FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 02:54:09 -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/2007/Dec/13/t1197538737puu4jnrunmjlhdf.htm/, Retrieved Sun, 05 May 2024 16:48:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3366, Retrieved Sun, 05 May 2024 16:48:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper CT Financië...] [2007-12-13 09:54:09] [142ab5472309a9ae9a3b52678758dc4a] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2
0
-2
1
-1
1
0
0
-2
2
0
1
-3
5
-2
0
0
2
-2
1
1
-3
-1
2
1
0
-1
-2
1
0
-1
0
-3
1
1
0
1
1
-1
1
-2
3
-2
-2
-2
1
1
1

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3366&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3366&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3366&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.02083333333333330.242785226230201-0.085809724326388
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.66458202961985
Winsorized Mean ( 1 / 16 )-0.06250.227549094539029-0.274666001754976
Winsorized Mean ( 2 / 16 )-0.1041666666666670.217251495219114-0.479475027601567
Winsorized Mean ( 3 / 16 )-0.04166666666666670.201849457045821-0.206424467404974
Winsorized Mean ( 4 / 16 )-0.04166666666666670.201849457045821-0.206424467404974
Winsorized Mean ( 5 / 16 )-0.04166666666666670.201849457045821-0.206424467404974
Winsorized Mean ( 6 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 7 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 8 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 9 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 10 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 11 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 12 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 13 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 14 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 15 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 16 / 16 )0.08333333333333330.129213844049660.644925734902727
Trimmed Mean ( 1 / 16 )-0.06521739130434780.218475556980889-0.298511157062997
Trimmed Mean ( 2 / 16 )-0.06818181818181820.206648805024624-0.329940539330454
Trimmed Mean ( 3 / 16 )-0.04761904761904760.198579101727042-0.23979888721877
Trimmed Mean ( 4 / 16 )-0.050.195952636872883-0.255163700769363
Trimmed Mean ( 5 / 16 )-0.05263157894736840.192118415730893-0.273953846366770
Trimmed Mean ( 6 / 16 )-0.05555555555555560.186634539941347-0.297670278893794
Trimmed Mean ( 7 / 16 )-0.02941176470588240.186368303621448-0.157815272953407
Trimmed Mean ( 8 / 16 )00.1851329077943390
Trimmed Mean ( 9 / 16 )0.03333333333333330.1824692279730700.182679204069702
Trimmed Mean ( 10 / 16 )0.07142857142857140.1776430895682490.402090346447893
Trimmed Mean ( 11 / 16 )0.1153846153846150.1694055041965020.68111491377975
Trimmed Mean ( 12 / 16 )0.1666666666666670.1554174680400521.07238052947636
Trimmed Mean ( 13 / 16 )0.1818181818181820.1562044896334951.16397539049476
Trimmed Mean ( 14 / 16 )0.20.1555973210431001.28536917383430
Trimmed Mean ( 15 / 16 )0.2222222222222220.1524431867933411.45773797371132
Trimmed Mean ( 16 / 16 )0.250.1443375672974061.73205080756888
Median0
Midrange1
Midmean - Weighted Average at Xnp-0.205128205128205
Midmean - Weighted Average at X(n+1)p0.333333333333333
Midmean - Empirical Distribution Function-0.205128205128205
Midmean - Empirical Distribution Function - Averaging0.333333333333333
Midmean - Empirical Distribution Function - Interpolation0.333333333333333
Midmean - Closest Observation-0.205128205128205
Midmean - True Basic - Statistics Graphics Toolkit0.333333333333333
Midmean - MS Excel (old versions)-0.205128205128205
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.0208333333333333 & 0.242785226230201 & -0.085809724326388 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.66458202961985 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -0.0625 & 0.227549094539029 & -0.274666001754976 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -0.104166666666667 & 0.217251495219114 & -0.479475027601567 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -0.0416666666666667 & 0.201849457045821 & -0.206424467404974 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -0.0416666666666667 & 0.201849457045821 & -0.206424467404974 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -0.0416666666666667 & 0.201849457045821 & -0.206424467404974 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -0.166666666666667 & 0.179472565845739 & -0.928647037954096 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -0.166666666666667 & 0.179472565845739 & -0.928647037954096 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -0.166666666666667 & 0.179472565845739 & -0.928647037954096 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -0.166666666666667 & 0.179472565845739 & -0.928647037954096 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -0.166666666666667 & 0.179472565845739 & -0.928647037954096 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -0.166666666666667 & 0.179472565845739 & -0.928647037954096 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 0.0833333333333333 & 0.12921384404966 & 0.644925734902727 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 0.0833333333333333 & 0.12921384404966 & 0.644925734902727 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 0.0833333333333333 & 0.12921384404966 & 0.644925734902727 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 0.0833333333333333 & 0.12921384404966 & 0.644925734902727 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 0.0833333333333333 & 0.12921384404966 & 0.644925734902727 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -0.0652173913043478 & 0.218475556980889 & -0.298511157062997 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -0.0681818181818182 & 0.206648805024624 & -0.329940539330454 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -0.0476190476190476 & 0.198579101727042 & -0.23979888721877 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -0.05 & 0.195952636872883 & -0.255163700769363 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -0.0526315789473684 & 0.192118415730893 & -0.273953846366770 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -0.0555555555555556 & 0.186634539941347 & -0.297670278893794 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -0.0294117647058824 & 0.186368303621448 & -0.157815272953407 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 0 & 0.185132907794339 & 0 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 0.0333333333333333 & 0.182469227973070 & 0.182679204069702 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 0.0714285714285714 & 0.177643089568249 & 0.402090346447893 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 0.115384615384615 & 0.169405504196502 & 0.68111491377975 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 0.166666666666667 & 0.155417468040052 & 1.07238052947636 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 0.181818181818182 & 0.156204489633495 & 1.16397539049476 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 0.2 & 0.155597321043100 & 1.28536917383430 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 0.222222222222222 & 0.152443186793341 & 1.45773797371132 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 0.25 & 0.144337567297406 & 1.73205080756888 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.205128205128205 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.333333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.205128205128205 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.333333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.333333333333333 &  &  \tabularnewline
Midmean - Closest Observation & -0.205128205128205 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.333333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.205128205128205 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3366&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]-0.0208333333333333[/C][C]0.242785226230201[/C][C]-0.085809724326388[/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]1.66458202961985[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-0.0625[/C][C]0.227549094539029[/C][C]-0.274666001754976[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-0.104166666666667[/C][C]0.217251495219114[/C][C]-0.479475027601567[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-0.0416666666666667[/C][C]0.201849457045821[/C][C]-0.206424467404974[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-0.0416666666666667[/C][C]0.201849457045821[/C][C]-0.206424467404974[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-0.0416666666666667[/C][C]0.201849457045821[/C][C]-0.206424467404974[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-0.166666666666667[/C][C]0.179472565845739[/C][C]-0.928647037954096[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-0.166666666666667[/C][C]0.179472565845739[/C][C]-0.928647037954096[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-0.166666666666667[/C][C]0.179472565845739[/C][C]-0.928647037954096[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-0.166666666666667[/C][C]0.179472565845739[/C][C]-0.928647037954096[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-0.166666666666667[/C][C]0.179472565845739[/C][C]-0.928647037954096[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-0.166666666666667[/C][C]0.179472565845739[/C][C]-0.928647037954096[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]0.0833333333333333[/C][C]0.12921384404966[/C][C]0.644925734902727[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]0.0833333333333333[/C][C]0.12921384404966[/C][C]0.644925734902727[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]0.0833333333333333[/C][C]0.12921384404966[/C][C]0.644925734902727[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]0.0833333333333333[/C][C]0.12921384404966[/C][C]0.644925734902727[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]0.0833333333333333[/C][C]0.12921384404966[/C][C]0.644925734902727[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-0.0652173913043478[/C][C]0.218475556980889[/C][C]-0.298511157062997[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-0.0681818181818182[/C][C]0.206648805024624[/C][C]-0.329940539330454[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-0.0476190476190476[/C][C]0.198579101727042[/C][C]-0.23979888721877[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-0.05[/C][C]0.195952636872883[/C][C]-0.255163700769363[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-0.0526315789473684[/C][C]0.192118415730893[/C][C]-0.273953846366770[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-0.0555555555555556[/C][C]0.186634539941347[/C][C]-0.297670278893794[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-0.0294117647058824[/C][C]0.186368303621448[/C][C]-0.157815272953407[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]0[/C][C]0.185132907794339[/C][C]0[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]0.0333333333333333[/C][C]0.182469227973070[/C][C]0.182679204069702[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]0.0714285714285714[/C][C]0.177643089568249[/C][C]0.402090346447893[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]0.115384615384615[/C][C]0.169405504196502[/C][C]0.68111491377975[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]0.166666666666667[/C][C]0.155417468040052[/C][C]1.07238052947636[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]0.181818181818182[/C][C]0.156204489633495[/C][C]1.16397539049476[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]0.2[/C][C]0.155597321043100[/C][C]1.28536917383430[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]0.222222222222222[/C][C]0.152443186793341[/C][C]1.45773797371132[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]0.25[/C][C]0.144337567297406[/C][C]1.73205080756888[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.205128205128205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.333333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.205128205128205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.333333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.333333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.205128205128205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.333333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.205128205128205[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3366&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3366&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.02083333333333330.242785226230201-0.085809724326388
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.66458202961985
Winsorized Mean ( 1 / 16 )-0.06250.227549094539029-0.274666001754976
Winsorized Mean ( 2 / 16 )-0.1041666666666670.217251495219114-0.479475027601567
Winsorized Mean ( 3 / 16 )-0.04166666666666670.201849457045821-0.206424467404974
Winsorized Mean ( 4 / 16 )-0.04166666666666670.201849457045821-0.206424467404974
Winsorized Mean ( 5 / 16 )-0.04166666666666670.201849457045821-0.206424467404974
Winsorized Mean ( 6 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 7 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 8 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 9 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 10 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 11 / 16 )-0.1666666666666670.179472565845739-0.928647037954096
Winsorized Mean ( 12 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 13 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 14 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 15 / 16 )0.08333333333333330.129213844049660.644925734902727
Winsorized Mean ( 16 / 16 )0.08333333333333330.129213844049660.644925734902727
Trimmed Mean ( 1 / 16 )-0.06521739130434780.218475556980889-0.298511157062997
Trimmed Mean ( 2 / 16 )-0.06818181818181820.206648805024624-0.329940539330454
Trimmed Mean ( 3 / 16 )-0.04761904761904760.198579101727042-0.23979888721877
Trimmed Mean ( 4 / 16 )-0.050.195952636872883-0.255163700769363
Trimmed Mean ( 5 / 16 )-0.05263157894736840.192118415730893-0.273953846366770
Trimmed Mean ( 6 / 16 )-0.05555555555555560.186634539941347-0.297670278893794
Trimmed Mean ( 7 / 16 )-0.02941176470588240.186368303621448-0.157815272953407
Trimmed Mean ( 8 / 16 )00.1851329077943390
Trimmed Mean ( 9 / 16 )0.03333333333333330.1824692279730700.182679204069702
Trimmed Mean ( 10 / 16 )0.07142857142857140.1776430895682490.402090346447893
Trimmed Mean ( 11 / 16 )0.1153846153846150.1694055041965020.68111491377975
Trimmed Mean ( 12 / 16 )0.1666666666666670.1554174680400521.07238052947636
Trimmed Mean ( 13 / 16 )0.1818181818181820.1562044896334951.16397539049476
Trimmed Mean ( 14 / 16 )0.20.1555973210431001.28536917383430
Trimmed Mean ( 15 / 16 )0.2222222222222220.1524431867933411.45773797371132
Trimmed Mean ( 16 / 16 )0.250.1443375672974061.73205080756888
Median0
Midrange1
Midmean - Weighted Average at Xnp-0.205128205128205
Midmean - Weighted Average at X(n+1)p0.333333333333333
Midmean - Empirical Distribution Function-0.205128205128205
Midmean - Empirical Distribution Function - Averaging0.333333333333333
Midmean - Empirical Distribution Function - Interpolation0.333333333333333
Midmean - Closest Observation-0.205128205128205
Midmean - True Basic - Statistics Graphics Toolkit0.333333333333333
Midmean - MS Excel (old versions)-0.205128205128205
Number of observations48


Figures (Output of Computation)

Input Parameters & R Code

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')