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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 19 May 2015 21:10:04 +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/2015/May/19/t14320662387jry8nz17lfn69s.htm/, Retrieved Sat, 04 May 2024 10:31:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279141, Retrieved Sat, 04 May 2024 10:31:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-05-19 20:10:04] [48df267a82852137cd18322add6deebf] [Current]
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Dataseries X:
5119676
4737614
5425255
5195396
5779583
6298652
6175944
6217653
6086619
5060250
3950207
3096398
3287215
2970037
3436547
3339099
3661160
3675026
3917675
3942501
3848079
3993974
3977059
4406890
4827736
4507189
5249062
5009908
5195771
5079423
5531062
5109363
4773753
5347125
5379543
6114549
6346091
5900935
7265533
6115096
7062343
7027841
6644644
7359822
7192534
7065705
7788175
6934803
7492202
8478866
8748316
8382956
8414863
7501787
8031203
9198243
8500998
9260617
9494903
8791918
8568871
8570003
8066695
7800532
8136832
7713840
7986953
7479868
7917564
8055845
7490221
7648110




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279141&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279141&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6252204.45833333211361.94131966929.5805593916142
Geometric Mean5977390.34227755
Harmonic Mean5687585.84416665
Quadratic Mean6500915.73362791
Winsorized Mean ( 1 / 24 )6250705.5210305.038837429.7220909900919
Winsorized Mean ( 2 / 24 )6254273.36111111208868.21015891129.9436345835144
Winsorized Mean ( 3 / 24 )6239504.98611111205272.11726110530.3962616519149
Winsorized Mean ( 4 / 24 )6242496.43055556203786.5468933130.632524696656
Winsorized Mean ( 5 / 24 )6245711.70833333198751.86915188331.4246690357436
Winsorized Mean ( 6 / 24 )6246772.875198525.09961127731.4659097878884
Winsorized Mean ( 7 / 24 )6256998.70833333194441.74222787432.1792976993619
Winsorized Mean ( 8 / 24 )6262272.48611111192705.40370947432.4966107102644
Winsorized Mean ( 9 / 24 )6257375.36111111190889.60235609732.7800743669539
Winsorized Mean ( 10 / 24 )6254014.11111111190004.40902083432.915099935525
Winsorized Mean ( 11 / 24 )6220514.22222222183566.13501474733.8870468767155
Winsorized Mean ( 12 / 24 )6211643.88888889181379.34991187234.2466983805322
Winsorized Mean ( 13 / 24 )6284239.13888889168814.64795828737.2256745187284
Winsorized Mean ( 14 / 24 )6298950.22222222165088.08966047538.1550857798211
Winsorized Mean ( 15 / 24 )6337736.68055556156593.96135599440.4724206838832
Winsorized Mean ( 16 / 24 )6330347.79166667153172.19263733841.3283095493375
Winsorized Mean ( 17 / 24 )6315461.22222222147375.35487631442.8528991670454
Winsorized Mean ( 18 / 24 )6357914.97222222140618.86475864145.2138124079936
Winsorized Mean ( 19 / 24 )6351583.48611111136045.19152525246.6873059966414
Winsorized Mean ( 20 / 24 )6338650.98611111132777.68912319647.7388259124609
Winsorized Mean ( 21 / 24 )6304705.94444444125782.98082594550.1236805094381
Winsorized Mean ( 22 / 24 )6304928.38888889124969.37874675250.4517862865086
Winsorized Mean ( 23 / 24 )6328483.90277778121682.35327071452.0082307144275
Winsorized Mean ( 24 / 24 )6325157.90277778121202.39058348152.1867421288293
Trimmed Mean ( 1 / 24 )6252768.3207062.21014758530.1975348159536
Trimmed Mean ( 2 / 24 )6254952.44117647203176.55906480430.785797682406
Trimmed Mean ( 3 / 24 )6255322.84848485199419.0278533731.3677331387067
Trimmed Mean ( 4 / 24 )6261254.546875196486.73382945331.8660421741738
Trimmed Mean ( 5 / 24 )6266700.4516129193425.30555310932.3985552650052
Trimmed Mean ( 6 / 24 )6271737.75191191.41703233132.8034482266504
Trimmed Mean ( 7 / 24 )6276902.89655172188428.43431676933.3118667536109
Trimmed Mean ( 8 / 24 )6280558.76785714185980.99476314833.7698955522611
Trimmed Mean ( 9 / 24 )6283606.48148148183259.59037473734.2880089856825
Trimmed Mean ( 10 / 24 )6287642.03846154180176.8797664334.8970525331133
Trimmed Mean ( 11 / 24 )6292484.46176402.41334541535.6711925912183
Trimmed Mean ( 12 / 24 )6302298.58333333172937.69873918936.4425953929107
Trimmed Mean ( 13 / 24 )6314123.10869565168859.93552387937.3926656379822
Trimmed Mean ( 14 / 24 )6317884.72727273166342.88759321937.9810932627472
Trimmed Mean ( 15 / 24 )6320203.23809524163685.15453074838.6119514394203
Trimmed Mean ( 16 / 24 )6318099.225161829.35060541439.0417387288746
Trimmed Mean ( 17 / 24 )6316648.73684211159816.43902583539.5243992129056
Trimmed Mean ( 18 / 24 )6316788.44444444158094.52728369439.9557692032516
Trimmed Mean ( 19 / 24 )6311950.02941176156893.23720216440.2308610745187
Trimmed Mean ( 20 / 24 )6307256.59375155820.61659958740.4776770326727
Trimmed Mean ( 21 / 24 )6303489.26666667154547.67172661340.7866983452019
Trimmed Mean ( 22 / 24 )6303340.28571429153951.8213284340.9435902175342
Trimmed Mean ( 23 / 24 )6303140.38461538152434.72798119841.3497663432236
Trimmed Mean ( 24 / 24 )6299834.70833333150284.18021712841.9194801424303
Median6196798.5
Midrange6232470
Midmean - Weighted Average at Xnp6276543.78378378
Midmean - Weighted Average at X(n+1)p6316788.44444444
Midmean - Empirical Distribution Function6276543.78378378
Midmean - Empirical Distribution Function - Averaging6316788.44444444
Midmean - Empirical Distribution Function - Interpolation6316788.44444444
Midmean - Closest Observation6276543.78378378
Midmean - True Basic - Statistics Graphics Toolkit6316788.44444444
Midmean - MS Excel (old versions)6316648.73684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6252204.45833333 & 211361.941319669 & 29.5805593916142 \tabularnewline
Geometric Mean & 5977390.34227755 &  &  \tabularnewline
Harmonic Mean & 5687585.84416665 &  &  \tabularnewline
Quadratic Mean & 6500915.73362791 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 6250705.5 & 210305.0388374 & 29.7220909900919 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6254273.36111111 & 208868.210158911 & 29.9436345835144 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 6239504.98611111 & 205272.117261105 & 30.3962616519149 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 6242496.43055556 & 203786.54689331 & 30.632524696656 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 6245711.70833333 & 198751.869151883 & 31.4246690357436 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 6246772.875 & 198525.099611277 & 31.4659097878884 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 6256998.70833333 & 194441.742227874 & 32.1792976993619 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 6262272.48611111 & 192705.403709474 & 32.4966107102644 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 6257375.36111111 & 190889.602356097 & 32.7800743669539 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 6254014.11111111 & 190004.409020834 & 32.915099935525 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6220514.22222222 & 183566.135014747 & 33.8870468767155 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 6211643.88888889 & 181379.349911872 & 34.2466983805322 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 6284239.13888889 & 168814.647958287 & 37.2256745187284 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 6298950.22222222 & 165088.089660475 & 38.1550857798211 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 6337736.68055556 & 156593.961355994 & 40.4724206838832 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6330347.79166667 & 153172.192637338 & 41.3283095493375 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6315461.22222222 & 147375.354876314 & 42.8528991670454 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6357914.97222222 & 140618.864758641 & 45.2138124079936 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6351583.48611111 & 136045.191525252 & 46.6873059966414 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6338650.98611111 & 132777.689123196 & 47.7388259124609 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 6304705.94444444 & 125782.980825945 & 50.1236805094381 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 6304928.38888889 & 124969.378746752 & 50.4517862865086 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 6328483.90277778 & 121682.353270714 & 52.0082307144275 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6325157.90277778 & 121202.390583481 & 52.1867421288293 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 6252768.3 & 207062.210147585 & 30.1975348159536 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 6254952.44117647 & 203176.559064804 & 30.785797682406 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 6255322.84848485 & 199419.02785337 & 31.3677331387067 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 6261254.546875 & 196486.733829453 & 31.8660421741738 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 6266700.4516129 & 193425.305553109 & 32.3985552650052 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 6271737.75 & 191191.417032331 & 32.8034482266504 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 6276902.89655172 & 188428.434316769 & 33.3118667536109 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 6280558.76785714 & 185980.994763148 & 33.7698955522611 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 6283606.48148148 & 183259.590374737 & 34.2880089856825 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 6287642.03846154 & 180176.87976643 & 34.8970525331133 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 6292484.46 & 176402.413345415 & 35.6711925912183 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 6302298.58333333 & 172937.698739189 & 36.4425953929107 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 6314123.10869565 & 168859.935523879 & 37.3926656379822 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 6317884.72727273 & 166342.887593219 & 37.9810932627472 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 6320203.23809524 & 163685.154530748 & 38.6119514394203 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 6318099.225 & 161829.350605414 & 39.0417387288746 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 6316648.73684211 & 159816.439025835 & 39.5243992129056 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6316788.44444444 & 158094.527283694 & 39.9557692032516 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6311950.02941176 & 156893.237202164 & 40.2308610745187 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6307256.59375 & 155820.616599587 & 40.4776770326727 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6303489.26666667 & 154547.671726613 & 40.7866983452019 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6303340.28571429 & 153951.82132843 & 40.9435902175342 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6303140.38461538 & 152434.727981198 & 41.3497663432236 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6299834.70833333 & 150284.180217128 & 41.9194801424303 \tabularnewline
Median & 6196798.5 &  &  \tabularnewline
Midrange & 6232470 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6276543.78378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6316788.44444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6276543.78378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6316788.44444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6316788.44444444 &  &  \tabularnewline
Midmean - Closest Observation & 6276543.78378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6316788.44444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6316648.73684211 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279141&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]6252204.45833333[/C][C]211361.941319669[/C][C]29.5805593916142[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5977390.34227755[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5687585.84416665[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6500915.73362791[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]6250705.5[/C][C]210305.0388374[/C][C]29.7220909900919[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6254273.36111111[/C][C]208868.210158911[/C][C]29.9436345835144[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]6239504.98611111[/C][C]205272.117261105[/C][C]30.3962616519149[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]6242496.43055556[/C][C]203786.54689331[/C][C]30.632524696656[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]6245711.70833333[/C][C]198751.869151883[/C][C]31.4246690357436[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]6246772.875[/C][C]198525.099611277[/C][C]31.4659097878884[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]6256998.70833333[/C][C]194441.742227874[/C][C]32.1792976993619[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]6262272.48611111[/C][C]192705.403709474[/C][C]32.4966107102644[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]6257375.36111111[/C][C]190889.602356097[/C][C]32.7800743669539[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]6254014.11111111[/C][C]190004.409020834[/C][C]32.915099935525[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6220514.22222222[/C][C]183566.135014747[/C][C]33.8870468767155[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]6211643.88888889[/C][C]181379.349911872[/C][C]34.2466983805322[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]6284239.13888889[/C][C]168814.647958287[/C][C]37.2256745187284[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]6298950.22222222[/C][C]165088.089660475[/C][C]38.1550857798211[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]6337736.68055556[/C][C]156593.961355994[/C][C]40.4724206838832[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6330347.79166667[/C][C]153172.192637338[/C][C]41.3283095493375[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6315461.22222222[/C][C]147375.354876314[/C][C]42.8528991670454[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6357914.97222222[/C][C]140618.864758641[/C][C]45.2138124079936[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6351583.48611111[/C][C]136045.191525252[/C][C]46.6873059966414[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6338650.98611111[/C][C]132777.689123196[/C][C]47.7388259124609[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]6304705.94444444[/C][C]125782.980825945[/C][C]50.1236805094381[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]6304928.38888889[/C][C]124969.378746752[/C][C]50.4517862865086[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]6328483.90277778[/C][C]121682.353270714[/C][C]52.0082307144275[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6325157.90277778[/C][C]121202.390583481[/C][C]52.1867421288293[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]6252768.3[/C][C]207062.210147585[/C][C]30.1975348159536[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]6254952.44117647[/C][C]203176.559064804[/C][C]30.785797682406[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]6255322.84848485[/C][C]199419.02785337[/C][C]31.3677331387067[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]6261254.546875[/C][C]196486.733829453[/C][C]31.8660421741738[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]6266700.4516129[/C][C]193425.305553109[/C][C]32.3985552650052[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]6271737.75[/C][C]191191.417032331[/C][C]32.8034482266504[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]6276902.89655172[/C][C]188428.434316769[/C][C]33.3118667536109[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]6280558.76785714[/C][C]185980.994763148[/C][C]33.7698955522611[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]6283606.48148148[/C][C]183259.590374737[/C][C]34.2880089856825[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]6287642.03846154[/C][C]180176.87976643[/C][C]34.8970525331133[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]6292484.46[/C][C]176402.413345415[/C][C]35.6711925912183[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]6302298.58333333[/C][C]172937.698739189[/C][C]36.4425953929107[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]6314123.10869565[/C][C]168859.935523879[/C][C]37.3926656379822[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]6317884.72727273[/C][C]166342.887593219[/C][C]37.9810932627472[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]6320203.23809524[/C][C]163685.154530748[/C][C]38.6119514394203[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]6318099.225[/C][C]161829.350605414[/C][C]39.0417387288746[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]6316648.73684211[/C][C]159816.439025835[/C][C]39.5243992129056[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6316788.44444444[/C][C]158094.527283694[/C][C]39.9557692032516[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6311950.02941176[/C][C]156893.237202164[/C][C]40.2308610745187[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6307256.59375[/C][C]155820.616599587[/C][C]40.4776770326727[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6303489.26666667[/C][C]154547.671726613[/C][C]40.7866983452019[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6303340.28571429[/C][C]153951.82132843[/C][C]40.9435902175342[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6303140.38461538[/C][C]152434.727981198[/C][C]41.3497663432236[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6299834.70833333[/C][C]150284.180217128[/C][C]41.9194801424303[/C][/ROW]
[ROW][C]Median[/C][C]6196798.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6232470[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6276543.78378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6316788.44444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6276543.78378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6316788.44444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6316788.44444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6276543.78378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6316788.44444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6316648.73684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279141&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 Mean6252204.45833333211361.94131966929.5805593916142
Geometric Mean5977390.34227755
Harmonic Mean5687585.84416665
Quadratic Mean6500915.73362791
Winsorized Mean ( 1 / 24 )6250705.5210305.038837429.7220909900919
Winsorized Mean ( 2 / 24 )6254273.36111111208868.21015891129.9436345835144
Winsorized Mean ( 3 / 24 )6239504.98611111205272.11726110530.3962616519149
Winsorized Mean ( 4 / 24 )6242496.43055556203786.5468933130.632524696656
Winsorized Mean ( 5 / 24 )6245711.70833333198751.86915188331.4246690357436
Winsorized Mean ( 6 / 24 )6246772.875198525.09961127731.4659097878884
Winsorized Mean ( 7 / 24 )6256998.70833333194441.74222787432.1792976993619
Winsorized Mean ( 8 / 24 )6262272.48611111192705.40370947432.4966107102644
Winsorized Mean ( 9 / 24 )6257375.36111111190889.60235609732.7800743669539
Winsorized Mean ( 10 / 24 )6254014.11111111190004.40902083432.915099935525
Winsorized Mean ( 11 / 24 )6220514.22222222183566.13501474733.8870468767155
Winsorized Mean ( 12 / 24 )6211643.88888889181379.34991187234.2466983805322
Winsorized Mean ( 13 / 24 )6284239.13888889168814.64795828737.2256745187284
Winsorized Mean ( 14 / 24 )6298950.22222222165088.08966047538.1550857798211
Winsorized Mean ( 15 / 24 )6337736.68055556156593.96135599440.4724206838832
Winsorized Mean ( 16 / 24 )6330347.79166667153172.19263733841.3283095493375
Winsorized Mean ( 17 / 24 )6315461.22222222147375.35487631442.8528991670454
Winsorized Mean ( 18 / 24 )6357914.97222222140618.86475864145.2138124079936
Winsorized Mean ( 19 / 24 )6351583.48611111136045.19152525246.6873059966414
Winsorized Mean ( 20 / 24 )6338650.98611111132777.68912319647.7388259124609
Winsorized Mean ( 21 / 24 )6304705.94444444125782.98082594550.1236805094381
Winsorized Mean ( 22 / 24 )6304928.38888889124969.37874675250.4517862865086
Winsorized Mean ( 23 / 24 )6328483.90277778121682.35327071452.0082307144275
Winsorized Mean ( 24 / 24 )6325157.90277778121202.39058348152.1867421288293
Trimmed Mean ( 1 / 24 )6252768.3207062.21014758530.1975348159536
Trimmed Mean ( 2 / 24 )6254952.44117647203176.55906480430.785797682406
Trimmed Mean ( 3 / 24 )6255322.84848485199419.0278533731.3677331387067
Trimmed Mean ( 4 / 24 )6261254.546875196486.73382945331.8660421741738
Trimmed Mean ( 5 / 24 )6266700.4516129193425.30555310932.3985552650052
Trimmed Mean ( 6 / 24 )6271737.75191191.41703233132.8034482266504
Trimmed Mean ( 7 / 24 )6276902.89655172188428.43431676933.3118667536109
Trimmed Mean ( 8 / 24 )6280558.76785714185980.99476314833.7698955522611
Trimmed Mean ( 9 / 24 )6283606.48148148183259.59037473734.2880089856825
Trimmed Mean ( 10 / 24 )6287642.03846154180176.8797664334.8970525331133
Trimmed Mean ( 11 / 24 )6292484.46176402.41334541535.6711925912183
Trimmed Mean ( 12 / 24 )6302298.58333333172937.69873918936.4425953929107
Trimmed Mean ( 13 / 24 )6314123.10869565168859.93552387937.3926656379822
Trimmed Mean ( 14 / 24 )6317884.72727273166342.88759321937.9810932627472
Trimmed Mean ( 15 / 24 )6320203.23809524163685.15453074838.6119514394203
Trimmed Mean ( 16 / 24 )6318099.225161829.35060541439.0417387288746
Trimmed Mean ( 17 / 24 )6316648.73684211159816.43902583539.5243992129056
Trimmed Mean ( 18 / 24 )6316788.44444444158094.52728369439.9557692032516
Trimmed Mean ( 19 / 24 )6311950.02941176156893.23720216440.2308610745187
Trimmed Mean ( 20 / 24 )6307256.59375155820.61659958740.4776770326727
Trimmed Mean ( 21 / 24 )6303489.26666667154547.67172661340.7866983452019
Trimmed Mean ( 22 / 24 )6303340.28571429153951.8213284340.9435902175342
Trimmed Mean ( 23 / 24 )6303140.38461538152434.72798119841.3497663432236
Trimmed Mean ( 24 / 24 )6299834.70833333150284.18021712841.9194801424303
Median6196798.5
Midrange6232470
Midmean - Weighted Average at Xnp6276543.78378378
Midmean - Weighted Average at X(n+1)p6316788.44444444
Midmean - Empirical Distribution Function6276543.78378378
Midmean - Empirical Distribution Function - Averaging6316788.44444444
Midmean - Empirical Distribution Function - Interpolation6316788.44444444
Midmean - Closest Observation6276543.78378378
Midmean - True Basic - Statistics Graphics Toolkit6316788.44444444
Midmean - MS Excel (old versions)6316648.73684211
Number of observations72



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')