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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 computationFri, 21 Nov 2008 07:16:19 -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/2008/Nov/21/t1227277153tokabtpwf4b21r5.htm/, Retrieved Sat, 18 May 2024 18:22:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25136, Retrieved Sat, 18 May 2024 18:22:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Exercise 1.13] [Exercise 1.13 (Wo...] [2008-10-01 13:28:34] [b98453cac15ba1066b407e146608df68]
F   P   [Exercise 1.13] [vraag 1 result 1 ...] [2008-10-10 13:06:35] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [] [2008-11-21 14:16:19] [fa8b44cd657c07c6ee11bb2476ca3f8d] [Current]
-    D        [Central Tendency] [] [2008-11-21 14:21:45] [fad8a251ac01c156a8ae23a83577546f]
-    D        [Central Tendency] [] [2008-11-21 14:26:00] [fad8a251ac01c156a8ae23a83577546f]
-    D        [Central Tendency] [] [2008-11-21 14:30:07] [fad8a251ac01c156a8ae23a83577546f]
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Dataseries X:
93,0
99,2
112,2
112,1
103,3
108,2
90,4
72,8
111,0
117,9
111,3
110,5
94,8
100,4
132,1
114,6
101,9
130,2
84,0
86,4
122,3
120,9
110,2
112,6
102,0
105,0
130,5
115,5
103,7
130,9
89,1
93,8
123,8
111,9
118,3
116,9
103,6
116,6
141,3
107,0
125,2
136,4
91,6
95,3
132,3
130,6
131,9
118,6
114,3
111,3
126,5
112,1
119,3
142,4
101,1
97,4
129,1
136,9
129,8
123,9




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25136&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25136&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25136&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112.8033333333331.9917016638770956.6366616944768
Geometric Mean111.725007824344
Harmonic Mean110.601533909002
Quadratic Mean113.836012169553
Winsorized Mean ( 1 / 20 )112.9716666666671.9314891238122258.4894138278616
Winsorized Mean ( 2 / 20 )112.9051.8775937615291960.1328159015854
Winsorized Mean ( 3 / 20 )113.0151.8411719815206661.3820985406581
Winsorized Mean ( 4 / 20 )112.8283333333331.7672844432070163.842769491361
Winsorized Mean ( 5 / 20 )112.9116666666671.7430541603823964.7780598176571
Winsorized Mean ( 6 / 20 )113.0316666666671.7109162504914966.064990986085
Winsorized Mean ( 7 / 20 )113.0083333333331.6710686923008167.6263841540456
Winsorized Mean ( 8 / 20 )113.1016666666671.6382029765774069.0400812864859
Winsorized Mean ( 9 / 20 )113.1616666666671.6213827043061069.7933105898622
Winsorized Mean ( 10 / 20 )113.4616666666671.5487941211649773.2580690462094
Winsorized Mean ( 11 / 20 )113.7183333333331.4788270120098976.8976576772003
Winsorized Mean ( 12 / 20 )113.8183333333331.413812994903380.5045177428986
Winsorized Mean ( 13 / 20 )113.4066666666671.2891131858864787.972621728077
Winsorized Mean ( 14 / 20 )113.291.2075976525298093.814359246781
Winsorized Mean ( 15 / 20 )112.991.1502632958229798.2296839430664
Winsorized Mean ( 16 / 20 )113.311.09089115076843103.869208142521
Winsorized Mean ( 17 / 20 )112.971.00962962387260111.892517145728
Winsorized Mean ( 18 / 20 )112.580.940440454567736119.709865152224
Winsorized Mean ( 19 / 20 )112.4850.800168855767402140.576578542439
Winsorized Mean ( 20 / 20 )112.9183333333330.662871222790495170.347315513230
Trimmed Mean ( 1 / 20 )112.9827586206901.8703146953050260.4084215903913
Trimmed Mean ( 2 / 20 )112.9946428571431.7949033538408062.953051268946
Trimmed Mean ( 3 / 20 )113.0444444444441.7378803982417965.0473096760922
Trimmed Mean ( 4 / 20 )113.0557692307691.6844900975815267.1157220770172
Trimmed Mean ( 5 / 20 )113.1241.6464198884183868.7090825346332
Trimmed Mean ( 6 / 20 )113.1770833333331.6058548671851370.4777783136275
Trimmed Mean ( 7 / 20 )113.2086956521741.5634713825731572.4085499191269
Trimmed Mean ( 8 / 20 )113.2477272727271.5198214282427874.5138377234651
Trimmed Mean ( 9 / 20 )113.2738095238101.4715263415228776.9770858512686
Trimmed Mean ( 10 / 20 )113.29251.4117155752433380.2516469937453
Trimmed Mean ( 11 / 20 )113.2657894736841.3521295374860083.768445502846
Trimmed Mean ( 12 / 20 )113.1972222222221.2907269153533787.7003654884125
Trimmed Mean ( 13 / 20 )113.1058823529411.2244460435897492.373104511282
Trimmed Mean ( 14 / 20 )113.06251.1702697338648096.612342204743
Trimmed Mean ( 15 / 20 )113.031.11758308595960101.137894282775
Trimmed Mean ( 16 / 20 )113.0357142857141.05835319673541106.803394778212
Trimmed Mean ( 17 / 20 )112.9961538461540.989257386889172114.223209595111
Trimmed Mean ( 18 / 20 )1130.914120310478323123.616113442301
Trimmed Mean ( 19 / 20 )113.0636363636360.822138101925906137.523897869200
Trimmed Mean ( 20 / 20 )113.1550.740180454526569152.874882480348
Median112.15
Midrange107.6
Midmean - Weighted Average at Xnp112.670967741935
Midmean - Weighted Average at X(n+1)p113.03
Midmean - Empirical Distribution Function112.670967741935
Midmean - Empirical Distribution Function - Averaging113.03
Midmean - Empirical Distribution Function - Interpolation113.03
Midmean - Closest Observation112.670967741935
Midmean - True Basic - Statistics Graphics Toolkit113.03
Midmean - MS Excel (old versions)113.0625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.803333333333 & 1.99170166387709 & 56.6366616944768 \tabularnewline
Geometric Mean & 111.725007824344 &  &  \tabularnewline
Harmonic Mean & 110.601533909002 &  &  \tabularnewline
Quadratic Mean & 113.836012169553 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 112.971666666667 & 1.93148912381222 & 58.4894138278616 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 112.905 & 1.87759376152919 & 60.1328159015854 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 113.015 & 1.84117198152066 & 61.3820985406581 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 112.828333333333 & 1.76728444320701 & 63.842769491361 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 112.911666666667 & 1.74305416038239 & 64.7780598176571 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 113.031666666667 & 1.71091625049149 & 66.064990986085 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 113.008333333333 & 1.67106869230081 & 67.6263841540456 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 113.101666666667 & 1.63820297657740 & 69.0400812864859 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 113.161666666667 & 1.62138270430610 & 69.7933105898622 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 113.461666666667 & 1.54879412116497 & 73.2580690462094 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 113.718333333333 & 1.47882701200989 & 76.8976576772003 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 113.818333333333 & 1.4138129949033 & 80.5045177428986 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 113.406666666667 & 1.28911318588647 & 87.972621728077 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 113.29 & 1.20759765252980 & 93.814359246781 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 112.99 & 1.15026329582297 & 98.2296839430664 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 113.31 & 1.09089115076843 & 103.869208142521 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 112.97 & 1.00962962387260 & 111.892517145728 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 112.58 & 0.940440454567736 & 119.709865152224 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 112.485 & 0.800168855767402 & 140.576578542439 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 112.918333333333 & 0.662871222790495 & 170.347315513230 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 112.982758620690 & 1.87031469530502 & 60.4084215903913 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 112.994642857143 & 1.79490335384080 & 62.953051268946 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 113.044444444444 & 1.73788039824179 & 65.0473096760922 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 113.055769230769 & 1.68449009758152 & 67.1157220770172 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 113.124 & 1.64641988841838 & 68.7090825346332 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 113.177083333333 & 1.60585486718513 & 70.4777783136275 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 113.208695652174 & 1.56347138257315 & 72.4085499191269 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 113.247727272727 & 1.51982142824278 & 74.5138377234651 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 113.273809523810 & 1.47152634152287 & 76.9770858512686 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 113.2925 & 1.41171557524333 & 80.2516469937453 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 113.265789473684 & 1.35212953748600 & 83.768445502846 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 113.197222222222 & 1.29072691535337 & 87.7003654884125 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 113.105882352941 & 1.22444604358974 & 92.373104511282 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 113.0625 & 1.17026973386480 & 96.612342204743 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 113.03 & 1.11758308595960 & 101.137894282775 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 113.035714285714 & 1.05835319673541 & 106.803394778212 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 112.996153846154 & 0.989257386889172 & 114.223209595111 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 113 & 0.914120310478323 & 123.616113442301 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 113.063636363636 & 0.822138101925906 & 137.523897869200 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 113.155 & 0.740180454526569 & 152.874882480348 \tabularnewline
Median & 112.15 &  &  \tabularnewline
Midrange & 107.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.670967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 113.03 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.670967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 113.03 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 113.03 &  &  \tabularnewline
Midmean - Closest Observation & 112.670967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 113.03 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 113.0625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25136&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]112.803333333333[/C][C]1.99170166387709[/C][C]56.6366616944768[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.725007824344[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.601533909002[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.836012169553[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]112.971666666667[/C][C]1.93148912381222[/C][C]58.4894138278616[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]112.905[/C][C]1.87759376152919[/C][C]60.1328159015854[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]113.015[/C][C]1.84117198152066[/C][C]61.3820985406581[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]112.828333333333[/C][C]1.76728444320701[/C][C]63.842769491361[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]112.911666666667[/C][C]1.74305416038239[/C][C]64.7780598176571[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]113.031666666667[/C][C]1.71091625049149[/C][C]66.064990986085[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]113.008333333333[/C][C]1.67106869230081[/C][C]67.6263841540456[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]113.101666666667[/C][C]1.63820297657740[/C][C]69.0400812864859[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]113.161666666667[/C][C]1.62138270430610[/C][C]69.7933105898622[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]113.461666666667[/C][C]1.54879412116497[/C][C]73.2580690462094[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]113.718333333333[/C][C]1.47882701200989[/C][C]76.8976576772003[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]113.818333333333[/C][C]1.4138129949033[/C][C]80.5045177428986[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]113.406666666667[/C][C]1.28911318588647[/C][C]87.972621728077[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]113.29[/C][C]1.20759765252980[/C][C]93.814359246781[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]112.99[/C][C]1.15026329582297[/C][C]98.2296839430664[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]113.31[/C][C]1.09089115076843[/C][C]103.869208142521[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]112.97[/C][C]1.00962962387260[/C][C]111.892517145728[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]112.58[/C][C]0.940440454567736[/C][C]119.709865152224[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]112.485[/C][C]0.800168855767402[/C][C]140.576578542439[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]112.918333333333[/C][C]0.662871222790495[/C][C]170.347315513230[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]112.982758620690[/C][C]1.87031469530502[/C][C]60.4084215903913[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]112.994642857143[/C][C]1.79490335384080[/C][C]62.953051268946[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]113.044444444444[/C][C]1.73788039824179[/C][C]65.0473096760922[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]113.055769230769[/C][C]1.68449009758152[/C][C]67.1157220770172[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]113.124[/C][C]1.64641988841838[/C][C]68.7090825346332[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]113.177083333333[/C][C]1.60585486718513[/C][C]70.4777783136275[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]113.208695652174[/C][C]1.56347138257315[/C][C]72.4085499191269[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]113.247727272727[/C][C]1.51982142824278[/C][C]74.5138377234651[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]113.273809523810[/C][C]1.47152634152287[/C][C]76.9770858512686[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]113.2925[/C][C]1.41171557524333[/C][C]80.2516469937453[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]113.265789473684[/C][C]1.35212953748600[/C][C]83.768445502846[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]113.197222222222[/C][C]1.29072691535337[/C][C]87.7003654884125[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]113.105882352941[/C][C]1.22444604358974[/C][C]92.373104511282[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]113.0625[/C][C]1.17026973386480[/C][C]96.612342204743[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]113.03[/C][C]1.11758308595960[/C][C]101.137894282775[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]113.035714285714[/C][C]1.05835319673541[/C][C]106.803394778212[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]112.996153846154[/C][C]0.989257386889172[/C][C]114.223209595111[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]113[/C][C]0.914120310478323[/C][C]123.616113442301[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]113.063636363636[/C][C]0.822138101925906[/C][C]137.523897869200[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]113.155[/C][C]0.740180454526569[/C][C]152.874882480348[/C][/ROW]
[ROW][C]Median[/C][C]112.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.670967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]113.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.670967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]113.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]113.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.670967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]113.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]113.0625[/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=25136&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25136&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 Mean112.8033333333331.9917016638770956.6366616944768
Geometric Mean111.725007824344
Harmonic Mean110.601533909002
Quadratic Mean113.836012169553
Winsorized Mean ( 1 / 20 )112.9716666666671.9314891238122258.4894138278616
Winsorized Mean ( 2 / 20 )112.9051.8775937615291960.1328159015854
Winsorized Mean ( 3 / 20 )113.0151.8411719815206661.3820985406581
Winsorized Mean ( 4 / 20 )112.8283333333331.7672844432070163.842769491361
Winsorized Mean ( 5 / 20 )112.9116666666671.7430541603823964.7780598176571
Winsorized Mean ( 6 / 20 )113.0316666666671.7109162504914966.064990986085
Winsorized Mean ( 7 / 20 )113.0083333333331.6710686923008167.6263841540456
Winsorized Mean ( 8 / 20 )113.1016666666671.6382029765774069.0400812864859
Winsorized Mean ( 9 / 20 )113.1616666666671.6213827043061069.7933105898622
Winsorized Mean ( 10 / 20 )113.4616666666671.5487941211649773.2580690462094
Winsorized Mean ( 11 / 20 )113.7183333333331.4788270120098976.8976576772003
Winsorized Mean ( 12 / 20 )113.8183333333331.413812994903380.5045177428986
Winsorized Mean ( 13 / 20 )113.4066666666671.2891131858864787.972621728077
Winsorized Mean ( 14 / 20 )113.291.2075976525298093.814359246781
Winsorized Mean ( 15 / 20 )112.991.1502632958229798.2296839430664
Winsorized Mean ( 16 / 20 )113.311.09089115076843103.869208142521
Winsorized Mean ( 17 / 20 )112.971.00962962387260111.892517145728
Winsorized Mean ( 18 / 20 )112.580.940440454567736119.709865152224
Winsorized Mean ( 19 / 20 )112.4850.800168855767402140.576578542439
Winsorized Mean ( 20 / 20 )112.9183333333330.662871222790495170.347315513230
Trimmed Mean ( 1 / 20 )112.9827586206901.8703146953050260.4084215903913
Trimmed Mean ( 2 / 20 )112.9946428571431.7949033538408062.953051268946
Trimmed Mean ( 3 / 20 )113.0444444444441.7378803982417965.0473096760922
Trimmed Mean ( 4 / 20 )113.0557692307691.6844900975815267.1157220770172
Trimmed Mean ( 5 / 20 )113.1241.6464198884183868.7090825346332
Trimmed Mean ( 6 / 20 )113.1770833333331.6058548671851370.4777783136275
Trimmed Mean ( 7 / 20 )113.2086956521741.5634713825731572.4085499191269
Trimmed Mean ( 8 / 20 )113.2477272727271.5198214282427874.5138377234651
Trimmed Mean ( 9 / 20 )113.2738095238101.4715263415228776.9770858512686
Trimmed Mean ( 10 / 20 )113.29251.4117155752433380.2516469937453
Trimmed Mean ( 11 / 20 )113.2657894736841.3521295374860083.768445502846
Trimmed Mean ( 12 / 20 )113.1972222222221.2907269153533787.7003654884125
Trimmed Mean ( 13 / 20 )113.1058823529411.2244460435897492.373104511282
Trimmed Mean ( 14 / 20 )113.06251.1702697338648096.612342204743
Trimmed Mean ( 15 / 20 )113.031.11758308595960101.137894282775
Trimmed Mean ( 16 / 20 )113.0357142857141.05835319673541106.803394778212
Trimmed Mean ( 17 / 20 )112.9961538461540.989257386889172114.223209595111
Trimmed Mean ( 18 / 20 )1130.914120310478323123.616113442301
Trimmed Mean ( 19 / 20 )113.0636363636360.822138101925906137.523897869200
Trimmed Mean ( 20 / 20 )113.1550.740180454526569152.874882480348
Median112.15
Midrange107.6
Midmean - Weighted Average at Xnp112.670967741935
Midmean - Weighted Average at X(n+1)p113.03
Midmean - Empirical Distribution Function112.670967741935
Midmean - Empirical Distribution Function - Averaging113.03
Midmean - Empirical Distribution Function - Interpolation113.03
Midmean - Closest Observation112.670967741935
Midmean - True Basic - Statistics Graphics Toolkit113.03
Midmean - MS Excel (old versions)113.0625
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')