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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Mar 2016 18:29:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/04/t14571167906oks35kvfkpimpc.htm/, Retrieved Sat, 18 May 2024 16:52:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293414, Retrieved Sat, 18 May 2024 16:52:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsopgave 5
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Trimmed Mean Plot ] [2016-03-04 18:29:40] [8fd6d867e46a5221be3e0a22eb2f8c7a] [Current]
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Dataseries X:
93,41
93
96,61
99,69
101,05
98
97,32
97,83
99,57
97,63
96,68
96,28
99,81
101,43
105,59
108,86
104,01
101,95
101,52
105,61
108,43
105,54
100,11
99,93
99,88
102,71
101,89
101,93
99,49
99,87
100,33
101,5
102,29
97,04
95,71
97,37
96,51
96,33
96,88
97,59
98,96
99,93
101,34
98,04
98,56
96,73
92,36
87,88
79,84
82,91
87,78
89,36
91,86
92,48
93,4
89,97
83,96
82,76
82,97
81,07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293414&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293414&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.82233333333330.851472216792696113.711676580642
Geometric Mean96.5912691508124
Harmonic Mean96.3494443526089
Quadratic Mean97.0429777126266
Winsorized Mean ( 1 / 20 )96.83566666666670.843063366494281114.861670563791
Winsorized Mean ( 2 / 20 )96.7980.806093943859947120.082777866419
Winsorized Mean ( 3 / 20 )96.80450.803702956377787120.448107390682
Winsorized Mean ( 4 / 20 )96.80516666666670.801915591161813120.717401848261
Winsorized Mean ( 5 / 20 )96.76016666666670.755831434726871128.018182654221
Winsorized Mean ( 6 / 20 )97.01216666666670.632536463818698153.37007779914
Winsorized Mean ( 7 / 20 )96.97483333333330.622360028583864155.817901021042
Winsorized Mean ( 8 / 20 )97.12683333333330.568459335817737170.85977344996
Winsorized Mean ( 9 / 20 )97.21533333333330.547155792616324177.673954375007
Winsorized Mean ( 10 / 20 )97.52366666666670.478991051581647203.602272619999
Winsorized Mean ( 11 / 20 )97.54750.450539640336035216.512580174397
Winsorized Mean ( 12 / 20 )97.56750.445275616100618219.117096180611
Winsorized Mean ( 13 / 20 )97.6650.42150708219315231.704291875329
Winsorized Mean ( 14 / 20 )97.73733333333330.401004801996317243.731079644854
Winsorized Mean ( 15 / 20 )97.66733333333330.389688334591582250.62934828597
Winsorized Mean ( 16 / 20 )98.08866666666670.254107774042089386.012065299584
Winsorized Mean ( 17 / 20 )98.18783333333330.220087821668316446.130242868721
Winsorized Mean ( 18 / 20 )98.14883333333330.210004047804232467.366388217568
Winsorized Mean ( 19 / 20 )98.20583333333330.201757712790449486.7513215484
Winsorized Mean ( 20 / 20 )98.22250.194632440058598504.656366484581
Trimmed Mean ( 1 / 20 )96.90758620689660.803198171375657120.652149943171
Trimmed Mean ( 2 / 20 )96.98464285714290.753533492920931128.706479231866
Trimmed Mean ( 3 / 20 )97.08833333333330.717054244083926135.398868543577
Trimmed Mean ( 4 / 20 )97.19750.672006005941254144.637844216673
Trimmed Mean ( 5 / 20 )97.31520.614422060615851158.38493803829
Trimmed Mean ( 6 / 20 )97.45395833333330.557351158420657174.851988483319
Trimmed Mean ( 7 / 20 )97.550.528953391917715184.420785442614
Trimmed Mean ( 8 / 20 )97.66204545454540.49449395188505197.498968556137
Trimmed Mean ( 9 / 20 )97.7576190476190.466624621823045209.499487330292
Trimmed Mean ( 10 / 20 )97.8480.436009909320466224.41691784597
Trimmed Mean ( 11 / 20 )97.89921052631580.41681382767212234.875150551211
Trimmed Mean ( 12 / 20 )97.95250.39878234804353245.628976509531
Trimmed Mean ( 13 / 20 )98.00911764705880.374942031799336261.398054458488
Trimmed Mean ( 14 / 20 )98.058750.349048172916188280.93185298966
Trimmed Mean ( 15 / 20 )98.10466666666670.318628791093037307.896428097802
Trimmed Mean ( 16 / 20 )98.16714285714290.275791241282155355.947282447272
Trimmed Mean ( 17 / 20 )98.17846153846150.268279815065535365.955454063805
Trimmed Mean ( 18 / 20 )98.17708333333330.267327405491942367.254091112229
Trimmed Mean ( 19 / 20 )98.18136363636360.267112421372197367.565698113143
Trimmed Mean ( 20 / 20 )98.17750.267108173435014367.557078982033
Median97.915
Midrange94.35
Midmean - Weighted Average at Xnp97.9529032258064
Midmean - Weighted Average at X(n+1)p98.1046666666666
Midmean - Empirical Distribution Function97.9529032258064
Midmean - Empirical Distribution Function - Averaging98.1046666666666
Midmean - Empirical Distribution Function - Interpolation98.1046666666666
Midmean - Closest Observation97.9529032258064
Midmean - True Basic - Statistics Graphics Toolkit98.1046666666666
Midmean - MS Excel (old versions)98.05875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.8223333333333 & 0.851472216792696 & 113.711676580642 \tabularnewline
Geometric Mean & 96.5912691508124 &  &  \tabularnewline
Harmonic Mean & 96.3494443526089 &  &  \tabularnewline
Quadratic Mean & 97.0429777126266 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 96.8356666666667 & 0.843063366494281 & 114.861670563791 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 96.798 & 0.806093943859947 & 120.082777866419 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96.8045 & 0.803702956377787 & 120.448107390682 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96.8051666666667 & 0.801915591161813 & 120.717401848261 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96.7601666666667 & 0.755831434726871 & 128.018182654221 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 97.0121666666667 & 0.632536463818698 & 153.37007779914 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 96.9748333333333 & 0.622360028583864 & 155.817901021042 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.1268333333333 & 0.568459335817737 & 170.85977344996 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.2153333333333 & 0.547155792616324 & 177.673954375007 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.5236666666667 & 0.478991051581647 & 203.602272619999 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.5475 & 0.450539640336035 & 216.512580174397 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.5675 & 0.445275616100618 & 219.117096180611 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.665 & 0.42150708219315 & 231.704291875329 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.7373333333333 & 0.401004801996317 & 243.731079644854 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.6673333333333 & 0.389688334591582 & 250.62934828597 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 98.0886666666667 & 0.254107774042089 & 386.012065299584 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 98.1878333333333 & 0.220087821668316 & 446.130242868721 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 98.1488333333333 & 0.210004047804232 & 467.366388217568 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 98.2058333333333 & 0.201757712790449 & 486.7513215484 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 98.2225 & 0.194632440058598 & 504.656366484581 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96.9075862068966 & 0.803198171375657 & 120.652149943171 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96.9846428571429 & 0.753533492920931 & 128.706479231866 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 97.0883333333333 & 0.717054244083926 & 135.398868543577 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 97.1975 & 0.672006005941254 & 144.637844216673 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.3152 & 0.614422060615851 & 158.38493803829 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.4539583333333 & 0.557351158420657 & 174.851988483319 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.55 & 0.528953391917715 & 184.420785442614 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.6620454545454 & 0.49449395188505 & 197.498968556137 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.757619047619 & 0.466624621823045 & 209.499487330292 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.848 & 0.436009909320466 & 224.41691784597 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.8992105263158 & 0.41681382767212 & 234.875150551211 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.9525 & 0.39878234804353 & 245.628976509531 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 98.0091176470588 & 0.374942031799336 & 261.398054458488 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 98.05875 & 0.349048172916188 & 280.93185298966 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 98.1046666666667 & 0.318628791093037 & 307.896428097802 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 98.1671428571429 & 0.275791241282155 & 355.947282447272 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 98.1784615384615 & 0.268279815065535 & 365.955454063805 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 98.1770833333333 & 0.267327405491942 & 367.254091112229 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 98.1813636363636 & 0.267112421372197 & 367.565698113143 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 98.1775 & 0.267108173435014 & 367.557078982033 \tabularnewline
Median & 97.915 &  &  \tabularnewline
Midrange & 94.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.9529032258064 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.1046666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.9529032258064 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.1046666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.1046666666666 &  &  \tabularnewline
Midmean - Closest Observation & 97.9529032258064 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.1046666666666 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.05875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293414&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]96.8223333333333[/C][C]0.851472216792696[/C][C]113.711676580642[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.5912691508124[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.3494443526089[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.0429777126266[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]96.8356666666667[/C][C]0.843063366494281[/C][C]114.861670563791[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]96.798[/C][C]0.806093943859947[/C][C]120.082777866419[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96.8045[/C][C]0.803702956377787[/C][C]120.448107390682[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96.8051666666667[/C][C]0.801915591161813[/C][C]120.717401848261[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96.7601666666667[/C][C]0.755831434726871[/C][C]128.018182654221[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]97.0121666666667[/C][C]0.632536463818698[/C][C]153.37007779914[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]96.9748333333333[/C][C]0.622360028583864[/C][C]155.817901021042[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.1268333333333[/C][C]0.568459335817737[/C][C]170.85977344996[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.2153333333333[/C][C]0.547155792616324[/C][C]177.673954375007[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.5236666666667[/C][C]0.478991051581647[/C][C]203.602272619999[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.5475[/C][C]0.450539640336035[/C][C]216.512580174397[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.5675[/C][C]0.445275616100618[/C][C]219.117096180611[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.665[/C][C]0.42150708219315[/C][C]231.704291875329[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.7373333333333[/C][C]0.401004801996317[/C][C]243.731079644854[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.6673333333333[/C][C]0.389688334591582[/C][C]250.62934828597[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]98.0886666666667[/C][C]0.254107774042089[/C][C]386.012065299584[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]98.1878333333333[/C][C]0.220087821668316[/C][C]446.130242868721[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]98.1488333333333[/C][C]0.210004047804232[/C][C]467.366388217568[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]98.2058333333333[/C][C]0.201757712790449[/C][C]486.7513215484[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]98.2225[/C][C]0.194632440058598[/C][C]504.656366484581[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96.9075862068966[/C][C]0.803198171375657[/C][C]120.652149943171[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96.9846428571429[/C][C]0.753533492920931[/C][C]128.706479231866[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]97.0883333333333[/C][C]0.717054244083926[/C][C]135.398868543577[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]97.1975[/C][C]0.672006005941254[/C][C]144.637844216673[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.3152[/C][C]0.614422060615851[/C][C]158.38493803829[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.4539583333333[/C][C]0.557351158420657[/C][C]174.851988483319[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.55[/C][C]0.528953391917715[/C][C]184.420785442614[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.6620454545454[/C][C]0.49449395188505[/C][C]197.498968556137[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.757619047619[/C][C]0.466624621823045[/C][C]209.499487330292[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.848[/C][C]0.436009909320466[/C][C]224.41691784597[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.8992105263158[/C][C]0.41681382767212[/C][C]234.875150551211[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.9525[/C][C]0.39878234804353[/C][C]245.628976509531[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]98.0091176470588[/C][C]0.374942031799336[/C][C]261.398054458488[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]98.05875[/C][C]0.349048172916188[/C][C]280.93185298966[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]98.1046666666667[/C][C]0.318628791093037[/C][C]307.896428097802[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]98.1671428571429[/C][C]0.275791241282155[/C][C]355.947282447272[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]98.1784615384615[/C][C]0.268279815065535[/C][C]365.955454063805[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]98.1770833333333[/C][C]0.267327405491942[/C][C]367.254091112229[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]98.1813636363636[/C][C]0.267112421372197[/C][C]367.565698113143[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]98.1775[/C][C]0.267108173435014[/C][C]367.557078982033[/C][/ROW]
[ROW][C]Median[/C][C]97.915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]94.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.9529032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.1046666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.9529032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.1046666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.1046666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.9529032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.1046666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.05875[/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=293414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293414&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 Mean96.82233333333330.851472216792696113.711676580642
Geometric Mean96.5912691508124
Harmonic Mean96.3494443526089
Quadratic Mean97.0429777126266
Winsorized Mean ( 1 / 20 )96.83566666666670.843063366494281114.861670563791
Winsorized Mean ( 2 / 20 )96.7980.806093943859947120.082777866419
Winsorized Mean ( 3 / 20 )96.80450.803702956377787120.448107390682
Winsorized Mean ( 4 / 20 )96.80516666666670.801915591161813120.717401848261
Winsorized Mean ( 5 / 20 )96.76016666666670.755831434726871128.018182654221
Winsorized Mean ( 6 / 20 )97.01216666666670.632536463818698153.37007779914
Winsorized Mean ( 7 / 20 )96.97483333333330.622360028583864155.817901021042
Winsorized Mean ( 8 / 20 )97.12683333333330.568459335817737170.85977344996
Winsorized Mean ( 9 / 20 )97.21533333333330.547155792616324177.673954375007
Winsorized Mean ( 10 / 20 )97.52366666666670.478991051581647203.602272619999
Winsorized Mean ( 11 / 20 )97.54750.450539640336035216.512580174397
Winsorized Mean ( 12 / 20 )97.56750.445275616100618219.117096180611
Winsorized Mean ( 13 / 20 )97.6650.42150708219315231.704291875329
Winsorized Mean ( 14 / 20 )97.73733333333330.401004801996317243.731079644854
Winsorized Mean ( 15 / 20 )97.66733333333330.389688334591582250.62934828597
Winsorized Mean ( 16 / 20 )98.08866666666670.254107774042089386.012065299584
Winsorized Mean ( 17 / 20 )98.18783333333330.220087821668316446.130242868721
Winsorized Mean ( 18 / 20 )98.14883333333330.210004047804232467.366388217568
Winsorized Mean ( 19 / 20 )98.20583333333330.201757712790449486.7513215484
Winsorized Mean ( 20 / 20 )98.22250.194632440058598504.656366484581
Trimmed Mean ( 1 / 20 )96.90758620689660.803198171375657120.652149943171
Trimmed Mean ( 2 / 20 )96.98464285714290.753533492920931128.706479231866
Trimmed Mean ( 3 / 20 )97.08833333333330.717054244083926135.398868543577
Trimmed Mean ( 4 / 20 )97.19750.672006005941254144.637844216673
Trimmed Mean ( 5 / 20 )97.31520.614422060615851158.38493803829
Trimmed Mean ( 6 / 20 )97.45395833333330.557351158420657174.851988483319
Trimmed Mean ( 7 / 20 )97.550.528953391917715184.420785442614
Trimmed Mean ( 8 / 20 )97.66204545454540.49449395188505197.498968556137
Trimmed Mean ( 9 / 20 )97.7576190476190.466624621823045209.499487330292
Trimmed Mean ( 10 / 20 )97.8480.436009909320466224.41691784597
Trimmed Mean ( 11 / 20 )97.89921052631580.41681382767212234.875150551211
Trimmed Mean ( 12 / 20 )97.95250.39878234804353245.628976509531
Trimmed Mean ( 13 / 20 )98.00911764705880.374942031799336261.398054458488
Trimmed Mean ( 14 / 20 )98.058750.349048172916188280.93185298966
Trimmed Mean ( 15 / 20 )98.10466666666670.318628791093037307.896428097802
Trimmed Mean ( 16 / 20 )98.16714285714290.275791241282155355.947282447272
Trimmed Mean ( 17 / 20 )98.17846153846150.268279815065535365.955454063805
Trimmed Mean ( 18 / 20 )98.17708333333330.267327405491942367.254091112229
Trimmed Mean ( 19 / 20 )98.18136363636360.267112421372197367.565698113143
Trimmed Mean ( 20 / 20 )98.17750.267108173435014367.557078982033
Median97.915
Midrange94.35
Midmean - Weighted Average at Xnp97.9529032258064
Midmean - Weighted Average at X(n+1)p98.1046666666666
Midmean - Empirical Distribution Function97.9529032258064
Midmean - Empirical Distribution Function - Averaging98.1046666666666
Midmean - Empirical Distribution Function - Interpolation98.1046666666666
Midmean - Closest Observation97.9529032258064
Midmean - True Basic - Statistics Graphics Toolkit98.1046666666666
Midmean - MS Excel (old versions)98.05875
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')