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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, 12 Apr 2011 18:41:57 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Apr/12/t13026335229yol17loj6ibi5l.htm/, Retrieved Thu, 09 May 2024 19:51:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120557, Retrieved Thu, 09 May 2024 19:51:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-04-12 18:41:57] [f0cd0ad4d4cb2a25864ed1f6cd7bfd87] [Current]
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Dataseries X:
7989
41102
9123
22109
47115
9105
5496
23102
6994
84101
5884
6383
6292
36109
49127
26116
63120
60115
77117
18110
3999
79105
2286
7487
7789
3788
83108
52100
93102
598
8983
3488
2780
7974
9171
3071
4166
7968
6580
7183
2779
5273
1568
1860
9853
6757
6745
5144
9444
2248
7349
8149
7949
3545
1043
4038
4335
5432
8027
8626
24
4829
931
232
9034
1337
5138
9736
7730
7133
8126
424




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120557&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120557&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120557&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'Herman Ole Andreas Wold' @ www.yougetit.org







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16169.06944444442732.435268869655.91745745220645
Geometric Mean7035.81374800811
Harmonic Mean1143.50470360894
Quadratic Mean28134.3061776405
Winsorized Mean ( 1 / 24 )16046.94444444442685.072615528445.97635399193339
Winsorized Mean ( 2 / 24 )16024.69444444442674.837292788995.99090437674282
Winsorized Mean ( 3 / 24 )15865.15277777782616.381128275436.06377740854413
Winsorized Mean ( 4 / 24 )15773.20833333332577.558542474196.11943747287024
Winsorized Mean ( 5 / 24 )14808.97222222222267.038321330366.53229902771645
Winsorized Mean ( 6 / 24 )14583.05555555562190.698056805446.65680763729765
Winsorized Mean ( 7 / 24 )13826.27777777781967.564554842737.02710248756382
Winsorized Mean ( 8 / 24 )13528.38888888891875.281192744327.21405885220404
Winsorized Mean ( 9 / 24 )13325.38888888891804.259202167327.38551804135575
Winsorized Mean ( 10 / 24 )12495.52777777781587.398424161817.87170226931263
Winsorized Mean ( 11 / 24 )11808.02777777781389.600875187158.4974239644081
Winsorized Mean ( 12 / 24 )10142.6944444444993.08021648248210.2133687451454
Winsorized Mean ( 13 / 24 )9651.04166666667866.23432188173411.1413752871181
Winsorized Mean ( 14 / 24 )9539.04166666667815.5817008335511.6959976626713
Winsorized Mean ( 15 / 24 )8717.79166666667636.85855480878813.6887407742903
Winsorized Mean ( 16 / 24 )6936.90277777778284.9032831250224.3482725144088
Winsorized Mean ( 17 / 24 )6959.09722222222273.25490913733525.4674188441557
Winsorized Mean ( 18 / 24 )6895.84722222222261.52293431367626.3680401121196
Winsorized Mean ( 19 / 24 )6857.58333333333246.61963670266727.8063151216181
Winsorized Mean ( 20 / 24 )6891.19444444444237.69288488920328.9920097846289
Winsorized Mean ( 21 / 24 )7030.02777777778215.69750649551132.5920679009985
Winsorized Mean ( 22 / 24 )7102.75199.40308100135435.6200614570834
Winsorized Mean ( 23 / 24 )7088.375196.92174855458435.9958971115635
Winsorized Mean ( 24 / 24 )7012.375175.12037826815340.0431695576988
Trimmed Mean ( 1 / 24 )15300.67142857142571.346331236645.95045142021489
Trimmed Mean ( 2 / 24 )14510.52431.32599269375.96814250479163
Trimmed Mean ( 3 / 24 )13684.57575757582263.680209409266.04527781825992
Trimmed Mean ( 4 / 24 )12866.8593752082.686785968076.17800980046034
Trimmed Mean ( 5 / 24 )12023.08064516131866.40345216976.44184440999851
Trimmed Mean ( 6 / 24 )11354.46666666671715.348845690156.61933384290605
Trimmed Mean ( 7 / 24 )10686.48275862071547.039567958246.90769840665714
Trimmed Mean ( 8 / 24 )10109.78571428571406.790477830937.18641892563388
Trimmed Mean ( 9 / 24 )9540.018518518521252.191768883357.61865614803224
Trimmed Mean ( 10 / 24 )8957.653846153851064.454193438158.4152553499939
Trimmed Mean ( 11 / 24 )8448.2883.9002723319939.55786559236047
Trimmed Mean ( 12 / 24 )7990.04166666667700.43044133914611.4073306856718
Trimmed Mean ( 13 / 24 )7709.26086956522600.91656356112312.8291701994017
Trimmed Mean ( 14 / 24 )7464.84090909091507.03298526121414.7225942415663
Trimmed Mean ( 15 / 24 )7210.85714285714383.62535496881118.7966125008692
Trimmed Mean ( 16 / 24 )7030.025277.21852550183325.3591457759684
Trimmed Mean ( 17 / 24 )7041.05263157895268.55288648831726.2184954466511
Trimmed Mean ( 18 / 24 )7050.69444444444259.55007719233427.1650639472539
Trimmed Mean ( 19 / 24 )7068.91176470588249.89470640993228.2875610542542
Trimmed Mean ( 20 / 24 )7093.9375240.12813673414329.5423001922262
Trimmed Mean ( 21 / 24 )7118.26666666667228.57288851476831.1422177534706
Trimmed Mean ( 22 / 24 )7129.07142857143219.01209727509232.551039496311
Trimmed Mean ( 23 / 24 )7132.38461538462210.01508427087333.9612968284955
Trimmed Mean ( 24 / 24 )7138.125196.38894336055536.3468781788542
Median7266
Midrange46563
Midmean - Weighted Average at Xnp6968.21621621622
Midmean - Weighted Average at X(n+1)p7050.69444444444
Midmean - Empirical Distribution Function6968.21621621622
Midmean - Empirical Distribution Function - Averaging7050.69444444444
Midmean - Empirical Distribution Function - Interpolation7050.69444444444
Midmean - Closest Observation6968.21621621622
Midmean - True Basic - Statistics Graphics Toolkit7050.69444444444
Midmean - MS Excel (old versions)7041.05263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16169.0694444444 & 2732.43526886965 & 5.91745745220645 \tabularnewline
Geometric Mean & 7035.81374800811 &  &  \tabularnewline
Harmonic Mean & 1143.50470360894 &  &  \tabularnewline
Quadratic Mean & 28134.3061776405 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16046.9444444444 & 2685.07261552844 & 5.97635399193339 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16024.6944444444 & 2674.83729278899 & 5.99090437674282 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 15865.1527777778 & 2616.38112827543 & 6.06377740854413 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 15773.2083333333 & 2577.55854247419 & 6.11943747287024 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 14808.9722222222 & 2267.03832133036 & 6.53229902771645 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 14583.0555555556 & 2190.69805680544 & 6.65680763729765 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 13826.2777777778 & 1967.56455484273 & 7.02710248756382 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13528.3888888889 & 1875.28119274432 & 7.21405885220404 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13325.3888888889 & 1804.25920216732 & 7.38551804135575 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 12495.5277777778 & 1587.39842416181 & 7.87170226931263 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 11808.0277777778 & 1389.60087518715 & 8.4974239644081 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 10142.6944444444 & 993.080216482482 & 10.2133687451454 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9651.04166666667 & 866.234321881734 & 11.1413752871181 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9539.04166666667 & 815.58170083355 & 11.6959976626713 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8717.79166666667 & 636.858554808788 & 13.6887407742903 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6936.90277777778 & 284.90328312502 & 24.3482725144088 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6959.09722222222 & 273.254909137335 & 25.4674188441557 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6895.84722222222 & 261.522934313676 & 26.3680401121196 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6857.58333333333 & 246.619636702667 & 27.8063151216181 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6891.19444444444 & 237.692884889203 & 28.9920097846289 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 7030.02777777778 & 215.697506495511 & 32.5920679009985 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 7102.75 & 199.403081001354 & 35.6200614570834 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 7088.375 & 196.921748554584 & 35.9958971115635 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 7012.375 & 175.120378268153 & 40.0431695576988 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 15300.6714285714 & 2571.34633123664 & 5.95045142021489 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 14510.5 & 2431.3259926937 & 5.96814250479163 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 13684.5757575758 & 2263.68020940926 & 6.04527781825992 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 12866.859375 & 2082.68678596807 & 6.17800980046034 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 12023.0806451613 & 1866.4034521697 & 6.44184440999851 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 11354.4666666667 & 1715.34884569015 & 6.61933384290605 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 10686.4827586207 & 1547.03956795824 & 6.90769840665714 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 10109.7857142857 & 1406.79047783093 & 7.18641892563388 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9540.01851851852 & 1252.19176888335 & 7.61865614803224 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8957.65384615385 & 1064.45419343815 & 8.4152553499939 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8448.2 & 883.900272331993 & 9.55786559236047 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 7990.04166666667 & 700.430441339146 & 11.4073306856718 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 7709.26086956522 & 600.916563561123 & 12.8291701994017 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 7464.84090909091 & 507.032985261214 & 14.7225942415663 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 7210.85714285714 & 383.625354968811 & 18.7966125008692 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 7030.025 & 277.218525501833 & 25.3591457759684 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 7041.05263157895 & 268.552886488317 & 26.2184954466511 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 7050.69444444444 & 259.550077192334 & 27.1650639472539 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 7068.91176470588 & 249.894706409932 & 28.2875610542542 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 7093.9375 & 240.128136734143 & 29.5423001922262 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 7118.26666666667 & 228.572888514768 & 31.1422177534706 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 7129.07142857143 & 219.012097275092 & 32.551039496311 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 7132.38461538462 & 210.015084270873 & 33.9612968284955 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 7138.125 & 196.388943360555 & 36.3468781788542 \tabularnewline
Median & 7266 &  &  \tabularnewline
Midrange & 46563 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6968.21621621622 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7050.69444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6968.21621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7050.69444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7050.69444444444 &  &  \tabularnewline
Midmean - Closest Observation & 6968.21621621622 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7050.69444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7041.05263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120557&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]16169.0694444444[/C][C]2732.43526886965[/C][C]5.91745745220645[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7035.81374800811[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1143.50470360894[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]28134.3061776405[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16046.9444444444[/C][C]2685.07261552844[/C][C]5.97635399193339[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16024.6944444444[/C][C]2674.83729278899[/C][C]5.99090437674282[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]15865.1527777778[/C][C]2616.38112827543[/C][C]6.06377740854413[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]15773.2083333333[/C][C]2577.55854247419[/C][C]6.11943747287024[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]14808.9722222222[/C][C]2267.03832133036[/C][C]6.53229902771645[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]14583.0555555556[/C][C]2190.69805680544[/C][C]6.65680763729765[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]13826.2777777778[/C][C]1967.56455484273[/C][C]7.02710248756382[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13528.3888888889[/C][C]1875.28119274432[/C][C]7.21405885220404[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13325.3888888889[/C][C]1804.25920216732[/C][C]7.38551804135575[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]12495.5277777778[/C][C]1587.39842416181[/C][C]7.87170226931263[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]11808.0277777778[/C][C]1389.60087518715[/C][C]8.4974239644081[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]10142.6944444444[/C][C]993.080216482482[/C][C]10.2133687451454[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9651.04166666667[/C][C]866.234321881734[/C][C]11.1413752871181[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9539.04166666667[/C][C]815.58170083355[/C][C]11.6959976626713[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8717.79166666667[/C][C]636.858554808788[/C][C]13.6887407742903[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6936.90277777778[/C][C]284.90328312502[/C][C]24.3482725144088[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6959.09722222222[/C][C]273.254909137335[/C][C]25.4674188441557[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6895.84722222222[/C][C]261.522934313676[/C][C]26.3680401121196[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6857.58333333333[/C][C]246.619636702667[/C][C]27.8063151216181[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6891.19444444444[/C][C]237.692884889203[/C][C]28.9920097846289[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]7030.02777777778[/C][C]215.697506495511[/C][C]32.5920679009985[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]7102.75[/C][C]199.403081001354[/C][C]35.6200614570834[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]7088.375[/C][C]196.921748554584[/C][C]35.9958971115635[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]7012.375[/C][C]175.120378268153[/C][C]40.0431695576988[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]15300.6714285714[/C][C]2571.34633123664[/C][C]5.95045142021489[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]14510.5[/C][C]2431.3259926937[/C][C]5.96814250479163[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]13684.5757575758[/C][C]2263.68020940926[/C][C]6.04527781825992[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]12866.859375[/C][C]2082.68678596807[/C][C]6.17800980046034[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]12023.0806451613[/C][C]1866.4034521697[/C][C]6.44184440999851[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]11354.4666666667[/C][C]1715.34884569015[/C][C]6.61933384290605[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]10686.4827586207[/C][C]1547.03956795824[/C][C]6.90769840665714[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]10109.7857142857[/C][C]1406.79047783093[/C][C]7.18641892563388[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9540.01851851852[/C][C]1252.19176888335[/C][C]7.61865614803224[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8957.65384615385[/C][C]1064.45419343815[/C][C]8.4152553499939[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8448.2[/C][C]883.900272331993[/C][C]9.55786559236047[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]7990.04166666667[/C][C]700.430441339146[/C][C]11.4073306856718[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]7709.26086956522[/C][C]600.916563561123[/C][C]12.8291701994017[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]7464.84090909091[/C][C]507.032985261214[/C][C]14.7225942415663[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]7210.85714285714[/C][C]383.625354968811[/C][C]18.7966125008692[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]7030.025[/C][C]277.218525501833[/C][C]25.3591457759684[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]7041.05263157895[/C][C]268.552886488317[/C][C]26.2184954466511[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]7050.69444444444[/C][C]259.550077192334[/C][C]27.1650639472539[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]7068.91176470588[/C][C]249.894706409932[/C][C]28.2875610542542[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]7093.9375[/C][C]240.128136734143[/C][C]29.5423001922262[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]7118.26666666667[/C][C]228.572888514768[/C][C]31.1422177534706[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]7129.07142857143[/C][C]219.012097275092[/C][C]32.551039496311[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]7132.38461538462[/C][C]210.015084270873[/C][C]33.9612968284955[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]7138.125[/C][C]196.388943360555[/C][C]36.3468781788542[/C][/ROW]
[ROW][C]Median[/C][C]7266[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]46563[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6968.21621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7050.69444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6968.21621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7050.69444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7050.69444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6968.21621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7050.69444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7041.05263157895[/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=120557&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120557&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 Mean16169.06944444442732.435268869655.91745745220645
Geometric Mean7035.81374800811
Harmonic Mean1143.50470360894
Quadratic Mean28134.3061776405
Winsorized Mean ( 1 / 24 )16046.94444444442685.072615528445.97635399193339
Winsorized Mean ( 2 / 24 )16024.69444444442674.837292788995.99090437674282
Winsorized Mean ( 3 / 24 )15865.15277777782616.381128275436.06377740854413
Winsorized Mean ( 4 / 24 )15773.20833333332577.558542474196.11943747287024
Winsorized Mean ( 5 / 24 )14808.97222222222267.038321330366.53229902771645
Winsorized Mean ( 6 / 24 )14583.05555555562190.698056805446.65680763729765
Winsorized Mean ( 7 / 24 )13826.27777777781967.564554842737.02710248756382
Winsorized Mean ( 8 / 24 )13528.38888888891875.281192744327.21405885220404
Winsorized Mean ( 9 / 24 )13325.38888888891804.259202167327.38551804135575
Winsorized Mean ( 10 / 24 )12495.52777777781587.398424161817.87170226931263
Winsorized Mean ( 11 / 24 )11808.02777777781389.600875187158.4974239644081
Winsorized Mean ( 12 / 24 )10142.6944444444993.08021648248210.2133687451454
Winsorized Mean ( 13 / 24 )9651.04166666667866.23432188173411.1413752871181
Winsorized Mean ( 14 / 24 )9539.04166666667815.5817008335511.6959976626713
Winsorized Mean ( 15 / 24 )8717.79166666667636.85855480878813.6887407742903
Winsorized Mean ( 16 / 24 )6936.90277777778284.9032831250224.3482725144088
Winsorized Mean ( 17 / 24 )6959.09722222222273.25490913733525.4674188441557
Winsorized Mean ( 18 / 24 )6895.84722222222261.52293431367626.3680401121196
Winsorized Mean ( 19 / 24 )6857.58333333333246.61963670266727.8063151216181
Winsorized Mean ( 20 / 24 )6891.19444444444237.69288488920328.9920097846289
Winsorized Mean ( 21 / 24 )7030.02777777778215.69750649551132.5920679009985
Winsorized Mean ( 22 / 24 )7102.75199.40308100135435.6200614570834
Winsorized Mean ( 23 / 24 )7088.375196.92174855458435.9958971115635
Winsorized Mean ( 24 / 24 )7012.375175.12037826815340.0431695576988
Trimmed Mean ( 1 / 24 )15300.67142857142571.346331236645.95045142021489
Trimmed Mean ( 2 / 24 )14510.52431.32599269375.96814250479163
Trimmed Mean ( 3 / 24 )13684.57575757582263.680209409266.04527781825992
Trimmed Mean ( 4 / 24 )12866.8593752082.686785968076.17800980046034
Trimmed Mean ( 5 / 24 )12023.08064516131866.40345216976.44184440999851
Trimmed Mean ( 6 / 24 )11354.46666666671715.348845690156.61933384290605
Trimmed Mean ( 7 / 24 )10686.48275862071547.039567958246.90769840665714
Trimmed Mean ( 8 / 24 )10109.78571428571406.790477830937.18641892563388
Trimmed Mean ( 9 / 24 )9540.018518518521252.191768883357.61865614803224
Trimmed Mean ( 10 / 24 )8957.653846153851064.454193438158.4152553499939
Trimmed Mean ( 11 / 24 )8448.2883.9002723319939.55786559236047
Trimmed Mean ( 12 / 24 )7990.04166666667700.43044133914611.4073306856718
Trimmed Mean ( 13 / 24 )7709.26086956522600.91656356112312.8291701994017
Trimmed Mean ( 14 / 24 )7464.84090909091507.03298526121414.7225942415663
Trimmed Mean ( 15 / 24 )7210.85714285714383.62535496881118.7966125008692
Trimmed Mean ( 16 / 24 )7030.025277.21852550183325.3591457759684
Trimmed Mean ( 17 / 24 )7041.05263157895268.55288648831726.2184954466511
Trimmed Mean ( 18 / 24 )7050.69444444444259.55007719233427.1650639472539
Trimmed Mean ( 19 / 24 )7068.91176470588249.89470640993228.2875610542542
Trimmed Mean ( 20 / 24 )7093.9375240.12813673414329.5423001922262
Trimmed Mean ( 21 / 24 )7118.26666666667228.57288851476831.1422177534706
Trimmed Mean ( 22 / 24 )7129.07142857143219.01209727509232.551039496311
Trimmed Mean ( 23 / 24 )7132.38461538462210.01508427087333.9612968284955
Trimmed Mean ( 24 / 24 )7138.125196.38894336055536.3468781788542
Median7266
Midrange46563
Midmean - Weighted Average at Xnp6968.21621621622
Midmean - Weighted Average at X(n+1)p7050.69444444444
Midmean - Empirical Distribution Function6968.21621621622
Midmean - Empirical Distribution Function - Averaging7050.69444444444
Midmean - Empirical Distribution Function - Interpolation7050.69444444444
Midmean - Closest Observation6968.21621621622
Midmean - True Basic - Statistics Graphics Toolkit7050.69444444444
Midmean - MS Excel (old versions)7041.05263157895
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')