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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 computationMon, 20 Oct 2008 14:11:42 -0600
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/Oct/20/t1224533542kqd07i8bhdjg7m9.htm/, Retrieved Tue, 28 May 2024 20:12:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18062, Retrieved Tue, 28 May 2024 20:12:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-10-20 20:11:42] [63db34dadd44fb018112addcdefe949f] [Current]
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Dataseries X:
95
96
97
96
96
96
95
97
97
97
98
98
97
98
98
99
99
98
97
99
100
100
100
100
99
101
101
101
101
101
100
102
102
102
103
103
102
103
103
103
103
103
101
104
104
104
104
104
103
105
104
105
106
106
105
107
108
108
109
110




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18062&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18062&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18062&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.2166666666670.474842624340709213.158342318573
Geometric Mean101.151309491989
Harmonic Mean101.086317129073
Quadratic Mean101.282361083590
Winsorized Mean ( 1 / 20 )101.20.469883986162518215.372310996353
Winsorized Mean ( 2 / 20 )101.20.453984245228019222.915224622324
Winsorized Mean ( 3 / 20 )101.20.453984245228019222.915224622324
Winsorized Mean ( 4 / 20 )101.1333333333330.437937298266323230.931080165342
Winsorized Mean ( 5 / 20 )101.050.42013247843392240.519372310069
Winsorized Mean ( 6 / 20 )101.150.401145957347254252.152609660825
Winsorized Mean ( 7 / 20 )101.0333333333330.378792809418346266.724528082977
Winsorized Mean ( 8 / 20 )101.0333333333330.378792809418346266.724528082977
Winsorized Mean ( 9 / 20 )101.0333333333330.378792809418346266.724528082977
Winsorized Mean ( 10 / 20 )100.8666666666670.351322494713763287.10563139103
Winsorized Mean ( 11 / 20 )100.8666666666670.351322494713763287.10563139103
Winsorized Mean ( 12 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 13 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 14 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 15 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 16 / 20 )100.80.276989465218098363.912757189633
Winsorized Mean ( 17 / 20 )101.0833333333330.230807556332681437.955043324639
Winsorized Mean ( 18 / 20 )101.0833333333330.230807556332681437.955043324639
Winsorized Mean ( 19 / 20 )101.0833333333330.230807556332681437.955043324639
Winsorized Mean ( 20 / 20 )101.0833333333330.230807556332681437.955043324639
Trimmed Mean ( 1 / 20 )101.1724137931030.454285190049883222.706828241515
Trimmed Mean ( 2 / 20 )101.1428571428570.435016473362188232.503510409932
Trimmed Mean ( 3 / 20 )101.1111111111110.421857947240137239.680470102783
Trimmed Mean ( 4 / 20 )101.0769230769230.405324808625497249.372653550832
Trimmed Mean ( 5 / 20 )101.060.391136491652263258.375278596727
Trimmed Mean ( 6 / 20 )101.06250.379443239478338266.344184017988
Trimmed Mean ( 7 / 20 )101.0434782608700.370345864903787272.835443395919
Trimmed Mean ( 8 / 20 )101.0454545454550.364889489851324276.920704366207
Trimmed Mean ( 9 / 20 )101.0476190476190.357355724406132282.764797501268
Trimmed Mean ( 10 / 20 )101.050.347057225754944291.162357389877
Trimmed Mean ( 11 / 20 )101.0789473684210.340240018509586297.081301050932
Trimmed Mean ( 12 / 20 )101.1111111111110.330410465690393306.016672019875
Trimmed Mean ( 13 / 20 )101.1176470588240.326393095137158309.803266568282
Trimmed Mean ( 14 / 20 )101.1250.319872706536673316.141383536285
Trimmed Mean ( 15 / 20 )101.1333333333330.30973972512096326.510696339769
Trimmed Mean ( 16 / 20 )101.1428571428570.294186555442074343.805164688338
Trimmed Mean ( 17 / 20 )101.1923076923080.282947294734608357.636597258234
Trimmed Mean ( 18 / 20 )101.2083333333330.282196140717319358.645348855836
Trimmed Mean ( 19 / 20 )101.2272727272730.278616077310713363.321721073489
Trimmed Mean ( 20 / 20 )101.250.270233816887291374.675535305892
Median101
Midrange102.5
Midmean - Weighted Average at Xnp101.263157894737
Midmean - Weighted Average at X(n+1)p101.263157894737
Midmean - Empirical Distribution Function101.263157894737
Midmean - Empirical Distribution Function - Averaging101.263157894737
Midmean - Empirical Distribution Function - Interpolation101.263157894737
Midmean - Closest Observation101.263157894737
Midmean - True Basic - Statistics Graphics Toolkit101.263157894737
Midmean - MS Excel (old versions)101.263157894737
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.216666666667 & 0.474842624340709 & 213.158342318573 \tabularnewline
Geometric Mean & 101.151309491989 &  &  \tabularnewline
Harmonic Mean & 101.086317129073 &  &  \tabularnewline
Quadratic Mean & 101.282361083590 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.2 & 0.469883986162518 & 215.372310996353 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.2 & 0.453984245228019 & 222.915224622324 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.2 & 0.453984245228019 & 222.915224622324 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.133333333333 & 0.437937298266323 & 230.931080165342 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.05 & 0.42013247843392 & 240.519372310069 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.15 & 0.401145957347254 & 252.152609660825 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.033333333333 & 0.378792809418346 & 266.724528082977 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.033333333333 & 0.378792809418346 & 266.724528082977 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.033333333333 & 0.378792809418346 & 266.724528082977 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 100.866666666667 & 0.351322494713763 & 287.10563139103 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 100.866666666667 & 0.351322494713763 & 287.10563139103 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.066666666667 & 0.316108637074574 & 319.721307212570 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.066666666667 & 0.316108637074574 & 319.721307212570 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.066666666667 & 0.316108637074574 & 319.721307212570 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.066666666667 & 0.316108637074574 & 319.721307212570 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 100.8 & 0.276989465218098 & 363.912757189633 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.083333333333 & 0.230807556332681 & 437.955043324639 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.083333333333 & 0.230807556332681 & 437.955043324639 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.083333333333 & 0.230807556332681 & 437.955043324639 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.083333333333 & 0.230807556332681 & 437.955043324639 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.172413793103 & 0.454285190049883 & 222.706828241515 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.142857142857 & 0.435016473362188 & 232.503510409932 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.111111111111 & 0.421857947240137 & 239.680470102783 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.076923076923 & 0.405324808625497 & 249.372653550832 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.06 & 0.391136491652263 & 258.375278596727 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.0625 & 0.379443239478338 & 266.344184017988 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.043478260870 & 0.370345864903787 & 272.835443395919 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.045454545455 & 0.364889489851324 & 276.920704366207 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.047619047619 & 0.357355724406132 & 282.764797501268 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.05 & 0.347057225754944 & 291.162357389877 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.078947368421 & 0.340240018509586 & 297.081301050932 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.111111111111 & 0.330410465690393 & 306.016672019875 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.117647058824 & 0.326393095137158 & 309.803266568282 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.125 & 0.319872706536673 & 316.141383536285 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.133333333333 & 0.30973972512096 & 326.510696339769 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.142857142857 & 0.294186555442074 & 343.805164688338 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.192307692308 & 0.282947294734608 & 357.636597258234 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.208333333333 & 0.282196140717319 & 358.645348855836 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.227272727273 & 0.278616077310713 & 363.321721073489 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.25 & 0.270233816887291 & 374.675535305892 \tabularnewline
Median & 101 &  &  \tabularnewline
Midrange & 102.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.263157894737 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.263157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.263157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.263157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.263157894737 &  &  \tabularnewline
Midmean - Closest Observation & 101.263157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.263157894737 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.263157894737 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18062&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]101.216666666667[/C][C]0.474842624340709[/C][C]213.158342318573[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.151309491989[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.086317129073[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.282361083590[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.2[/C][C]0.469883986162518[/C][C]215.372310996353[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.2[/C][C]0.453984245228019[/C][C]222.915224622324[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.2[/C][C]0.453984245228019[/C][C]222.915224622324[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.133333333333[/C][C]0.437937298266323[/C][C]230.931080165342[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.05[/C][C]0.42013247843392[/C][C]240.519372310069[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.15[/C][C]0.401145957347254[/C][C]252.152609660825[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.033333333333[/C][C]0.378792809418346[/C][C]266.724528082977[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.033333333333[/C][C]0.378792809418346[/C][C]266.724528082977[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.033333333333[/C][C]0.378792809418346[/C][C]266.724528082977[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]100.866666666667[/C][C]0.351322494713763[/C][C]287.10563139103[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]100.866666666667[/C][C]0.351322494713763[/C][C]287.10563139103[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.066666666667[/C][C]0.316108637074574[/C][C]319.721307212570[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.066666666667[/C][C]0.316108637074574[/C][C]319.721307212570[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.066666666667[/C][C]0.316108637074574[/C][C]319.721307212570[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.066666666667[/C][C]0.316108637074574[/C][C]319.721307212570[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]100.8[/C][C]0.276989465218098[/C][C]363.912757189633[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.083333333333[/C][C]0.230807556332681[/C][C]437.955043324639[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.083333333333[/C][C]0.230807556332681[/C][C]437.955043324639[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.083333333333[/C][C]0.230807556332681[/C][C]437.955043324639[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.083333333333[/C][C]0.230807556332681[/C][C]437.955043324639[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.172413793103[/C][C]0.454285190049883[/C][C]222.706828241515[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.142857142857[/C][C]0.435016473362188[/C][C]232.503510409932[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.111111111111[/C][C]0.421857947240137[/C][C]239.680470102783[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.076923076923[/C][C]0.405324808625497[/C][C]249.372653550832[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.06[/C][C]0.391136491652263[/C][C]258.375278596727[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.0625[/C][C]0.379443239478338[/C][C]266.344184017988[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.043478260870[/C][C]0.370345864903787[/C][C]272.835443395919[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.045454545455[/C][C]0.364889489851324[/C][C]276.920704366207[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.047619047619[/C][C]0.357355724406132[/C][C]282.764797501268[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.05[/C][C]0.347057225754944[/C][C]291.162357389877[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.078947368421[/C][C]0.340240018509586[/C][C]297.081301050932[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.111111111111[/C][C]0.330410465690393[/C][C]306.016672019875[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.117647058824[/C][C]0.326393095137158[/C][C]309.803266568282[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.125[/C][C]0.319872706536673[/C][C]316.141383536285[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.133333333333[/C][C]0.30973972512096[/C][C]326.510696339769[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.142857142857[/C][C]0.294186555442074[/C][C]343.805164688338[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.192307692308[/C][C]0.282947294734608[/C][C]357.636597258234[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.208333333333[/C][C]0.282196140717319[/C][C]358.645348855836[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.227272727273[/C][C]0.278616077310713[/C][C]363.321721073489[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.25[/C][C]0.270233816887291[/C][C]374.675535305892[/C][/ROW]
[ROW][C]Median[/C][C]101[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.263157894737[/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=18062&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18062&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 Mean101.2166666666670.474842624340709213.158342318573
Geometric Mean101.151309491989
Harmonic Mean101.086317129073
Quadratic Mean101.282361083590
Winsorized Mean ( 1 / 20 )101.20.469883986162518215.372310996353
Winsorized Mean ( 2 / 20 )101.20.453984245228019222.915224622324
Winsorized Mean ( 3 / 20 )101.20.453984245228019222.915224622324
Winsorized Mean ( 4 / 20 )101.1333333333330.437937298266323230.931080165342
Winsorized Mean ( 5 / 20 )101.050.42013247843392240.519372310069
Winsorized Mean ( 6 / 20 )101.150.401145957347254252.152609660825
Winsorized Mean ( 7 / 20 )101.0333333333330.378792809418346266.724528082977
Winsorized Mean ( 8 / 20 )101.0333333333330.378792809418346266.724528082977
Winsorized Mean ( 9 / 20 )101.0333333333330.378792809418346266.724528082977
Winsorized Mean ( 10 / 20 )100.8666666666670.351322494713763287.10563139103
Winsorized Mean ( 11 / 20 )100.8666666666670.351322494713763287.10563139103
Winsorized Mean ( 12 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 13 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 14 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 15 / 20 )101.0666666666670.316108637074574319.721307212570
Winsorized Mean ( 16 / 20 )100.80.276989465218098363.912757189633
Winsorized Mean ( 17 / 20 )101.0833333333330.230807556332681437.955043324639
Winsorized Mean ( 18 / 20 )101.0833333333330.230807556332681437.955043324639
Winsorized Mean ( 19 / 20 )101.0833333333330.230807556332681437.955043324639
Winsorized Mean ( 20 / 20 )101.0833333333330.230807556332681437.955043324639
Trimmed Mean ( 1 / 20 )101.1724137931030.454285190049883222.706828241515
Trimmed Mean ( 2 / 20 )101.1428571428570.435016473362188232.503510409932
Trimmed Mean ( 3 / 20 )101.1111111111110.421857947240137239.680470102783
Trimmed Mean ( 4 / 20 )101.0769230769230.405324808625497249.372653550832
Trimmed Mean ( 5 / 20 )101.060.391136491652263258.375278596727
Trimmed Mean ( 6 / 20 )101.06250.379443239478338266.344184017988
Trimmed Mean ( 7 / 20 )101.0434782608700.370345864903787272.835443395919
Trimmed Mean ( 8 / 20 )101.0454545454550.364889489851324276.920704366207
Trimmed Mean ( 9 / 20 )101.0476190476190.357355724406132282.764797501268
Trimmed Mean ( 10 / 20 )101.050.347057225754944291.162357389877
Trimmed Mean ( 11 / 20 )101.0789473684210.340240018509586297.081301050932
Trimmed Mean ( 12 / 20 )101.1111111111110.330410465690393306.016672019875
Trimmed Mean ( 13 / 20 )101.1176470588240.326393095137158309.803266568282
Trimmed Mean ( 14 / 20 )101.1250.319872706536673316.141383536285
Trimmed Mean ( 15 / 20 )101.1333333333330.30973972512096326.510696339769
Trimmed Mean ( 16 / 20 )101.1428571428570.294186555442074343.805164688338
Trimmed Mean ( 17 / 20 )101.1923076923080.282947294734608357.636597258234
Trimmed Mean ( 18 / 20 )101.2083333333330.282196140717319358.645348855836
Trimmed Mean ( 19 / 20 )101.2272727272730.278616077310713363.321721073489
Trimmed Mean ( 20 / 20 )101.250.270233816887291374.675535305892
Median101
Midrange102.5
Midmean - Weighted Average at Xnp101.263157894737
Midmean - Weighted Average at X(n+1)p101.263157894737
Midmean - Empirical Distribution Function101.263157894737
Midmean - Empirical Distribution Function - Averaging101.263157894737
Midmean - Empirical Distribution Function - Interpolation101.263157894737
Midmean - Closest Observation101.263157894737
Midmean - True Basic - Statistics Graphics Toolkit101.263157894737
Midmean - MS Excel (old versions)101.263157894737
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')