )318804.563073.82788892658103.715813480803
Trimmed Mean ( 6 / 20 )318786.9583333332926.26600230996108.939842817326
Trimmed Mean ( 7 / 20 )318890.8478260872781.62228878337114.642037889898
Trimmed Mean ( 8 / 20 )319024.3409090912628.7917277987121.357784846742
Trimmed Mean ( 9 / 20 )319001.690476192541.58539246414125.512875318704
Trimmed Mean ( 10 / 20 )318940.12482.97674633101128.45069953687
Trimmed Mean ( 11 / 20 )318867.6315789472412.49258356338132.17351785926
Trimmed Mean ( 12 / 20 )318808.6388888892349.60810989488135.685877805024
Trimmed Mean ( 13 / 20 )318779.0294117652287.64064741446139.348384883813
Trimmed Mean ( 14 / 20 )318754.3752245.8957848734141.927500441864
Trimmed Mean ( 15 / 20 )318705.5666666672192.09748382283145.388409511274
Trimmed Mean ( 16 / 20 )318676.7142857142139.87821122636148.92282776368
Trimmed Mean ( 17 / 20 )318646.2692307692058.35139599833154.806545592873
Trimmed Mean ( 18 / 20 )318680.0833333331974.71835536904161.380017796906
Trimmed Mean ( 19 / 20 )318706.7272727271854.44589241279171.860893098403
Trimmed Mean ( 20 / 20 )318686.751701.31798425592187.317569642561
Median316988.5
Midrange329527.5
Midmean - Weighted Average at Xnp318076.806451613
Midmean - Weighted Average at X(n+1)p318705.566666667
Midmean - Empirical Distribution Function318076.806451613
Midmean - Empirical Distribution Function - Averaging318705.566666667
Midmean - Empirical Distribution Function - Interpolation318705.566666667
Midmean - Closest Observation318076.806451613
Midmean - True Basic - Statistics Graphics Toolkit318705.566666667
Midmean - MS Excel (old versions)318754.375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 319823.05 & 4056.83967683183 & 78.8355161843035 \tabularnewline
Geometric Mean & 318316.520084859 &  &  \tabularnewline
Harmonic Mean & 316819.864682112 &  &  \tabularnewline
Quadratic Mean & 321337.520767417 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 319649.833333333 & 3999.8579044794 & 79.9152972347744 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 319726.333333333 & 3921.84059907557 & 81.5245610463355 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 319634.233333333 & 3778.35895455589 & 84.5960474316298 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 319117.633333333 & 3617.65612487343 & 88.2111572571033 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 318874.966666667 & 3456.76942401842 & 92.2465248769707 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 318309.066666667 & 3323.9391404671 & 95.7626037105889 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 318205.583333333 & 3214.3210213688 & 98.9962051761175 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 319151.183333333 & 2846.51702104963 & 112.11989282806 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 319371.233333333 & 2639.69513384447 & 120.987923657759 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 319399.066666667 & 2601.00204743713 & 122.798467990974 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 319256.983333333 & 2474.17594870222 & 129.035682971857 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 319009.983333333 & 2374.79971198187 & 134.331321384196 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 318949.966666667 & 2201.34940228525 & 144.888388156628 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 319096.033333333 & 2160.18014523515 & 147.717325352325 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 318907.533333333 & 2055.72823769809 & 155.131173218903 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 318887.8 & 2043.62259399006 & 156.040455286506 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 318416.333333333 & 1914.41289825612 & 166.325839960327 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 318504.233333333 & 1863.83061373729 & 170.886898726639 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 318833.25 & 1752.86692148061 & 181.89244493854 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 319731.25 & 1443.58449360736 & 221.484264631457 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 319488.413793103 & 3832.42615602704 & 83.3645322273626 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 319315.464285714 & 3625.06028288114 & 88.0855597887955 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 319087.203703704 & 3420.23784898967 & 93.2938636995555 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 318876.807692308 & 3236.8604554216 & 98.5142276239319 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 318804.56 & 3073.82788892658 & 103.715813480803 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 318786.958333333 & 2926.26600230996 & 108.939842817326 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 318890.847826087 & 2781.62228878337 & 114.642037889898 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 319024.340909091 & 2628.7917277987 & 121.357784846742 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 319001.69047619 & 2541.58539246414 & 125.512875318704 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 318940.1 & 2482.97674633101 & 128.45069953687 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 318867.631578947 & 2412.49258356338 & 132.17351785926 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 318808.638888889 & 2349.60810989488 & 135.685877805024 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 318779.029411765 & 2287.64064741446 & 139.348384883813 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 318754.375 & 2245.8957848734 & 141.927500441864 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 318705.566666667 & 2192.09748382283 & 145.388409511274 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 318676.714285714 & 2139.87821122636 & 148.92282776368 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 318646.269230769 & 2058.35139599833 & 154.806545592873 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 318680.083333333 & 1974.71835536904 & 161.380017796906 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 318706.727272727 & 1854.44589241279 & 171.860893098403 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 318686.75 & 1701.31798425592 & 187.317569642561 \tabularnewline
Median & 316988.5 &  &  \tabularnewline
Midrange & 329527.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 318076.806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 318705.566666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 318076.806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 318705.566666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 318705.566666667 &  &  \tabularnewline
Midmean - Closest Observation & 318076.806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 318705.566666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 318754.375 &  &  \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]319823.05[/C][C]4056.83967683183[/C][C]78.8355161843035[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]318316.520084859[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]316819.864682112[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]321337.520767417[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]319649.833333333[/C][C]3999.8579044794[/C][C]79.9152972347744[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]319726.333333333[/C][C]3921.84059907557[/C][C]81.5245610463355[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]319634.233333333[/C][C]3778.35895455589[/C][C]84.5960474316298[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]319117.633333333[/C][C]3617.65612487343[/C][C]88.2111572571033[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]318874.966666667[/C][C]3456.76942401842[/C][C]92.2465248769707[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]318309.066666667[/C][C]3323.9391404671[/C][C]95.7626037105889[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]318205.583333333[/C][C]3214.3210213688[/C][C]98.9962051761175[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]319151.183333333[/C][C]2846.51702104963[/C][C]112.11989282806[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]319371.233333333[/C][C]2639.69513384447[/C][C]120.987923657759[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]319399.066666667[/C][C]2601.00204743713[/C][C]122.798467990974[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]319256.983333333[/C][C]2474.17594870222[/C][C]129.035682971857[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]319009.983333333[/C][C]2374.79971198187[/C][C]134.331321384196[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]318949.966666667[/C][C]2201.34940228525[/C][C]144.888388156628[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]319096.033333333[/C][C]2160.18014523515[/C][C]147.717325352325[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]318907.533333333[/C][C]2055.72823769809[/C][C]155.131173218903[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]318887.8[/C][C]2043.62259399006[/C][C]156.040455286506[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]318416.333333333[/C][C]1914.41289825612[/C][C]166.325839960327[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]318504.233333333[/C][C]1863.83061373729[/C][C]170.886898726639[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]318833.25[/C][C]1752.86692148061[/C][C]181.89244493854[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]319731.25[/C][C]1443.58449360736[/C][C]221.484264631457[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]319488.413793103[/C][C]3832.42615602704[/C][C]83.3645322273626[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]319315.464285714[/C][C]3625.06028288114[/C][C]88.0855597887955[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]319087.203703704[/C][C]3420.23784898967[/C][C]93.2938636995555[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]318876.807692308[/C][C]3236.8604554216[/C][C]98.5142276239319[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]318804.56[/C][C]3073.82788892658[/C][C]103.715813480803[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]318786.958333333[/C][C]2926.26600230996[/C][C]108.939842817326[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]318890.847826087[/C][C]2781.62228878337[/C][C]114.642037889898[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]319024.340909091[/C][C]2628.7917277987[/C][C]121.357784846742[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]319001.69047619[/C][C]2541.58539246414[/C][C]125.512875318704[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]318940.1[/C][C]2482.97674633101[/C][C]128.45069953687[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]318867.631578947[/C][C]2412.49258356338[/C][C]132.17351785926[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]318808.638888889[/C][C]2349.60810989488[/C][C]135.685877805024[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]318779.029411765[/C][C]2287.64064741446[/C][C]139.348384883813[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]318754.375[/C][C]2245.8957848734[/C][C]141.927500441864[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]318705.566666667[/C][C]2192.09748382283[/C][C]145.388409511274[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]318676.714285714[/C][C]2139.87821122636[/C][C]148.92282776368[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]318646.269230769[/C][C]2058.35139599833[/C][C]154.806545592873[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]318680.083333333[/C][C]1974.71835536904[/C][C]161.380017796906[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]318706.727272727[/C][C]1854.44589241279[/C][C]171.860893098403[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]318686.75[/C][C]1701.31798425592[/C][C]187.317569642561[/C][/ROW]
[ROW][C]Median[/C][C]316988.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]329527.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]318076.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]318705.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]318076.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]318705.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]318705.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]318076.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]318705.566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]318754.375[/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 Mean319823.054056.8396768318378.8355161843035
Geometric Mean318316.520084859
Harmonic Mean316819.864682112
Quadratic Mean321337.520767417
Winsorized Mean ( 1 / 20 )319649.8333333333999.857904479479.9152972347744
Winsorized Mean ( 2 / 20 )319726.3333333333921.8405990755781.5245610463355
Winsorized Mean ( 3 / 20 )319634.2333333333778.3589545558984.5960474316298
Winsorized Mean ( 4 / 20 )319117.6333333333617.6561248734388.2111572571033
Winsorized Mean ( 5 / 20 )318874.9666666673456.7694240184292.2465248769707
Winsorized Mean ( 6 / 20 )318309.0666666673323.939140467195.7626037105889
Winsorized Mean ( 7 / 20 )318205.5833333333214.321021368898.9962051761175
Winsorized Mean ( 8 / 20 )319151.1833333332846.51702104963112.11989282806
Winsorized Mean ( 9 / 20 )319371.2333333332639.69513384447120.987923657759
Winsorized Mean ( 10 / 20 )319399.0666666672601.00204743713122.798467990974
Winsorized Mean ( 11 / 20 )319256.9833333332474.17594870222129.035682971857
Winsorized Mean ( 12 / 20 )319009.9833333332374.79971198187134.331321384196
Winsorized Mean ( 13 / 20 )318949.9666666672201.34940228525144.888388156628
Winsorized Mean ( 14 / 20 )319096.0333333332160.18014523515147.717325352325
Winsorized Mean ( 15 / 20 )318907.5333333332055.72823769809155.131173218903
Winsorized Mean ( 16 / 20 )318887.82043.62259399006156.040455286506
Winsorized Mean ( 17 / 20 )318416.3333333331914.41289825612166.325839960327
Winsorized Mean ( 18 / 20 )318504.2333333331863.83061373729170.886898726639
Winsorized Mean ( 19 / 20 )318833.251752.86692148061181.89244493854
Winsorized Mean ( 20 / 20 )319731.251443.58449360736221.484264631457
Trimmed Mean ( 1 / 20 )319488.4137931033832.4261560270483.3645322273626
Trimmed Mean ( 2 / 20 )319315.4642857143625.0602828811488.0855597887955
Trimmed Mean ( 3 / 20 )319087.2037037043420.2378489896793.2938636995555
Trimmed Mean ( 4 / 20 )318876.8076923083236.860455421698.5142276239319
Trimmed Mean ( 5 / 20 )318804.563073.82788892658103.715813480803
Trimmed Mean ( 6 / 20 )318786.9583333332926.26600230996108.939842817326
Trimmed Mean ( 7 / 20 )318890.8478260872781.62228878337114.642037889898
Trimmed Mean ( 8 / 20 )319024.3409090912628.7917277987121.357784846742
Trimmed Mean ( 9 / 20 )319001.690476192541.58539246414125.512875318704
Trimmed Mean ( 10 / 20 )318940.12482.97674633101128.45069953687
Trimmed Mean ( 11 / 20 )318867.6315789472412.49258356338132.17351785926
Trimmed Mean ( 12 / 20 )318808.6388888892349.60810989488135.685877805024
Trimmed Mean ( 13 / 20 )318779.0294117652287.64064741446139.348384883813
Trimmed Mean ( 14 / 20 )318754.3752245.8957848734141.927500441864
Trimmed Mean ( 15 / 20 )318705.5666666672192.09748382283145.388409511274
Trimmed Mean ( 16 / 20 )318676.7142857142139.87821122636148.92282776368
Trimmed Mean ( 17 / 20 )318646.2692307692058.35139599833154.806545592873
Trimmed Mean ( 18 / 20 )318680.0833333331974.71835536904161.380017796906
Trimmed Mean ( 19 / 20 )318706.7272727271854.44589241279171.860893098403
Trimmed Mean ( 20 / 20 )318686.751701.31798425592187.317569642561
Median316988.5
Midrange329527.5
Midmean - Weighted Average at Xnp318076.806451613
Midmean - Weighted Average at X(n+1)p318705.566666667
Midmean - Empirical Distribution Function318076.806451613
Midmean - Empirical Distribution Function - Averaging318705.566666667
Midmean - Empirical Distribution Function - Interpolation318705.566666667
Midmean - Closest Observation318076.806451613
Midmean - True Basic - Statistics Graphics Toolkit318705.566666667
Midmean - MS Excel (old versions)318754.375
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')