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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Nov 2011 15:36:04 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321389499yhzbnmmxupdl2ll.htm/, Retrieved Thu, 25 Apr 2024 12:53:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143512, Retrieved Thu, 25 Apr 2024 12:53:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [WS VI-linear regr...] [2011-11-15 15:40:01] [74be16979710d4c4e7c6647856088456]
-    D      [Central Tendency] [WS VI-minitutoria...] [2011-11-15 20:36:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
122,0
104,1
102,9
105,1
151,5
155,0
99,2
91,7
144,3
118,9
196,5
96,4
121,8
101,4
102,5
98,1
162,9
102,1
108,7
74,4
72,7
100,6
108,7
126,8
130,9
125,2
93,9
116,5
140,4
77,8
82,7
92,6
91,5
101,7
96,7
118,7
123,1
121,0
129,6
133,9
147,7
28,2
16,9
26,1
27,7
42,6
104,5
151,7
72,6
67,3
113,4
99,9
112,8
121,2
97,9
109,9
135,7
137,1
126,6
121,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143512&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143512&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143512&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.7616666666674.3589171487860624.4927038120923
Geometric Mean98.9533777216863
Harmonic Mean85.9322038713519
Quadratic Mean111.88861797937
Winsorized Mean ( 1 / 20 )106.3554.143621075999725.6671635869456
Winsorized Mean ( 2 / 20 )106.1454.0688706806458226.0870910704767
Winsorized Mean ( 3 / 20 )106.0054.0280369284770926.3167895136647
Winsorized Mean ( 4 / 20 )106.9516666666673.7271476891078328.6953122301058
Winsorized Mean ( 5 / 20 )108.6933333333333.1231465614736134.8025080456192
Winsorized Mean ( 6 / 20 )108.8833333333332.937242034992737.0699220684427
Winsorized Mean ( 7 / 20 )108.442.8449163700436638.1171134385001
Winsorized Mean ( 8 / 20 )108.2266666666672.7152559853379139.8587342228795
Winsorized Mean ( 9 / 20 )108.5266666666672.5719882465691142.1956308748437
Winsorized Mean ( 10 / 20 )109.0433333333332.3580950449578246.2421281815992
Winsorized Mean ( 11 / 20 )110.1066666666671.9763400898274455.7124086251169
Winsorized Mean ( 12 / 20 )109.8866666666671.9241807511480157.108287046893
Winsorized Mean ( 13 / 20 )109.4751.7904590595899761.1435371357057
Winsorized Mean ( 14 / 20 )109.7316666666671.7350922599847963.2425544147309
Winsorized Mean ( 15 / 20 )110.0066666666671.5838251392003869.4563206151695
Winsorized Mean ( 16 / 20 )109.5266666666671.4831118351732273.8492297540558
Winsorized Mean ( 17 / 20 )109.5551.3860369570569579.0419039277455
Winsorized Mean ( 18 / 20 )109.5551.3683889347828680.0613021745786
Winsorized Mean ( 19 / 20 )109.7766666666671.3004505231220984.4143354282466
Winsorized Mean ( 20 / 20 )109.9433333333331.2584794130795387.362043582659
Trimmed Mean ( 1 / 20 )106.7637931034483.9327557828634427.1473234032634
Trimmed Mean ( 2 / 20 )107.2017857142863.6690974252598229.2174813828211
Trimmed Mean ( 3 / 20 )107.7888888888893.3874018114053731.8205205316842
Trimmed Mean ( 4 / 20 )108.4753.0427408793427635.6504231880011
Trimmed Mean ( 5 / 20 )108.9322.736885523244839.8014455024967
Trimmed Mean ( 6 / 20 )108.9916666666672.5884595101978742.1067690018976
Trimmed Mean ( 7 / 20 )109.0152173913042.4617282476206444.2840177410614
Trimmed Mean ( 8 / 20 )109.1272727272732.3264345494464246.9075189556654
Trimmed Mean ( 9 / 20 )109.2880952380952.1888912927627449.9285165962516
Trimmed Mean ( 10 / 20 )109.4152.0507645541139753.3532724566096
Trimmed Mean ( 11 / 20 )109.4736842105261.9318866736011356.6667215559089
Trimmed Mean ( 12 / 20 )109.3777777777781.8824549620916258.1037952994354
Trimmed Mean ( 13 / 20 )109.3029411764711.8265592820784259.8408944340947
Trimmed Mean ( 14 / 20 )109.2781251.7842824887040661.2448565133705
Trimmed Mean ( 15 / 20 )109.2133333333331.7358739117654562.9154759416017
Trimmed Mean ( 16 / 20 )109.11.706438166747163.9343412061462
Trimmed Mean ( 17 / 20 )109.0384615384621.6877666346440664.6051766282587
Trimmed Mean ( 18 / 20 )108.96251.6807500536229764.829687058539
Trimmed Mean ( 19 / 20 )108.8727272727271.6621477502449265.5012331224375
Trimmed Mean ( 20 / 20 )108.731.6427528244094666.1876810585222
Median106.9
Midrange106.7
Midmean - Weighted Average at Xnp108.71935483871
Midmean - Weighted Average at X(n+1)p109.213333333333
Midmean - Empirical Distribution Function108.71935483871
Midmean - Empirical Distribution Function - Averaging109.213333333333
Midmean - Empirical Distribution Function - Interpolation109.213333333333
Midmean - Closest Observation108.71935483871
Midmean - True Basic - Statistics Graphics Toolkit109.213333333333
Midmean - MS Excel (old versions)109.278125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.761666666667 & 4.35891714878606 & 24.4927038120923 \tabularnewline
Geometric Mean & 98.9533777216863 &  &  \tabularnewline
Harmonic Mean & 85.9322038713519 &  &  \tabularnewline
Quadratic Mean & 111.88861797937 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 106.355 & 4.1436210759997 & 25.6671635869456 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 106.145 & 4.06887068064582 & 26.0870910704767 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 106.005 & 4.02803692847709 & 26.3167895136647 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 106.951666666667 & 3.72714768910783 & 28.6953122301058 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 108.693333333333 & 3.12314656147361 & 34.8025080456192 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 108.883333333333 & 2.9372420349927 & 37.0699220684427 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 108.44 & 2.84491637004366 & 38.1171134385001 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 108.226666666667 & 2.71525598533791 & 39.8587342228795 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 108.526666666667 & 2.57198824656911 & 42.1956308748437 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 109.043333333333 & 2.35809504495782 & 46.2421281815992 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 110.106666666667 & 1.97634008982744 & 55.7124086251169 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 109.886666666667 & 1.92418075114801 & 57.108287046893 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 109.475 & 1.79045905958997 & 61.1435371357057 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 109.731666666667 & 1.73509225998479 & 63.2425544147309 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 110.006666666667 & 1.58382513920038 & 69.4563206151695 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 109.526666666667 & 1.48311183517322 & 73.8492297540558 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 109.555 & 1.38603695705695 & 79.0419039277455 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 109.555 & 1.36838893478286 & 80.0613021745786 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 109.776666666667 & 1.30045052312209 & 84.4143354282466 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 109.943333333333 & 1.25847941307953 & 87.362043582659 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 106.763793103448 & 3.93275578286344 & 27.1473234032634 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 107.201785714286 & 3.66909742525982 & 29.2174813828211 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 107.788888888889 & 3.38740181140537 & 31.8205205316842 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 108.475 & 3.04274087934276 & 35.6504231880011 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 108.932 & 2.7368855232448 & 39.8014455024967 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 108.991666666667 & 2.58845951019787 & 42.1067690018976 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 109.015217391304 & 2.46172824762064 & 44.2840177410614 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 109.127272727273 & 2.32643454944642 & 46.9075189556654 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 109.288095238095 & 2.18889129276274 & 49.9285165962516 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 109.415 & 2.05076455411397 & 53.3532724566096 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109.473684210526 & 1.93188667360113 & 56.6667215559089 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109.377777777778 & 1.88245496209162 & 58.1037952994354 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 109.302941176471 & 1.82655928207842 & 59.8408944340947 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 109.278125 & 1.78428248870406 & 61.2448565133705 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 109.213333333333 & 1.73587391176545 & 62.9154759416017 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 109.1 & 1.7064381667471 & 63.9343412061462 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 109.038461538462 & 1.68776663464406 & 64.6051766282587 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 108.9625 & 1.68075005362297 & 64.829687058539 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 108.872727272727 & 1.66214775024492 & 65.5012331224375 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 108.73 & 1.64275282440946 & 66.1876810585222 \tabularnewline
Median & 106.9 &  &  \tabularnewline
Midrange & 106.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.71935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.213333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.71935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.213333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.213333333333 &  &  \tabularnewline
Midmean - Closest Observation & 108.71935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.213333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.278125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143512&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]106.761666666667[/C][C]4.35891714878606[/C][C]24.4927038120923[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.9533777216863[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.9322038713519[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.88861797937[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]106.355[/C][C]4.1436210759997[/C][C]25.6671635869456[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]106.145[/C][C]4.06887068064582[/C][C]26.0870910704767[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]106.005[/C][C]4.02803692847709[/C][C]26.3167895136647[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]106.951666666667[/C][C]3.72714768910783[/C][C]28.6953122301058[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]108.693333333333[/C][C]3.12314656147361[/C][C]34.8025080456192[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]108.883333333333[/C][C]2.9372420349927[/C][C]37.0699220684427[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]108.44[/C][C]2.84491637004366[/C][C]38.1171134385001[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]108.226666666667[/C][C]2.71525598533791[/C][C]39.8587342228795[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]108.526666666667[/C][C]2.57198824656911[/C][C]42.1956308748437[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]109.043333333333[/C][C]2.35809504495782[/C][C]46.2421281815992[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]110.106666666667[/C][C]1.97634008982744[/C][C]55.7124086251169[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]109.886666666667[/C][C]1.92418075114801[/C][C]57.108287046893[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]109.475[/C][C]1.79045905958997[/C][C]61.1435371357057[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]109.731666666667[/C][C]1.73509225998479[/C][C]63.2425544147309[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]110.006666666667[/C][C]1.58382513920038[/C][C]69.4563206151695[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]109.526666666667[/C][C]1.48311183517322[/C][C]73.8492297540558[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]109.555[/C][C]1.38603695705695[/C][C]79.0419039277455[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]109.555[/C][C]1.36838893478286[/C][C]80.0613021745786[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]109.776666666667[/C][C]1.30045052312209[/C][C]84.4143354282466[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]109.943333333333[/C][C]1.25847941307953[/C][C]87.362043582659[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]106.763793103448[/C][C]3.93275578286344[/C][C]27.1473234032634[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]107.201785714286[/C][C]3.66909742525982[/C][C]29.2174813828211[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]107.788888888889[/C][C]3.38740181140537[/C][C]31.8205205316842[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]108.475[/C][C]3.04274087934276[/C][C]35.6504231880011[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]108.932[/C][C]2.7368855232448[/C][C]39.8014455024967[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]108.991666666667[/C][C]2.58845951019787[/C][C]42.1067690018976[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]109.015217391304[/C][C]2.46172824762064[/C][C]44.2840177410614[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]109.127272727273[/C][C]2.32643454944642[/C][C]46.9075189556654[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]109.288095238095[/C][C]2.18889129276274[/C][C]49.9285165962516[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]109.415[/C][C]2.05076455411397[/C][C]53.3532724566096[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109.473684210526[/C][C]1.93188667360113[/C][C]56.6667215559089[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109.377777777778[/C][C]1.88245496209162[/C][C]58.1037952994354[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]109.302941176471[/C][C]1.82655928207842[/C][C]59.8408944340947[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]109.278125[/C][C]1.78428248870406[/C][C]61.2448565133705[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]109.213333333333[/C][C]1.73587391176545[/C][C]62.9154759416017[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]109.1[/C][C]1.7064381667471[/C][C]63.9343412061462[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]109.038461538462[/C][C]1.68776663464406[/C][C]64.6051766282587[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]108.9625[/C][C]1.68075005362297[/C][C]64.829687058539[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]108.872727272727[/C][C]1.66214775024492[/C][C]65.5012331224375[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]108.73[/C][C]1.64275282440946[/C][C]66.1876810585222[/C][/ROW]
[ROW][C]Median[/C][C]106.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.71935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.213333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.71935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.213333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.213333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.71935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.213333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.278125[/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=143512&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143512&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 Mean106.7616666666674.3589171487860624.4927038120923
Geometric Mean98.9533777216863
Harmonic Mean85.9322038713519
Quadratic Mean111.88861797937
Winsorized Mean ( 1 / 20 )106.3554.143621075999725.6671635869456
Winsorized Mean ( 2 / 20 )106.1454.0688706806458226.0870910704767
Winsorized Mean ( 3 / 20 )106.0054.0280369284770926.3167895136647
Winsorized Mean ( 4 / 20 )106.9516666666673.7271476891078328.6953122301058
Winsorized Mean ( 5 / 20 )108.6933333333333.1231465614736134.8025080456192
Winsorized Mean ( 6 / 20 )108.8833333333332.937242034992737.0699220684427
Winsorized Mean ( 7 / 20 )108.442.8449163700436638.1171134385001
Winsorized Mean ( 8 / 20 )108.2266666666672.7152559853379139.8587342228795
Winsorized Mean ( 9 / 20 )108.5266666666672.5719882465691142.1956308748437
Winsorized Mean ( 10 / 20 )109.0433333333332.3580950449578246.2421281815992
Winsorized Mean ( 11 / 20 )110.1066666666671.9763400898274455.7124086251169
Winsorized Mean ( 12 / 20 )109.8866666666671.9241807511480157.108287046893
Winsorized Mean ( 13 / 20 )109.4751.7904590595899761.1435371357057
Winsorized Mean ( 14 / 20 )109.7316666666671.7350922599847963.2425544147309
Winsorized Mean ( 15 / 20 )110.0066666666671.5838251392003869.4563206151695
Winsorized Mean ( 16 / 20 )109.5266666666671.4831118351732273.8492297540558
Winsorized Mean ( 17 / 20 )109.5551.3860369570569579.0419039277455
Winsorized Mean ( 18 / 20 )109.5551.3683889347828680.0613021745786
Winsorized Mean ( 19 / 20 )109.7766666666671.3004505231220984.4143354282466
Winsorized Mean ( 20 / 20 )109.9433333333331.2584794130795387.362043582659
Trimmed Mean ( 1 / 20 )106.7637931034483.9327557828634427.1473234032634
Trimmed Mean ( 2 / 20 )107.2017857142863.6690974252598229.2174813828211
Trimmed Mean ( 3 / 20 )107.7888888888893.3874018114053731.8205205316842
Trimmed Mean ( 4 / 20 )108.4753.0427408793427635.6504231880011
Trimmed Mean ( 5 / 20 )108.9322.736885523244839.8014455024967
Trimmed Mean ( 6 / 20 )108.9916666666672.5884595101978742.1067690018976
Trimmed Mean ( 7 / 20 )109.0152173913042.4617282476206444.2840177410614
Trimmed Mean ( 8 / 20 )109.1272727272732.3264345494464246.9075189556654
Trimmed Mean ( 9 / 20 )109.2880952380952.1888912927627449.9285165962516
Trimmed Mean ( 10 / 20 )109.4152.0507645541139753.3532724566096
Trimmed Mean ( 11 / 20 )109.4736842105261.9318866736011356.6667215559089
Trimmed Mean ( 12 / 20 )109.3777777777781.8824549620916258.1037952994354
Trimmed Mean ( 13 / 20 )109.3029411764711.8265592820784259.8408944340947
Trimmed Mean ( 14 / 20 )109.2781251.7842824887040661.2448565133705
Trimmed Mean ( 15 / 20 )109.2133333333331.7358739117654562.9154759416017
Trimmed Mean ( 16 / 20 )109.11.706438166747163.9343412061462
Trimmed Mean ( 17 / 20 )109.0384615384621.6877666346440664.6051766282587
Trimmed Mean ( 18 / 20 )108.96251.6807500536229764.829687058539
Trimmed Mean ( 19 / 20 )108.8727272727271.6621477502449265.5012331224375
Trimmed Mean ( 20 / 20 )108.731.6427528244094666.1876810585222
Median106.9
Midrange106.7
Midmean - Weighted Average at Xnp108.71935483871
Midmean - Weighted Average at X(n+1)p109.213333333333
Midmean - Empirical Distribution Function108.71935483871
Midmean - Empirical Distribution Function - Averaging109.213333333333
Midmean - Empirical Distribution Function - Interpolation109.213333333333
Midmean - Closest Observation108.71935483871
Midmean - True Basic - Statistics Graphics Toolkit109.213333333333
Midmean - MS Excel (old versions)109.278125
Number of observations60



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')