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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 19 Dec 2008 06:13:17 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/19/t12296924618n3gzkil8wjkdk8.htm/, Retrieved Wed, 15 May 2024 23:30:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35104, Retrieved Wed, 15 May 2024 23:30:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [ARIMA forecasting] [2008-12-10 17:08:10] [2a0ad3a9bcadca2da0acb91636601c6c]
F       [ARIMA Forecasting] [ARIMA Forecasting...] [2008-12-11 18:38:00] [888addc516c3b812dd7be4bd54caa358]
- RMPD      [Central Tendency] [feedback op blog] [2008-12-19 13:13:17] [f4b2017b314c03698059f43b95818e67] [Current]
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Post a new message
Dataseries X:
5.7
5.7
5.6
5.8
5.6
5.6
5.6
5.5
5.4
5.4
5.5
5.4
5.4
5.2
5.4
5.2
5.1
5.1
5.0
5.0
4.9
5.1
5.0
5.0
4.8
4.7
4.7
4.7
4.7
4.7
4.6
4.7
4.7
4.5
4.4
4.5
4.4
4.6
4.5
4.4
4.5
4.5
4.6
4.7
4.7
4.7
4.8
4.7
5.0
4.9
4.8
5.1
5.0
5.5
5.5
5.7
6.1
6.1
6.5
6.7




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=35104&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=35104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35104&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 Mean5.098333333333330.068043342230122574.9277323281795
Geometric Mean5.07280028517334
Harmonic Mean5.04846365195397
Quadratic Mean5.125052845256
Winsorized Mean ( 1 / 20 )5.0950.066783442922535676.291364701126
Winsorized Mean ( 2 / 20 )5.081666666666670.06254903914171581.2429213365425
Winsorized Mean ( 3 / 20 )5.086666666666670.061683842469852582.4635182082365
Winsorized Mean ( 4 / 20 )5.066666666666670.056681619828347889.3881770141775
Winsorized Mean ( 5 / 20 )5.058333333333330.054941759953766792.067187829256
Winsorized Mean ( 6 / 20 )5.058333333333330.054941759953766792.067187829256
Winsorized Mean ( 7 / 20 )5.058333333333330.054941759953766792.067187829256
Winsorized Mean ( 8 / 20 )5.058333333333330.0502137615158871100.735997077871
Winsorized Mean ( 9 / 20 )5.058333333333330.0502137615158871100.735997077871
Winsorized Mean ( 10 / 20 )5.058333333333330.0502137615158871100.735997077871
Winsorized Mean ( 11 / 20 )5.076666666666670.047560052236496106.742243289022
Winsorized Mean ( 12 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 13 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 14 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 15 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 16 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 17 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 18 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 19 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 20 / 20 )5.030.0395811402901264127.080724888938
Trimmed Mean ( 1 / 20 )5.082758620689660.063481277090520680.0670505327412
Trimmed Mean ( 2 / 20 )5.069642857142860.059320811861028885.4614543883779
Trimmed Mean ( 3 / 20 )5.062962962962960.057083575267436188.6938657791321
Trimmed Mean ( 4 / 20 )5.053846153846150.054680033116122392.4258063837207
Trimmed Mean ( 5 / 20 )5.050.053699846083464394.0412378864348
Trimmed Mean ( 6 / 20 )5.047916666666670.053011237880354895.223519927222
Trimmed Mean ( 7 / 20 )5.045652173913040.052078213358930396.8860459773784
Trimmed Mean ( 8 / 20 )5.043181818181820.050827999066861699.2205459740364
Trimmed Mean ( 9 / 20 )5.040476190476190.050440512888080299.9291224825615
Trimmed Mean ( 10 / 20 )5.03750.04983144666697101.090783770864
Trimmed Mean ( 11 / 20 )5.034210526315790.0489253380422963102.895774004948
Trimmed Mean ( 12 / 20 )5.027777777777780.0482406518802054104.222840733229
Trimmed Mean ( 13 / 20 )5.023529411764710.0481491339521909104.332705480285
Trimmed Mean ( 14 / 20 )5.018750.0478230736252673104.944112110526
Trimmed Mean ( 15 / 20 )5.013333333333330.0471567046057295106.312206827197
Trimmed Mean ( 16 / 20 )5.007142857142860.045983828371019108.889212458408
Trimmed Mean ( 17 / 20 )5.003846153846150.045566779137292109.813470440157
Trimmed Mean ( 18 / 20 )50.0446402690761201112.006493318265
Trimmed Mean ( 19 / 20 )4.995454545454550.0428817324184391116.493767012699
Trimmed Mean ( 20 / 20 )4.990.0396696888130764125.788735664474
Median5
Midrange5.55
Midmean - Weighted Average at Xnp5.01891891891892
Midmean - Weighted Average at X(n+1)p5.01891891891892
Midmean - Empirical Distribution Function5.01891891891892
Midmean - Empirical Distribution Function - Averaging5.01891891891892
Midmean - Empirical Distribution Function - Interpolation5.01891891891892
Midmean - Closest Observation5.01891891891892
Midmean - True Basic - Statistics Graphics Toolkit5.01891891891892
Midmean - MS Excel (old versions)5.01891891891892
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.09833333333333 & 0.0680433422301225 & 74.9277323281795 \tabularnewline
Geometric Mean & 5.07280028517334 &  &  \tabularnewline
Harmonic Mean & 5.04846365195397 &  &  \tabularnewline
Quadratic Mean & 5.125052845256 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 5.095 & 0.0667834429225356 & 76.291364701126 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 5.08166666666667 & 0.062549039141715 & 81.2429213365425 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 5.08666666666667 & 0.0616838424698525 & 82.4635182082365 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 5.06666666666667 & 0.0566816198283478 & 89.3881770141775 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 5.05833333333333 & 0.0549417599537667 & 92.067187829256 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 5.05833333333333 & 0.0549417599537667 & 92.067187829256 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 5.05833333333333 & 0.0549417599537667 & 92.067187829256 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 5.05833333333333 & 0.0502137615158871 & 100.735997077871 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 5.05833333333333 & 0.0502137615158871 & 100.735997077871 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 5.05833333333333 & 0.0502137615158871 & 100.735997077871 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 5.07666666666667 & 0.047560052236496 & 106.742243289022 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 5.05666666666667 & 0.0439803928236097 & 114.975477525797 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 5.05666666666667 & 0.0439803928236097 & 114.975477525797 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 5.05666666666667 & 0.0439803928236097 & 114.975477525797 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 5.05666666666667 & 0.0439803928236097 & 114.975477525797 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 5.03 & 0.0395811402901264 & 127.080724888938 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 5.03 & 0.0395811402901264 & 127.080724888938 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 5.03 & 0.0395811402901264 & 127.080724888938 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 5.03 & 0.0395811402901264 & 127.080724888938 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 5.03 & 0.0395811402901264 & 127.080724888938 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 5.08275862068966 & 0.0634812770905206 & 80.0670505327412 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 5.06964285714286 & 0.0593208118610288 & 85.4614543883779 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 5.06296296296296 & 0.0570835752674361 & 88.6938657791321 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 5.05384615384615 & 0.0546800331161223 & 92.4258063837207 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 5.05 & 0.0536998460834643 & 94.0412378864348 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 5.04791666666667 & 0.0530112378803548 & 95.223519927222 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 5.04565217391304 & 0.0520782133589303 & 96.8860459773784 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 5.04318181818182 & 0.0508279990668616 & 99.2205459740364 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 5.04047619047619 & 0.0504405128880802 & 99.9291224825615 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 5.0375 & 0.04983144666697 & 101.090783770864 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 5.03421052631579 & 0.0489253380422963 & 102.895774004948 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 5.02777777777778 & 0.0482406518802054 & 104.222840733229 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 5.02352941176471 & 0.0481491339521909 & 104.332705480285 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 5.01875 & 0.0478230736252673 & 104.944112110526 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 5.01333333333333 & 0.0471567046057295 & 106.312206827197 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 5.00714285714286 & 0.045983828371019 & 108.889212458408 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 5.00384615384615 & 0.045566779137292 & 109.813470440157 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 5 & 0.0446402690761201 & 112.006493318265 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4.99545454545455 & 0.0428817324184391 & 116.493767012699 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4.99 & 0.0396696888130764 & 125.788735664474 \tabularnewline
Median & 5 &  &  \tabularnewline
Midrange & 5.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.01891891891892 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.01891891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.01891891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.01891891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.01891891891892 &  &  \tabularnewline
Midmean - Closest Observation & 5.01891891891892 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.01891891891892 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.01891891891892 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35104&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]5.09833333333333[/C][C]0.0680433422301225[/C][C]74.9277323281795[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.07280028517334[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5.04846365195397[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.125052845256[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]5.095[/C][C]0.0667834429225356[/C][C]76.291364701126[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]5.08166666666667[/C][C]0.062549039141715[/C][C]81.2429213365425[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]5.08666666666667[/C][C]0.0616838424698525[/C][C]82.4635182082365[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]5.06666666666667[/C][C]0.0566816198283478[/C][C]89.3881770141775[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]5.05833333333333[/C][C]0.0549417599537667[/C][C]92.067187829256[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]5.05833333333333[/C][C]0.0549417599537667[/C][C]92.067187829256[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]5.05833333333333[/C][C]0.0549417599537667[/C][C]92.067187829256[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]5.05833333333333[/C][C]0.0502137615158871[/C][C]100.735997077871[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]5.05833333333333[/C][C]0.0502137615158871[/C][C]100.735997077871[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]5.05833333333333[/C][C]0.0502137615158871[/C][C]100.735997077871[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]5.07666666666667[/C][C]0.047560052236496[/C][C]106.742243289022[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]5.05666666666667[/C][C]0.0439803928236097[/C][C]114.975477525797[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]5.05666666666667[/C][C]0.0439803928236097[/C][C]114.975477525797[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]5.05666666666667[/C][C]0.0439803928236097[/C][C]114.975477525797[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]5.05666666666667[/C][C]0.0439803928236097[/C][C]114.975477525797[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]5.03[/C][C]0.0395811402901264[/C][C]127.080724888938[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]5.03[/C][C]0.0395811402901264[/C][C]127.080724888938[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]5.03[/C][C]0.0395811402901264[/C][C]127.080724888938[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]5.03[/C][C]0.0395811402901264[/C][C]127.080724888938[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]5.03[/C][C]0.0395811402901264[/C][C]127.080724888938[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]5.08275862068966[/C][C]0.0634812770905206[/C][C]80.0670505327412[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]5.06964285714286[/C][C]0.0593208118610288[/C][C]85.4614543883779[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]5.06296296296296[/C][C]0.0570835752674361[/C][C]88.6938657791321[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]5.05384615384615[/C][C]0.0546800331161223[/C][C]92.4258063837207[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]5.05[/C][C]0.0536998460834643[/C][C]94.0412378864348[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]5.04791666666667[/C][C]0.0530112378803548[/C][C]95.223519927222[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]5.04565217391304[/C][C]0.0520782133589303[/C][C]96.8860459773784[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]5.04318181818182[/C][C]0.0508279990668616[/C][C]99.2205459740364[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]5.04047619047619[/C][C]0.0504405128880802[/C][C]99.9291224825615[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]5.0375[/C][C]0.04983144666697[/C][C]101.090783770864[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]5.03421052631579[/C][C]0.0489253380422963[/C][C]102.895774004948[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]5.02777777777778[/C][C]0.0482406518802054[/C][C]104.222840733229[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]5.02352941176471[/C][C]0.0481491339521909[/C][C]104.332705480285[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]5.01875[/C][C]0.0478230736252673[/C][C]104.944112110526[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]5.01333333333333[/C][C]0.0471567046057295[/C][C]106.312206827197[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]5.00714285714286[/C][C]0.045983828371019[/C][C]108.889212458408[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]5.00384615384615[/C][C]0.045566779137292[/C][C]109.813470440157[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]5[/C][C]0.0446402690761201[/C][C]112.006493318265[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4.99545454545455[/C][C]0.0428817324184391[/C][C]116.493767012699[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4.99[/C][C]0.0396696888130764[/C][C]125.788735664474[/C][/ROW]
[ROW][C]Median[/C][C]5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.01891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.01891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.01891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.01891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.01891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.01891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.01891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.01891891891892[/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=35104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35104&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 Mean5.098333333333330.068043342230122574.9277323281795
Geometric Mean5.07280028517334
Harmonic Mean5.04846365195397
Quadratic Mean5.125052845256
Winsorized Mean ( 1 / 20 )5.0950.066783442922535676.291364701126
Winsorized Mean ( 2 / 20 )5.081666666666670.06254903914171581.2429213365425
Winsorized Mean ( 3 / 20 )5.086666666666670.061683842469852582.4635182082365
Winsorized Mean ( 4 / 20 )5.066666666666670.056681619828347889.3881770141775
Winsorized Mean ( 5 / 20 )5.058333333333330.054941759953766792.067187829256
Winsorized Mean ( 6 / 20 )5.058333333333330.054941759953766792.067187829256
Winsorized Mean ( 7 / 20 )5.058333333333330.054941759953766792.067187829256
Winsorized Mean ( 8 / 20 )5.058333333333330.0502137615158871100.735997077871
Winsorized Mean ( 9 / 20 )5.058333333333330.0502137615158871100.735997077871
Winsorized Mean ( 10 / 20 )5.058333333333330.0502137615158871100.735997077871
Winsorized Mean ( 11 / 20 )5.076666666666670.047560052236496106.742243289022
Winsorized Mean ( 12 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 13 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 14 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 15 / 20 )5.056666666666670.0439803928236097114.975477525797
Winsorized Mean ( 16 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 17 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 18 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 19 / 20 )5.030.0395811402901264127.080724888938
Winsorized Mean ( 20 / 20 )5.030.0395811402901264127.080724888938
Trimmed Mean ( 1 / 20 )5.082758620689660.063481277090520680.0670505327412
Trimmed Mean ( 2 / 20 )5.069642857142860.059320811861028885.4614543883779
Trimmed Mean ( 3 / 20 )5.062962962962960.057083575267436188.6938657791321
Trimmed Mean ( 4 / 20 )5.053846153846150.054680033116122392.4258063837207
Trimmed Mean ( 5 / 20 )5.050.053699846083464394.0412378864348
Trimmed Mean ( 6 / 20 )5.047916666666670.053011237880354895.223519927222
Trimmed Mean ( 7 / 20 )5.045652173913040.052078213358930396.8860459773784
Trimmed Mean ( 8 / 20 )5.043181818181820.050827999066861699.2205459740364
Trimmed Mean ( 9 / 20 )5.040476190476190.050440512888080299.9291224825615
Trimmed Mean ( 10 / 20 )5.03750.04983144666697101.090783770864
Trimmed Mean ( 11 / 20 )5.034210526315790.0489253380422963102.895774004948
Trimmed Mean ( 12 / 20 )5.027777777777780.0482406518802054104.222840733229
Trimmed Mean ( 13 / 20 )5.023529411764710.0481491339521909104.332705480285
Trimmed Mean ( 14 / 20 )5.018750.0478230736252673104.944112110526
Trimmed Mean ( 15 / 20 )5.013333333333330.0471567046057295106.312206827197
Trimmed Mean ( 16 / 20 )5.007142857142860.045983828371019108.889212458408
Trimmed Mean ( 17 / 20 )5.003846153846150.045566779137292109.813470440157
Trimmed Mean ( 18 / 20 )50.0446402690761201112.006493318265
Trimmed Mean ( 19 / 20 )4.995454545454550.0428817324184391116.493767012699
Trimmed Mean ( 20 / 20 )4.990.0396696888130764125.788735664474
Median5
Midrange5.55
Midmean - Weighted Average at Xnp5.01891891891892
Midmean - Weighted Average at X(n+1)p5.01891891891892
Midmean - Empirical Distribution Function5.01891891891892
Midmean - Empirical Distribution Function - Averaging5.01891891891892
Midmean - Empirical Distribution Function - Interpolation5.01891891891892
Midmean - Closest Observation5.01891891891892
Midmean - True Basic - Statistics Graphics Toolkit5.01891891891892
Midmean - MS Excel (old versions)5.01891891891892
Number of observations60



Parameters (Session):
par1 = FALSE ; par2 = 0.1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;
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')