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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 14:24:34 -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/2012/Oct/21/t1350843889qtmwpdjdyj9sr6f.htm/, Retrieved Mon, 29 Apr 2024 05:53:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=181138, Retrieved Mon, 29 Apr 2024 05:53:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-21 18:24:34] [682ec54b5cb44a03479f999543600eb2] [Current]
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Dataseries X:
1,55
1,56
1,56
1,57
1,57
1,58
1,58
1,58
1,58
1,59
1,59
1,60
1,60
1,61
1,62
1,62
1,63
1,63
1,63
1,63
1,63
1,63
1,64
1,64
1,64
1,65
1,65
1,66
1,67
1,67
1,68
1,68
1,69
1,70
1,71
1,72
1,72
1,73
1,73
1,73
1,73
1,74
1,75
1,75
1,75
1,76
1,76
1,76
1,77
1,78
1,78
1,79
1,79
1,79
1,79
1,79
1,83
1,83
1,83
1,83
1,84
1,84
1,84
1,85
1,85
1,85
1,86
1,86
1,86
1,87
1,87
1,88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181138&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=181138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181138&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.712777777777780.0116971804552795146.426549913122
Geometric Mean1.70994362722056
Harmonic Mean1.70711495647038
Quadratic Mean1.71561132609406
Winsorized Mean ( 1 / 24 )1.712777777777780.0116435421767536147.101092758297
Winsorized Mean ( 2 / 24 )1.712777777777780.0116435421767536147.101092758297
Winsorized Mean ( 3 / 24 )1.712777777777780.0114913422915374149.049409052859
Winsorized Mean ( 4 / 24 )1.712777777777780.0114913422915374149.049409052859
Winsorized Mean ( 5 / 24 )1.713472222222220.0113731689479198150.659172484695
Winsorized Mean ( 6 / 24 )1.712638888888890.0112257268230443152.563741830343
Winsorized Mean ( 7 / 24 )1.712638888888890.0112257268230443152.563741830343
Winsorized Mean ( 8 / 24 )1.712638888888890.0112257268230443152.563741830343
Winsorized Mean ( 9 / 24 )1.712638888888890.0108102734992299158.426971252013
Winsorized Mean ( 10 / 24 )1.712638888888890.0108102734992299158.426971252013
Winsorized Mean ( 11 / 24 )1.714166666666670.0105719644307424162.14268198652
Winsorized Mean ( 12 / 24 )1.71250.0102982708182799166.29005298251
Winsorized Mean ( 13 / 24 )1.714305555555560.0100270104484053170.968761265049
Winsorized Mean ( 14 / 24 )1.716250.00974927769083217176.038682497873
Winsorized Mean ( 15 / 24 )1.716250.00974927769083217176.038682497873
Winsorized Mean ( 16 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 17 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 18 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 19 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 20 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 21 / 24 )1.706666666666670.00767594865755545222.339510437813
Winsorized Mean ( 22 / 24 )1.709722222222220.00725397797677712235.694432447372
Winsorized Mean ( 23 / 24 )1.706527777777780.00682660186657227249.982027827653
Winsorized Mean ( 24 / 24 )1.703194444444440.00639966007046954266.138267609498
Trimmed Mean ( 1 / 24 )1.712714285714290.0115558262013369148.212188023055
Trimmed Mean ( 2 / 24 )1.712647058823530.0114463623871946149.623697109182
Trimmed Mean ( 3 / 24 )1.712575757575760.0113110516042689151.407297702489
Trimmed Mean ( 4 / 24 )1.71250.0112113533725614152.746947053793
Trimmed Mean ( 5 / 24 )1.712419354838710.0110851840460258154.478206922747
Trimmed Mean ( 6 / 24 )1.712166666666670.010962420829048156.185088436835
Trimmed Mean ( 7 / 24 )1.712068965517240.0108466699629665157.842819165947
Trimmed Mean ( 8 / 24 )1.711964285714290.0106977957520118160.029629037583
Trimmed Mean ( 9 / 24 )1.711851851851850.010507971996388162.909822412953
Trimmed Mean ( 10 / 24 )1.711730769230770.0103619312604076165.194183035281
Trimmed Mean ( 11 / 24 )1.71160.0101714285714286168.275280898876
Trimmed Mean ( 12 / 24 )1.711250.00997614619518988171.534174271133
Trimmed Mean ( 13 / 24 )1.711086956521740.0097813203660518174.934149223906
Trimmed Mean ( 14 / 24 )1.710681818181820.00958106465499119178.548196863555
Trimmed Mean ( 15 / 24 )1.710.00937042571331637182.489040766836
Trimmed Mean ( 16 / 24 )1.709250.00908215706333452188.198683207142
Trimmed Mean ( 17 / 24 )1.709210526315790.00907830310864784188.274229870957
Trimmed Mean ( 18 / 24 )1.709166666666670.00904464236747676188.970066170066
Trimmed Mean ( 19 / 24 )1.709117647058820.00896982112964521190.540883965924
Trimmed Mean ( 20 / 24 )1.70906250.00883723079847324193.393444052097
Trimmed Mean ( 21 / 24 )1.7090.00862167810425172198.221271930486
Trimmed Mean ( 22 / 24 )1.709285714285710.00840333411137823203.405659186075
Trimmed Mean ( 23 / 24 )1.709230769230770.00818860515825925208.732834981889
Trimmed Mean ( 24 / 24 )1.709583333333330.00797366968293524214.403580949946
Median1.72
Midrange1.715
Midmean - Weighted Average at Xnp1.70925
Midmean - Weighted Average at X(n+1)p1.70925
Midmean - Empirical Distribution Function1.70925
Midmean - Empirical Distribution Function - Averaging1.70925
Midmean - Empirical Distribution Function - Interpolation1.70925
Midmean - Closest Observation1.70925
Midmean - True Basic - Statistics Graphics Toolkit1.70925
Midmean - MS Excel (old versions)1.70925
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.71277777777778 & 0.0116971804552795 & 146.426549913122 \tabularnewline
Geometric Mean & 1.70994362722056 &  &  \tabularnewline
Harmonic Mean & 1.70711495647038 &  &  \tabularnewline
Quadratic Mean & 1.71561132609406 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.71277777777778 & 0.0116435421767536 & 147.101092758297 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.71277777777778 & 0.0116435421767536 & 147.101092758297 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.71277777777778 & 0.0114913422915374 & 149.049409052859 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.71277777777778 & 0.0114913422915374 & 149.049409052859 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.71347222222222 & 0.0113731689479198 & 150.659172484695 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.71263888888889 & 0.0112257268230443 & 152.563741830343 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.71263888888889 & 0.0112257268230443 & 152.563741830343 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.71263888888889 & 0.0112257268230443 & 152.563741830343 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.71263888888889 & 0.0108102734992299 & 158.426971252013 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.71263888888889 & 0.0108102734992299 & 158.426971252013 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.71416666666667 & 0.0105719644307424 & 162.14268198652 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.7125 & 0.0102982708182799 & 166.29005298251 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.71430555555556 & 0.0100270104484053 & 170.968761265049 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.71625 & 0.00974927769083217 & 176.038682497873 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.71625 & 0.00974927769083217 & 176.038682497873 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.70958333333333 & 0.00807689351918099 & 211.663473001522 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.70958333333333 & 0.00807689351918099 & 211.663473001522 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.70958333333333 & 0.00807689351918099 & 211.663473001522 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.70958333333333 & 0.00807689351918099 & 211.663473001522 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.70958333333333 & 0.00807689351918099 & 211.663473001522 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.70666666666667 & 0.00767594865755545 & 222.339510437813 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.70972222222222 & 0.00725397797677712 & 235.694432447372 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.70652777777778 & 0.00682660186657227 & 249.982027827653 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.70319444444444 & 0.00639966007046954 & 266.138267609498 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.71271428571429 & 0.0115558262013369 & 148.212188023055 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.71264705882353 & 0.0114463623871946 & 149.623697109182 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.71257575757576 & 0.0113110516042689 & 151.407297702489 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.7125 & 0.0112113533725614 & 152.746947053793 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.71241935483871 & 0.0110851840460258 & 154.478206922747 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.71216666666667 & 0.010962420829048 & 156.185088436835 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.71206896551724 & 0.0108466699629665 & 157.842819165947 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.71196428571429 & 0.0106977957520118 & 160.029629037583 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.71185185185185 & 0.010507971996388 & 162.909822412953 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.71173076923077 & 0.0103619312604076 & 165.194183035281 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.7116 & 0.0101714285714286 & 168.275280898876 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.71125 & 0.00997614619518988 & 171.534174271133 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.71108695652174 & 0.0097813203660518 & 174.934149223906 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.71068181818182 & 0.00958106465499119 & 178.548196863555 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.71 & 0.00937042571331637 & 182.489040766836 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.70925 & 0.00908215706333452 & 188.198683207142 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.70921052631579 & 0.00907830310864784 & 188.274229870957 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.70916666666667 & 0.00904464236747676 & 188.970066170066 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.70911764705882 & 0.00896982112964521 & 190.540883965924 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.7090625 & 0.00883723079847324 & 193.393444052097 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.709 & 0.00862167810425172 & 198.221271930486 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.70928571428571 & 0.00840333411137823 & 203.405659186075 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.70923076923077 & 0.00818860515825925 & 208.732834981889 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.70958333333333 & 0.00797366968293524 & 214.403580949946 \tabularnewline
Median & 1.72 &  &  \tabularnewline
Midrange & 1.715 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.70925 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.70925 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.70925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.70925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.70925 &  &  \tabularnewline
Midmean - Closest Observation & 1.70925 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.70925 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.70925 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181138&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]1.71277777777778[/C][C]0.0116971804552795[/C][C]146.426549913122[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.70994362722056[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.70711495647038[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.71561132609406[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.71277777777778[/C][C]0.0116435421767536[/C][C]147.101092758297[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.71277777777778[/C][C]0.0116435421767536[/C][C]147.101092758297[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.71277777777778[/C][C]0.0114913422915374[/C][C]149.049409052859[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.71277777777778[/C][C]0.0114913422915374[/C][C]149.049409052859[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.71347222222222[/C][C]0.0113731689479198[/C][C]150.659172484695[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.71263888888889[/C][C]0.0112257268230443[/C][C]152.563741830343[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.71263888888889[/C][C]0.0112257268230443[/C][C]152.563741830343[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.71263888888889[/C][C]0.0112257268230443[/C][C]152.563741830343[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.71263888888889[/C][C]0.0108102734992299[/C][C]158.426971252013[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.71263888888889[/C][C]0.0108102734992299[/C][C]158.426971252013[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.71416666666667[/C][C]0.0105719644307424[/C][C]162.14268198652[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.7125[/C][C]0.0102982708182799[/C][C]166.29005298251[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.71430555555556[/C][C]0.0100270104484053[/C][C]170.968761265049[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.71625[/C][C]0.00974927769083217[/C][C]176.038682497873[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.71625[/C][C]0.00974927769083217[/C][C]176.038682497873[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.70958333333333[/C][C]0.00807689351918099[/C][C]211.663473001522[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.70958333333333[/C][C]0.00807689351918099[/C][C]211.663473001522[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.70958333333333[/C][C]0.00807689351918099[/C][C]211.663473001522[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.70958333333333[/C][C]0.00807689351918099[/C][C]211.663473001522[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.70958333333333[/C][C]0.00807689351918099[/C][C]211.663473001522[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.70666666666667[/C][C]0.00767594865755545[/C][C]222.339510437813[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.70972222222222[/C][C]0.00725397797677712[/C][C]235.694432447372[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.70652777777778[/C][C]0.00682660186657227[/C][C]249.982027827653[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.70319444444444[/C][C]0.00639966007046954[/C][C]266.138267609498[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.71271428571429[/C][C]0.0115558262013369[/C][C]148.212188023055[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.71264705882353[/C][C]0.0114463623871946[/C][C]149.623697109182[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.71257575757576[/C][C]0.0113110516042689[/C][C]151.407297702489[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.7125[/C][C]0.0112113533725614[/C][C]152.746947053793[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.71241935483871[/C][C]0.0110851840460258[/C][C]154.478206922747[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.71216666666667[/C][C]0.010962420829048[/C][C]156.185088436835[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.71206896551724[/C][C]0.0108466699629665[/C][C]157.842819165947[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.71196428571429[/C][C]0.0106977957520118[/C][C]160.029629037583[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.71185185185185[/C][C]0.010507971996388[/C][C]162.909822412953[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.71173076923077[/C][C]0.0103619312604076[/C][C]165.194183035281[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.7116[/C][C]0.0101714285714286[/C][C]168.275280898876[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.71125[/C][C]0.00997614619518988[/C][C]171.534174271133[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.71108695652174[/C][C]0.0097813203660518[/C][C]174.934149223906[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.71068181818182[/C][C]0.00958106465499119[/C][C]178.548196863555[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.71[/C][C]0.00937042571331637[/C][C]182.489040766836[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.70925[/C][C]0.00908215706333452[/C][C]188.198683207142[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.70921052631579[/C][C]0.00907830310864784[/C][C]188.274229870957[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.70916666666667[/C][C]0.00904464236747676[/C][C]188.970066170066[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.70911764705882[/C][C]0.00896982112964521[/C][C]190.540883965924[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.7090625[/C][C]0.00883723079847324[/C][C]193.393444052097[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.709[/C][C]0.00862167810425172[/C][C]198.221271930486[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.70928571428571[/C][C]0.00840333411137823[/C][C]203.405659186075[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.70923076923077[/C][C]0.00818860515825925[/C][C]208.732834981889[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.70958333333333[/C][C]0.00797366968293524[/C][C]214.403580949946[/C][/ROW]
[ROW][C]Median[/C][C]1.72[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.70925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.70925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.70925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.70925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.70925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.70925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.70925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.70925[/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=181138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181138&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 Mean1.712777777777780.0116971804552795146.426549913122
Geometric Mean1.70994362722056
Harmonic Mean1.70711495647038
Quadratic Mean1.71561132609406
Winsorized Mean ( 1 / 24 )1.712777777777780.0116435421767536147.101092758297
Winsorized Mean ( 2 / 24 )1.712777777777780.0116435421767536147.101092758297
Winsorized Mean ( 3 / 24 )1.712777777777780.0114913422915374149.049409052859
Winsorized Mean ( 4 / 24 )1.712777777777780.0114913422915374149.049409052859
Winsorized Mean ( 5 / 24 )1.713472222222220.0113731689479198150.659172484695
Winsorized Mean ( 6 / 24 )1.712638888888890.0112257268230443152.563741830343
Winsorized Mean ( 7 / 24 )1.712638888888890.0112257268230443152.563741830343
Winsorized Mean ( 8 / 24 )1.712638888888890.0112257268230443152.563741830343
Winsorized Mean ( 9 / 24 )1.712638888888890.0108102734992299158.426971252013
Winsorized Mean ( 10 / 24 )1.712638888888890.0108102734992299158.426971252013
Winsorized Mean ( 11 / 24 )1.714166666666670.0105719644307424162.14268198652
Winsorized Mean ( 12 / 24 )1.71250.0102982708182799166.29005298251
Winsorized Mean ( 13 / 24 )1.714305555555560.0100270104484053170.968761265049
Winsorized Mean ( 14 / 24 )1.716250.00974927769083217176.038682497873
Winsorized Mean ( 15 / 24 )1.716250.00974927769083217176.038682497873
Winsorized Mean ( 16 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 17 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 18 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 19 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 20 / 24 )1.709583333333330.00807689351918099211.663473001522
Winsorized Mean ( 21 / 24 )1.706666666666670.00767594865755545222.339510437813
Winsorized Mean ( 22 / 24 )1.709722222222220.00725397797677712235.694432447372
Winsorized Mean ( 23 / 24 )1.706527777777780.00682660186657227249.982027827653
Winsorized Mean ( 24 / 24 )1.703194444444440.00639966007046954266.138267609498
Trimmed Mean ( 1 / 24 )1.712714285714290.0115558262013369148.212188023055
Trimmed Mean ( 2 / 24 )1.712647058823530.0114463623871946149.623697109182
Trimmed Mean ( 3 / 24 )1.712575757575760.0113110516042689151.407297702489
Trimmed Mean ( 4 / 24 )1.71250.0112113533725614152.746947053793
Trimmed Mean ( 5 / 24 )1.712419354838710.0110851840460258154.478206922747
Trimmed Mean ( 6 / 24 )1.712166666666670.010962420829048156.185088436835
Trimmed Mean ( 7 / 24 )1.712068965517240.0108466699629665157.842819165947
Trimmed Mean ( 8 / 24 )1.711964285714290.0106977957520118160.029629037583
Trimmed Mean ( 9 / 24 )1.711851851851850.010507971996388162.909822412953
Trimmed Mean ( 10 / 24 )1.711730769230770.0103619312604076165.194183035281
Trimmed Mean ( 11 / 24 )1.71160.0101714285714286168.275280898876
Trimmed Mean ( 12 / 24 )1.711250.00997614619518988171.534174271133
Trimmed Mean ( 13 / 24 )1.711086956521740.0097813203660518174.934149223906
Trimmed Mean ( 14 / 24 )1.710681818181820.00958106465499119178.548196863555
Trimmed Mean ( 15 / 24 )1.710.00937042571331637182.489040766836
Trimmed Mean ( 16 / 24 )1.709250.00908215706333452188.198683207142
Trimmed Mean ( 17 / 24 )1.709210526315790.00907830310864784188.274229870957
Trimmed Mean ( 18 / 24 )1.709166666666670.00904464236747676188.970066170066
Trimmed Mean ( 19 / 24 )1.709117647058820.00896982112964521190.540883965924
Trimmed Mean ( 20 / 24 )1.70906250.00883723079847324193.393444052097
Trimmed Mean ( 21 / 24 )1.7090.00862167810425172198.221271930486
Trimmed Mean ( 22 / 24 )1.709285714285710.00840333411137823203.405659186075
Trimmed Mean ( 23 / 24 )1.709230769230770.00818860515825925208.732834981889
Trimmed Mean ( 24 / 24 )1.709583333333330.00797366968293524214.403580949946
Median1.72
Midrange1.715
Midmean - Weighted Average at Xnp1.70925
Midmean - Weighted Average at X(n+1)p1.70925
Midmean - Empirical Distribution Function1.70925
Midmean - Empirical Distribution Function - Averaging1.70925
Midmean - Empirical Distribution Function - Interpolation1.70925
Midmean - Closest Observation1.70925
Midmean - True Basic - Statistics Graphics Toolkit1.70925
Midmean - MS Excel (old versions)1.70925
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')