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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 computationSat, 18 Dec 2010 14:35:41 +0000
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/Dec/18/t1292682815eivp7hvqc00l6nr.htm/, Retrieved Tue, 30 Apr 2024 06:54:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112009, Retrieved Tue, 30 Apr 2024 06:54:23 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
17.0
20.5
17.4
11.2
10.3
6.7
2.5
0.1
2.9
9.7
11.3
15.8
19.4
18.7
16.5
14.4
12.5
6.7
3.6
0.7
2.8
6.9
10.5
14.0
17.6
18.0
16.1
16.4
9.3
6.3
6.1
6.5
4.1
6.8
10.4
14.1
17.2
17.2
17.5
14.6
14.3
8.0
6.8
7.2
5.9
9.1
14.2
18.4
16.3
23.0
17.3
14.2
9.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112009&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112009&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112009&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11.59056603773580.78343825654678714.7944856418224
Geometric Mean9.20347261192109
Harmonic Mean3.08410585119221
Quadratic Mean12.8940896215984
Winsorized Mean ( 1 / 17 )11.55471698113210.76840534759519215.037267787495
Winsorized Mean ( 2 / 17 )11.58113207547170.74230966100984115.6014836984833
Winsorized Mean ( 3 / 17 )11.55849056603770.73061515506180215.8202173688281
Winsorized Mean ( 4 / 17 )11.54339622641510.72469156360859715.9287023695085
Winsorized Mean ( 5 / 17 )11.57169811320750.70316193064950216.4566618424847
Winsorized Mean ( 6 / 17 )11.58301886792450.6832100863765716.9538171331098
Winsorized Mean ( 7 / 17 )11.80754716981130.63449378160966518.6093977782673
Winsorized Mean ( 8 / 17 )11.8226415094340.62654535515903718.8695701150526
Winsorized Mean ( 9 / 17 )11.83962264150940.61773698391498519.1661223948004
Winsorized Mean ( 10 / 17 )11.85849056603770.60808792835295919.5012760706451
Winsorized Mean ( 11 / 17 )11.90.60111773006552519.7964548453809
Winsorized Mean ( 12 / 17 )11.85471698113210.593503570281719.9741291792151
Winsorized Mean ( 13 / 17 )11.75660377358490.56934580028706320.6493202683804
Winsorized Mean ( 14 / 17 )11.73018867924530.56513086521275120.7565882547033
Winsorized Mean ( 15 / 17 )11.73018867924530.5559063057708521.1010174870738
Winsorized Mean ( 16 / 17 )11.76037735849060.53134915789466222.1330497729367
Winsorized Mean ( 17 / 17 )11.92075471698110.4746273344508125.1160307291922
Trimmed Mean ( 1 / 17 )11.59215686274510.7486869192374715.4833169444868
Trimmed Mean ( 2 / 17 )11.63265306122450.72353762763093816.0774680085582
Trimmed Mean ( 3 / 17 )11.66170212765960.70923310194233316.4426929534484
Trimmed Mean ( 4 / 17 )11.70222222222220.6960820287845816.8115563084646
Trimmed Mean ( 5 / 17 )11.75116279069770.68074589484231617.2621867861864
Trimmed Mean ( 6 / 17 )11.79756097560980.66779111496801217.6665437906805
Trimmed Mean ( 7 / 17 )11.84615384615380.65629769826113418.0499701241377
Trimmed Mean ( 8 / 17 )11.85405405405410.65474239707341718.1049128741923
Trimmed Mean ( 9 / 17 )11.860.65281806697687918.1673893538551
Trimmed Mean ( 10 / 17 )11.86363636363640.6503469089096818.2420123800173
Trimmed Mean ( 11 / 17 )11.86451612903230.64707029395105818.3357453431939
Trimmed Mean ( 12 / 17 )11.85862068965520.64159048909643118.4831615979158
Trimmed Mean ( 13 / 17 )11.85925925925930.63291167383252118.7376212978455
Trimmed Mean ( 14 / 17 )11.8760.62458733042972719.0141545007471
Trimmed Mean ( 15 / 17 )11.90.6092501709076419.5322062565396
Trimmed Mean ( 16 / 17 )11.92857142857140.58440620483093620.4114387047315
Trimmed Mean ( 17 / 17 )11.95789473684210.55056142475237221.719456175522
Median11.3
Midrange11.55
Midmean - Weighted Average at Xnp11.6807692307692
Midmean - Weighted Average at X(n+1)p11.8592592592593
Midmean - Empirical Distribution Function11.8592592592593
Midmean - Empirical Distribution Function - Averaging11.8592592592593
Midmean - Empirical Distribution Function - Interpolation11.8592592592593
Midmean - Closest Observation11.5034482758621
Midmean - True Basic - Statistics Graphics Toolkit11.8592592592593
Midmean - MS Excel (old versions)11.8592592592593
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11.5905660377358 & 0.783438256546787 & 14.7944856418224 \tabularnewline
Geometric Mean & 9.20347261192109 &  &  \tabularnewline
Harmonic Mean & 3.08410585119221 &  &  \tabularnewline
Quadratic Mean & 12.8940896215984 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 11.5547169811321 & 0.768405347595192 & 15.037267787495 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 11.5811320754717 & 0.742309661009841 & 15.6014836984833 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 11.5584905660377 & 0.730615155061802 & 15.8202173688281 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 11.5433962264151 & 0.724691563608597 & 15.9287023695085 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 11.5716981132075 & 0.703161930649502 & 16.4566618424847 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 11.5830188679245 & 0.68321008637657 & 16.9538171331098 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 11.8075471698113 & 0.634493781609665 & 18.6093977782673 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 11.822641509434 & 0.626545355159037 & 18.8695701150526 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 11.8396226415094 & 0.617736983914985 & 19.1661223948004 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 11.8584905660377 & 0.608087928352959 & 19.5012760706451 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 11.9 & 0.601117730065525 & 19.7964548453809 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 11.8547169811321 & 0.5935035702817 & 19.9741291792151 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 11.7566037735849 & 0.569345800287063 & 20.6493202683804 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 11.7301886792453 & 0.565130865212751 & 20.7565882547033 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 11.7301886792453 & 0.55590630577085 & 21.1010174870738 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 11.7603773584906 & 0.531349157894662 & 22.1330497729367 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 11.9207547169811 & 0.47462733445081 & 25.1160307291922 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 11.5921568627451 & 0.74868691923747 & 15.4833169444868 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 11.6326530612245 & 0.723537627630938 & 16.0774680085582 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 11.6617021276596 & 0.709233101942333 & 16.4426929534484 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 11.7022222222222 & 0.69608202878458 & 16.8115563084646 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 11.7511627906977 & 0.680745894842316 & 17.2621867861864 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 11.7975609756098 & 0.667791114968012 & 17.6665437906805 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 11.8461538461538 & 0.656297698261134 & 18.0499701241377 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 11.8540540540541 & 0.654742397073417 & 18.1049128741923 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 11.86 & 0.652818066976879 & 18.1673893538551 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 11.8636363636364 & 0.65034690890968 & 18.2420123800173 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 11.8645161290323 & 0.647070293951058 & 18.3357453431939 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 11.8586206896552 & 0.641590489096431 & 18.4831615979158 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 11.8592592592593 & 0.632911673832521 & 18.7376212978455 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 11.876 & 0.624587330429727 & 19.0141545007471 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 11.9 & 0.60925017090764 & 19.5322062565396 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 11.9285714285714 & 0.584406204830936 & 20.4114387047315 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 11.9578947368421 & 0.550561424752372 & 21.719456175522 \tabularnewline
Median & 11.3 &  &  \tabularnewline
Midrange & 11.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.6807692307692 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.8592592592593 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.8592592592593 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.8592592592593 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.8592592592593 &  &  \tabularnewline
Midmean - Closest Observation & 11.5034482758621 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.8592592592593 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.8592592592593 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112009&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]11.5905660377358[/C][C]0.783438256546787[/C][C]14.7944856418224[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.20347261192109[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.08410585119221[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]12.8940896215984[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]11.5547169811321[/C][C]0.768405347595192[/C][C]15.037267787495[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]11.5811320754717[/C][C]0.742309661009841[/C][C]15.6014836984833[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]11.5584905660377[/C][C]0.730615155061802[/C][C]15.8202173688281[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]11.5433962264151[/C][C]0.724691563608597[/C][C]15.9287023695085[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]11.5716981132075[/C][C]0.703161930649502[/C][C]16.4566618424847[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]11.5830188679245[/C][C]0.68321008637657[/C][C]16.9538171331098[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]11.8075471698113[/C][C]0.634493781609665[/C][C]18.6093977782673[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]11.822641509434[/C][C]0.626545355159037[/C][C]18.8695701150526[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]11.8396226415094[/C][C]0.617736983914985[/C][C]19.1661223948004[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]11.8584905660377[/C][C]0.608087928352959[/C][C]19.5012760706451[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]11.9[/C][C]0.601117730065525[/C][C]19.7964548453809[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]11.8547169811321[/C][C]0.5935035702817[/C][C]19.9741291792151[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]11.7566037735849[/C][C]0.569345800287063[/C][C]20.6493202683804[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]11.7301886792453[/C][C]0.565130865212751[/C][C]20.7565882547033[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]11.7301886792453[/C][C]0.55590630577085[/C][C]21.1010174870738[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]11.7603773584906[/C][C]0.531349157894662[/C][C]22.1330497729367[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]11.9207547169811[/C][C]0.47462733445081[/C][C]25.1160307291922[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]11.5921568627451[/C][C]0.74868691923747[/C][C]15.4833169444868[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]11.6326530612245[/C][C]0.723537627630938[/C][C]16.0774680085582[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]11.6617021276596[/C][C]0.709233101942333[/C][C]16.4426929534484[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]11.7022222222222[/C][C]0.69608202878458[/C][C]16.8115563084646[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]11.7511627906977[/C][C]0.680745894842316[/C][C]17.2621867861864[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]11.7975609756098[/C][C]0.667791114968012[/C][C]17.6665437906805[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]11.8461538461538[/C][C]0.656297698261134[/C][C]18.0499701241377[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]11.8540540540541[/C][C]0.654742397073417[/C][C]18.1049128741923[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]11.86[/C][C]0.652818066976879[/C][C]18.1673893538551[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]11.8636363636364[/C][C]0.65034690890968[/C][C]18.2420123800173[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]11.8645161290323[/C][C]0.647070293951058[/C][C]18.3357453431939[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]11.8586206896552[/C][C]0.641590489096431[/C][C]18.4831615979158[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]11.8592592592593[/C][C]0.632911673832521[/C][C]18.7376212978455[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]11.876[/C][C]0.624587330429727[/C][C]19.0141545007471[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]11.9[/C][C]0.60925017090764[/C][C]19.5322062565396[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]11.9285714285714[/C][C]0.584406204830936[/C][C]20.4114387047315[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]11.9578947368421[/C][C]0.550561424752372[/C][C]21.719456175522[/C][/ROW]
[ROW][C]Median[/C][C]11.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.6807692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.8592592592593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.8592592592593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.8592592592593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.8592592592593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.5034482758621[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.8592592592593[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.8592592592593[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]53[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112009&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112009&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 Mean11.59056603773580.78343825654678714.7944856418224
Geometric Mean9.20347261192109
Harmonic Mean3.08410585119221
Quadratic Mean12.8940896215984
Winsorized Mean ( 1 / 17 )11.55471698113210.76840534759519215.037267787495
Winsorized Mean ( 2 / 17 )11.58113207547170.74230966100984115.6014836984833
Winsorized Mean ( 3 / 17 )11.55849056603770.73061515506180215.8202173688281
Winsorized Mean ( 4 / 17 )11.54339622641510.72469156360859715.9287023695085
Winsorized Mean ( 5 / 17 )11.57169811320750.70316193064950216.4566618424847
Winsorized Mean ( 6 / 17 )11.58301886792450.6832100863765716.9538171331098
Winsorized Mean ( 7 / 17 )11.80754716981130.63449378160966518.6093977782673
Winsorized Mean ( 8 / 17 )11.8226415094340.62654535515903718.8695701150526
Winsorized Mean ( 9 / 17 )11.83962264150940.61773698391498519.1661223948004
Winsorized Mean ( 10 / 17 )11.85849056603770.60808792835295919.5012760706451
Winsorized Mean ( 11 / 17 )11.90.60111773006552519.7964548453809
Winsorized Mean ( 12 / 17 )11.85471698113210.593503570281719.9741291792151
Winsorized Mean ( 13 / 17 )11.75660377358490.56934580028706320.6493202683804
Winsorized Mean ( 14 / 17 )11.73018867924530.56513086521275120.7565882547033
Winsorized Mean ( 15 / 17 )11.73018867924530.5559063057708521.1010174870738
Winsorized Mean ( 16 / 17 )11.76037735849060.53134915789466222.1330497729367
Winsorized Mean ( 17 / 17 )11.92075471698110.4746273344508125.1160307291922
Trimmed Mean ( 1 / 17 )11.59215686274510.7486869192374715.4833169444868
Trimmed Mean ( 2 / 17 )11.63265306122450.72353762763093816.0774680085582
Trimmed Mean ( 3 / 17 )11.66170212765960.70923310194233316.4426929534484
Trimmed Mean ( 4 / 17 )11.70222222222220.6960820287845816.8115563084646
Trimmed Mean ( 5 / 17 )11.75116279069770.68074589484231617.2621867861864
Trimmed Mean ( 6 / 17 )11.79756097560980.66779111496801217.6665437906805
Trimmed Mean ( 7 / 17 )11.84615384615380.65629769826113418.0499701241377
Trimmed Mean ( 8 / 17 )11.85405405405410.65474239707341718.1049128741923
Trimmed Mean ( 9 / 17 )11.860.65281806697687918.1673893538551
Trimmed Mean ( 10 / 17 )11.86363636363640.6503469089096818.2420123800173
Trimmed Mean ( 11 / 17 )11.86451612903230.64707029395105818.3357453431939
Trimmed Mean ( 12 / 17 )11.85862068965520.64159048909643118.4831615979158
Trimmed Mean ( 13 / 17 )11.85925925925930.63291167383252118.7376212978455
Trimmed Mean ( 14 / 17 )11.8760.62458733042972719.0141545007471
Trimmed Mean ( 15 / 17 )11.90.6092501709076419.5322062565396
Trimmed Mean ( 16 / 17 )11.92857142857140.58440620483093620.4114387047315
Trimmed Mean ( 17 / 17 )11.95789473684210.55056142475237221.719456175522
Median11.3
Midrange11.55
Midmean - Weighted Average at Xnp11.6807692307692
Midmean - Weighted Average at X(n+1)p11.8592592592593
Midmean - Empirical Distribution Function11.8592592592593
Midmean - Empirical Distribution Function - Averaging11.8592592592593
Midmean - Empirical Distribution Function - Interpolation11.8592592592593
Midmean - Closest Observation11.5034482758621
Midmean - True Basic - Statistics Graphics Toolkit11.8592592592593
Midmean - MS Excel (old versions)11.8592592592593
Number of observations53



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')