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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 computationSun, 13 Dec 2009 09:14:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/13/t12607209506fqx3oq48971zmk.htm/, Retrieved Sun, 28 Apr 2024 12:03:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67355, Retrieved Sun, 28 Apr 2024 12:03:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Central Tendency] [WS 3: Part 1: Cen...] [2009-10-18 15:24:12] [8cf9233b7464ea02e32be3b30fdac052]
-  M D          [Central Tendency] [Paper: Central Te...] [2009-12-13 16:14:14] [b9056af0304697100f456398102f1287] [Current]
-    D            [Central Tendency] [Paper: Central Te...] [2009-12-13 16:40:32] [8cf9233b7464ea02e32be3b30fdac052]
-    D            [Central Tendency] [Faillissementen V...] [2010-12-09 12:14:12] [13c73ac943380855a1c72833078e44d2]
-    D            [Central Tendency] [Faillissementen V...] [2010-12-09 12:25:53] [13c73ac943380855a1c72833078e44d2]
-    D            [Central Tendency] [Faillissementen W...] [2010-12-09 12:29:38] [049b50ae610f671f7417ed8e2d1295c1]
-    D            [Central Tendency] [] [2010-12-09 12:43:52] [049b50ae610f671f7417ed8e2d1295c1]
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Dataseries X:
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67355&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67355&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.7666666666672.4785368686820448.7249829496722
Geometric Mean119.303343736826
Harmonic Mean117.877409767096
Quadratic Mean122.258060402304
Winsorized Mean ( 1 / 20 )120.82.4617755752811549.0702731853223
Winsorized Mean ( 2 / 20 )120.8666666666672.3830221834742450.7199083184587
Winsorized Mean ( 3 / 20 )120.8666666666672.3830221834742450.7199083184587
Winsorized Mean ( 4 / 20 )120.7333333333332.2909631688559852.6998141980708
Winsorized Mean ( 5 / 20 )120.4833333333332.2330961590903153.9534909156865
Winsorized Mean ( 6 / 20 )120.9833333333332.1040036715971257.5014839406133
Winsorized Mean ( 7 / 20 )121.12.0855570053582558.06602250088
Winsorized Mean ( 8 / 20 )121.52.0268675562047759.94471598702
Winsorized Mean ( 9 / 20 )121.21.9588708842705661.8723780996582
Winsorized Mean ( 10 / 20 )120.71.8496144047686565.2568447179115
Winsorized Mean ( 11 / 20 )119.7833333333331.6614763815589972.0945146514445
Winsorized Mean ( 12 / 20 )119.5833333333331.5543435889361976.9349416593131
Winsorized Mean ( 13 / 20 )119.3666666666671.4415086781921282.8067624375117
Winsorized Mean ( 14 / 20 )119.1333333333331.3990446027116785.1533490086204
Winsorized Mean ( 15 / 20 )118.8833333333331.2738330577959293.3272477156731
Winsorized Mean ( 16 / 20 )118.6166666666671.14390837279408103.694202689449
Winsorized Mean ( 17 / 20 )118.6166666666671.14390837279408103.694202689449
Winsorized Mean ( 18 / 20 )117.7166666666670.996630386883856118.114667399144
Winsorized Mean ( 19 / 20 )117.7166666666670.806082690052023146.035472687138
Winsorized Mean ( 20 / 20 )117.3833333333330.755803036349537155.30942280979
Trimmed Mean ( 1 / 20 )120.6896551724142.3779597594142950.7534472333294
Trimmed Mean ( 2 / 20 )120.5714285714292.2744854053165853.0104208580957
Trimmed Mean ( 3 / 20 )120.4074074074072.1994406439852154.7445586843567
Trimmed Mean ( 4 / 20 )120.2307692307692.1051927797666057.1115246006586
Trimmed Mean ( 5 / 20 )120.082.0245110268801259.3130876570477
Trimmed Mean ( 6 / 20 )119.9791666666671.9430019873415661.7493792843845
Trimmed Mean ( 7 / 20 )119.7608695652171.8795067660638863.7193074947127
Trimmed Mean ( 8 / 20 )119.51.8013091316422766.3406396497033
Trimmed Mean ( 9 / 20 )119.1428571428571.7130270253308569.5510668431202
Trimmed Mean ( 10 / 20 )118.81.6157081483092273.5281307606944
Trimmed Mean ( 11 / 20 )118.51.5188479200589678.0196611095863
Trimmed Mean ( 12 / 20 )118.3055555555561.4473947281644281.7368982030146
Trimmed Mean ( 13 / 20 )118.1176470588241.3802559282965585.5766272307186
Trimmed Mean ( 14 / 20 )117.93751.3197762976377789.3617351751909
Trimmed Mean ( 15 / 20 )117.7666666666671.2453899664692994.5620808239993
Trimmed Mean ( 16 / 20 )117.6071428571431.1788920519469299.7607394696715
Trimmed Mean ( 17 / 20 )117.4615384615381.12486685602652104.422614847467
Trimmed Mean ( 18 / 20 )117.2916666666671.03643614334268113.168252014428
Trimmed Mean ( 19 / 20 )117.2272727272730.96459357832709121.530223050605
Trimmed Mean ( 20 / 20 )117.150.9326673689224125.607482263859
Median116.5
Midrange123
Midmean - Weighted Average at Xnp117.09375
Midmean - Weighted Average at X(n+1)p117.766666666667
Midmean - Empirical Distribution Function117.09375
Midmean - Empirical Distribution Function - Averaging117.766666666667
Midmean - Empirical Distribution Function - Interpolation117.766666666667
Midmean - Closest Observation117.09375
Midmean - True Basic - Statistics Graphics Toolkit117.766666666667
Midmean - MS Excel (old versions)117.606060606061
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.766666666667 & 2.47853686868204 & 48.7249829496722 \tabularnewline
Geometric Mean & 119.303343736826 &  &  \tabularnewline
Harmonic Mean & 117.877409767096 &  &  \tabularnewline
Quadratic Mean & 122.258060402304 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 120.8 & 2.46177557528115 & 49.0702731853223 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 120.866666666667 & 2.38302218347424 & 50.7199083184587 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 120.866666666667 & 2.38302218347424 & 50.7199083184587 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 120.733333333333 & 2.29096316885598 & 52.6998141980708 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 120.483333333333 & 2.23309615909031 & 53.9534909156865 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 120.983333333333 & 2.10400367159712 & 57.5014839406133 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 121.1 & 2.08555700535825 & 58.06602250088 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 121.5 & 2.02686755620477 & 59.94471598702 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 121.2 & 1.95887088427056 & 61.8723780996582 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 120.7 & 1.84961440476865 & 65.2568447179115 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 119.783333333333 & 1.66147638155899 & 72.0945146514445 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 119.583333333333 & 1.55434358893619 & 76.9349416593131 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 119.366666666667 & 1.44150867819212 & 82.8067624375117 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 119.133333333333 & 1.39904460271167 & 85.1533490086204 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 118.883333333333 & 1.27383305779592 & 93.3272477156731 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 118.616666666667 & 1.14390837279408 & 103.694202689449 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 118.616666666667 & 1.14390837279408 & 103.694202689449 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 117.716666666667 & 0.996630386883856 & 118.114667399144 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 117.716666666667 & 0.806082690052023 & 146.035472687138 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 117.383333333333 & 0.755803036349537 & 155.30942280979 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 120.689655172414 & 2.37795975941429 & 50.7534472333294 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 120.571428571429 & 2.27448540531658 & 53.0104208580957 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 120.407407407407 & 2.19944064398521 & 54.7445586843567 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 120.230769230769 & 2.10519277976660 & 57.1115246006586 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 120.08 & 2.02451102688012 & 59.3130876570477 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 119.979166666667 & 1.94300198734156 & 61.7493792843845 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 119.760869565217 & 1.87950676606388 & 63.7193074947127 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 119.5 & 1.80130913164227 & 66.3406396497033 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 119.142857142857 & 1.71302702533085 & 69.5510668431202 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 118.8 & 1.61570814830922 & 73.5281307606944 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 118.5 & 1.51884792005896 & 78.0196611095863 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 118.305555555556 & 1.44739472816442 & 81.7368982030146 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 118.117647058824 & 1.38025592829655 & 85.5766272307186 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 117.9375 & 1.31977629763777 & 89.3617351751909 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 117.766666666667 & 1.24538996646929 & 94.5620808239993 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 117.607142857143 & 1.17889205194692 & 99.7607394696715 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 117.461538461538 & 1.12486685602652 & 104.422614847467 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 117.291666666667 & 1.03643614334268 & 113.168252014428 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 117.227272727273 & 0.96459357832709 & 121.530223050605 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 117.15 & 0.9326673689224 & 125.607482263859 \tabularnewline
Median & 116.5 &  &  \tabularnewline
Midrange & 123 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 117.09375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 117.766666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 117.09375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 117.766666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 117.766666666667 &  &  \tabularnewline
Midmean - Closest Observation & 117.09375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 117.766666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 117.606060606061 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67355&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]120.766666666667[/C][C]2.47853686868204[/C][C]48.7249829496722[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]119.303343736826[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]117.877409767096[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]122.258060402304[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]120.8[/C][C]2.46177557528115[/C][C]49.0702731853223[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]120.866666666667[/C][C]2.38302218347424[/C][C]50.7199083184587[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]120.866666666667[/C][C]2.38302218347424[/C][C]50.7199083184587[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]120.733333333333[/C][C]2.29096316885598[/C][C]52.6998141980708[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]120.483333333333[/C][C]2.23309615909031[/C][C]53.9534909156865[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]120.983333333333[/C][C]2.10400367159712[/C][C]57.5014839406133[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]121.1[/C][C]2.08555700535825[/C][C]58.06602250088[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]121.5[/C][C]2.02686755620477[/C][C]59.94471598702[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]121.2[/C][C]1.95887088427056[/C][C]61.8723780996582[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]120.7[/C][C]1.84961440476865[/C][C]65.2568447179115[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]119.783333333333[/C][C]1.66147638155899[/C][C]72.0945146514445[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]119.583333333333[/C][C]1.55434358893619[/C][C]76.9349416593131[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]119.366666666667[/C][C]1.44150867819212[/C][C]82.8067624375117[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]119.133333333333[/C][C]1.39904460271167[/C][C]85.1533490086204[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]118.883333333333[/C][C]1.27383305779592[/C][C]93.3272477156731[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]118.616666666667[/C][C]1.14390837279408[/C][C]103.694202689449[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]118.616666666667[/C][C]1.14390837279408[/C][C]103.694202689449[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]117.716666666667[/C][C]0.996630386883856[/C][C]118.114667399144[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]117.716666666667[/C][C]0.806082690052023[/C][C]146.035472687138[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]117.383333333333[/C][C]0.755803036349537[/C][C]155.30942280979[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]120.689655172414[/C][C]2.37795975941429[/C][C]50.7534472333294[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]120.571428571429[/C][C]2.27448540531658[/C][C]53.0104208580957[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]120.407407407407[/C][C]2.19944064398521[/C][C]54.7445586843567[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]120.230769230769[/C][C]2.10519277976660[/C][C]57.1115246006586[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]120.08[/C][C]2.02451102688012[/C][C]59.3130876570477[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]119.979166666667[/C][C]1.94300198734156[/C][C]61.7493792843845[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]119.760869565217[/C][C]1.87950676606388[/C][C]63.7193074947127[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]119.5[/C][C]1.80130913164227[/C][C]66.3406396497033[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]119.142857142857[/C][C]1.71302702533085[/C][C]69.5510668431202[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]118.8[/C][C]1.61570814830922[/C][C]73.5281307606944[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]118.5[/C][C]1.51884792005896[/C][C]78.0196611095863[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]118.305555555556[/C][C]1.44739472816442[/C][C]81.7368982030146[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]118.117647058824[/C][C]1.38025592829655[/C][C]85.5766272307186[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]117.9375[/C][C]1.31977629763777[/C][C]89.3617351751909[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]117.766666666667[/C][C]1.24538996646929[/C][C]94.5620808239993[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]117.607142857143[/C][C]1.17889205194692[/C][C]99.7607394696715[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]117.461538461538[/C][C]1.12486685602652[/C][C]104.422614847467[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]117.291666666667[/C][C]1.03643614334268[/C][C]113.168252014428[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]117.227272727273[/C][C]0.96459357832709[/C][C]121.530223050605[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]117.15[/C][C]0.9326673689224[/C][C]125.607482263859[/C][/ROW]
[ROW][C]Median[/C][C]116.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]123[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]117.09375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]117.766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]117.09375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]117.766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]117.766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]117.09375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]117.766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]117.606060606061[/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=67355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67355&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 Mean120.7666666666672.4785368686820448.7249829496722
Geometric Mean119.303343736826
Harmonic Mean117.877409767096
Quadratic Mean122.258060402304
Winsorized Mean ( 1 / 20 )120.82.4617755752811549.0702731853223
Winsorized Mean ( 2 / 20 )120.8666666666672.3830221834742450.7199083184587
Winsorized Mean ( 3 / 20 )120.8666666666672.3830221834742450.7199083184587
Winsorized Mean ( 4 / 20 )120.7333333333332.2909631688559852.6998141980708
Winsorized Mean ( 5 / 20 )120.4833333333332.2330961590903153.9534909156865
Winsorized Mean ( 6 / 20 )120.9833333333332.1040036715971257.5014839406133
Winsorized Mean ( 7 / 20 )121.12.0855570053582558.06602250088
Winsorized Mean ( 8 / 20 )121.52.0268675562047759.94471598702
Winsorized Mean ( 9 / 20 )121.21.9588708842705661.8723780996582
Winsorized Mean ( 10 / 20 )120.71.8496144047686565.2568447179115
Winsorized Mean ( 11 / 20 )119.7833333333331.6614763815589972.0945146514445
Winsorized Mean ( 12 / 20 )119.5833333333331.5543435889361976.9349416593131
Winsorized Mean ( 13 / 20 )119.3666666666671.4415086781921282.8067624375117
Winsorized Mean ( 14 / 20 )119.1333333333331.3990446027116785.1533490086204
Winsorized Mean ( 15 / 20 )118.8833333333331.2738330577959293.3272477156731
Winsorized Mean ( 16 / 20 )118.6166666666671.14390837279408103.694202689449
Winsorized Mean ( 17 / 20 )118.6166666666671.14390837279408103.694202689449
Winsorized Mean ( 18 / 20 )117.7166666666670.996630386883856118.114667399144
Winsorized Mean ( 19 / 20 )117.7166666666670.806082690052023146.035472687138
Winsorized Mean ( 20 / 20 )117.3833333333330.755803036349537155.30942280979
Trimmed Mean ( 1 / 20 )120.6896551724142.3779597594142950.7534472333294
Trimmed Mean ( 2 / 20 )120.5714285714292.2744854053165853.0104208580957
Trimmed Mean ( 3 / 20 )120.4074074074072.1994406439852154.7445586843567
Trimmed Mean ( 4 / 20 )120.2307692307692.1051927797666057.1115246006586
Trimmed Mean ( 5 / 20 )120.082.0245110268801259.3130876570477
Trimmed Mean ( 6 / 20 )119.9791666666671.9430019873415661.7493792843845
Trimmed Mean ( 7 / 20 )119.7608695652171.8795067660638863.7193074947127
Trimmed Mean ( 8 / 20 )119.51.8013091316422766.3406396497033
Trimmed Mean ( 9 / 20 )119.1428571428571.7130270253308569.5510668431202
Trimmed Mean ( 10 / 20 )118.81.6157081483092273.5281307606944
Trimmed Mean ( 11 / 20 )118.51.5188479200589678.0196611095863
Trimmed Mean ( 12 / 20 )118.3055555555561.4473947281644281.7368982030146
Trimmed Mean ( 13 / 20 )118.1176470588241.3802559282965585.5766272307186
Trimmed Mean ( 14 / 20 )117.93751.3197762976377789.3617351751909
Trimmed Mean ( 15 / 20 )117.7666666666671.2453899664692994.5620808239993
Trimmed Mean ( 16 / 20 )117.6071428571431.1788920519469299.7607394696715
Trimmed Mean ( 17 / 20 )117.4615384615381.12486685602652104.422614847467
Trimmed Mean ( 18 / 20 )117.2916666666671.03643614334268113.168252014428
Trimmed Mean ( 19 / 20 )117.2272727272730.96459357832709121.530223050605
Trimmed Mean ( 20 / 20 )117.150.9326673689224125.607482263859
Median116.5
Midrange123
Midmean - Weighted Average at Xnp117.09375
Midmean - Weighted Average at X(n+1)p117.766666666667
Midmean - Empirical Distribution Function117.09375
Midmean - Empirical Distribution Function - Averaging117.766666666667
Midmean - Empirical Distribution Function - Interpolation117.766666666667
Midmean - Closest Observation117.09375
Midmean - True Basic - Statistics Graphics Toolkit117.766666666667
Midmean - MS Excel (old versions)117.606060606061
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')