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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 20 Oct 2008 10:45:54 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224521240lylz95wugte42qc.htm/, Retrieved Fri, 17 May 2024 04:44:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17632, Retrieved Fri, 17 May 2024 04:44:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
- R  D    [Central Tendency] [Central Tendency ...] [2008-10-20 16:45:54] [270782e2502ae87124d0ebdcd1862d6a] [Current]

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Boxplots

1.4
0.7
9.5
1.4
4.1
6.6
18.4
16.9
9.2
-4.3
-5.9
-7.7
-5.4
-2.3
-4.8
2.3
-5.2
-10
-17.1
-14.4
-3.9
3.7
6.5
0.9
-4.1
-7
-12.2
-2.5
4.4
13.7
12.3
13.4
2.2
1.7
-7.2
-4.8
-2.9
-2.4
-2.5
-5.3
-7.1
-8
-8.9
-7.7
-1.1
4
9.6
10.9
13
14.9
20.1
10.8
11
3.8
10.8
7.6
10.2
2.2
-0.1
-1.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17632&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17632&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17632&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.52833333333333	1.10240131235589	1.38636748360468
Geometric Mean	NaN
Harmonic Mean	-7.7960049052048
Quadratic Mean	8.6045240038792
Winsorized Mean ( 1 / 20 )	1.545	1.08254623731839	1.42719077184839
Winsorized Mean ( 2 / 20 )	1.56833333333333	1.05247218159532	1.49014231516892
Winsorized Mean ( 3 / 20 )	1.57833333333333	1.00592058538707	1.56904367627193
Winsorized Mean ( 4 / 20 )	1.57166666666667	0.974659412240077	1.6125291018885
Winsorized Mean ( 5 / 20 )	1.62166666666667	0.956184424409848	1.69597686938642
Winsorized Mean ( 6 / 20 )	1.61166666666667	0.94284427142061	1.70936676980423
Winsorized Mean ( 7 / 20 )	1.53	0.926436279941022	1.65148972803332
Winsorized Mean ( 8 / 20 )	1.42333333333333	0.882233191903604	1.61333006556032
Winsorized Mean ( 9 / 20 )	1.42333333333333	0.877001718964058	1.62295386948000
Winsorized Mean ( 10 / 20 )	1.42333333333333	0.871216976829326	1.63373002499717
Winsorized Mean ( 11 / 20 )	1.625	0.839348768946618	1.93602476124362
Winsorized Mean ( 12 / 20 )	1.605	0.802332140953346	2.0004184278258
Winsorized Mean ( 13 / 20 )	1.49666666666667	0.775806366235011	1.92917554148207
Winsorized Mean ( 14 / 20 )	1.49666666666667	0.768224773879043	1.94821452985623
Winsorized Mean ( 15 / 20 )	1.52166666666667	0.740385041323902	2.05523691287136
Winsorized Mean ( 16 / 20 )	1.095	0.667533722883302	1.64036656495844
Winsorized Mean ( 17 / 20 )	0.953333333333333	0.600397545636245	1.58783682622000
Winsorized Mean ( 18 / 20 )	0.983333333333333	0.586761516472243	1.67586541674611
Winsorized Mean ( 19 / 20 )	0.381666666666667	0.476199002143205	0.801485649799597
Winsorized Mean ( 20 / 20 )	0.615	0.412309363584475	1.49159843146273
Trimmed Mean ( 1 / 20 )	1.52931034482759	1.04499501013548	1.46346186344882
Trimmed Mean ( 2 / 20 )	1.5125	0.998671398252855	1.51451218353312
Trimmed Mean ( 3 / 20 )	1.48148148148148	0.961698627062926	1.54048413899269
Trimmed Mean ( 4 / 20 )	1.44423076923077	0.938333996908986	1.53914360343788
Trimmed Mean ( 5 / 20 )	1.406	0.920897565710005	1.52677132870471
Trimmed Mean ( 6 / 20 )	1.35208333333333	0.904397205223891	1.49501051697591
Trimmed Mean ( 7 / 20 )	1.29565217391304	0.886696940322992	1.46121195979438
Trimmed Mean ( 8 / 20 )	1.25	0.867973143844623	1.44013672411939
Trimmed Mean ( 9 / 20 )	1.21904761904762	0.855020278065311	1.42575287431312
Trimmed Mean ( 10 / 20 )	1.185	0.838156937143666	1.41381637195336
Trimmed Mean ( 11 / 20 )	1.14736842105263	0.816096395253487	1.40592266762341
Trimmed Mean ( 12 / 20 )	1.075	0.793519135905127	1.35472473360558
Trimmed Mean ( 13 / 20 )	0.997058823529412	0.771593315226304	1.29220770042180
Trimmed Mean ( 14 / 20 )	0.925	0.747414899676254	1.23759909041239
Trimmed Mean ( 15 / 20 )	0.843333333333333	0.713509753670106	1.18195067270692
Trimmed Mean ( 16 / 20 )	0.746428571428571	0.67157877133463	1.11145349330383
Trimmed Mean ( 17 / 20 )	0.696153846153846	0.63629893239023	1.09406728617126
Trimmed Mean ( 18 / 20 )	0.658333333333333	0.606902227718487	1.08474364282397
Trimmed Mean ( 19 / 20 )	0.609090909090909	0.563112450262899	1.08165058116997
Trimmed Mean ( 20 / 20 )	0.645	0.542337775890537	1.18929572800067
Median	1.15
Midrange	1.5
Midmean - Weighted Average at Xnp	0.648387096774194
Midmean - Weighted Average at X(n+1)p	0.843333333333333
Midmean - Empirical Distribution Function	0.648387096774194
Midmean - Empirical Distribution Function - Averaging	0.843333333333333
Midmean - Empirical Distribution Function - Interpolation	0.843333333333333
Midmean - Closest Observation	0.648387096774194
Midmean - True Basic - Statistics Graphics Toolkit	0.843333333333333
Midmean - MS Excel (old versions)	0.925
Number of observations	60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.52833333333333 & 1.10240131235589 & 1.38636748360468 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -7.7960049052048 &  &  \tabularnewline
Quadratic Mean & 8.6045240038792 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.545 & 1.08254623731839 & 1.42719077184839 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.56833333333333 & 1.05247218159532 & 1.49014231516892 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.57833333333333 & 1.00592058538707 & 1.56904367627193 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.57166666666667 & 0.974659412240077 & 1.6125291018885 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.62166666666667 & 0.956184424409848 & 1.69597686938642 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.61166666666667 & 0.94284427142061 & 1.70936676980423 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.53 & 0.926436279941022 & 1.65148972803332 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.42333333333333 & 0.882233191903604 & 1.61333006556032 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.42333333333333 & 0.877001718964058 & 1.62295386948000 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.42333333333333 & 0.871216976829326 & 1.63373002499717 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.625 & 0.839348768946618 & 1.93602476124362 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.605 & 0.802332140953346 & 2.0004184278258 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.49666666666667 & 0.775806366235011 & 1.92917554148207 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.49666666666667 & 0.768224773879043 & 1.94821452985623 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.52166666666667 & 0.740385041323902 & 2.05523691287136 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.095 & 0.667533722883302 & 1.64036656495844 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.953333333333333 & 0.600397545636245 & 1.58783682622000 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.983333333333333 & 0.586761516472243 & 1.67586541674611 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.381666666666667 & 0.476199002143205 & 0.801485649799597 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.615 & 0.412309363584475 & 1.49159843146273 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.52931034482759 & 1.04499501013548 & 1.46346186344882 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.5125 & 0.998671398252855 & 1.51451218353312 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.48148148148148 & 0.961698627062926 & 1.54048413899269 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.44423076923077 & 0.938333996908986 & 1.53914360343788 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.406 & 0.920897565710005 & 1.52677132870471 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.35208333333333 & 0.904397205223891 & 1.49501051697591 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.29565217391304 & 0.886696940322992 & 1.46121195979438 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.25 & 0.867973143844623 & 1.44013672411939 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.21904761904762 & 0.855020278065311 & 1.42575287431312 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.185 & 0.838156937143666 & 1.41381637195336 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.14736842105263 & 0.816096395253487 & 1.40592266762341 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.075 & 0.793519135905127 & 1.35472473360558 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.997058823529412 & 0.771593315226304 & 1.29220770042180 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.925 & 0.747414899676254 & 1.23759909041239 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.843333333333333 & 0.713509753670106 & 1.18195067270692 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.746428571428571 & 0.67157877133463 & 1.11145349330383 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.696153846153846 & 0.63629893239023 & 1.09406728617126 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.658333333333333 & 0.606902227718487 & 1.08474364282397 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.609090909090909 & 0.563112450262899 & 1.08165058116997 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.645 & 0.542337775890537 & 1.18929572800067 \tabularnewline
Median & 1.15 &  &  \tabularnewline
Midrange & 1.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.648387096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.843333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.648387096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.843333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.843333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 0.648387096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.843333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.925 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17632&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.52833333333333[/C][C]1.10240131235589[/C][C]1.38636748360468[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-7.7960049052048[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.6045240038792[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.545[/C][C]1.08254623731839[/C][C]1.42719077184839[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.56833333333333[/C][C]1.05247218159532[/C][C]1.49014231516892[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.57833333333333[/C][C]1.00592058538707[/C][C]1.56904367627193[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.57166666666667[/C][C]0.974659412240077[/C][C]1.6125291018885[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.62166666666667[/C][C]0.956184424409848[/C][C]1.69597686938642[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.61166666666667[/C][C]0.94284427142061[/C][C]1.70936676980423[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.53[/C][C]0.926436279941022[/C][C]1.65148972803332[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.42333333333333[/C][C]0.882233191903604[/C][C]1.61333006556032[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.42333333333333[/C][C]0.877001718964058[/C][C]1.62295386948000[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.42333333333333[/C][C]0.871216976829326[/C][C]1.63373002499717[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.625[/C][C]0.839348768946618[/C][C]1.93602476124362[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.605[/C][C]0.802332140953346[/C][C]2.0004184278258[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.49666666666667[/C][C]0.775806366235011[/C][C]1.92917554148207[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.49666666666667[/C][C]0.768224773879043[/C][C]1.94821452985623[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.52166666666667[/C][C]0.740385041323902[/C][C]2.05523691287136[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.095[/C][C]0.667533722883302[/C][C]1.64036656495844[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.953333333333333[/C][C]0.600397545636245[/C][C]1.58783682622000[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.983333333333333[/C][C]0.586761516472243[/C][C]1.67586541674611[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.381666666666667[/C][C]0.476199002143205[/C][C]0.801485649799597[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.615[/C][C]0.412309363584475[/C][C]1.49159843146273[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.52931034482759[/C][C]1.04499501013548[/C][C]1.46346186344882[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.5125[/C][C]0.998671398252855[/C][C]1.51451218353312[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.48148148148148[/C][C]0.961698627062926[/C][C]1.54048413899269[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.44423076923077[/C][C]0.938333996908986[/C][C]1.53914360343788[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.406[/C][C]0.920897565710005[/C][C]1.52677132870471[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.35208333333333[/C][C]0.904397205223891[/C][C]1.49501051697591[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.29565217391304[/C][C]0.886696940322992[/C][C]1.46121195979438[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.25[/C][C]0.867973143844623[/C][C]1.44013672411939[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.21904761904762[/C][C]0.855020278065311[/C][C]1.42575287431312[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.185[/C][C]0.838156937143666[/C][C]1.41381637195336[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.14736842105263[/C][C]0.816096395253487[/C][C]1.40592266762341[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.075[/C][C]0.793519135905127[/C][C]1.35472473360558[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.997058823529412[/C][C]0.771593315226304[/C][C]1.29220770042180[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.925[/C][C]0.747414899676254[/C][C]1.23759909041239[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.843333333333333[/C][C]0.713509753670106[/C][C]1.18195067270692[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.746428571428571[/C][C]0.67157877133463[/C][C]1.11145349330383[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.696153846153846[/C][C]0.63629893239023[/C][C]1.09406728617126[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.658333333333333[/C][C]0.606902227718487[/C][C]1.08474364282397[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.609090909090909[/C][C]0.563112450262899[/C][C]1.08165058116997[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.645[/C][C]0.542337775890537[/C][C]1.18929572800067[/C][/ROW]
[ROW][C]Median[/C][C]1.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.648387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.843333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.648387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.843333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.843333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.648387096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.843333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17632&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17632&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.52833333333333	1.10240131235589	1.38636748360468
Geometric Mean	NaN
Harmonic Mean	-7.7960049052048
Quadratic Mean	8.6045240038792
Winsorized Mean ( 1 / 20 )	1.545	1.08254623731839	1.42719077184839
Winsorized Mean ( 2 / 20 )	1.56833333333333	1.05247218159532	1.49014231516892
Winsorized Mean ( 3 / 20 )	1.57833333333333	1.00592058538707	1.56904367627193
Winsorized Mean ( 4 / 20 )	1.57166666666667	0.974659412240077	1.6125291018885
Winsorized Mean ( 5 / 20 )	1.62166666666667	0.956184424409848	1.69597686938642
Winsorized Mean ( 6 / 20 )	1.61166666666667	0.94284427142061	1.70936676980423
Winsorized Mean ( 7 / 20 )	1.53	0.926436279941022	1.65148972803332
Winsorized Mean ( 8 / 20 )	1.42333333333333	0.882233191903604	1.61333006556032
Winsorized Mean ( 9 / 20 )	1.42333333333333	0.877001718964058	1.62295386948000
Winsorized Mean ( 10 / 20 )	1.42333333333333	0.871216976829326	1.63373002499717
Winsorized Mean ( 11 / 20 )	1.625	0.839348768946618	1.93602476124362
Winsorized Mean ( 12 / 20 )	1.605	0.802332140953346	2.0004184278258
Winsorized Mean ( 13 / 20 )	1.49666666666667	0.775806366235011	1.92917554148207
Winsorized Mean ( 14 / 20 )	1.49666666666667	0.768224773879043	1.94821452985623
Winsorized Mean ( 15 / 20 )	1.52166666666667	0.740385041323902	2.05523691287136
Winsorized Mean ( 16 / 20 )	1.095	0.667533722883302	1.64036656495844
Winsorized Mean ( 17 / 20 )	0.953333333333333	0.600397545636245	1.58783682622000
Winsorized Mean ( 18 / 20 )	0.983333333333333	0.586761516472243	1.67586541674611
Winsorized Mean ( 19 / 20 )	0.381666666666667	0.476199002143205	0.801485649799597
Winsorized Mean ( 20 / 20 )	0.615	0.412309363584475	1.49159843146273
Trimmed Mean ( 1 / 20 )	1.52931034482759	1.04499501013548	1.46346186344882
Trimmed Mean ( 2 / 20 )	1.5125	0.998671398252855	1.51451218353312
Trimmed Mean ( 3 / 20 )	1.48148148148148	0.961698627062926	1.54048413899269
Trimmed Mean ( 4 / 20 )	1.44423076923077	0.938333996908986	1.53914360343788
Trimmed Mean ( 5 / 20 )	1.406	0.920897565710005	1.52677132870471
Trimmed Mean ( 6 / 20 )	1.35208333333333	0.904397205223891	1.49501051697591
Trimmed Mean ( 7 / 20 )	1.29565217391304	0.886696940322992	1.46121195979438
Trimmed Mean ( 8 / 20 )	1.25	0.867973143844623	1.44013672411939
Trimmed Mean ( 9 / 20 )	1.21904761904762	0.855020278065311	1.42575287431312
Trimmed Mean ( 10 / 20 )	1.185	0.838156937143666	1.41381637195336
Trimmed Mean ( 11 / 20 )	1.14736842105263	0.816096395253487	1.40592266762341
Trimmed Mean ( 12 / 20 )	1.075	0.793519135905127	1.35472473360558
Trimmed Mean ( 13 / 20 )	0.997058823529412	0.771593315226304	1.29220770042180
Trimmed Mean ( 14 / 20 )	0.925	0.747414899676254	1.23759909041239
Trimmed Mean ( 15 / 20 )	0.843333333333333	0.713509753670106	1.18195067270692
Trimmed Mean ( 16 / 20 )	0.746428571428571	0.67157877133463	1.11145349330383
Trimmed Mean ( 17 / 20 )	0.696153846153846	0.63629893239023	1.09406728617126
Trimmed Mean ( 18 / 20 )	0.658333333333333	0.606902227718487	1.08474364282397
Trimmed Mean ( 19 / 20 )	0.609090909090909	0.563112450262899	1.08165058116997
Trimmed Mean ( 20 / 20 )	0.645	0.542337775890537	1.18929572800067
Median	1.15
Midrange	1.5
Midmean - Weighted Average at Xnp	0.648387096774194
Midmean - Weighted Average at X(n+1)p	0.843333333333333
Midmean - Empirical Distribution Function	0.648387096774194
Midmean - Empirical Distribution Function - Averaging	0.843333333333333
Midmean - Empirical Distribution Function - Interpolation	0.843333333333333
Midmean - Closest Observation	0.648387096774194
Midmean - True Basic - Statistics Graphics Toolkit	0.843333333333333
Midmean - MS Excel (old versions)	0.925
Number of observations	60

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code