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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, 19 Oct 2008 07:21:07 -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/19/t12244225729g9lgmoqnmv3zs7.htm/, Retrieved Sun, 19 May 2024 16:31:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16820, Retrieved Sun, 19 May 2024 16:31:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
- R  D    [Central Tendency] [Central Tendency ...] [2008-10-19 13:21:07] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]
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Dataseries X:
99.29
98.69
107.92
101.03
97.55
103.02
94.08
94.12
115.08
116.48
103.42
112.51
95.55
97.53
119.26
100.94
97.73
115.25
92.8
99.2
118.69
110.12
110.26
112.9
102.17
99.38
116.1
103.77
101.81
113.74
89.67
99.5
122.89
108.61
114.37
110.5
104.08
103.64
121.61
101.14
115.97
120.12
95.97
105.01
124.68
123.89
123.61
114.76
108.75
106.09
123.17
106.16
115.18
120.6
109.48
114.44
121.44
129.48
124.32
112.59




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=16820&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=16820&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16820&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 Mean109.0351666666671.2687511652421185.9389686912014
Geometric Mean108.598867723453
Harmonic Mean108.162701222704
Quadratic Mean109.469820551907
Winsorized Mean ( 1 / 20 )109.0073333333331.2366503615658088.147253840861
Winsorized Mean ( 2 / 20 )109.0381.2249369821217389.0151914681634
Winsorized Mean ( 3 / 20 )109.01851.2200288462135789.3573134261087
Winsorized Mean ( 4 / 20 )109.0951666666671.1971688233576791.127637588064
Winsorized Mean ( 5 / 20 )109.09351.1830571291801492.2132138078589
Winsorized Mean ( 6 / 20 )109.22151.1492799962963895.0347176945327
Winsorized Mean ( 7 / 20 )109.07451.1196437444146297.4189339637025
Winsorized Mean ( 8 / 20 )109.0758333333331.1111853825224098.1616884535778
Winsorized Mean ( 9 / 20 )109.0938333333331.06333047548453102.596357245965
Winsorized Mean ( 10 / 20 )109.0988333333331.03483165725215105.426648449305
Winsorized Mean ( 11 / 20 )108.9576666666671.00420188863844108.501754377696
Winsorized Mean ( 12 / 20 )108.8616666666670.981673429038702110.893972930763
Winsorized Mean ( 13 / 20 )108.4088333333330.900171832048085120.431265980274
Winsorized Mean ( 14 / 20 )108.6561666666670.832054705790127130.587767739966
Winsorized Mean ( 15 / 20 )108.6461666666670.823609874587411131.914599398281
Winsorized Mean ( 16 / 20 )108.48350.790596207298233137.217329147997
Winsorized Mean ( 17 / 20 )108.65350.758239368053082143.297096639796
Winsorized Mean ( 18 / 20 )108.73150.737456685503867147.441201818801
Winsorized Mean ( 19 / 20 )108.8993333333330.682726912948936159.506431148230
Winsorized Mean ( 20 / 20 )108.9260.647936803781754168.112074147111
Trimmed Mean ( 1 / 20 )109.0165517241381.2181106519105389.4964275644027
Trimmed Mean ( 2 / 20 )109.0264285714291.1948341032640691.248172674005
Trimmed Mean ( 3 / 20 )109.021.1732823209322592.918812509999
Trimmed Mean ( 4 / 20 )109.0205769230771.1482621275362494.9439803932192
Trimmed Mean ( 5 / 20 )108.99821.1252836264693496.8628685569605
Trimmed Mean ( 6 / 20 )108.9743751.1003996254363599.0316358539176
Trimmed Mean ( 7 / 20 )108.9206521739131.07833130175531101.008523073207
Trimmed Mean ( 8 / 20 )108.8906818181821.05770151483031102.950293907493
Trimmed Mean ( 9 / 20 )108.8576190476191.03216273338603105.465558411036
Trimmed Mean ( 10 / 20 )108.818251.01059254562323107.677669374548
Trimmed Mean ( 11 / 20 )108.7739473684210.98816211858865110.0770261501
Trimmed Mean ( 12 / 20 )108.7461111111110.9648498754661112.707804474326
Trimmed Mean ( 13 / 20 )108.7291176470590.93760973144120115.964152249072
Trimmed Mean ( 14 / 20 )108.77531250.920774238596357118.134617521249
Trimmed Mean ( 15 / 20 )108.7923333333330.913494450509203119.094684453408
Trimmed Mean ( 16 / 20 )108.8132142857140.901355395259756120.721765086186
Trimmed Mean ( 17 / 20 )108.8607692307690.889110691919295122.437813671743
Trimmed Mean ( 18 / 20 )108.891250.87659612444874124.220546912043
Trimmed Mean ( 19 / 20 )108.9154545454550.858720917142454126.834519075056
Trimmed Mean ( 20 / 20 )108.9180.845676807745072128.793883198028
Median109.115
Midrange109.575
Midmean - Weighted Average at Xnp108.539032258065
Midmean - Weighted Average at X(n+1)p108.792333333333
Midmean - Empirical Distribution Function108.539032258065
Midmean - Empirical Distribution Function - Averaging108.792333333333
Midmean - Empirical Distribution Function - Interpolation108.792333333333
Midmean - Closest Observation108.539032258065
Midmean - True Basic - Statistics Graphics Toolkit108.792333333333
Midmean - MS Excel (old versions)108.7753125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.035166666667 & 1.26875116524211 & 85.9389686912014 \tabularnewline
Geometric Mean & 108.598867723453 &  &  \tabularnewline
Harmonic Mean & 108.162701222704 &  &  \tabularnewline
Quadratic Mean & 109.469820551907 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 109.007333333333 & 1.23665036156580 & 88.147253840861 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 109.038 & 1.22493698212173 & 89.0151914681634 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 109.0185 & 1.22002884621357 & 89.3573134261087 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 109.095166666667 & 1.19716882335767 & 91.127637588064 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 109.0935 & 1.18305712918014 & 92.2132138078589 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 109.2215 & 1.14927999629638 & 95.0347176945327 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 109.0745 & 1.11964374441462 & 97.4189339637025 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 109.075833333333 & 1.11118538252240 & 98.1616884535778 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 109.093833333333 & 1.06333047548453 & 102.596357245965 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 109.098833333333 & 1.03483165725215 & 105.426648449305 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 108.957666666667 & 1.00420188863844 & 108.501754377696 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 108.861666666667 & 0.981673429038702 & 110.893972930763 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 108.408833333333 & 0.900171832048085 & 120.431265980274 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 108.656166666667 & 0.832054705790127 & 130.587767739966 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 108.646166666667 & 0.823609874587411 & 131.914599398281 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 108.4835 & 0.790596207298233 & 137.217329147997 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 108.6535 & 0.758239368053082 & 143.297096639796 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 108.7315 & 0.737456685503867 & 147.441201818801 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 108.899333333333 & 0.682726912948936 & 159.506431148230 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 108.926 & 0.647936803781754 & 168.112074147111 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 109.016551724138 & 1.21811065191053 & 89.4964275644027 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 109.026428571429 & 1.19483410326406 & 91.248172674005 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 109.02 & 1.17328232093225 & 92.918812509999 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 109.020576923077 & 1.14826212753624 & 94.9439803932192 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 108.9982 & 1.12528362646934 & 96.8628685569605 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 108.974375 & 1.10039962543635 & 99.0316358539176 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 108.920652173913 & 1.07833130175531 & 101.008523073207 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 108.890681818182 & 1.05770151483031 & 102.950293907493 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 108.857619047619 & 1.03216273338603 & 105.465558411036 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 108.81825 & 1.01059254562323 & 107.677669374548 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 108.773947368421 & 0.98816211858865 & 110.0770261501 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 108.746111111111 & 0.9648498754661 & 112.707804474326 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 108.729117647059 & 0.93760973144120 & 115.964152249072 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 108.7753125 & 0.920774238596357 & 118.134617521249 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 108.792333333333 & 0.913494450509203 & 119.094684453408 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 108.813214285714 & 0.901355395259756 & 120.721765086186 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 108.860769230769 & 0.889110691919295 & 122.437813671743 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 108.89125 & 0.87659612444874 & 124.220546912043 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 108.915454545455 & 0.858720917142454 & 126.834519075056 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 108.918 & 0.845676807745072 & 128.793883198028 \tabularnewline
Median & 109.115 &  &  \tabularnewline
Midrange & 109.575 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.539032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.792333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.539032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.792333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.792333333333 &  &  \tabularnewline
Midmean - Closest Observation & 108.539032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.792333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.7753125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16820&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]109.035166666667[/C][C]1.26875116524211[/C][C]85.9389686912014[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.598867723453[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.162701222704[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.469820551907[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]109.007333333333[/C][C]1.23665036156580[/C][C]88.147253840861[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]109.038[/C][C]1.22493698212173[/C][C]89.0151914681634[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]109.0185[/C][C]1.22002884621357[/C][C]89.3573134261087[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]109.095166666667[/C][C]1.19716882335767[/C][C]91.127637588064[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]109.0935[/C][C]1.18305712918014[/C][C]92.2132138078589[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]109.2215[/C][C]1.14927999629638[/C][C]95.0347176945327[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]109.0745[/C][C]1.11964374441462[/C][C]97.4189339637025[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]109.075833333333[/C][C]1.11118538252240[/C][C]98.1616884535778[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]109.093833333333[/C][C]1.06333047548453[/C][C]102.596357245965[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]109.098833333333[/C][C]1.03483165725215[/C][C]105.426648449305[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]108.957666666667[/C][C]1.00420188863844[/C][C]108.501754377696[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]108.861666666667[/C][C]0.981673429038702[/C][C]110.893972930763[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]108.408833333333[/C][C]0.900171832048085[/C][C]120.431265980274[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]108.656166666667[/C][C]0.832054705790127[/C][C]130.587767739966[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]108.646166666667[/C][C]0.823609874587411[/C][C]131.914599398281[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]108.4835[/C][C]0.790596207298233[/C][C]137.217329147997[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]108.6535[/C][C]0.758239368053082[/C][C]143.297096639796[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]108.7315[/C][C]0.737456685503867[/C][C]147.441201818801[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]108.899333333333[/C][C]0.682726912948936[/C][C]159.506431148230[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]108.926[/C][C]0.647936803781754[/C][C]168.112074147111[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]109.016551724138[/C][C]1.21811065191053[/C][C]89.4964275644027[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]109.026428571429[/C][C]1.19483410326406[/C][C]91.248172674005[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]109.02[/C][C]1.17328232093225[/C][C]92.918812509999[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]109.020576923077[/C][C]1.14826212753624[/C][C]94.9439803932192[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]108.9982[/C][C]1.12528362646934[/C][C]96.8628685569605[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]108.974375[/C][C]1.10039962543635[/C][C]99.0316358539176[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]108.920652173913[/C][C]1.07833130175531[/C][C]101.008523073207[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]108.890681818182[/C][C]1.05770151483031[/C][C]102.950293907493[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]108.857619047619[/C][C]1.03216273338603[/C][C]105.465558411036[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]108.81825[/C][C]1.01059254562323[/C][C]107.677669374548[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]108.773947368421[/C][C]0.98816211858865[/C][C]110.0770261501[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]108.746111111111[/C][C]0.9648498754661[/C][C]112.707804474326[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]108.729117647059[/C][C]0.93760973144120[/C][C]115.964152249072[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]108.7753125[/C][C]0.920774238596357[/C][C]118.134617521249[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]108.792333333333[/C][C]0.913494450509203[/C][C]119.094684453408[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]108.813214285714[/C][C]0.901355395259756[/C][C]120.721765086186[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]108.860769230769[/C][C]0.889110691919295[/C][C]122.437813671743[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]108.89125[/C][C]0.87659612444874[/C][C]124.220546912043[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]108.915454545455[/C][C]0.858720917142454[/C][C]126.834519075056[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]108.918[/C][C]0.845676807745072[/C][C]128.793883198028[/C][/ROW]
[ROW][C]Median[/C][C]109.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.539032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.792333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.539032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.792333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.792333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.539032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.792333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.7753125[/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=16820&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16820&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 Mean109.0351666666671.2687511652421185.9389686912014
Geometric Mean108.598867723453
Harmonic Mean108.162701222704
Quadratic Mean109.469820551907
Winsorized Mean ( 1 / 20 )109.0073333333331.2366503615658088.147253840861
Winsorized Mean ( 2 / 20 )109.0381.2249369821217389.0151914681634
Winsorized Mean ( 3 / 20 )109.01851.2200288462135789.3573134261087
Winsorized Mean ( 4 / 20 )109.0951666666671.1971688233576791.127637588064
Winsorized Mean ( 5 / 20 )109.09351.1830571291801492.2132138078589
Winsorized Mean ( 6 / 20 )109.22151.1492799962963895.0347176945327
Winsorized Mean ( 7 / 20 )109.07451.1196437444146297.4189339637025
Winsorized Mean ( 8 / 20 )109.0758333333331.1111853825224098.1616884535778
Winsorized Mean ( 9 / 20 )109.0938333333331.06333047548453102.596357245965
Winsorized Mean ( 10 / 20 )109.0988333333331.03483165725215105.426648449305
Winsorized Mean ( 11 / 20 )108.9576666666671.00420188863844108.501754377696
Winsorized Mean ( 12 / 20 )108.8616666666670.981673429038702110.893972930763
Winsorized Mean ( 13 / 20 )108.4088333333330.900171832048085120.431265980274
Winsorized Mean ( 14 / 20 )108.6561666666670.832054705790127130.587767739966
Winsorized Mean ( 15 / 20 )108.6461666666670.823609874587411131.914599398281
Winsorized Mean ( 16 / 20 )108.48350.790596207298233137.217329147997
Winsorized Mean ( 17 / 20 )108.65350.758239368053082143.297096639796
Winsorized Mean ( 18 / 20 )108.73150.737456685503867147.441201818801
Winsorized Mean ( 19 / 20 )108.8993333333330.682726912948936159.506431148230
Winsorized Mean ( 20 / 20 )108.9260.647936803781754168.112074147111
Trimmed Mean ( 1 / 20 )109.0165517241381.2181106519105389.4964275644027
Trimmed Mean ( 2 / 20 )109.0264285714291.1948341032640691.248172674005
Trimmed Mean ( 3 / 20 )109.021.1732823209322592.918812509999
Trimmed Mean ( 4 / 20 )109.0205769230771.1482621275362494.9439803932192
Trimmed Mean ( 5 / 20 )108.99821.1252836264693496.8628685569605
Trimmed Mean ( 6 / 20 )108.9743751.1003996254363599.0316358539176
Trimmed Mean ( 7 / 20 )108.9206521739131.07833130175531101.008523073207
Trimmed Mean ( 8 / 20 )108.8906818181821.05770151483031102.950293907493
Trimmed Mean ( 9 / 20 )108.8576190476191.03216273338603105.465558411036
Trimmed Mean ( 10 / 20 )108.818251.01059254562323107.677669374548
Trimmed Mean ( 11 / 20 )108.7739473684210.98816211858865110.0770261501
Trimmed Mean ( 12 / 20 )108.7461111111110.9648498754661112.707804474326
Trimmed Mean ( 13 / 20 )108.7291176470590.93760973144120115.964152249072
Trimmed Mean ( 14 / 20 )108.77531250.920774238596357118.134617521249
Trimmed Mean ( 15 / 20 )108.7923333333330.913494450509203119.094684453408
Trimmed Mean ( 16 / 20 )108.8132142857140.901355395259756120.721765086186
Trimmed Mean ( 17 / 20 )108.8607692307690.889110691919295122.437813671743
Trimmed Mean ( 18 / 20 )108.891250.87659612444874124.220546912043
Trimmed Mean ( 19 / 20 )108.9154545454550.858720917142454126.834519075056
Trimmed Mean ( 20 / 20 )108.9180.845676807745072128.793883198028
Median109.115
Midrange109.575
Midmean - Weighted Average at Xnp108.539032258065
Midmean - Weighted Average at X(n+1)p108.792333333333
Midmean - Empirical Distribution Function108.539032258065
Midmean - Empirical Distribution Function - Averaging108.792333333333
Midmean - Empirical Distribution Function - Interpolation108.792333333333
Midmean - Closest Observation108.539032258065
Midmean - True Basic - Statistics Graphics Toolkit108.792333333333
Midmean - MS Excel (old versions)108.7753125
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')