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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 06:29:55 -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/2007/Oct/20/r5y4i597scdra811192886850.htm/, Retrieved Thu, 02 May 2024 21:20:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1164, Retrieved Thu, 02 May 2024 21:20:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [mannen onder 25 jaar] [2007-10-20 13:29:55] [a1ee67c0c4cd462b4e85e70c1c0a96bd] [Current]
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Dataseries X:
18
18
18
18
21,6
21,6
21,6
20,1
20,1
20,1
22,9
22,9
22,9
24
24
24
20,3
20,3
20,3
15,8
15,8
15,8
23,3
23,3
23,3
20,9
20,9
20,9
19,8
19,8
19,8
20,6
20,6
20,6
21,1
21,1
21,1
22,4
22,4
22,4
20,5
20,5
20,5
18,4
18,4
18,4
17,6
17,6
17,6
18,5
18,5
18,5
17,3
17,3
17,3
16,2
16,2
16,2
18
18
18




Summary of compuational 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 compuational 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=1164&T=0

[TABLE]
[ROW][C]Summary of compuational 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=1164&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1164&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 compuational 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 Mean19.83442622950820.29351725399523867.5749924732874
Geometric Mean19.7030963722260
Harmonic Mean19.5710996442660
Quadratic Mean19.9643083165277
Winsorized Mean ( 1 / 20 )19.83442622950820.29351725399523867.5749924732874
Winsorized Mean ( 2 / 20 )19.83442622950820.29351725399523867.5749924732874
Winsorized Mean ( 3 / 20 )19.81967213114750.28152414674926670.4013220890765
Winsorized Mean ( 4 / 20 )19.81967213114750.28152414674926670.4013220890765
Winsorized Mean ( 5 / 20 )19.81967213114750.28152414674926670.4013220890765
Winsorized Mean ( 6 / 20 )19.88852459016390.25259417289091778.7370680904535
Winsorized Mean ( 7 / 20 )19.88852459016390.25259417289091778.7370680904535
Winsorized Mean ( 8 / 20 )19.88852459016390.25259417289091778.7370680904535
Winsorized Mean ( 9 / 20 )19.85901639344260.23108649350808085.9375902588105
Winsorized Mean ( 10 / 20 )19.85901639344260.23108649350808085.9375902588105
Winsorized Mean ( 11 / 20 )19.85901639344260.23108649350808085.9375902588105
Winsorized Mean ( 12 / 20 )19.78032786885250.191482848496873103.300781370899
Winsorized Mean ( 13 / 20 )19.78032786885250.191482848496873103.300781370899
Winsorized Mean ( 14 / 20 )19.78032786885250.191482848496873103.300781370899
Winsorized Mean ( 15 / 20 )19.65737704918030.1731492141559113.528537481442
Winsorized Mean ( 16 / 20 )19.65737704918030.1731492141559113.528537481442
Winsorized Mean ( 17 / 20 )19.65737704918030.1731492141559113.528537481442
Winsorized Mean ( 18 / 20 )19.59836065573770.165170747937401118.655154744261
Winsorized Mean ( 19 / 20 )19.72295081967210.145654607595457135.409041603757
Winsorized Mean ( 20 / 20 )19.72295081967210.145654607595457135.409041603757
Trimmed Mean ( 1 / 20 )19.83220338983050.28690941350937469.1235716083695
Trimmed Mean ( 2 / 20 )19.82982456140350.27877017906079671.1332346530469
Trimmed Mean ( 3 / 20 )19.82727272727270.26869750111870873.790313064777
Trimmed Mean ( 4 / 20 )19.83018867924530.26201996547062575.681975774737
Trimmed Mean ( 5 / 20 )19.83333333333330.25359635468813678.2082745539605
Trimmed Mean ( 6 / 20 )19.83673469387760.24290430000057181.6648148831905
Trimmed Mean ( 7 / 20 )19.82553191489360.23847084709268583.136082068716
Trimmed Mean ( 8 / 20 )19.81333333333330.23258755275588185.1865592056381
Trimmed Mean ( 9 / 20 )19.80.22479226290465288.0813233700949
Trimmed Mean ( 10 / 20 )19.79024390243900.22038781998040889.797357695168
Trimmed Mean ( 11 / 20 )19.77948717948720.21427401476434892.3093133866002
Trimmed Mean ( 12 / 20 )19.76756756756760.20581100305812396.0471853974932
Trimmed Mean ( 13 / 20 )19.76571428571430.20485464644588496.4865314438241
Trimmed Mean ( 14 / 20 )19.76363636363640.20285921104089097.4253831621807
Trimmed Mean ( 15 / 20 )19.76129032258060.19939032986090399.108569289024
Trimmed Mean ( 16 / 20 )19.77586206896550.19874329138932299.5045514780482
Trimmed Mean ( 17 / 20 )19.79259259259260.196690997040988100.627852267524
Trimmed Mean ( 18 / 20 )19.8120.192468179188145102.936496222750
Trimmed Mean ( 19 / 20 )19.84347826086960.187222900587002105.988520627840
Trimmed Mean ( 20 / 20 )19.86190476190480.185994903985002106.787359956412
Median20.1
Midrange19.9
Midmean - Weighted Average at Xnp19.6058823529412
Midmean - Weighted Average at X(n+1)p19.6058823529412
Midmean - Empirical Distribution Function19.6058823529412
Midmean - Empirical Distribution Function - Averaging19.6058823529412
Midmean - Empirical Distribution Function - Interpolation19.6058823529412
Midmean - Closest Observation19.6058823529412
Midmean - True Basic - Statistics Graphics Toolkit19.6058823529412
Midmean - MS Excel (old versions)19.6058823529412
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19.8344262295082 & 0.293517253995238 & 67.5749924732874 \tabularnewline
Geometric Mean & 19.7030963722260 &  &  \tabularnewline
Harmonic Mean & 19.5710996442660 &  &  \tabularnewline
Quadratic Mean & 19.9643083165277 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 19.8344262295082 & 0.293517253995238 & 67.5749924732874 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 19.8344262295082 & 0.293517253995238 & 67.5749924732874 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 19.8196721311475 & 0.281524146749266 & 70.4013220890765 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 19.8196721311475 & 0.281524146749266 & 70.4013220890765 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 19.8196721311475 & 0.281524146749266 & 70.4013220890765 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 19.8885245901639 & 0.252594172890917 & 78.7370680904535 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 19.8885245901639 & 0.252594172890917 & 78.7370680904535 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 19.8885245901639 & 0.252594172890917 & 78.7370680904535 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 19.8590163934426 & 0.231086493508080 & 85.9375902588105 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 19.8590163934426 & 0.231086493508080 & 85.9375902588105 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 19.8590163934426 & 0.231086493508080 & 85.9375902588105 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 19.7803278688525 & 0.191482848496873 & 103.300781370899 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 19.7803278688525 & 0.191482848496873 & 103.300781370899 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 19.7803278688525 & 0.191482848496873 & 103.300781370899 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 19.6573770491803 & 0.1731492141559 & 113.528537481442 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 19.6573770491803 & 0.1731492141559 & 113.528537481442 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 19.6573770491803 & 0.1731492141559 & 113.528537481442 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 19.5983606557377 & 0.165170747937401 & 118.655154744261 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 19.7229508196721 & 0.145654607595457 & 135.409041603757 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 19.7229508196721 & 0.145654607595457 & 135.409041603757 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 19.8322033898305 & 0.286909413509374 & 69.1235716083695 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 19.8298245614035 & 0.278770179060796 & 71.1332346530469 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 19.8272727272727 & 0.268697501118708 & 73.790313064777 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 19.8301886792453 & 0.262019965470625 & 75.681975774737 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 19.8333333333333 & 0.253596354688136 & 78.2082745539605 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 19.8367346938776 & 0.242904300000571 & 81.6648148831905 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 19.8255319148936 & 0.238470847092685 & 83.136082068716 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 19.8133333333333 & 0.232587552755881 & 85.1865592056381 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 19.8 & 0.224792262904652 & 88.0813233700949 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 19.7902439024390 & 0.220387819980408 & 89.797357695168 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 19.7794871794872 & 0.214274014764348 & 92.3093133866002 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 19.7675675675676 & 0.205811003058123 & 96.0471853974932 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 19.7657142857143 & 0.204854646445884 & 96.4865314438241 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 19.7636363636364 & 0.202859211040890 & 97.4253831621807 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 19.7612903225806 & 0.199390329860903 & 99.108569289024 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 19.7758620689655 & 0.198743291389322 & 99.5045514780482 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 19.7925925925926 & 0.196690997040988 & 100.627852267524 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 19.812 & 0.192468179188145 & 102.936496222750 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 19.8434782608696 & 0.187222900587002 & 105.988520627840 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 19.8619047619048 & 0.185994903985002 & 106.787359956412 \tabularnewline
Median & 20.1 &  &  \tabularnewline
Midrange & 19.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 19.6058823529412 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.6058823529412 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.6058823529412 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.6058823529412 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.6058823529412 &  &  \tabularnewline
Midmean - Closest Observation & 19.6058823529412 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.6058823529412 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.6058823529412 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1164&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]19.8344262295082[/C][C]0.293517253995238[/C][C]67.5749924732874[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19.7030963722260[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19.5710996442660[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19.9643083165277[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]19.8344262295082[/C][C]0.293517253995238[/C][C]67.5749924732874[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]19.8344262295082[/C][C]0.293517253995238[/C][C]67.5749924732874[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]19.8196721311475[/C][C]0.281524146749266[/C][C]70.4013220890765[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]19.8196721311475[/C][C]0.281524146749266[/C][C]70.4013220890765[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]19.8196721311475[/C][C]0.281524146749266[/C][C]70.4013220890765[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]19.8885245901639[/C][C]0.252594172890917[/C][C]78.7370680904535[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]19.8885245901639[/C][C]0.252594172890917[/C][C]78.7370680904535[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]19.8885245901639[/C][C]0.252594172890917[/C][C]78.7370680904535[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]19.8590163934426[/C][C]0.231086493508080[/C][C]85.9375902588105[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]19.8590163934426[/C][C]0.231086493508080[/C][C]85.9375902588105[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]19.8590163934426[/C][C]0.231086493508080[/C][C]85.9375902588105[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]19.7803278688525[/C][C]0.191482848496873[/C][C]103.300781370899[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]19.7803278688525[/C][C]0.191482848496873[/C][C]103.300781370899[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]19.7803278688525[/C][C]0.191482848496873[/C][C]103.300781370899[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]19.6573770491803[/C][C]0.1731492141559[/C][C]113.528537481442[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]19.6573770491803[/C][C]0.1731492141559[/C][C]113.528537481442[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]19.6573770491803[/C][C]0.1731492141559[/C][C]113.528537481442[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]19.5983606557377[/C][C]0.165170747937401[/C][C]118.655154744261[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]19.7229508196721[/C][C]0.145654607595457[/C][C]135.409041603757[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]19.7229508196721[/C][C]0.145654607595457[/C][C]135.409041603757[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]19.8322033898305[/C][C]0.286909413509374[/C][C]69.1235716083695[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]19.8298245614035[/C][C]0.278770179060796[/C][C]71.1332346530469[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]19.8272727272727[/C][C]0.268697501118708[/C][C]73.790313064777[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]19.8301886792453[/C][C]0.262019965470625[/C][C]75.681975774737[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]19.8333333333333[/C][C]0.253596354688136[/C][C]78.2082745539605[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]19.8367346938776[/C][C]0.242904300000571[/C][C]81.6648148831905[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]19.8255319148936[/C][C]0.238470847092685[/C][C]83.136082068716[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]19.8133333333333[/C][C]0.232587552755881[/C][C]85.1865592056381[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]19.8[/C][C]0.224792262904652[/C][C]88.0813233700949[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]19.7902439024390[/C][C]0.220387819980408[/C][C]89.797357695168[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]19.7794871794872[/C][C]0.214274014764348[/C][C]92.3093133866002[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]19.7675675675676[/C][C]0.205811003058123[/C][C]96.0471853974932[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]19.7657142857143[/C][C]0.204854646445884[/C][C]96.4865314438241[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]19.7636363636364[/C][C]0.202859211040890[/C][C]97.4253831621807[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]19.7612903225806[/C][C]0.199390329860903[/C][C]99.108569289024[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]19.7758620689655[/C][C]0.198743291389322[/C][C]99.5045514780482[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]19.7925925925926[/C][C]0.196690997040988[/C][C]100.627852267524[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]19.812[/C][C]0.192468179188145[/C][C]102.936496222750[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]19.8434782608696[/C][C]0.187222900587002[/C][C]105.988520627840[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]19.8619047619048[/C][C]0.185994903985002[/C][C]106.787359956412[/C][/ROW]
[ROW][C]Median[/C][C]20.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.6058823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1164&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1164&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 Mean19.83442622950820.29351725399523867.5749924732874
Geometric Mean19.7030963722260
Harmonic Mean19.5710996442660
Quadratic Mean19.9643083165277
Winsorized Mean ( 1 / 20 )19.83442622950820.29351725399523867.5749924732874
Winsorized Mean ( 2 / 20 )19.83442622950820.29351725399523867.5749924732874
Winsorized Mean ( 3 / 20 )19.81967213114750.28152414674926670.4013220890765
Winsorized Mean ( 4 / 20 )19.81967213114750.28152414674926670.4013220890765
Winsorized Mean ( 5 / 20 )19.81967213114750.28152414674926670.4013220890765
Winsorized Mean ( 6 / 20 )19.88852459016390.25259417289091778.7370680904535
Winsorized Mean ( 7 / 20 )19.88852459016390.25259417289091778.7370680904535
Winsorized Mean ( 8 / 20 )19.88852459016390.25259417289091778.7370680904535
Winsorized Mean ( 9 / 20 )19.85901639344260.23108649350808085.9375902588105
Winsorized Mean ( 10 / 20 )19.85901639344260.23108649350808085.9375902588105
Winsorized Mean ( 11 / 20 )19.85901639344260.23108649350808085.9375902588105
Winsorized Mean ( 12 / 20 )19.78032786885250.191482848496873103.300781370899
Winsorized Mean ( 13 / 20 )19.78032786885250.191482848496873103.300781370899
Winsorized Mean ( 14 / 20 )19.78032786885250.191482848496873103.300781370899
Winsorized Mean ( 15 / 20 )19.65737704918030.1731492141559113.528537481442
Winsorized Mean ( 16 / 20 )19.65737704918030.1731492141559113.528537481442
Winsorized Mean ( 17 / 20 )19.65737704918030.1731492141559113.528537481442
Winsorized Mean ( 18 / 20 )19.59836065573770.165170747937401118.655154744261
Winsorized Mean ( 19 / 20 )19.72295081967210.145654607595457135.409041603757
Winsorized Mean ( 20 / 20 )19.72295081967210.145654607595457135.409041603757
Trimmed Mean ( 1 / 20 )19.83220338983050.28690941350937469.1235716083695
Trimmed Mean ( 2 / 20 )19.82982456140350.27877017906079671.1332346530469
Trimmed Mean ( 3 / 20 )19.82727272727270.26869750111870873.790313064777
Trimmed Mean ( 4 / 20 )19.83018867924530.26201996547062575.681975774737
Trimmed Mean ( 5 / 20 )19.83333333333330.25359635468813678.2082745539605
Trimmed Mean ( 6 / 20 )19.83673469387760.24290430000057181.6648148831905
Trimmed Mean ( 7 / 20 )19.82553191489360.23847084709268583.136082068716
Trimmed Mean ( 8 / 20 )19.81333333333330.23258755275588185.1865592056381
Trimmed Mean ( 9 / 20 )19.80.22479226290465288.0813233700949
Trimmed Mean ( 10 / 20 )19.79024390243900.22038781998040889.797357695168
Trimmed Mean ( 11 / 20 )19.77948717948720.21427401476434892.3093133866002
Trimmed Mean ( 12 / 20 )19.76756756756760.20581100305812396.0471853974932
Trimmed Mean ( 13 / 20 )19.76571428571430.20485464644588496.4865314438241
Trimmed Mean ( 14 / 20 )19.76363636363640.20285921104089097.4253831621807
Trimmed Mean ( 15 / 20 )19.76129032258060.19939032986090399.108569289024
Trimmed Mean ( 16 / 20 )19.77586206896550.19874329138932299.5045514780482
Trimmed Mean ( 17 / 20 )19.79259259259260.196690997040988100.627852267524
Trimmed Mean ( 18 / 20 )19.8120.192468179188145102.936496222750
Trimmed Mean ( 19 / 20 )19.84347826086960.187222900587002105.988520627840
Trimmed Mean ( 20 / 20 )19.86190476190480.185994903985002106.787359956412
Median20.1
Midrange19.9
Midmean - Weighted Average at Xnp19.6058823529412
Midmean - Weighted Average at X(n+1)p19.6058823529412
Midmean - Empirical Distribution Function19.6058823529412
Midmean - Empirical Distribution Function - Averaging19.6058823529412
Midmean - Empirical Distribution Function - Interpolation19.6058823529412
Midmean - Closest Observation19.6058823529412
Midmean - True Basic - Statistics Graphics Toolkit19.6058823529412
Midmean - MS Excel (old versions)19.6058823529412
Number of observations61



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')