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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 09:37:09 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256053107zmhjwsrg6x6sogq.htm/, Retrieved Thu, 02 May 2024 17:55:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48738, Retrieved Thu, 02 May 2024 17:55:57 +0000
QR Codes:

Original text written by user:sebastien.willemse@student.lessius.eu
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Ws 3 part 2 ex 2] [2009-10-20 15:37:09] [ba02bcb7e07025bbb7f8a074d38ad767] [Current]
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Dataseries X:
-19,4
-19,6
-18,8
-18,7
-19,8
-18,2
-18,2
-18
-18,3
-18,6
-17,5
-19,1
-19,4
-18,2
-17,6
-17,2
-17,9
-17,4
-16,9
-17,6
-17,3
-17,2
-17,3
-17,5
-18,1
-17,2
-17,2
-16,9
-18,5
-16,6
-17
-17,1
-17,7
-18,2
-17,8
-18,4
-18,8
-17,6
-16,9
-16,7
-18,4
-16,6
-17,5
-17,1
-16,9
-17,1
-17,6
-17,5
-18
-17
-16,6
-16,6
-18,3
-16,4
-17,4
-16,7
-16,8
-17,1
-17,1
-17,4
-17,8
-16,9
-16,7
-16,1
-18
-16,2
-16,5
-16,5
-16,8
-17,1
-17,4
-17,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48738&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48738&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-17.55555555555560.0983209765628508-178.553510850590
Geometric MeanNaN
Harmonic Mean-17.5175934960416
Quadratic Mean17.5750928557686
Winsorized Mean ( 1 / 24 )-17.55416666666670.097181273513742-180.633223171174
Winsorized Mean ( 2 / 24 )-17.55416666666670.0945696433806286-185.621580447478
Winsorized Mean ( 3 / 24 )-17.55833333333330.0938806470996206-187.028252102922
Winsorized Mean ( 4 / 24 )-17.54166666666670.0895290669789193-195.932642421004
Winsorized Mean ( 5 / 24 )-17.52777777777780.083619747758929-209.612899435064
Winsorized Mean ( 6 / 24 )-17.52777777777780.083619747758929-209.612899435064
Winsorized Mean ( 7 / 24 )-17.51805555555560.0815855779491648-214.720003166134
Winsorized Mean ( 8 / 24 )-17.50694444444440.079373682604347-220.563590727056
Winsorized Mean ( 9 / 24 )-17.50694444444440.0750411047737744-233.2980637375
Winsorized Mean ( 10 / 24 )-17.49305555555560.0725223614775179-241.209127766454
Winsorized Mean ( 11 / 24 )-17.49305555555560.0725223614775179-241.209127766454
Winsorized Mean ( 12 / 24 )-17.49305555555560.0671440183885027-260.530364065177
Winsorized Mean ( 13 / 24 )-17.49305555555560.0671440183885027-260.530364065177
Winsorized Mean ( 14 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 15 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 16 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 17 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 18 / 24 )-17.46805555555560.057184406043584-305.468864050840
Winsorized Mean ( 19 / 24 )-17.46805555555560.0495214338796173-352.73727327886
Winsorized Mean ( 20 / 24 )-17.46805555555560.0495214338796173-352.73727327886
Winsorized Mean ( 21 / 24 )-17.49722222222220.0457921164319469-382.101190894406
Winsorized Mean ( 22 / 24 )-17.46666666666670.0411588776345724-424.371792198607
Winsorized Mean ( 23 / 24 )-17.43472222222220.0365341032087834-477.21774153281
Winsorized Mean ( 24 / 24 )-17.43472222222220.0365341032087834-477.21774153281
Trimmed Mean ( 1 / 24 )-17.54428571428570.0935306044682572-187.578021269391
Trimmed Mean ( 2 / 24 )-17.53382352941180.0891529324524502-196.671304544732
Trimmed Mean ( 3 / 24 )-17.52272727272730.0856020895586588-204.699760987958
Trimmed Mean ( 4 / 24 )-17.5093750.0816107300538393-214.547461938509
Trimmed Mean ( 5 / 24 )-17.50.0784905185474709-222.956865667998
Trimmed Mean ( 6 / 24 )-17.49333333333330.0766482414607192-228.228762982101
Trimmed Mean ( 7 / 24 )-17.48620689655170.0743777687589104-235.099912088407
Trimmed Mean ( 8 / 24 )-17.48035714285710.0721389191415876-242.315207253775
Trimmed Mean ( 9 / 24 )-17.47592592592590.0699373376906125-249.879770992079
Trimmed Mean ( 10 / 24 )-17.47115384615380.0682321771855529-256.054468240728
Trimmed Mean ( 11 / 24 )-17.4680.0666663945572678-262.021069475936
Trimmed Mean ( 12 / 24 )-17.46458333333330.0646519310823072-270.1324313283
Trimmed Mean ( 13 / 24 )-17.46086956521740.0632820739069669-275.921259958819
Trimmed Mean ( 14 / 24 )-17.45681818181820.0614653451986421-284.010740123588
Trimmed Mean ( 15 / 24 )-17.45238095238100.0604126436872559-288.886231212268
Trimmed Mean ( 16 / 24 )-17.44750.0589423338352726-296.009656637637
Trimmed Mean ( 17 / 24 )-17.44210526315790.0569034493285053-306.521053978013
Trimmed Mean ( 18 / 24 )-17.43611111111110.0540653305245296-322.500777151456
Trimmed Mean ( 19 / 24 )-17.43235294117650.0513143797165231-339.716723411222
Trimmed Mean ( 20 / 24 )-17.4281250.0496427509488968-351.070894881326
Trimmed Mean ( 21 / 24 )-17.42333333333330.0471445157360288-369.572856170374
Trimmed Mean ( 22 / 24 )-17.41428571428570.0444586145211457-391.696545244409
Trimmed Mean ( 23 / 24 )-17.40769230769230.0422166853354223-412.341522537446
Trimmed Mean ( 24 / 24 )-17.40416666666670.0405930522838553-428.747425666945
Median-17.4
Midrange-17.95
Midmean - Weighted Average at Xnp-17.4568181818182
Midmean - Weighted Average at X(n+1)p-17.3825
Midmean - Empirical Distribution Function-17.4568181818182
Midmean - Empirical Distribution Function - Averaging-17.3825
Midmean - Empirical Distribution Function - Interpolation-17.3825
Midmean - Closest Observation-17.4568181818182
Midmean - True Basic - Statistics Graphics Toolkit-17.3825
Midmean - MS Excel (old versions)-17.4568181818182
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -17.5555555555556 & 0.0983209765628508 & -178.553510850590 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -17.5175934960416 &  &  \tabularnewline
Quadratic Mean & 17.5750928557686 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -17.5541666666667 & 0.097181273513742 & -180.633223171174 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -17.5541666666667 & 0.0945696433806286 & -185.621580447478 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -17.5583333333333 & 0.0938806470996206 & -187.028252102922 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -17.5416666666667 & 0.0895290669789193 & -195.932642421004 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -17.5277777777778 & 0.083619747758929 & -209.612899435064 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -17.5277777777778 & 0.083619747758929 & -209.612899435064 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -17.5180555555556 & 0.0815855779491648 & -214.720003166134 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -17.5069444444444 & 0.079373682604347 & -220.563590727056 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -17.5069444444444 & 0.0750411047737744 & -233.2980637375 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -17.4930555555556 & 0.0725223614775179 & -241.209127766454 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -17.4930555555556 & 0.0725223614775179 & -241.209127766454 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -17.4930555555556 & 0.0671440183885027 & -260.530364065177 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -17.4930555555556 & 0.0671440183885027 & -260.530364065177 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -17.4930555555556 & 0.0611677696517229 & -285.984852074181 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -17.4930555555556 & 0.0611677696517229 & -285.984852074181 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -17.4930555555556 & 0.0611677696517229 & -285.984852074181 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -17.4930555555556 & 0.0611677696517229 & -285.984852074181 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -17.4680555555556 & 0.057184406043584 & -305.468864050840 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -17.4680555555556 & 0.0495214338796173 & -352.73727327886 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -17.4680555555556 & 0.0495214338796173 & -352.73727327886 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -17.4972222222222 & 0.0457921164319469 & -382.101190894406 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -17.4666666666667 & 0.0411588776345724 & -424.371792198607 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -17.4347222222222 & 0.0365341032087834 & -477.21774153281 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -17.4347222222222 & 0.0365341032087834 & -477.21774153281 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -17.5442857142857 & 0.0935306044682572 & -187.578021269391 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -17.5338235294118 & 0.0891529324524502 & -196.671304544732 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -17.5227272727273 & 0.0856020895586588 & -204.699760987958 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -17.509375 & 0.0816107300538393 & -214.547461938509 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -17.5 & 0.0784905185474709 & -222.956865667998 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -17.4933333333333 & 0.0766482414607192 & -228.228762982101 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -17.4862068965517 & 0.0743777687589104 & -235.099912088407 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -17.4803571428571 & 0.0721389191415876 & -242.315207253775 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -17.4759259259259 & 0.0699373376906125 & -249.879770992079 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -17.4711538461538 & 0.0682321771855529 & -256.054468240728 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -17.468 & 0.0666663945572678 & -262.021069475936 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -17.4645833333333 & 0.0646519310823072 & -270.1324313283 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -17.4608695652174 & 0.0632820739069669 & -275.921259958819 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -17.4568181818182 & 0.0614653451986421 & -284.010740123588 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -17.4523809523810 & 0.0604126436872559 & -288.886231212268 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -17.4475 & 0.0589423338352726 & -296.009656637637 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -17.4421052631579 & 0.0569034493285053 & -306.521053978013 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -17.4361111111111 & 0.0540653305245296 & -322.500777151456 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -17.4323529411765 & 0.0513143797165231 & -339.716723411222 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -17.428125 & 0.0496427509488968 & -351.070894881326 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -17.4233333333333 & 0.0471445157360288 & -369.572856170374 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -17.4142857142857 & 0.0444586145211457 & -391.696545244409 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -17.4076923076923 & 0.0422166853354223 & -412.341522537446 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -17.4041666666667 & 0.0405930522838553 & -428.747425666945 \tabularnewline
Median & -17.4 &  &  \tabularnewline
Midrange & -17.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -17.4568181818182 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -17.3825 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -17.4568181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -17.3825 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -17.3825 &  &  \tabularnewline
Midmean - Closest Observation & -17.4568181818182 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -17.3825 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -17.4568181818182 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48738&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]-17.5555555555556[/C][C]0.0983209765628508[/C][C]-178.553510850590[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-17.5175934960416[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.5750928557686[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-17.5541666666667[/C][C]0.097181273513742[/C][C]-180.633223171174[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-17.5541666666667[/C][C]0.0945696433806286[/C][C]-185.621580447478[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-17.5583333333333[/C][C]0.0938806470996206[/C][C]-187.028252102922[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-17.5416666666667[/C][C]0.0895290669789193[/C][C]-195.932642421004[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-17.5277777777778[/C][C]0.083619747758929[/C][C]-209.612899435064[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-17.5277777777778[/C][C]0.083619747758929[/C][C]-209.612899435064[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-17.5180555555556[/C][C]0.0815855779491648[/C][C]-214.720003166134[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-17.5069444444444[/C][C]0.079373682604347[/C][C]-220.563590727056[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-17.5069444444444[/C][C]0.0750411047737744[/C][C]-233.2980637375[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-17.4930555555556[/C][C]0.0725223614775179[/C][C]-241.209127766454[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-17.4930555555556[/C][C]0.0725223614775179[/C][C]-241.209127766454[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-17.4930555555556[/C][C]0.0671440183885027[/C][C]-260.530364065177[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-17.4930555555556[/C][C]0.0671440183885027[/C][C]-260.530364065177[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-17.4930555555556[/C][C]0.0611677696517229[/C][C]-285.984852074181[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-17.4930555555556[/C][C]0.0611677696517229[/C][C]-285.984852074181[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-17.4930555555556[/C][C]0.0611677696517229[/C][C]-285.984852074181[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-17.4930555555556[/C][C]0.0611677696517229[/C][C]-285.984852074181[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-17.4680555555556[/C][C]0.057184406043584[/C][C]-305.468864050840[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-17.4680555555556[/C][C]0.0495214338796173[/C][C]-352.73727327886[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-17.4680555555556[/C][C]0.0495214338796173[/C][C]-352.73727327886[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-17.4972222222222[/C][C]0.0457921164319469[/C][C]-382.101190894406[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-17.4666666666667[/C][C]0.0411588776345724[/C][C]-424.371792198607[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-17.4347222222222[/C][C]0.0365341032087834[/C][C]-477.21774153281[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-17.4347222222222[/C][C]0.0365341032087834[/C][C]-477.21774153281[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-17.5442857142857[/C][C]0.0935306044682572[/C][C]-187.578021269391[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-17.5338235294118[/C][C]0.0891529324524502[/C][C]-196.671304544732[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-17.5227272727273[/C][C]0.0856020895586588[/C][C]-204.699760987958[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-17.509375[/C][C]0.0816107300538393[/C][C]-214.547461938509[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-17.5[/C][C]0.0784905185474709[/C][C]-222.956865667998[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-17.4933333333333[/C][C]0.0766482414607192[/C][C]-228.228762982101[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-17.4862068965517[/C][C]0.0743777687589104[/C][C]-235.099912088407[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-17.4803571428571[/C][C]0.0721389191415876[/C][C]-242.315207253775[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-17.4759259259259[/C][C]0.0699373376906125[/C][C]-249.879770992079[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-17.4711538461538[/C][C]0.0682321771855529[/C][C]-256.054468240728[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-17.468[/C][C]0.0666663945572678[/C][C]-262.021069475936[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-17.4645833333333[/C][C]0.0646519310823072[/C][C]-270.1324313283[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-17.4608695652174[/C][C]0.0632820739069669[/C][C]-275.921259958819[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-17.4568181818182[/C][C]0.0614653451986421[/C][C]-284.010740123588[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-17.4523809523810[/C][C]0.0604126436872559[/C][C]-288.886231212268[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-17.4475[/C][C]0.0589423338352726[/C][C]-296.009656637637[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-17.4421052631579[/C][C]0.0569034493285053[/C][C]-306.521053978013[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-17.4361111111111[/C][C]0.0540653305245296[/C][C]-322.500777151456[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-17.4323529411765[/C][C]0.0513143797165231[/C][C]-339.716723411222[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-17.428125[/C][C]0.0496427509488968[/C][C]-351.070894881326[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-17.4233333333333[/C][C]0.0471445157360288[/C][C]-369.572856170374[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-17.4142857142857[/C][C]0.0444586145211457[/C][C]-391.696545244409[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-17.4076923076923[/C][C]0.0422166853354223[/C][C]-412.341522537446[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-17.4041666666667[/C][C]0.0405930522838553[/C][C]-428.747425666945[/C][/ROW]
[ROW][C]Median[/C][C]-17.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-17.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-17.4568181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-17.3825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-17.4568181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-17.3825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-17.3825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-17.4568181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-17.3825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-17.4568181818182[/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=48738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48738&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 Mean-17.55555555555560.0983209765628508-178.553510850590
Geometric MeanNaN
Harmonic Mean-17.5175934960416
Quadratic Mean17.5750928557686
Winsorized Mean ( 1 / 24 )-17.55416666666670.097181273513742-180.633223171174
Winsorized Mean ( 2 / 24 )-17.55416666666670.0945696433806286-185.621580447478
Winsorized Mean ( 3 / 24 )-17.55833333333330.0938806470996206-187.028252102922
Winsorized Mean ( 4 / 24 )-17.54166666666670.0895290669789193-195.932642421004
Winsorized Mean ( 5 / 24 )-17.52777777777780.083619747758929-209.612899435064
Winsorized Mean ( 6 / 24 )-17.52777777777780.083619747758929-209.612899435064
Winsorized Mean ( 7 / 24 )-17.51805555555560.0815855779491648-214.720003166134
Winsorized Mean ( 8 / 24 )-17.50694444444440.079373682604347-220.563590727056
Winsorized Mean ( 9 / 24 )-17.50694444444440.0750411047737744-233.2980637375
Winsorized Mean ( 10 / 24 )-17.49305555555560.0725223614775179-241.209127766454
Winsorized Mean ( 11 / 24 )-17.49305555555560.0725223614775179-241.209127766454
Winsorized Mean ( 12 / 24 )-17.49305555555560.0671440183885027-260.530364065177
Winsorized Mean ( 13 / 24 )-17.49305555555560.0671440183885027-260.530364065177
Winsorized Mean ( 14 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 15 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 16 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 17 / 24 )-17.49305555555560.0611677696517229-285.984852074181
Winsorized Mean ( 18 / 24 )-17.46805555555560.057184406043584-305.468864050840
Winsorized Mean ( 19 / 24 )-17.46805555555560.0495214338796173-352.73727327886
Winsorized Mean ( 20 / 24 )-17.46805555555560.0495214338796173-352.73727327886
Winsorized Mean ( 21 / 24 )-17.49722222222220.0457921164319469-382.101190894406
Winsorized Mean ( 22 / 24 )-17.46666666666670.0411588776345724-424.371792198607
Winsorized Mean ( 23 / 24 )-17.43472222222220.0365341032087834-477.21774153281
Winsorized Mean ( 24 / 24 )-17.43472222222220.0365341032087834-477.21774153281
Trimmed Mean ( 1 / 24 )-17.54428571428570.0935306044682572-187.578021269391
Trimmed Mean ( 2 / 24 )-17.53382352941180.0891529324524502-196.671304544732
Trimmed Mean ( 3 / 24 )-17.52272727272730.0856020895586588-204.699760987958
Trimmed Mean ( 4 / 24 )-17.5093750.0816107300538393-214.547461938509
Trimmed Mean ( 5 / 24 )-17.50.0784905185474709-222.956865667998
Trimmed Mean ( 6 / 24 )-17.49333333333330.0766482414607192-228.228762982101
Trimmed Mean ( 7 / 24 )-17.48620689655170.0743777687589104-235.099912088407
Trimmed Mean ( 8 / 24 )-17.48035714285710.0721389191415876-242.315207253775
Trimmed Mean ( 9 / 24 )-17.47592592592590.0699373376906125-249.879770992079
Trimmed Mean ( 10 / 24 )-17.47115384615380.0682321771855529-256.054468240728
Trimmed Mean ( 11 / 24 )-17.4680.0666663945572678-262.021069475936
Trimmed Mean ( 12 / 24 )-17.46458333333330.0646519310823072-270.1324313283
Trimmed Mean ( 13 / 24 )-17.46086956521740.0632820739069669-275.921259958819
Trimmed Mean ( 14 / 24 )-17.45681818181820.0614653451986421-284.010740123588
Trimmed Mean ( 15 / 24 )-17.45238095238100.0604126436872559-288.886231212268
Trimmed Mean ( 16 / 24 )-17.44750.0589423338352726-296.009656637637
Trimmed Mean ( 17 / 24 )-17.44210526315790.0569034493285053-306.521053978013
Trimmed Mean ( 18 / 24 )-17.43611111111110.0540653305245296-322.500777151456
Trimmed Mean ( 19 / 24 )-17.43235294117650.0513143797165231-339.716723411222
Trimmed Mean ( 20 / 24 )-17.4281250.0496427509488968-351.070894881326
Trimmed Mean ( 21 / 24 )-17.42333333333330.0471445157360288-369.572856170374
Trimmed Mean ( 22 / 24 )-17.41428571428570.0444586145211457-391.696545244409
Trimmed Mean ( 23 / 24 )-17.40769230769230.0422166853354223-412.341522537446
Trimmed Mean ( 24 / 24 )-17.40416666666670.0405930522838553-428.747425666945
Median-17.4
Midrange-17.95
Midmean - Weighted Average at Xnp-17.4568181818182
Midmean - Weighted Average at X(n+1)p-17.3825
Midmean - Empirical Distribution Function-17.4568181818182
Midmean - Empirical Distribution Function - Averaging-17.3825
Midmean - Empirical Distribution Function - Interpolation-17.3825
Midmean - Closest Observation-17.4568181818182
Midmean - True Basic - Statistics Graphics Toolkit-17.3825
Midmean - MS Excel (old versions)-17.4568181818182
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')