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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 computationTue, 15 Dec 2009 13:10:21 -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/2009/Dec/15/t1260907857iheov981z95qv7g.htm/, Retrieved Wed, 08 May 2024 23:55:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68112, Retrieved Wed, 08 May 2024 23:55:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper central ten...] [2009-12-15 20:10:21] [ba02bcb7e07025bbb7f8a074d38ad767] [Current]
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Dataseries X:
96.2
96.1
106
103.1
102
104.7
86
92.1
106.9
112.6
101.7
92
97.4
97
105.4
102.7
98.1
104.5
87.4
89.9
109.8
111.7
98.6
96.9
95.1
97
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68112&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68112&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68112&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.9783333333331.0875439900620893.769387045679
Geometric Mean101.629291991473
Harmonic Mean101.273055539749
Quadratic Mean102.319904384891
Winsorized Mean ( 1 / 20 )102.0366666666671.0615572365531496.1197975513577
Winsorized Mean ( 2 / 20 )102.0333333333331.0514065549916897.0446045337246
Winsorized Mean ( 3 / 20 )102.0933333333331.0318511330752298.9419210395832
Winsorized Mean ( 4 / 20 )102.061.0251090613054999.5601383817887
Winsorized Mean ( 5 / 20 )102.2516666666670.974051738398537104.975601023803
Winsorized Mean ( 6 / 20 )102.3916666666670.917159985386807111.639919205027
Winsorized Mean ( 7 / 20 )102.3683333333330.90798557589114112.742246189169
Winsorized Mean ( 8 / 20 )102.6750.84351171044018121.723265639572
Winsorized Mean ( 9 / 20 )102.7350.828543835295182123.994646539611
Winsorized Mean ( 10 / 20 )102.6850.783393404356139131.077182203743
Winsorized Mean ( 11 / 20 )102.6666666666670.76721179342465133.81789428495
Winsorized Mean ( 12 / 20 )102.4866666666670.719720075319097142.397954678738
Winsorized Mean ( 13 / 20 )102.4216666666670.700645754067655146.181813094634
Winsorized Mean ( 14 / 20 )102.5383333333330.675792448274623151.730510743536
Winsorized Mean ( 15 / 20 )102.3133333333330.627466732936192163.057781333784
Winsorized Mean ( 16 / 20 )101.8333333333330.538394068743336189.142747376512
Winsorized Mean ( 17 / 20 )101.5783333333330.498857970722047203.621750668449
Winsorized Mean ( 18 / 20 )101.6683333333330.47588449713553213.640776165857
Winsorized Mean ( 19 / 20 )101.510.452405372944361224.378413853374
Winsorized Mean ( 20 / 20 )101.510.383315155550334264.821253556385
Trimmed Mean ( 1 / 20 )102.0913793103451.0334727121896698.7847846451989
Trimmed Mean ( 2 / 20 )102.150.998771973247875102.275597169414
Trimmed Mean ( 3 / 20 )102.2148148148150.962498813044028106.197341159879
Trimmed Mean ( 4 / 20 )102.2615384615380.926886620513118110.327990714687
Trimmed Mean ( 5 / 20 )102.3220.884604327553585115.669793616064
Trimmed Mean ( 6 / 20 )102.3395833333330.849701342939195120.441828395059
Trimmed Mean ( 7 / 20 )102.3282608695650.823552238947325124.252301226650
Trimmed Mean ( 8 / 20 )102.3204545454550.792262926608304129.149618275704
Trimmed Mean ( 9 / 20 )102.2571428571430.76965641501865132.860768599798
Trimmed Mean ( 10 / 20 )102.17750.743178270879667137.487200586552
Trimmed Mean ( 11 / 20 )102.0973684210530.719930521008614141.815585590142
Trimmed Mean ( 12 / 20 )102.0111111111110.692084243172221147.396956537452
Trimmed Mean ( 13 / 20 )101.9411764705880.667358611235634152.753219564877
Trimmed Mean ( 14 / 20 )101.8718750.637570906477303159.781247803261
Trimmed Mean ( 15 / 20 )101.7766666666670.601142271555862169.305456432553
Trimmed Mean ( 16 / 20 )101.70.564749323985252180.079896833406
Trimmed Mean ( 17 / 20 )101.6807692307690.543465213118395187.097107186174
Trimmed Mean ( 18 / 20 )101.6958333333330.523729628176555194.176208222939
Trimmed Mean ( 19 / 20 )101.70.499523582550223203.593991460403
Trimmed Mean ( 20 / 20 )101.730.467586186820423217.564168633300
Median102
Midrange98.7
Midmean - Weighted Average at Xnp101.616129032258
Midmean - Weighted Average at X(n+1)p101.776666666667
Midmean - Empirical Distribution Function101.616129032258
Midmean - Empirical Distribution Function - Averaging101.776666666667
Midmean - Empirical Distribution Function - Interpolation101.776666666667
Midmean - Closest Observation101.616129032258
Midmean - True Basic - Statistics Graphics Toolkit101.776666666667
Midmean - MS Excel (old versions)101.871875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.978333333333 & 1.08754399006208 & 93.769387045679 \tabularnewline
Geometric Mean & 101.629291991473 &  &  \tabularnewline
Harmonic Mean & 101.273055539749 &  &  \tabularnewline
Quadratic Mean & 102.319904384891 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 102.036666666667 & 1.06155723655314 & 96.1197975513577 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 102.033333333333 & 1.05140655499168 & 97.0446045337246 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 102.093333333333 & 1.03185113307522 & 98.9419210395832 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 102.06 & 1.02510906130549 & 99.5601383817887 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 102.251666666667 & 0.974051738398537 & 104.975601023803 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 102.391666666667 & 0.917159985386807 & 111.639919205027 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 102.368333333333 & 0.90798557589114 & 112.742246189169 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 102.675 & 0.84351171044018 & 121.723265639572 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 102.735 & 0.828543835295182 & 123.994646539611 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 102.685 & 0.783393404356139 & 131.077182203743 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 102.666666666667 & 0.76721179342465 & 133.81789428495 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 102.486666666667 & 0.719720075319097 & 142.397954678738 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 102.421666666667 & 0.700645754067655 & 146.181813094634 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 102.538333333333 & 0.675792448274623 & 151.730510743536 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 102.313333333333 & 0.627466732936192 & 163.057781333784 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.833333333333 & 0.538394068743336 & 189.142747376512 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.578333333333 & 0.498857970722047 & 203.621750668449 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.668333333333 & 0.47588449713553 & 213.640776165857 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.51 & 0.452405372944361 & 224.378413853374 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.51 & 0.383315155550334 & 264.821253556385 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 102.091379310345 & 1.03347271218966 & 98.7847846451989 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 102.15 & 0.998771973247875 & 102.275597169414 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 102.214814814815 & 0.962498813044028 & 106.197341159879 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 102.261538461538 & 0.926886620513118 & 110.327990714687 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 102.322 & 0.884604327553585 & 115.669793616064 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 102.339583333333 & 0.849701342939195 & 120.441828395059 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 102.328260869565 & 0.823552238947325 & 124.252301226650 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 102.320454545455 & 0.792262926608304 & 129.149618275704 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 102.257142857143 & 0.76965641501865 & 132.860768599798 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 102.1775 & 0.743178270879667 & 137.487200586552 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 102.097368421053 & 0.719930521008614 & 141.815585590142 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 102.011111111111 & 0.692084243172221 & 147.396956537452 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.941176470588 & 0.667358611235634 & 152.753219564877 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.871875 & 0.637570906477303 & 159.781247803261 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.776666666667 & 0.601142271555862 & 169.305456432553 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.7 & 0.564749323985252 & 180.079896833406 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.680769230769 & 0.543465213118395 & 187.097107186174 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.695833333333 & 0.523729628176555 & 194.176208222939 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.7 & 0.499523582550223 & 203.593991460403 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.73 & 0.467586186820423 & 217.564168633300 \tabularnewline
Median & 102 &  &  \tabularnewline
Midrange & 98.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.616129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.776666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.616129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.776666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.776666666667 &  &  \tabularnewline
Midmean - Closest Observation & 101.616129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.776666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.871875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68112&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]101.978333333333[/C][C]1.08754399006208[/C][C]93.769387045679[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.629291991473[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.273055539749[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]102.319904384891[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]102.036666666667[/C][C]1.06155723655314[/C][C]96.1197975513577[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]102.033333333333[/C][C]1.05140655499168[/C][C]97.0446045337246[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]102.093333333333[/C][C]1.03185113307522[/C][C]98.9419210395832[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]102.06[/C][C]1.02510906130549[/C][C]99.5601383817887[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]102.251666666667[/C][C]0.974051738398537[/C][C]104.975601023803[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]102.391666666667[/C][C]0.917159985386807[/C][C]111.639919205027[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]102.368333333333[/C][C]0.90798557589114[/C][C]112.742246189169[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]102.675[/C][C]0.84351171044018[/C][C]121.723265639572[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]102.735[/C][C]0.828543835295182[/C][C]123.994646539611[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]102.685[/C][C]0.783393404356139[/C][C]131.077182203743[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]102.666666666667[/C][C]0.76721179342465[/C][C]133.81789428495[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]102.486666666667[/C][C]0.719720075319097[/C][C]142.397954678738[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]102.421666666667[/C][C]0.700645754067655[/C][C]146.181813094634[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]102.538333333333[/C][C]0.675792448274623[/C][C]151.730510743536[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]102.313333333333[/C][C]0.627466732936192[/C][C]163.057781333784[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.833333333333[/C][C]0.538394068743336[/C][C]189.142747376512[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.578333333333[/C][C]0.498857970722047[/C][C]203.621750668449[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.668333333333[/C][C]0.47588449713553[/C][C]213.640776165857[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.51[/C][C]0.452405372944361[/C][C]224.378413853374[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.51[/C][C]0.383315155550334[/C][C]264.821253556385[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]102.091379310345[/C][C]1.03347271218966[/C][C]98.7847846451989[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]102.15[/C][C]0.998771973247875[/C][C]102.275597169414[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]102.214814814815[/C][C]0.962498813044028[/C][C]106.197341159879[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]102.261538461538[/C][C]0.926886620513118[/C][C]110.327990714687[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]102.322[/C][C]0.884604327553585[/C][C]115.669793616064[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]102.339583333333[/C][C]0.849701342939195[/C][C]120.441828395059[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]102.328260869565[/C][C]0.823552238947325[/C][C]124.252301226650[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]102.320454545455[/C][C]0.792262926608304[/C][C]129.149618275704[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]102.257142857143[/C][C]0.76965641501865[/C][C]132.860768599798[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]102.1775[/C][C]0.743178270879667[/C][C]137.487200586552[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]102.097368421053[/C][C]0.719930521008614[/C][C]141.815585590142[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]102.011111111111[/C][C]0.692084243172221[/C][C]147.396956537452[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.941176470588[/C][C]0.667358611235634[/C][C]152.753219564877[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.871875[/C][C]0.637570906477303[/C][C]159.781247803261[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.776666666667[/C][C]0.601142271555862[/C][C]169.305456432553[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.7[/C][C]0.564749323985252[/C][C]180.079896833406[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.680769230769[/C][C]0.543465213118395[/C][C]187.097107186174[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.695833333333[/C][C]0.523729628176555[/C][C]194.176208222939[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.7[/C][C]0.499523582550223[/C][C]203.593991460403[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.73[/C][C]0.467586186820423[/C][C]217.564168633300[/C][/ROW]
[ROW][C]Median[/C][C]102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.616129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.776666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.616129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.776666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.776666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.616129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.776666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.871875[/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=68112&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68112&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 Mean101.9783333333331.0875439900620893.769387045679
Geometric Mean101.629291991473
Harmonic Mean101.273055539749
Quadratic Mean102.319904384891
Winsorized Mean ( 1 / 20 )102.0366666666671.0615572365531496.1197975513577
Winsorized Mean ( 2 / 20 )102.0333333333331.0514065549916897.0446045337246
Winsorized Mean ( 3 / 20 )102.0933333333331.0318511330752298.9419210395832
Winsorized Mean ( 4 / 20 )102.061.0251090613054999.5601383817887
Winsorized Mean ( 5 / 20 )102.2516666666670.974051738398537104.975601023803
Winsorized Mean ( 6 / 20 )102.3916666666670.917159985386807111.639919205027
Winsorized Mean ( 7 / 20 )102.3683333333330.90798557589114112.742246189169
Winsorized Mean ( 8 / 20 )102.6750.84351171044018121.723265639572
Winsorized Mean ( 9 / 20 )102.7350.828543835295182123.994646539611
Winsorized Mean ( 10 / 20 )102.6850.783393404356139131.077182203743
Winsorized Mean ( 11 / 20 )102.6666666666670.76721179342465133.81789428495
Winsorized Mean ( 12 / 20 )102.4866666666670.719720075319097142.397954678738
Winsorized Mean ( 13 / 20 )102.4216666666670.700645754067655146.181813094634
Winsorized Mean ( 14 / 20 )102.5383333333330.675792448274623151.730510743536
Winsorized Mean ( 15 / 20 )102.3133333333330.627466732936192163.057781333784
Winsorized Mean ( 16 / 20 )101.8333333333330.538394068743336189.142747376512
Winsorized Mean ( 17 / 20 )101.5783333333330.498857970722047203.621750668449
Winsorized Mean ( 18 / 20 )101.6683333333330.47588449713553213.640776165857
Winsorized Mean ( 19 / 20 )101.510.452405372944361224.378413853374
Winsorized Mean ( 20 / 20 )101.510.383315155550334264.821253556385
Trimmed Mean ( 1 / 20 )102.0913793103451.0334727121896698.7847846451989
Trimmed Mean ( 2 / 20 )102.150.998771973247875102.275597169414
Trimmed Mean ( 3 / 20 )102.2148148148150.962498813044028106.197341159879
Trimmed Mean ( 4 / 20 )102.2615384615380.926886620513118110.327990714687
Trimmed Mean ( 5 / 20 )102.3220.884604327553585115.669793616064
Trimmed Mean ( 6 / 20 )102.3395833333330.849701342939195120.441828395059
Trimmed Mean ( 7 / 20 )102.3282608695650.823552238947325124.252301226650
Trimmed Mean ( 8 / 20 )102.3204545454550.792262926608304129.149618275704
Trimmed Mean ( 9 / 20 )102.2571428571430.76965641501865132.860768599798
Trimmed Mean ( 10 / 20 )102.17750.743178270879667137.487200586552
Trimmed Mean ( 11 / 20 )102.0973684210530.719930521008614141.815585590142
Trimmed Mean ( 12 / 20 )102.0111111111110.692084243172221147.396956537452
Trimmed Mean ( 13 / 20 )101.9411764705880.667358611235634152.753219564877
Trimmed Mean ( 14 / 20 )101.8718750.637570906477303159.781247803261
Trimmed Mean ( 15 / 20 )101.7766666666670.601142271555862169.305456432553
Trimmed Mean ( 16 / 20 )101.70.564749323985252180.079896833406
Trimmed Mean ( 17 / 20 )101.6807692307690.543465213118395187.097107186174
Trimmed Mean ( 18 / 20 )101.6958333333330.523729628176555194.176208222939
Trimmed Mean ( 19 / 20 )101.70.499523582550223203.593991460403
Trimmed Mean ( 20 / 20 )101.730.467586186820423217.564168633300
Median102
Midrange98.7
Midmean - Weighted Average at Xnp101.616129032258
Midmean - Weighted Average at X(n+1)p101.776666666667
Midmean - Empirical Distribution Function101.616129032258
Midmean - Empirical Distribution Function - Averaging101.776666666667
Midmean - Empirical Distribution Function - Interpolation101.776666666667
Midmean - Closest Observation101.616129032258
Midmean - True Basic - Statistics Graphics Toolkit101.776666666667
Midmean - MS Excel (old versions)101.871875
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')