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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Oct 2011 08:50:11 -0400
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/Oct/15/t1318683048ltb8el91lht7xyo.htm/, Retrieved Wed, 15 May 2024 09:29:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=129786, Retrieved Wed, 15 May 2024 09:29:53 +0000
QR Codes:

Original text written by user:opgave 5 oefening 2 stap één
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-15 12:50:11] [25a1dad2033db3c79b30421a00eb9df6] [Current]
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Dataseries X:
3,32
3,32
3,32
3,32
3,32
3,32
3,32
3,33
3,41
3,42
3,42
3,42
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,5
3,52
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,58
3,58
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,61
3,71
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,98
3,98
3,98
3,98




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129786&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129786&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.637222222222220.0256146829089319141.99755020016
Geometric Mean3.63085057033372
Harmonic Mean3.62452071184885
Quadratic Mean3.64362037600577
Winsorized Mean ( 1 / 24 )3.637222222222220.0256146829089319141.99755020016
Winsorized Mean ( 2 / 24 )3.637222222222220.0256146829089319141.99755020016
Winsorized Mean ( 3 / 24 )3.637222222222220.0256146829089319141.99755020016
Winsorized Mean ( 4 / 24 )3.633888888888890.0250317134966285145.171399847571
Winsorized Mean ( 5 / 24 )3.633888888888890.0250317134966285145.171399847571
Winsorized Mean ( 6 / 24 )3.633888888888890.0250317134966285145.171399847571
Winsorized Mean ( 7 / 24 )3.634861111111110.0248618979426287146.202076748079
Winsorized Mean ( 8 / 24 )3.643750.0234666192347739155.273751346361
Winsorized Mean ( 9 / 24 )3.6450.0232938969217866156.478755454218
Winsorized Mean ( 10 / 24 )3.6450.0232938969217866156.478755454218
Winsorized Mean ( 11 / 24 )3.6450.0232938969217866156.478755454218
Winsorized Mean ( 12 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 13 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 14 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 15 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 16 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 17 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 18 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 19 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 20 / 24 )3.646111111111110.0174381935113807209.087662017947
Winsorized Mean ( 21 / 24 )3.651944444444440.0167703802261584217.761576970577
Winsorized Mean ( 22 / 24 )3.6550.016437390103883222.358901072536
Winsorized Mean ( 23 / 24 )3.6550.016437390103883222.358901072536
Winsorized Mean ( 24 / 24 )3.6550.016437390103883222.358901072536
Trimmed Mean ( 1 / 24 )3.636857142857140.0254805108466841142.730935213194
Trimmed Mean ( 2 / 24 )3.636470588235290.0253065183886202143.696992703293
Trimmed Mean ( 3 / 24 )3.636060606060610.0250852892820204144.947924067462
Trimmed Mean ( 4 / 24 )3.6356250.024807667905403146.55246973893
Trimmed Mean ( 5 / 24 )3.636129032258060.0246652413760123147.419154624382
Trimmed Mean ( 6 / 24 )3.636666666666670.024473745492992148.594609995762
Trimmed Mean ( 7 / 24 )3.637241379310340.024222692763888150.158424365307
Trimmed Mean ( 8 / 24 )3.637678571428570.0239412037793519151.942174877852
Trimmed Mean ( 9 / 24 )3.636666666666670.0238926670504585152.208485515093
Trimmed Mean ( 10 / 24 )3.635384615384620.0238339870678859152.529436431681
Trimmed Mean ( 11 / 24 )3.6340.02372461048905153.174274522958
Trimmed Mean ( 12 / 24 )3.63250.0235510988134131154.239087898997
Trimmed Mean ( 13 / 24 )3.630652173913040.0233383062483618155.566223841453
Trimmed Mean ( 14 / 24 )3.628636363636360.0230281354456377157.574041207221
Trimmed Mean ( 15 / 24 )3.626428571428570.0225901765741344160.531218493476
Trimmed Mean ( 16 / 24 )3.6240.0219813440712684164.867079476586
Trimmed Mean ( 17 / 24 )3.623684210526320.0218894839962121165.544524080759
Trimmed Mean ( 18 / 24 )3.623333333333330.021705094128133166.934697999626
Trimmed Mean ( 19 / 24 )3.622941176470590.0213932261913504169.349921515596
Trimmed Mean ( 20 / 24 )3.62250.0209020372521514173.308465404594
Trimmed Mean ( 21 / 24 )3.619666666666670.0207640457009161174.323767092603
Trimmed Mean ( 22 / 24 )3.615714285714290.0205893881039319175.610575091535
Trimmed Mean ( 23 / 24 )3.610769230769230.0202516709808054178.294879182638
Trimmed Mean ( 24 / 24 )3.6050.019560385876873184.301067611469
Median3.59
Midrange3.65
Midmean - Weighted Average at Xnp3.60636363636364
Midmean - Weighted Average at X(n+1)p3.60636363636364
Midmean - Empirical Distribution Function3.60636363636364
Midmean - Empirical Distribution Function - Averaging3.60636363636364
Midmean - Empirical Distribution Function - Interpolation3.60636363636364
Midmean - Closest Observation3.60636363636364
Midmean - True Basic - Statistics Graphics Toolkit3.60636363636364
Midmean - MS Excel (old versions)3.60636363636364
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.63722222222222 & 0.0256146829089319 & 141.99755020016 \tabularnewline
Geometric Mean & 3.63085057033372 &  &  \tabularnewline
Harmonic Mean & 3.62452071184885 &  &  \tabularnewline
Quadratic Mean & 3.64362037600577 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.63722222222222 & 0.0256146829089319 & 141.99755020016 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.63722222222222 & 0.0256146829089319 & 141.99755020016 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.63722222222222 & 0.0256146829089319 & 141.99755020016 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.63388888888889 & 0.0250317134966285 & 145.171399847571 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.63388888888889 & 0.0250317134966285 & 145.171399847571 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.63388888888889 & 0.0250317134966285 & 145.171399847571 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.63486111111111 & 0.0248618979426287 & 146.202076748079 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.64375 & 0.0234666192347739 & 155.273751346361 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.645 & 0.0232938969217866 & 156.478755454218 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.645 & 0.0232938969217866 & 156.478755454218 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.645 & 0.0232938969217866 & 156.478755454218 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.64666666666667 & 0.0230702811355755 & 158.067716870746 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.64666666666667 & 0.0230702811355755 & 158.067716870746 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.64666666666667 & 0.0230702811355755 & 158.067716870746 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.64666666666667 & 0.0230702811355755 & 158.067716870746 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.62666666666667 & 0.0199490744448209 & 181.796237048391 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.62666666666667 & 0.0199490744448209 & 181.796237048391 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.62666666666667 & 0.0199490744448209 & 181.796237048391 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.62666666666667 & 0.0199490744448209 & 181.796237048391 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.64611111111111 & 0.0174381935113807 & 209.087662017947 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.65194444444444 & 0.0167703802261584 & 217.761576970577 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.655 & 0.016437390103883 & 222.358901072536 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.655 & 0.016437390103883 & 222.358901072536 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.655 & 0.016437390103883 & 222.358901072536 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.63685714285714 & 0.0254805108466841 & 142.730935213194 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.63647058823529 & 0.0253065183886202 & 143.696992703293 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.63606060606061 & 0.0250852892820204 & 144.947924067462 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.635625 & 0.024807667905403 & 146.55246973893 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.63612903225806 & 0.0246652413760123 & 147.419154624382 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.63666666666667 & 0.024473745492992 & 148.594609995762 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.63724137931034 & 0.024222692763888 & 150.158424365307 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.63767857142857 & 0.0239412037793519 & 151.942174877852 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.63666666666667 & 0.0238926670504585 & 152.208485515093 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.63538461538462 & 0.0238339870678859 & 152.529436431681 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.634 & 0.02372461048905 & 153.174274522958 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.6325 & 0.0235510988134131 & 154.239087898997 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.63065217391304 & 0.0233383062483618 & 155.566223841453 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.62863636363636 & 0.0230281354456377 & 157.574041207221 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.62642857142857 & 0.0225901765741344 & 160.531218493476 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.624 & 0.0219813440712684 & 164.867079476586 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.62368421052632 & 0.0218894839962121 & 165.544524080759 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.62333333333333 & 0.021705094128133 & 166.934697999626 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.62294117647059 & 0.0213932261913504 & 169.349921515596 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.6225 & 0.0209020372521514 & 173.308465404594 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.61966666666667 & 0.0207640457009161 & 174.323767092603 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.61571428571429 & 0.0205893881039319 & 175.610575091535 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.61076923076923 & 0.0202516709808054 & 178.294879182638 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.605 & 0.019560385876873 & 184.301067611469 \tabularnewline
Median & 3.59 &  &  \tabularnewline
Midrange & 3.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.60636363636364 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.60636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.60636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.60636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.60636363636364 &  &  \tabularnewline
Midmean - Closest Observation & 3.60636363636364 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.60636363636364 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.60636363636364 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129786&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]3.63722222222222[/C][C]0.0256146829089319[/C][C]141.99755020016[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.63085057033372[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.62452071184885[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.64362037600577[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.63722222222222[/C][C]0.0256146829089319[/C][C]141.99755020016[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.63722222222222[/C][C]0.0256146829089319[/C][C]141.99755020016[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.63722222222222[/C][C]0.0256146829089319[/C][C]141.99755020016[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.63388888888889[/C][C]0.0250317134966285[/C][C]145.171399847571[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.63388888888889[/C][C]0.0250317134966285[/C][C]145.171399847571[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.63388888888889[/C][C]0.0250317134966285[/C][C]145.171399847571[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.63486111111111[/C][C]0.0248618979426287[/C][C]146.202076748079[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.64375[/C][C]0.0234666192347739[/C][C]155.273751346361[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.645[/C][C]0.0232938969217866[/C][C]156.478755454218[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.645[/C][C]0.0232938969217866[/C][C]156.478755454218[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.645[/C][C]0.0232938969217866[/C][C]156.478755454218[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.64666666666667[/C][C]0.0230702811355755[/C][C]158.067716870746[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.64666666666667[/C][C]0.0230702811355755[/C][C]158.067716870746[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.64666666666667[/C][C]0.0230702811355755[/C][C]158.067716870746[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.64666666666667[/C][C]0.0230702811355755[/C][C]158.067716870746[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.62666666666667[/C][C]0.0199490744448209[/C][C]181.796237048391[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.62666666666667[/C][C]0.0199490744448209[/C][C]181.796237048391[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.62666666666667[/C][C]0.0199490744448209[/C][C]181.796237048391[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.62666666666667[/C][C]0.0199490744448209[/C][C]181.796237048391[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.64611111111111[/C][C]0.0174381935113807[/C][C]209.087662017947[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.65194444444444[/C][C]0.0167703802261584[/C][C]217.761576970577[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.655[/C][C]0.016437390103883[/C][C]222.358901072536[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.655[/C][C]0.016437390103883[/C][C]222.358901072536[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.655[/C][C]0.016437390103883[/C][C]222.358901072536[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.63685714285714[/C][C]0.0254805108466841[/C][C]142.730935213194[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.63647058823529[/C][C]0.0253065183886202[/C][C]143.696992703293[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.63606060606061[/C][C]0.0250852892820204[/C][C]144.947924067462[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.635625[/C][C]0.024807667905403[/C][C]146.55246973893[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.63612903225806[/C][C]0.0246652413760123[/C][C]147.419154624382[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.63666666666667[/C][C]0.024473745492992[/C][C]148.594609995762[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.63724137931034[/C][C]0.024222692763888[/C][C]150.158424365307[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.63767857142857[/C][C]0.0239412037793519[/C][C]151.942174877852[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.63666666666667[/C][C]0.0238926670504585[/C][C]152.208485515093[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.63538461538462[/C][C]0.0238339870678859[/C][C]152.529436431681[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.634[/C][C]0.02372461048905[/C][C]153.174274522958[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.6325[/C][C]0.0235510988134131[/C][C]154.239087898997[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.63065217391304[/C][C]0.0233383062483618[/C][C]155.566223841453[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.62863636363636[/C][C]0.0230281354456377[/C][C]157.574041207221[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.62642857142857[/C][C]0.0225901765741344[/C][C]160.531218493476[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.624[/C][C]0.0219813440712684[/C][C]164.867079476586[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.62368421052632[/C][C]0.0218894839962121[/C][C]165.544524080759[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.62333333333333[/C][C]0.021705094128133[/C][C]166.934697999626[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.62294117647059[/C][C]0.0213932261913504[/C][C]169.349921515596[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.6225[/C][C]0.0209020372521514[/C][C]173.308465404594[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.61966666666667[/C][C]0.0207640457009161[/C][C]174.323767092603[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.61571428571429[/C][C]0.0205893881039319[/C][C]175.610575091535[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.61076923076923[/C][C]0.0202516709808054[/C][C]178.294879182638[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.605[/C][C]0.019560385876873[/C][C]184.301067611469[/C][/ROW]
[ROW][C]Median[/C][C]3.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.60636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.60636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.60636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.60636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.60636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.60636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.60636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.60636363636364[/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=129786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129786&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 Mean3.637222222222220.0256146829089319141.99755020016
Geometric Mean3.63085057033372
Harmonic Mean3.62452071184885
Quadratic Mean3.64362037600577
Winsorized Mean ( 1 / 24 )3.637222222222220.0256146829089319141.99755020016
Winsorized Mean ( 2 / 24 )3.637222222222220.0256146829089319141.99755020016
Winsorized Mean ( 3 / 24 )3.637222222222220.0256146829089319141.99755020016
Winsorized Mean ( 4 / 24 )3.633888888888890.0250317134966285145.171399847571
Winsorized Mean ( 5 / 24 )3.633888888888890.0250317134966285145.171399847571
Winsorized Mean ( 6 / 24 )3.633888888888890.0250317134966285145.171399847571
Winsorized Mean ( 7 / 24 )3.634861111111110.0248618979426287146.202076748079
Winsorized Mean ( 8 / 24 )3.643750.0234666192347739155.273751346361
Winsorized Mean ( 9 / 24 )3.6450.0232938969217866156.478755454218
Winsorized Mean ( 10 / 24 )3.6450.0232938969217866156.478755454218
Winsorized Mean ( 11 / 24 )3.6450.0232938969217866156.478755454218
Winsorized Mean ( 12 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 13 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 14 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 15 / 24 )3.646666666666670.0230702811355755158.067716870746
Winsorized Mean ( 16 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 17 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 18 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 19 / 24 )3.626666666666670.0199490744448209181.796237048391
Winsorized Mean ( 20 / 24 )3.646111111111110.0174381935113807209.087662017947
Winsorized Mean ( 21 / 24 )3.651944444444440.0167703802261584217.761576970577
Winsorized Mean ( 22 / 24 )3.6550.016437390103883222.358901072536
Winsorized Mean ( 23 / 24 )3.6550.016437390103883222.358901072536
Winsorized Mean ( 24 / 24 )3.6550.016437390103883222.358901072536
Trimmed Mean ( 1 / 24 )3.636857142857140.0254805108466841142.730935213194
Trimmed Mean ( 2 / 24 )3.636470588235290.0253065183886202143.696992703293
Trimmed Mean ( 3 / 24 )3.636060606060610.0250852892820204144.947924067462
Trimmed Mean ( 4 / 24 )3.6356250.024807667905403146.55246973893
Trimmed Mean ( 5 / 24 )3.636129032258060.0246652413760123147.419154624382
Trimmed Mean ( 6 / 24 )3.636666666666670.024473745492992148.594609995762
Trimmed Mean ( 7 / 24 )3.637241379310340.024222692763888150.158424365307
Trimmed Mean ( 8 / 24 )3.637678571428570.0239412037793519151.942174877852
Trimmed Mean ( 9 / 24 )3.636666666666670.0238926670504585152.208485515093
Trimmed Mean ( 10 / 24 )3.635384615384620.0238339870678859152.529436431681
Trimmed Mean ( 11 / 24 )3.6340.02372461048905153.174274522958
Trimmed Mean ( 12 / 24 )3.63250.0235510988134131154.239087898997
Trimmed Mean ( 13 / 24 )3.630652173913040.0233383062483618155.566223841453
Trimmed Mean ( 14 / 24 )3.628636363636360.0230281354456377157.574041207221
Trimmed Mean ( 15 / 24 )3.626428571428570.0225901765741344160.531218493476
Trimmed Mean ( 16 / 24 )3.6240.0219813440712684164.867079476586
Trimmed Mean ( 17 / 24 )3.623684210526320.0218894839962121165.544524080759
Trimmed Mean ( 18 / 24 )3.623333333333330.021705094128133166.934697999626
Trimmed Mean ( 19 / 24 )3.622941176470590.0213932261913504169.349921515596
Trimmed Mean ( 20 / 24 )3.62250.0209020372521514173.308465404594
Trimmed Mean ( 21 / 24 )3.619666666666670.0207640457009161174.323767092603
Trimmed Mean ( 22 / 24 )3.615714285714290.0205893881039319175.610575091535
Trimmed Mean ( 23 / 24 )3.610769230769230.0202516709808054178.294879182638
Trimmed Mean ( 24 / 24 )3.6050.019560385876873184.301067611469
Median3.59
Midrange3.65
Midmean - Weighted Average at Xnp3.60636363636364
Midmean - Weighted Average at X(n+1)p3.60636363636364
Midmean - Empirical Distribution Function3.60636363636364
Midmean - Empirical Distribution Function - Averaging3.60636363636364
Midmean - Empirical Distribution Function - Interpolation3.60636363636364
Midmean - Closest Observation3.60636363636364
Midmean - True Basic - Statistics Graphics Toolkit3.60636363636364
Midmean - MS Excel (old versions)3.60636363636364
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')