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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 07:26:00 -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/t12272776643tx4hhefzb2iiid.htm/, Retrieved Mon, 20 May 2024 07:29:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25139, Retrieved Mon, 20 May 2024 07:29:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172
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] [fad8a251ac01c156a8ae23a83577546f]
-    D        [Central Tendency] [] [2008-11-21 14:26:00] [fa8b44cd657c07c6ee11bb2476ca3f8d] [Current]
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Dataseries X:
95,9
95,3
100,4
97,3
82,3
97,0
93,5
90,9
107,8
110,9
98,1
106,5
93,4
95,7
109,0
97,6
92,7
107,5
91,7
95,7
111,4
106,0
104,8
108,7
97,3
97,1
106,1
98,6
98,5
105,5
86,2
98,3
111,3
105,0
105,7
103,5
96,9
98,1
111,7
94,7
104,2
109,7
91,3
102,6
114,2
115,8
113,5
107,1
104,5
101,9
116,0
102,0
108,1
112,9
104,5
109,1
113,4
123,9
117,7
108,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25139&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25139&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.0883333333331.0687790480188196.4542985048478
Geometric Mean102.758562378598
Harmonic Mean102.425578141720
Quadratic Mean103.414696731171
Winsorized Mean ( 1 / 20 )103.051.01917353245928101.111338469847
Winsorized Mean ( 2 / 20 )103.150.966970047853773106.673417888119
Winsorized Mean ( 3 / 20 )103.160.960488340953363107.403698307889
Winsorized Mean ( 4 / 20 )103.080.93224351223363110.571968211421
Winsorized Mean ( 5 / 20 )103.1050.903900602630084114.066745502763
Winsorized Mean ( 6 / 20 )103.1650.888599561552312116.098414250598
Winsorized Mean ( 7 / 20 )103.1183333333330.875206163498199117.821763184539
Winsorized Mean ( 8 / 20 )103.1183333333330.816868388553784126.236165798873
Winsorized Mean ( 9 / 20 )103.1633333333330.793479666511757130.013833608180
Winsorized Mean ( 10 / 20 )103.2133333333330.779502473030967132.409244234987
Winsorized Mean ( 11 / 20 )103.140.766764425111011134.513282857466
Winsorized Mean ( 12 / 20 )102.940.720448698856217142.883178446192
Winsorized Mean ( 13 / 20 )103.0266666666670.665144590145914154.893639958893
Winsorized Mean ( 14 / 20 )103.0266666666670.657910863515302156.596694750079
Winsorized Mean ( 15 / 20 )102.9766666666670.642599622590085160.250120053923
Winsorized Mean ( 16 / 20 )102.9233333333330.618442396765261166.423475931905
Winsorized Mean ( 17 / 20 )102.8666666666670.610148016989759168.592970561754
Winsorized Mean ( 18 / 20 )102.8666666666670.58330669834269176.350909322548
Winsorized Mean ( 19 / 20 )102.930.545755579488083188.600911962362
Winsorized Mean ( 20 / 20 )102.7966666666670.527063963713679195.036416343785
Trimmed Mean ( 1 / 20 )103.0879310344830.98051518486189105.136496227749
Trimmed Mean ( 2 / 20 )103.1285714285710.932740391651891110.565139401683
Trimmed Mean ( 3 / 20 )103.1166666666670.908919040675102113.449781610996
Trimmed Mean ( 4 / 20 )103.10.882176452937646116.870043013138
Trimmed Mean ( 5 / 20 )103.1060.859688647958417119.934118293705
Trimmed Mean ( 6 / 20 )103.106250.840673732735446122.647164988140
Trimmed Mean ( 7 / 20 )103.0934782608700.820689012834094125.618202082243
Trimmed Mean ( 8 / 20 )103.0886363636360.798387751129225129.121014466755
Trimmed Mean ( 9 / 20 )103.0833333333330.7851253379944131.295384755585
Trimmed Mean ( 10 / 20 )103.070.77282531943446133.367783647959
Trimmed Mean ( 11 / 20 )103.0473684210530.758852326927974135.793704208847
Trimmed Mean ( 12 / 20 )103.0333333333330.742154735074601138.829988496909
Trimmed Mean ( 13 / 20 )103.0470588235290.730458251086013141.071797971100
Trimmed Mean ( 14 / 20 )103.050.726957868060787141.755120244992
Trimmed Mean ( 15 / 20 )103.0533333333330.720978475188978142.935381401396
Trimmed Mean ( 16 / 20 )103.0642857142860.713535320121733144.441743537941
Trimmed Mean ( 17 / 20 )103.0846153846150.706294606383142145.951299150507
Trimmed Mean ( 18 / 20 )103.1166666666670.693673968719619148.652928200548
Trimmed Mean ( 19 / 20 )103.1545454545450.679340375025443151.845156341079
Trimmed Mean ( 20 / 20 )103.190.666408283261846154.845014072934
Median104.35
Midrange103.1
Midmean - Weighted Average at Xnp102.858064516129
Midmean - Weighted Average at X(n+1)p103.053333333333
Midmean - Empirical Distribution Function102.858064516129
Midmean - Empirical Distribution Function - Averaging103.053333333333
Midmean - Empirical Distribution Function - Interpolation103.053333333333
Midmean - Closest Observation102.858064516129
Midmean - True Basic - Statistics Graphics Toolkit103.053333333333
Midmean - MS Excel (old versions)103.05
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.088333333333 & 1.06877904801881 & 96.4542985048478 \tabularnewline
Geometric Mean & 102.758562378598 &  &  \tabularnewline
Harmonic Mean & 102.425578141720 &  &  \tabularnewline
Quadratic Mean & 103.414696731171 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.05 & 1.01917353245928 & 101.111338469847 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.15 & 0.966970047853773 & 106.673417888119 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.16 & 0.960488340953363 & 107.403698307889 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.08 & 0.93224351223363 & 110.571968211421 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.105 & 0.903900602630084 & 114.066745502763 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.165 & 0.888599561552312 & 116.098414250598 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.118333333333 & 0.875206163498199 & 117.821763184539 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.118333333333 & 0.816868388553784 & 126.236165798873 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.163333333333 & 0.793479666511757 & 130.013833608180 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 103.213333333333 & 0.779502473030967 & 132.409244234987 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.14 & 0.766764425111011 & 134.513282857466 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 102.94 & 0.720448698856217 & 142.883178446192 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.026666666667 & 0.665144590145914 & 154.893639958893 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.026666666667 & 0.657910863515302 & 156.596694750079 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 102.976666666667 & 0.642599622590085 & 160.250120053923 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 102.923333333333 & 0.618442396765261 & 166.423475931905 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 102.866666666667 & 0.610148016989759 & 168.592970561754 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 102.866666666667 & 0.58330669834269 & 176.350909322548 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 102.93 & 0.545755579488083 & 188.600911962362 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 102.796666666667 & 0.527063963713679 & 195.036416343785 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.087931034483 & 0.98051518486189 & 105.136496227749 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.128571428571 & 0.932740391651891 & 110.565139401683 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.116666666667 & 0.908919040675102 & 113.449781610996 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.1 & 0.882176452937646 & 116.870043013138 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.106 & 0.859688647958417 & 119.934118293705 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.10625 & 0.840673732735446 & 122.647164988140 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.093478260870 & 0.820689012834094 & 125.618202082243 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.088636363636 & 0.798387751129225 & 129.121014466755 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.083333333333 & 0.7851253379944 & 131.295384755585 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.07 & 0.77282531943446 & 133.367783647959 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.047368421053 & 0.758852326927974 & 135.793704208847 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.033333333333 & 0.742154735074601 & 138.829988496909 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.047058823529 & 0.730458251086013 & 141.071797971100 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.05 & 0.726957868060787 & 141.755120244992 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.053333333333 & 0.720978475188978 & 142.935381401396 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.064285714286 & 0.713535320121733 & 144.441743537941 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 103.084615384615 & 0.706294606383142 & 145.951299150507 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 103.116666666667 & 0.693673968719619 & 148.652928200548 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 103.154545454545 & 0.679340375025443 & 151.845156341079 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.19 & 0.666408283261846 & 154.845014072934 \tabularnewline
Median & 104.35 &  &  \tabularnewline
Midrange & 103.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.858064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.053333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.858064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.053333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.053333333333 &  &  \tabularnewline
Midmean - Closest Observation & 102.858064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.053333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.05 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25139&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]103.088333333333[/C][C]1.06877904801881[/C][C]96.4542985048478[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.758562378598[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.425578141720[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.414696731171[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.05[/C][C]1.01917353245928[/C][C]101.111338469847[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.15[/C][C]0.966970047853773[/C][C]106.673417888119[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.16[/C][C]0.960488340953363[/C][C]107.403698307889[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.08[/C][C]0.93224351223363[/C][C]110.571968211421[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.105[/C][C]0.903900602630084[/C][C]114.066745502763[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.165[/C][C]0.888599561552312[/C][C]116.098414250598[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.118333333333[/C][C]0.875206163498199[/C][C]117.821763184539[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.118333333333[/C][C]0.816868388553784[/C][C]126.236165798873[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.163333333333[/C][C]0.793479666511757[/C][C]130.013833608180[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]103.213333333333[/C][C]0.779502473030967[/C][C]132.409244234987[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.14[/C][C]0.766764425111011[/C][C]134.513282857466[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]102.94[/C][C]0.720448698856217[/C][C]142.883178446192[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.026666666667[/C][C]0.665144590145914[/C][C]154.893639958893[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.026666666667[/C][C]0.657910863515302[/C][C]156.596694750079[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]102.976666666667[/C][C]0.642599622590085[/C][C]160.250120053923[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]102.923333333333[/C][C]0.618442396765261[/C][C]166.423475931905[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]102.866666666667[/C][C]0.610148016989759[/C][C]168.592970561754[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]102.866666666667[/C][C]0.58330669834269[/C][C]176.350909322548[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]102.93[/C][C]0.545755579488083[/C][C]188.600911962362[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]102.796666666667[/C][C]0.527063963713679[/C][C]195.036416343785[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.087931034483[/C][C]0.98051518486189[/C][C]105.136496227749[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.128571428571[/C][C]0.932740391651891[/C][C]110.565139401683[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.116666666667[/C][C]0.908919040675102[/C][C]113.449781610996[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.1[/C][C]0.882176452937646[/C][C]116.870043013138[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.106[/C][C]0.859688647958417[/C][C]119.934118293705[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.10625[/C][C]0.840673732735446[/C][C]122.647164988140[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.093478260870[/C][C]0.820689012834094[/C][C]125.618202082243[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.088636363636[/C][C]0.798387751129225[/C][C]129.121014466755[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.083333333333[/C][C]0.7851253379944[/C][C]131.295384755585[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.07[/C][C]0.77282531943446[/C][C]133.367783647959[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.047368421053[/C][C]0.758852326927974[/C][C]135.793704208847[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.033333333333[/C][C]0.742154735074601[/C][C]138.829988496909[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.047058823529[/C][C]0.730458251086013[/C][C]141.071797971100[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.05[/C][C]0.726957868060787[/C][C]141.755120244992[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.053333333333[/C][C]0.720978475188978[/C][C]142.935381401396[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.064285714286[/C][C]0.713535320121733[/C][C]144.441743537941[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]103.084615384615[/C][C]0.706294606383142[/C][C]145.951299150507[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]103.116666666667[/C][C]0.693673968719619[/C][C]148.652928200548[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]103.154545454545[/C][C]0.679340375025443[/C][C]151.845156341079[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.19[/C][C]0.666408283261846[/C][C]154.845014072934[/C][/ROW]
[ROW][C]Median[/C][C]104.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.858064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.053333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.05[/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=25139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25139&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 Mean103.0883333333331.0687790480188196.4542985048478
Geometric Mean102.758562378598
Harmonic Mean102.425578141720
Quadratic Mean103.414696731171
Winsorized Mean ( 1 / 20 )103.051.01917353245928101.111338469847
Winsorized Mean ( 2 / 20 )103.150.966970047853773106.673417888119
Winsorized Mean ( 3 / 20 )103.160.960488340953363107.403698307889
Winsorized Mean ( 4 / 20 )103.080.93224351223363110.571968211421
Winsorized Mean ( 5 / 20 )103.1050.903900602630084114.066745502763
Winsorized Mean ( 6 / 20 )103.1650.888599561552312116.098414250598
Winsorized Mean ( 7 / 20 )103.1183333333330.875206163498199117.821763184539
Winsorized Mean ( 8 / 20 )103.1183333333330.816868388553784126.236165798873
Winsorized Mean ( 9 / 20 )103.1633333333330.793479666511757130.013833608180
Winsorized Mean ( 10 / 20 )103.2133333333330.779502473030967132.409244234987
Winsorized Mean ( 11 / 20 )103.140.766764425111011134.513282857466
Winsorized Mean ( 12 / 20 )102.940.720448698856217142.883178446192
Winsorized Mean ( 13 / 20 )103.0266666666670.665144590145914154.893639958893
Winsorized Mean ( 14 / 20 )103.0266666666670.657910863515302156.596694750079
Winsorized Mean ( 15 / 20 )102.9766666666670.642599622590085160.250120053923
Winsorized Mean ( 16 / 20 )102.9233333333330.618442396765261166.423475931905
Winsorized Mean ( 17 / 20 )102.8666666666670.610148016989759168.592970561754
Winsorized Mean ( 18 / 20 )102.8666666666670.58330669834269176.350909322548
Winsorized Mean ( 19 / 20 )102.930.545755579488083188.600911962362
Winsorized Mean ( 20 / 20 )102.7966666666670.527063963713679195.036416343785
Trimmed Mean ( 1 / 20 )103.0879310344830.98051518486189105.136496227749
Trimmed Mean ( 2 / 20 )103.1285714285710.932740391651891110.565139401683
Trimmed Mean ( 3 / 20 )103.1166666666670.908919040675102113.449781610996
Trimmed Mean ( 4 / 20 )103.10.882176452937646116.870043013138
Trimmed Mean ( 5 / 20 )103.1060.859688647958417119.934118293705
Trimmed Mean ( 6 / 20 )103.106250.840673732735446122.647164988140
Trimmed Mean ( 7 / 20 )103.0934782608700.820689012834094125.618202082243
Trimmed Mean ( 8 / 20 )103.0886363636360.798387751129225129.121014466755
Trimmed Mean ( 9 / 20 )103.0833333333330.7851253379944131.295384755585
Trimmed Mean ( 10 / 20 )103.070.77282531943446133.367783647959
Trimmed Mean ( 11 / 20 )103.0473684210530.758852326927974135.793704208847
Trimmed Mean ( 12 / 20 )103.0333333333330.742154735074601138.829988496909
Trimmed Mean ( 13 / 20 )103.0470588235290.730458251086013141.071797971100
Trimmed Mean ( 14 / 20 )103.050.726957868060787141.755120244992
Trimmed Mean ( 15 / 20 )103.0533333333330.720978475188978142.935381401396
Trimmed Mean ( 16 / 20 )103.0642857142860.713535320121733144.441743537941
Trimmed Mean ( 17 / 20 )103.0846153846150.706294606383142145.951299150507
Trimmed Mean ( 18 / 20 )103.1166666666670.693673968719619148.652928200548
Trimmed Mean ( 19 / 20 )103.1545454545450.679340375025443151.845156341079
Trimmed Mean ( 20 / 20 )103.190.666408283261846154.845014072934
Median104.35
Midrange103.1
Midmean - Weighted Average at Xnp102.858064516129
Midmean - Weighted Average at X(n+1)p103.053333333333
Midmean - Empirical Distribution Function102.858064516129
Midmean - Empirical Distribution Function - Averaging103.053333333333
Midmean - Empirical Distribution Function - Interpolation103.053333333333
Midmean - Closest Observation102.858064516129
Midmean - True Basic - Statistics Graphics Toolkit103.053333333333
Midmean - MS Excel (old versions)103.05
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')