Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 13 Mar 2010 02:26:42 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/13/t1268472595bc0nrzindcvmzf2.htm/, Retrieved Tue, 05 Jul 2022 13:18:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74367, Retrieved Tue, 05 Jul 2022 13:18:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact172
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Consumentenvertro...] [2010-03-13 09:26:42] [181f2439255053cc457d7672472fa443] [Current]
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Dataseries X:
-15
-15
-10
-12
-11
-11
-17
-18
-19
-22
-24
-24
-20
-25
-22
-17
-9
-11
-13
-11
-9
-7
-3
-3
-6
-4
-8
-1
-2
-2
-1
1
2
2
-1
1
-1
-8
1
2
-2
-2
-2
-2
-6
-4
-5
-2
-1
-5
-9
-8
-14
-10
-11
-11
-11
-5
-2
-3
-6
-6
-7
-6
-2
-2
-4
0
-6
-4
-3
-1
-3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74367&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74367&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-7.369863013698630.809359925549123-9.10579184989723
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.0737010107902
Winsorized Mean ( 1 / 24 )-7.356164383561640.805321405300232-9.13444537193096
Winsorized Mean ( 2 / 24 )-7.356164383561640.805321405300232-9.13444537193096
Winsorized Mean ( 3 / 24 )-7.315068493150680.776332926591736-9.42259208979499
Winsorized Mean ( 4 / 24 )-7.315068493150680.776332926591736-9.42259208979499
Winsorized Mean ( 5 / 24 )-7.178082191780820.741861594042929-9.6757700485105
Winsorized Mean ( 6 / 24 )-7.178082191780820.7104199633029-10.1039984270829
Winsorized Mean ( 7 / 24 )-7.178082191780820.675833795233593-10.6210761320390
Winsorized Mean ( 8 / 24 )-7.068493150684930.652045361455372-10.8404929603486
Winsorized Mean ( 9 / 24 )-7.068493150684930.652045361455372-10.8404929603486
Winsorized Mean ( 10 / 24 )-6.79452054794520.596781991899896-11.3852640330423
Winsorized Mean ( 11 / 24 )-6.79452054794520.596781991899896-11.3852640330423
Winsorized Mean ( 12 / 24 )-6.630136986301370.56620544260907-11.7097726149536
Winsorized Mean ( 13 / 24 )-6.630136986301370.511104561363451-12.9721733819288
Winsorized Mean ( 14 / 24 )-6.438356164383560.479006098318148-13.4410734790005
Winsorized Mean ( 15 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 16 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 17 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 18 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 19 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 20 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 21 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 22 / 24 )-5.931506849315070.403715980949109-14.6922765736707
Winsorized Mean ( 23 / 24 )-6.246575342465750.362733587113002-17.2208352476600
Winsorized Mean ( 24 / 24 )-5.917808219178080.31680087558394-18.6798985585824
Trimmed Mean ( 1 / 24 )-7.253521126760560.782535298182177-9.26925742980596
Trimmed Mean ( 2 / 24 )-7.144927536231880.755281309222522-9.45995544837034
Trimmed Mean ( 3 / 24 )-7.029850746268660.722441883234331-9.73067994728713
Trimmed Mean ( 4 / 24 )-6.923076923076920.696594633083142-9.9384586017197
Trimmed Mean ( 5 / 24 )-6.809523809523810.665073804795731-10.2387490838183
Trimmed Mean ( 6 / 24 )-6.721311475409840.638531078763583-10.5262088235777
Trimmed Mean ( 7 / 24 )-6.62711864406780.615358802113722-10.7695195409638
Trimmed Mean ( 8 / 24 )-6.526315789473680.596094885277772-10.9484512460336
Trimmed Mean ( 9 / 24 )-6.436363636363640.578377875828805-11.1283019377953
Trimmed Mean ( 10 / 24 )-6.339622641509430.555969971979969-11.4028148299668
Trimmed Mean ( 11 / 24 )-6.274509803921570.54165934694726-11.5838669438349
Trimmed Mean ( 12 / 24 )-6.204081632653060.523251536002711-11.8567862792111
Trimmed Mean ( 13 / 24 )-6.148936170212770.5070992066345-12.1257065476829
Trimmed Mean ( 14 / 24 )-6.088888888888890.498302393102764-12.2192647941652
Trimmed Mean ( 15 / 24 )-6.046511627906980.493539085343813-12.2513328882449
Trimmed Mean ( 16 / 24 )-6.024390243902440.493232005071537-12.2141105645176
Trimmed Mean ( 17 / 24 )-60.491493084480105-12.207699740774
Trimmed Mean ( 18 / 24 )-5.972972972972970.487819328673185-12.2442318741629
Trimmed Mean ( 19 / 24 )-5.942857142857140.481494272752935-12.3425292452161
Trimmed Mean ( 20 / 24 )-5.909090909090910.471465390378837-12.5334563886922
Trimmed Mean ( 21 / 24 )-5.870967741935480.456121884021797-12.8714888445364
Trimmed Mean ( 22 / 24 )-5.827586206896550.432853305442634-13.4631898003812
Trimmed Mean ( 23 / 24 )-5.814814814814810.413576703362518-14.0598219569391
Trimmed Mean ( 24 / 24 )-5.760.396988664825584-14.5092303895645
Median-6
Midrange-11.5
Midmean - Weighted Average at Xnp-5.86666666666667
Midmean - Weighted Average at X(n+1)p-5.86666666666667
Midmean - Empirical Distribution Function-5.86666666666667
Midmean - Empirical Distribution Function - Averaging-5.86666666666667
Midmean - Empirical Distribution Function - Interpolation-5.86666666666667
Midmean - Closest Observation-5.86666666666667
Midmean - True Basic - Statistics Graphics Toolkit-5.86666666666667
Midmean - MS Excel (old versions)-5.86666666666667
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -7.36986301369863 & 0.809359925549123 & -9.10579184989723 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 10.0737010107902 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -7.35616438356164 & 0.805321405300232 & -9.13444537193096 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -7.35616438356164 & 0.805321405300232 & -9.13444537193096 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -7.31506849315068 & 0.776332926591736 & -9.42259208979499 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -7.31506849315068 & 0.776332926591736 & -9.42259208979499 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -7.17808219178082 & 0.741861594042929 & -9.6757700485105 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -7.17808219178082 & 0.7104199633029 & -10.1039984270829 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -7.17808219178082 & 0.675833795233593 & -10.6210761320390 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -7.06849315068493 & 0.652045361455372 & -10.8404929603486 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -7.06849315068493 & 0.652045361455372 & -10.8404929603486 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -6.7945205479452 & 0.596781991899896 & -11.3852640330423 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -6.7945205479452 & 0.596781991899896 & -11.3852640330423 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -6.63013698630137 & 0.56620544260907 & -11.7097726149536 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -6.63013698630137 & 0.511104561363451 & -12.9721733819288 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -6.43835616438356 & 0.479006098318148 & -13.4410734790005 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -6.23287671232877 & 0.447179792815415 & -13.9381895435994 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -6.23287671232877 & 0.447179792815415 & -13.9381895435994 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -6.23287671232877 & 0.447179792815415 & -13.9381895435994 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -6.23287671232877 & 0.447179792815415 & -13.9381895435994 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -6.23287671232877 & 0.447179792815415 & -13.9381895435994 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -6.23287671232877 & 0.447179792815415 & -13.9381895435994 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -6.23287671232877 & 0.447179792815415 & -13.9381895435994 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -5.93150684931507 & 0.403715980949109 & -14.6922765736707 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -6.24657534246575 & 0.362733587113002 & -17.2208352476600 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -5.91780821917808 & 0.31680087558394 & -18.6798985585824 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -7.25352112676056 & 0.782535298182177 & -9.26925742980596 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -7.14492753623188 & 0.755281309222522 & -9.45995544837034 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -7.02985074626866 & 0.722441883234331 & -9.73067994728713 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -6.92307692307692 & 0.696594633083142 & -9.9384586017197 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -6.80952380952381 & 0.665073804795731 & -10.2387490838183 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -6.72131147540984 & 0.638531078763583 & -10.5262088235777 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -6.6271186440678 & 0.615358802113722 & -10.7695195409638 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -6.52631578947368 & 0.596094885277772 & -10.9484512460336 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -6.43636363636364 & 0.578377875828805 & -11.1283019377953 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -6.33962264150943 & 0.555969971979969 & -11.4028148299668 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -6.27450980392157 & 0.54165934694726 & -11.5838669438349 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -6.20408163265306 & 0.523251536002711 & -11.8567862792111 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -6.14893617021277 & 0.5070992066345 & -12.1257065476829 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -6.08888888888889 & 0.498302393102764 & -12.2192647941652 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -6.04651162790698 & 0.493539085343813 & -12.2513328882449 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -6.02439024390244 & 0.493232005071537 & -12.2141105645176 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -6 & 0.491493084480105 & -12.207699740774 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -5.97297297297297 & 0.487819328673185 & -12.2442318741629 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -5.94285714285714 & 0.481494272752935 & -12.3425292452161 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -5.90909090909091 & 0.471465390378837 & -12.5334563886922 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -5.87096774193548 & 0.456121884021797 & -12.8714888445364 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -5.82758620689655 & 0.432853305442634 & -13.4631898003812 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -5.81481481481481 & 0.413576703362518 & -14.0598219569391 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -5.76 & 0.396988664825584 & -14.5092303895645 \tabularnewline
Median & -6 &  &  \tabularnewline
Midrange & -11.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -5.86666666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -5.86666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -5.86666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -5.86666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -5.86666666666667 &  &  \tabularnewline
Midmean - Closest Observation & -5.86666666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -5.86666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -5.86666666666667 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74367&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]-7.36986301369863[/C][C]0.809359925549123[/C][C]-9.10579184989723[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.0737010107902[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-7.35616438356164[/C][C]0.805321405300232[/C][C]-9.13444537193096[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-7.35616438356164[/C][C]0.805321405300232[/C][C]-9.13444537193096[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-7.31506849315068[/C][C]0.776332926591736[/C][C]-9.42259208979499[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-7.31506849315068[/C][C]0.776332926591736[/C][C]-9.42259208979499[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-7.17808219178082[/C][C]0.741861594042929[/C][C]-9.6757700485105[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-7.17808219178082[/C][C]0.7104199633029[/C][C]-10.1039984270829[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-7.17808219178082[/C][C]0.675833795233593[/C][C]-10.6210761320390[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-7.06849315068493[/C][C]0.652045361455372[/C][C]-10.8404929603486[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-7.06849315068493[/C][C]0.652045361455372[/C][C]-10.8404929603486[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-6.7945205479452[/C][C]0.596781991899896[/C][C]-11.3852640330423[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-6.7945205479452[/C][C]0.596781991899896[/C][C]-11.3852640330423[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-6.63013698630137[/C][C]0.56620544260907[/C][C]-11.7097726149536[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-6.63013698630137[/C][C]0.511104561363451[/C][C]-12.9721733819288[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-6.43835616438356[/C][C]0.479006098318148[/C][C]-13.4410734790005[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-6.23287671232877[/C][C]0.447179792815415[/C][C]-13.9381895435994[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-6.23287671232877[/C][C]0.447179792815415[/C][C]-13.9381895435994[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-6.23287671232877[/C][C]0.447179792815415[/C][C]-13.9381895435994[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-6.23287671232877[/C][C]0.447179792815415[/C][C]-13.9381895435994[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-6.23287671232877[/C][C]0.447179792815415[/C][C]-13.9381895435994[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-6.23287671232877[/C][C]0.447179792815415[/C][C]-13.9381895435994[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-6.23287671232877[/C][C]0.447179792815415[/C][C]-13.9381895435994[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-5.93150684931507[/C][C]0.403715980949109[/C][C]-14.6922765736707[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-6.24657534246575[/C][C]0.362733587113002[/C][C]-17.2208352476600[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-5.91780821917808[/C][C]0.31680087558394[/C][C]-18.6798985585824[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-7.25352112676056[/C][C]0.782535298182177[/C][C]-9.26925742980596[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-7.14492753623188[/C][C]0.755281309222522[/C][C]-9.45995544837034[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-7.02985074626866[/C][C]0.722441883234331[/C][C]-9.73067994728713[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-6.92307692307692[/C][C]0.696594633083142[/C][C]-9.9384586017197[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-6.80952380952381[/C][C]0.665073804795731[/C][C]-10.2387490838183[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-6.72131147540984[/C][C]0.638531078763583[/C][C]-10.5262088235777[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-6.6271186440678[/C][C]0.615358802113722[/C][C]-10.7695195409638[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-6.52631578947368[/C][C]0.596094885277772[/C][C]-10.9484512460336[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-6.43636363636364[/C][C]0.578377875828805[/C][C]-11.1283019377953[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-6.33962264150943[/C][C]0.555969971979969[/C][C]-11.4028148299668[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-6.27450980392157[/C][C]0.54165934694726[/C][C]-11.5838669438349[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-6.20408163265306[/C][C]0.523251536002711[/C][C]-11.8567862792111[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-6.14893617021277[/C][C]0.5070992066345[/C][C]-12.1257065476829[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-6.08888888888889[/C][C]0.498302393102764[/C][C]-12.2192647941652[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-6.04651162790698[/C][C]0.493539085343813[/C][C]-12.2513328882449[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-6.02439024390244[/C][C]0.493232005071537[/C][C]-12.2141105645176[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-6[/C][C]0.491493084480105[/C][C]-12.207699740774[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-5.97297297297297[/C][C]0.487819328673185[/C][C]-12.2442318741629[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-5.94285714285714[/C][C]0.481494272752935[/C][C]-12.3425292452161[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-5.90909090909091[/C][C]0.471465390378837[/C][C]-12.5334563886922[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-5.87096774193548[/C][C]0.456121884021797[/C][C]-12.8714888445364[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-5.82758620689655[/C][C]0.432853305442634[/C][C]-13.4631898003812[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-5.81481481481481[/C][C]0.413576703362518[/C][C]-14.0598219569391[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-5.76[/C][C]0.396988664825584[/C][C]-14.5092303895645[/C][/ROW]
[ROW][C]Median[/C][C]-6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-11.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-5.86666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74367&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-7.369863013698630.809359925549123-9.10579184989723
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.0737010107902
Winsorized Mean ( 1 / 24 )-7.356164383561640.805321405300232-9.13444537193096
Winsorized Mean ( 2 / 24 )-7.356164383561640.805321405300232-9.13444537193096
Winsorized Mean ( 3 / 24 )-7.315068493150680.776332926591736-9.42259208979499
Winsorized Mean ( 4 / 24 )-7.315068493150680.776332926591736-9.42259208979499
Winsorized Mean ( 5 / 24 )-7.178082191780820.741861594042929-9.6757700485105
Winsorized Mean ( 6 / 24 )-7.178082191780820.7104199633029-10.1039984270829
Winsorized Mean ( 7 / 24 )-7.178082191780820.675833795233593-10.6210761320390
Winsorized Mean ( 8 / 24 )-7.068493150684930.652045361455372-10.8404929603486
Winsorized Mean ( 9 / 24 )-7.068493150684930.652045361455372-10.8404929603486
Winsorized Mean ( 10 / 24 )-6.79452054794520.596781991899896-11.3852640330423
Winsorized Mean ( 11 / 24 )-6.79452054794520.596781991899896-11.3852640330423
Winsorized Mean ( 12 / 24 )-6.630136986301370.56620544260907-11.7097726149536
Winsorized Mean ( 13 / 24 )-6.630136986301370.511104561363451-12.9721733819288
Winsorized Mean ( 14 / 24 )-6.438356164383560.479006098318148-13.4410734790005
Winsorized Mean ( 15 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 16 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 17 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 18 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 19 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 20 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 21 / 24 )-6.232876712328770.447179792815415-13.9381895435994
Winsorized Mean ( 22 / 24 )-5.931506849315070.403715980949109-14.6922765736707
Winsorized Mean ( 23 / 24 )-6.246575342465750.362733587113002-17.2208352476600
Winsorized Mean ( 24 / 24 )-5.917808219178080.31680087558394-18.6798985585824
Trimmed Mean ( 1 / 24 )-7.253521126760560.782535298182177-9.26925742980596
Trimmed Mean ( 2 / 24 )-7.144927536231880.755281309222522-9.45995544837034
Trimmed Mean ( 3 / 24 )-7.029850746268660.722441883234331-9.73067994728713
Trimmed Mean ( 4 / 24 )-6.923076923076920.696594633083142-9.9384586017197
Trimmed Mean ( 5 / 24 )-6.809523809523810.665073804795731-10.2387490838183
Trimmed Mean ( 6 / 24 )-6.721311475409840.638531078763583-10.5262088235777
Trimmed Mean ( 7 / 24 )-6.62711864406780.615358802113722-10.7695195409638
Trimmed Mean ( 8 / 24 )-6.526315789473680.596094885277772-10.9484512460336
Trimmed Mean ( 9 / 24 )-6.436363636363640.578377875828805-11.1283019377953
Trimmed Mean ( 10 / 24 )-6.339622641509430.555969971979969-11.4028148299668
Trimmed Mean ( 11 / 24 )-6.274509803921570.54165934694726-11.5838669438349
Trimmed Mean ( 12 / 24 )-6.204081632653060.523251536002711-11.8567862792111
Trimmed Mean ( 13 / 24 )-6.148936170212770.5070992066345-12.1257065476829
Trimmed Mean ( 14 / 24 )-6.088888888888890.498302393102764-12.2192647941652
Trimmed Mean ( 15 / 24 )-6.046511627906980.493539085343813-12.2513328882449
Trimmed Mean ( 16 / 24 )-6.024390243902440.493232005071537-12.2141105645176
Trimmed Mean ( 17 / 24 )-60.491493084480105-12.207699740774
Trimmed Mean ( 18 / 24 )-5.972972972972970.487819328673185-12.2442318741629
Trimmed Mean ( 19 / 24 )-5.942857142857140.481494272752935-12.3425292452161
Trimmed Mean ( 20 / 24 )-5.909090909090910.471465390378837-12.5334563886922
Trimmed Mean ( 21 / 24 )-5.870967741935480.456121884021797-12.8714888445364
Trimmed Mean ( 22 / 24 )-5.827586206896550.432853305442634-13.4631898003812
Trimmed Mean ( 23 / 24 )-5.814814814814810.413576703362518-14.0598219569391
Trimmed Mean ( 24 / 24 )-5.760.396988664825584-14.5092303895645
Median-6
Midrange-11.5
Midmean - Weighted Average at Xnp-5.86666666666667
Midmean - Weighted Average at X(n+1)p-5.86666666666667
Midmean - Empirical Distribution Function-5.86666666666667
Midmean - Empirical Distribution Function - Averaging-5.86666666666667
Midmean - Empirical Distribution Function - Interpolation-5.86666666666667
Midmean - Closest Observation-5.86666666666667
Midmean - True Basic - Statistics Graphics Toolkit-5.86666666666667
Midmean - MS Excel (old versions)-5.86666666666667
Number of observations73



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')